Aboveground tree biomass, carbon stocks and tree diversity in a mixed forest plantation in Northern Vietnam

Máster Gestión Forestal basada en Ciencia de Datos/ Forest Management based on Data Science (DATAFOREST) Aboveground tree biomass, carbon stocks and tree diversity in a mixed forest plantation in Northern Vietnam Student: Doan Thi Nhat Minh Co-advisors: Prof. Felipe Bravo Oviedo– University of Valladolid Prof. Vu Van Manh – Vietnam National University, University of Science July, 2019 Aboveground tree biomass, carbon stocks and tree diversity in a mixed forest plantation in Northern Vietnam Thi Nhat Minh Doan Máster en Gestión Forestal basada en Ciencia de Datos - Master on Forest Management based on Data Science (DATAFOREST) 3 TABLE OF CONTENTS ABSTRACT .................................................................................................................... 4 RESUMEN ...................................................................................................................... 5 1.- INTRODUCTION ....................................................................................................... 8 2.-OBJECTIVES ........................................................................................................... 10 3.- MATERIAL AND METHODS ................................................................................... 11 3.1. Study site ............................................................................................................ 11 3.2. Data gathering and preparation .......................................................................... 13 3.1.1. Tree level ................................................................................................................... 13 3.2.2. Stand level ................................................................................................................. 22 3.3. Statistical Ananlysis ............................................................................................ 22 4.- RESULTS ................................................................................................................ 26 4.1. Stand characteristic ............................................................................................ 26 4.2. Stand diversity .................................................................................................... 31 4.3. Tree distribution pattern ...................................................................................... 32 4.3.1. Species Intermingling .............................................................................................. 32 4.3.2. Vertical Spatial Pattern ............................................................................................ 34 4.3.3. Horizontal Spatial Pattern ....................................................................................... 36 4.4. Statistical Analysis .............................................................................................. 40 4.4.1. Statistical analysis for Acacia mangium ............................................................... 40 4.4.2. Statistical analysis for Acacia auriculiformis ........................................................ 43 5.- DISCUSSION ........................................................................................................... 48 6. - CONCLUSION ........................................................................................................ 52 7.- AKNOWLEDGES .................................................................................................... 53 8.- REFERENCES ........................................................................................................ 53 ANNEX ......................................................................................................................... 60 Aboveground tree biomass, carbon stocks and tree diversity in a mixed forest plantation in Northern Vietnam Thi Nhat Minh Doan Máster en Gestión Forestal basada en Ciencia de Datos - Master on Forest Management based on Data Science (DATAFOREST) 4 ABSTRACT Tropical forests reserve a huge amount of carbon stocks and contribute to the amount of biomass accumulation aboveand below-ground and the global carbon cycle. Forest plantations in the tropics have long been recognized as an effective solution in reducing the rate of increase in CO2 in the atmosphere. Moreover, the information on forest biomass and carbon content is necessary to support sustainable forest resource management in the world generally and in Vietnam particularly. Most of the forest plantations included only one tree species nevertheless, the use of two or more tree species during the planting phase and the plantation diversification are becoming more and more frequent. Within the framework of BioEcoN project, a Marteloscope, covered an area of 1 hectare, was set up in Hoa Lac Campus of Vietnam National University, Hanoi, Vietnam. Data collected from the Marteloscope include diameter at breast height (1,3 m above the ground), total height, species identity and position of 507 trees. Carbon stocks and above ground tree biomass by compartments were calculated using different biomass equations obtained from the relevant literature. The relationship between above ground tree biomass and species diversity were examined using regression analysis in which predictor variables are a set of parameters for the characterization of mixed stand structure include stand density and diversity, species intermingling, horizontal and vertical tree distribution pattern. The results show that the study area embraces 110.66 tons/ha of tree aboveground biomass and 55.33 tons/ha of carbon. Furthermore, results from the calculation of indices for characterizing species richness and diversity indicates high diversity and high evenness in the community. Although the study area is said to be a plantation, the results from a set of measures, indices, and methods for characterization of tree distribution patterns illustrate random distribution patterns. The sensitivity analysis of the optimum model fitted to explain the relationship between above ground tree biomass and species diversity indicates that above-ground biomass and carbon content decrease as the species diversity increase. Key words: Tropical forests, marteloscope, model selection, spatial pattern, forest structure Aboveground tree biomass, carbon stocks and tree diversity in a mixed forest plantation in Northern Vietnam Thi Nhat Minh Doan Máster en Gestión Forestal basada en Ciencia de Datos - Master on Forest Management based on Data Science (DATAFOREST) 5 RESUMEN Los bosques tropicales almacenan una gran cantidad de reservas de carbono y contribuyen a la acumulación de biomasa tanto aérea como subterránea y al ciclo global del carbono. Las plantaciones forestales en los trópicos han sido reconocidas durante mucho tiempo como una solución efectiva para reducir la tasa de aumento del CO2 en la atmósfera. Además, la información sobre la biomasa forestal y la concentración de carbono es necesaria para apoyar la gestión sostenible de los recursos forestales tanto a nivel global como en Vietnam en particular. La mayoría de las plantaciones forestales incluyen solo una especie arbórea, sin embargo, el uso de dos o más especies arbóreas durante la fase de plantación y la diversificación de las plantaciones es cada vez más frecuente. En el marco del proyecto BioEcoN se estableció, en el Campus Hoa Lac de la Universidad Nacional de Vietnam, Hanoi, Vietnam, un aula de señalamiento (Marteloscope) de una superficie igual a 1 hectárea. Los datos recopilados en esta aula de señalamiento fueron el diámetro a la altura del pecho (1.3 m sobre el suelo), la altura total, la identidad de la especie y la posición de 507 árboles. Las reservas de carbono y la biomasa arbórea sobre el suelo por compartimientos se calcularon utilizando diferentes ecuaciones de biomasa obtenidas de la literatura relevante. La relación entre la biomasa arbórea aérea y la diversidad de especies se estudió mediante modelos lineales, en los que las variables predictoras fueron un conjunto de parámetros que caracterizan la estructura de los rodales como son la densidad y la diversidad del rodal, la mezcla de especies, el patrón de distribución horizontal y vertical de árboles. Los resultados muestran que en el área de estudio se almacenan 110.66 toneladas / ha de biomasa aérea y 55.33 toneladas / ha de carbono. Además, los resultados del cálculo de los índices para caracterizar la riqueza y diversidad de las especies indican una alta diversidad y una alta uniformidad en el rodal. Aunque el área de estudio es una plantación, los resultados de un conjunto de medidas, índices y métodos para la caracterización de patrones de distribución espacial de árboles se hayo un patrón de distribución aleatorio. El análisis de sensibilidad del modelo óptimo ajustado para explicar la relación entre la biomasa aérea y la diversidad de especies indica que la biomasa aérea y la cantidad de carbono disminuyen a medida que aumenta la diversidad de especies. Palabras clave: Bosque tropical, aula de señalamiento, selección de modelos, patrón espacial, estructura forestal. Aboveground tree biomass, carbon stocks and tree diversity in a mixed forest plantation in Northern Vietnam Thi Nhat Minh Doan Máster en Gestión Forestal basada en Ciencia de Datos - Master on Forest Management based on Data Science (DATAFOREST) 6 LIST OF FIGURES Figure 1: Study area location (105o30’51’’E and 21o0’35’’N) .......................................... 11 Figure 2: Marteloscope A43 of VNU .............................................................................. 12 Figure 3: Walter and Lieth climate diagrams of study area ............................................ 13 Figure 4: Illustration of the Mingling index for 4 neighbours ........................................... 18 Figure 5: Calculation of uniform angle index W and possible values for structural group of 4 neighbours around the reference 𝑖-tree ...................................................................... 22 Figure 6: DBH distribution of the Marteloscope ............................................................. 26 Figure 7: Tree position in the VNU A43 Marteloscope ................................................... 27 Figure 8: Propotion of biomass by compartments from total ABG of Acacia auriculiformis ...................................................................................................................................... 30 Figure 9: Propotion of biomass by compartments from total ABG of Acacia mangium... 30 Figure 10: Stand diversity indices of the Marteloscope .................................................. 31 Figure 11: Above ground biomass vs stand density and stand diversity ........................ 32 Figure 12: Segregation index for each species .............................................................. 33 Figure 13: Percentage frequency distribution of Mingling Index (Mi) in each quadrants. 33 Figure 14: Spatial Diversity Index (MSi) of each quadrant ............................................ 34 Figure 15: Vertical Species profile A for each zone in each quadrants .......................... 35 Figure 16: Height Differentiation Index (TH) in each quandrant ..................................... 35 Figure 17: TH class by two most abundant species ....................................................... 36 Figure 18: L – function for the whole Marteloscope ....................................................... 36 Figure 19: L – function for quandrants 1 to 16 ............................................................... 37 Figure 20: L – function for quandrants 1 and 9 .............................................................. 38 Figure 21: Agregation index calculated for each quadrant and species ......................... 38 Figure 22: Percentage frequency distribution of Uniform Angle Index (W) in each quadrants ...................................................................................................................... 39 Figure 23: Regression diagnostic plots of Model (1.1) .................................................. 40 Figure 22: Pearson’s correlation matrix between tree above ground biomass and input variables for Acacia mangium ....................................................................................... 41 Figure 25: Sensitivity analysis 3D plot of Model (1.1) in different angles ....................... 43 Figure 26: Pearson’s correlation matrix between tree above ground biomass and input variables for Acacia auriculiformis ................................................................................. 44 Figure 27: Regression diagnostic plots of Model (2.1) ................................................... 46 Figure 28: Sensitivity analysis plot of Model (2.1) .......................................................... 47 Figure 29: Distribution of Acacia species ....................................................................... 48 Aboveground tree biomass, carbon stocks and tree diversity in a mixed forest plantation in Northern Vietnam Thi Nhat Minh Doan Máster en Gestión Forestal basada en Ciencia de Datos - Master on Forest Management based on Data Science (DATAFOREST) 7 Figure 30: Relation between tree above ground calculated by biomass equations and by sum of biomass in compartments .................................................................................. 49 Figure 31: Tree above groud biomass and Shannon index of each quadrants .............. 50 LIST OF TABLES Table 1: Biomass allometric equations for different species in the Marteloscope........... 14 Table 2: Categorization of different indices used ........................................................... 15 Table 3: Contingency table summarizing the number of trees of both species (A and B) ...................................................................................................................................... 17 Table 4: Model forms for statistical annalysis ................................................................ 23 Table 5: General characteristic of each species ............................................................ 28 Table 6: General characteristics of each quadrants ....................................................... 29 Table 7: 10 best fitted model for Acacia mangium ......................................................... 42 Table 8: 10 best fitted model for Acacia auriculiformis ................................................... 45 Aboveground tree biomass, carbon stocks and tree diversity in a mixed forest plantation in Northern Vietnam Thi Nhat Minh Doan Máster en Gestión Forestal basada en Ciencia de Datos - Master on Forest Management based on Data Science (DATAFOREST) 8 1.- INTRODUCTION Biomass was defined as all organic matter in the living form (still in the tree) and died on or below ground (Brown et al., 1997). It is also material from flora and fauna which are used for energy production or in different industrial processes as raw material for various products. (Ur-Rehman et al., 2015) According to the European Commission and the European Biomass Association (AEBIOM), biomass provides an efficient source of energy and a neutral carbon source, with can ensure up to 15% of the industrial demand of industrialized countries by 2020 (AEBIOM, 2017; European Commission, 2014). Additionally, biomass could reduce emissions of CO2 (the main gas causing global warming) by nearly 1000 tons/nm - equivalent to the combined emissions of Canada and Italy combined (Bauen et al., 2004). Forests play an important part in the global carbon cycle because it contributes 80% of the above ground biomass. Intergovernmental Panel on Climate Change (IPPC) determines the carbon pools in ecosystem biomass, namely biomass on the surface soil, below ground biomass, litter, woody debris and organic matter in the soil Among all carbon pools, above-ground biomass accounts for the majority or 45% of dry biomass of plant parts, forest ecosystems, about 72% of the earth's carbon stocks. (Malhi et al., 2002). The carbon in biomass of forest ecosystems is often concentrated in four main parts: the terrestrial vegetation, down debris, tree roots, and forest soil. Determining the amount of carbon in the forest is usually done through the determination of forest biomass (Mckenzie et al., 2000). Due to difficulties in collecting below ground biomass, most studies predict biomass based only on above ground biomass (AGB) (Lu, 2006). Forest biomass estimation is important for many applications, from trade to timber use (Morgan & Moss, 1985) to the analysis of the global carbon cycle. Forest biomass assessment and management play a key role in sustainable use of forest ecosystems. Biomass is an important source of energy in Vietnam, approximately 90% of domestic energy consumption in rural areas is derived from biomass such as fuel wood, agricultural residues (e.g. rice straw and husks) and charcoal. (Zwebe, 2012) It is well known that tree biomass is closely related with diameter at breast height and total height (Brown et al., 1989; Chave et al., 2005; Picard et al., 2012). However, different approaches have been used leading to different biomass compartment definitions, scope of the analyisis (local vs regional studies) and statistical approaches (system equations, proportion estimation, …). Beside the ground data, forest biomass has been assessed base on satellite an other remote sensing data (Roy & Ravan, 1996). Biomass were also determined by using carbon dioxide method in which biomass is assessed by determining the rate of CO2 assimilation. Parts of shrubs and trees under the forest canopy contribute a significant part of the biomass of the forest. There are many methods for estimating biomass for this unit, including the following methods: (1) Sampling whole plants (Quadrants); (2) Line and planar intersect method; (3) Objective measurement; (4) Double sampling method using correlation (Ali et al., 2015; J. K. Brown, 1976; Catchpole & Wheeler, 1992; Pitt & Schwab, 1988). However, the assessment of biomass is not easy, especially the forest subterranean biomass, such as the root system, so the clarification of the problem requires more and more intensive research. Whether in any different regions such as tropical or temperate, terrestrial or aquatic, all species are not equally common. Various methods of mensuration have been created Aboveground tree biomass, carbon stocks and tree diversity in a mixed forest plantation in Northern Vietnam Thi Nhat Minh Doan Máster en Gestión Forestal basada en Ciencia de Datos - Master on Forest Management based on Data Science (DATAFOREST) 9 in order to empirically measure biodiversity. The basic purpose of a diversity index is to obtain a quantitative estimation of biological variability (Help et al., 1998). For tropical ecology, the understanding of how species diversity, species distribution and structural pattern change across different environmental regions is very important. In the past 40 years, many studies were carried out focused on the relationship between species diversity and the ecosystem functions in which one of the most common topics is the relationship between productivity and species richness (Hooper et al., 2005; Keddy, 2005; Mittelbach et al., 2001). Although from many studies, it is said that the relationship between species diversity and productivity are commonly positive. A reverse case was found in Central Europe which indicates a negative relationship between above ground biomass and species diversity (Szwagrzyk & Gazda, 2007). Along with various studies on the productivity and species diversity relationship, another topic which has been much less studied is the relationship between forest stand structural diversity and productivity. Stand structure can be described in terms of the stand density or vertical and horizontal tree distribution patterns. For mixed-species stands, many aspects of structural were increased which led to higher productivity compared to monocultures (Riofrío et al., 2017). A positive relationship between aboveground biomass and stand structural diversity in Canadian forest were also found although the relationship was showed to be a quite weak correlation (Wang et al., 2011). In recent years, research methods for quantifying, building models for forecasting forest tree biomass have been applied through the relationship between tree biomass and basic measurement factors such as diameter at breast height, tree height which help to quickly predict biomass and save costs ((Bảo, 2017; S. Brown et al., 1989; Huy et al., 2016; Riofrío et al., 2015; Vũ Tấn, 2005). Methods based on biomass measurement can be divided into two groups, which are direct and indirect (Overman et al., 1994). Direct measurement methods include felling trees to identify births. The block is used to measure the actual weight of plant parts such as stems, branches, leaves and weigh the biomass weight after being dried (Supriya Devi & Yadava, 2009). Direct measurement method regional limits and small sample size, accurate biomass determination but it takes a lot of time and effort, large costs. The method is not feasible for large area sizes and does not apply to species that are threatened, much applied to the subjects of vegetation, shrubs and grassland. Other indirect methods aimed at building a relationship between biomass with parameters such as diameter, height, plant density by or wood density regression analysis method (Brown et al., 1989; Vũ et al., 2016). Correlation equation is one of the most attractive methods of quantifying carbon accumulation in forest biomass because it allows easy use of variables such as diameter, height and tree volume. This method allows the estimation of individual tree biomass from measuring tree size. The development and application of the correlation equation are the criteria for estimating above ground biomass (Návar, 2009). Correlation equations were developed and applied for forest inventories to assess forest biomass and carbon stocks. Many researchers have developed the method of predicting the overall biomass for different forest types and species (Basuki et al., 2009). Some construction works for mixed forest with many different trees, some for specific species on a small scale or for regional and global. Tropical forests have the largest carbon stock and are the habitat for various world's species (Baccini & Asner, 2013). Up to the present, most researches in the world has Aboveground tree biomass, carbon stocks and tree diversity in a mixed forest plantation in Northern Vietnam Thi Nhat Minh Doan Máster en Gestión Forestal basada en Ciencia de Datos - Master on Forest Management based on Data Science (DATAFOREST) 16 different species. Therefore, the index is less sensitive to species richness. Simpson’s index was calculated as follows: 𝐷=1−∑𝑛𝑖×(𝑛𝑖−1) 𝑅 𝑖=1 𝑁×(𝑁−1) Where:  𝑛𝑖 is the total number of a particular species  𝑁 is the total number of all species in the dataset  R – richness (total number of species types in dataset). The value of Simpson’s Diversity index ranges between 0 and 1. The greater value indicates the greater sample diversity. Value close to 1 indicates high diversity and low value (close to 0) indicates low diversity. Shannon's index (H’) accounts for abundance and evenness of the species observed in the stand. (Shannon et al., 1949). The Shannon index reflects the manner in which abundance is distributed amongst the different species constituting the community. The index is based on the relative frequencies of species in the population, thus taking into account both species richness and evenness. However, the value of the index is most strongly related to species richness. Shannon’s index was calculated as follows: 𝐻′=−∑𝑝𝑖×ln (𝑝𝑖) 𝑠 𝑝𝑖 Where:  𝑠 is the number of a particular species in the stand.  𝑝𝑖 is the proportion of individuals found in species 𝑖 . For a well-sampled community, we can estimate this proportion as 𝑝𝑖 = 𝑛𝑖/𝑁, where 𝑛𝑖 is the number of individuals in species i and N is the total number of individuals in the community.  𝑙𝑛(𝑝𝑖) is natural logarithm of this 𝑝𝑖 which value ranges from 0 to ln (S). When all species in the dataset are equally common, all 𝑝𝑖 values equal 1/𝑆, and the Shannon index then equal to 𝐼𝑛(𝑆). If practically all abundance is concentrated in one species, and the other species area very rare (even if there are many of them), the value approaches 0. If there are only one species in the dataset, the value equals to 0 Berger-Parker index (D) (Berger & Parker, 1970) focuses on quantifying the abundance of individuals of each species in the stand. If the Berger-Parker index is high, this means that the stand dominated by the most common species. Berger-parker index was calculated as follows: 𝐷= 𝑁𝑚𝑎𝑥 𝑁 Where:  𝑁𝑚𝑎𝑥 is the number of individuals in the most abundant species  𝑁 is the total number of individuals in the stand 1/𝐷 is the reciprocal of the index, which is often used in order to illustrate that, an increase of the value of the index followed by an increase in diversity and a reduction in the dominance. Aboveground tree biomass, carbon stocks and tree diversity in a mixed forest plantation in Northern Vietnam Thi Nhat Minh Doan Máster en Gestión Forestal basada en Ciencia de Datos - Master on Forest Management based on Data Science (DATAFOREST) 17 Species evenness tells us how evenly the species are distributed in the stand. The Evenness index (𝐸) (Pielou, 1975) compares the actual diversity value (the ShannonWiener Index, 𝐻′) to the maximum possible diversity value (when all species are equally common, 𝐻𝑚𝑎𝑥=𝑙𝑛 𝑆, where 𝑆 is the total number of species). Evennes index is computed as follows: 𝐸= 𝐻′ 𝑙𝑛 𝑆 Where:  𝐻′ is the number derived from the Shannon index  𝐻𝑚𝑎𝑥=𝑙𝑛 𝑆 where 𝐻𝑚𝑎𝑥 is the maximum possible value of 𝐻′ The Evenness index is constrained between 0 and 1. The more variation in abundances between different species within the community, the lower the Evenness index. The segregation index (S) by (Pielou, 1961) is commonly used to describe the intermingling of two tree species A and B. The Segregation index (S) describes the relative mixing of two species regardless of their spatial pattern. This method is based on the nearest neighbor distances and compares the observed number of mixed pairs with the one expected under random conditions. S is considered as the ratio of the observed propability (𝑝𝑖𝑗) that the reference tree 𝑖 and its neareast neighbor 𝑗 belong to different species along with the same probaility for completely random distributed or independent species attributes (Río et al., 2018) .The segregation index S is computed as follows: 𝑆=1− 𝑝𝑖𝑗 𝐸(𝑝𝑖𝑗)=1−𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑜𝑏𝑠𝑒𝑟𝑣𝑒𝑑 𝑚𝑖𝑥𝑒𝑑 𝑝𝑎𝑖𝑟𝑠 𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑒𝑥𝑝𝑒𝑐𝑡𝑒𝑑 𝑚𝑖𝑥𝑒𝑑 𝑝𝑎𝑖𝑟𝑠 =1− 𝑁(𝑏+𝑐) 𝑚1𝑛2+𝑚2𝑛1 Values of S vary between –1 and 1.  If 0 < 𝑆 < 1 indicates that the nearest neighbors are always different species (spatial separation of species)  If –1 < 𝑆 < 0, spatial association between two species is observed.  If both species are randomly distributed, then 𝑆 = 0  𝑆=−1 indicates that all neighbours are of different species  𝑆=1 indicates that the reference tree is surrounded by the same speciess Table 3: Contingency table summarizing the number of trees of both species (A and B) (adapted from (Pielou, 1961)) Nearest-neighbor species (𝑗) Species A Species B Species A+B Reference tree (𝑖) Species A 𝑎 𝑏 𝑛1=𝑎+ 𝑏 Species B 𝑐 𝑑 𝑛2=𝑐+𝑑 Species A+B 𝑚1=𝑎+𝑐 𝑚2=𝑏+𝑑 𝑁 Aboveground tree biomass, carbon stocks and tree diversity in a mixed forest plantation in Northern Vietnam Thi Nhat Minh Doan Máster en Gestión Forestal basada en Ciencia de Datos - Master on Forest Management based on Data Science (DATAFOREST) 18 Quantification of species diversity is an important aspect connected with forest management. Several parameters have been developed to describe species diversity. The Mingling index (Mi) (Füldner, 1995) describes the species pattern around the reference tree. Mingling index is expressed by the proportion of the 𝑛 nearest neighbour trees of the 𝑖𝑡ℎ reference tree that do not belong to the same species. This index is generall used to derive a distribution of trees that belong to a certain structure class. (Aguirre et al., 2003). The Mingling index was calculated as follow: 𝑀𝑖=1 𝑛∑𝑣𝑗 𝑛 𝑗=1 𝑣𝑗={1,𝑠𝑝𝑒𝑐𝑖𝑒𝑗 ≠𝑠𝑝𝑒𝑐𝑖𝑒𝑖 0, 𝑠𝑝𝑒𝑐𝑖𝑒𝑗 𝑖𝑠 𝑡ℎ𝑒 𝑠𝑎𝑚𝑒 𝑎𝑠 𝑠𝑝𝑒𝑐𝑖𝑒𝑖 Where:  n is the number of nearest neighbor trees considered  𝑣𝑗 produces binary output The Mingling index range from 0 to 1 (0≤𝑀𝑖≤1). The larger the mingling variable Mi, the more the different tree species are intermingled. A high value of mean mingling Mi represents a high intermingling of the different species. On the other hand, a small value near 0 will indicates large groups of one single species and segregation. 𝑀𝑖=0 4=0 𝑀𝑖=1 4=0.25 𝑀𝑖=2 4=0.5 𝑀𝑖=3 4=0.75 𝑀𝑖=4 4=1 Zero mingling Weak mingling Moderate mingling High mingling Very high mingling Figure 4: Illustration of the Mingling index for 𝒏 = 𝟒 neighbours. n = neighbours. The neighbours are numbered according to increasing distance from the reference tree (adapted from (Pommerening & Stoyan, 2006)) Spatial diversity status (MS) is improvement of the Mingling index, which considers not only the spatial mingling, but also the number of tree species. Spatial diversity status of a particular tree species is determined by the relative species richness within the stand or analyzed spatial unit 𝑖 and the degree of mingling of the reference tree (Río et al., 2018). The Spatial diversity status was calculated as follow: 𝑀𝑆𝑖=𝑆𝑖 𝑛𝑚𝑎𝑥×𝑀𝑖 Where:  𝑆𝑖 is the number of tree species in the neighborhood of the reference tree 𝑖, including tree 𝑖  𝑛𝑚𝑎𝑥 is the maximum number of species in this structure unit Aboveground tree biomass, carbon stocks and tree diversity in a mixed forest plantation in Northern Vietnam Thi Nhat Minh Doan Máster en Gestión Forestal basada en Ciencia de Datos - Master on Forest Management based on Data Science (DATAFOREST) 19  𝑀𝑖 is the species Mingling value. The Spatial diversity status range from 0 to 1 (0≤𝑀𝑆𝑖≤1). A reference tree of a common species is more likely to have neighbors of the same species, which is reflected by low values of 𝑀𝑆𝑖. In contrast, a rare species is likely to produce a high proportion of high 𝑀𝑆𝑖 values. Thus, 𝑀𝑆𝑖 is especially sensitive to rare species. (Gadow & Hui, 2002) Tree spatial distribution pattern and population structure of trees are the direct consequence of comprehensive interactions among characteristics of species, environmental factor, and intraspecific and interspecific interactions between each individual tree over a long time. Tree spatial distribution pattern depends on the biological characteristics of the tree at a small scale and on environmental heterogeneity, such as soil, pH, nutrition, water, canopy cover, and terrain, at large scales. (Condit et al., 2000) Vertical species profile (𝐴) (Pretzsch, 1995) is based on the common diversity index of Shannon (Shannon, 1948). 𝐴 index takes into account the presence of the species in different height zones in addition to the proportion of the species within a stand. The Vertical species profile was calculated as follow: 𝐴=−∑∑𝑝𝑖𝑗×ln(𝑝𝑖𝑗) 𝑍 𝑖=1 𝑆 𝑖=1 Where  S is the number of species present in the stand  Z is the number of height zones (in this study Z = 3)  N is the total number of individual trees  𝑝𝑖𝑗 is the proportion of a species in the height zone 𝑝𝑖𝑗 =𝑛𝑖𝑗/𝑁,  𝑛𝑖𝑗 is the number of individuals of the species 𝑖 in the zone 𝑗 The value of Vertical species profile is greater than 0 (𝐴>0) is for a single-layered pure stand. The more heterogeneous the vertical profile, the higher the A value. In order to calculate the Vertical Species profile A by using R-studio, the Height were devided into 3 zones. Assume the height of the highest tree in the stand is 100%, zone I extends from 100% to 80% of maximal tree height (Hmax), zone 2 from 80% to 50% of Hmax and zone 3 from 50% to the forest ground which is 0% of Hmax. A tree is considerd in the zone where the top of the tree is located. Standardization of 𝐴 can be calculated as follow: 𝐴𝑟𝑒𝑙=−∑ ∑ 𝑝𝑖𝑗×𝑙𝑛(𝑝𝑖𝑗) 𝑍 𝑖=1 𝑆 𝑖=1 𝑙𝑛(𝑆×𝑍) where 𝐴𝑚𝑎𝑥 =𝑙𝑛(𝑆×𝑍) 𝐴𝑟𝑒𝑙 indicates how close a given stand stucture is to the maximum structuring posible with the given species abundance. Height Differentiation index (TH) was developed by (Klaus v. Gadow, 1993).It measures the differences of size between the reference tree 𝑖 and its neighboring trees on a continuous scale and describes spatial distribution of tree sizes. TH reveals smallscale variability in the height for the 𝑖 reference tree and its 𝑛 nearest neighbours 𝑗 (𝑗= 1…𝑛). The average of TH can be calculated at a whole stand level and at species level by summing up TH values and divided it by the number of trees or individuals of the Aboveground tree biomass, carbon stocks and tree diversity in a mixed forest plantation in Northern Vietnam Thi Nhat Minh Doan Máster en Gestión Forestal basada en Ciencia de Datos - Master on Forest Management based on Data Science (DATAFOREST) 20 subpopulation. Further, it can be demonstrated in frequency histogram by each species based on its classes defined. The Height Differentiation index was calculated as follow: 𝑇𝐻𝑖𝑗=1−𝑀𝐼𝑁(𝐻𝑖, 𝐻𝑗) 𝑀𝐴𝑋(𝐻𝑖, 𝐻𝑗) Where  𝐻𝑖 the height of reference tree 𝑖  𝐻𝑗 the height of neighbour tree 𝑗 The Height Differentiation index (TH) range from 0 to 1 (0 ≤ 𝑇𝐻 ≤ 1)  If TH=1, the neighbour trees have high differentiation in height  If TH=0 means the neightbour trees have an equal height To define the spatial distribution of the trees the L-function defined by Besag (1977) was used. L-function was calculatedby dividing the 𝐾 – function (Ripley, 1977) by 𝜋 and by taking the square root of the quotient, which yields the 𝐿 -function with both statistical and graphical advantages over the 𝐾 -function. The 𝐿 – function allowed tree distribution patterns to be quantified more precisely. For 𝑛 tres on an experimental plot with size 𝐴 , the L-function is calculated as follows: 𝐿(𝑟)=√𝐾 (𝑟) 𝜋,𝑓𝑜𝑟 𝑟≥0 𝐾 (𝑟)=1 𝜆×∑∑𝑃𝑖𝑗(𝑟) 𝑛−1 𝑛 𝑗=1 𝑛 𝑖=1 ,𝑤𝑖𝑡ℎ 𝑃𝑖𝑗(𝑟)={1 𝑖𝑓 𝑟𝑖𝑗≤𝑟 0 𝑖𝑓 𝑟𝑖𝑗>𝑟 Where:  𝑟 denotes radius centred at the typical point (tree) i of the point pattern  𝑟𝑖𝑗 is the distance between tree 𝑖 and tree 𝑗  𝜆=𝑛/𝐴 represents the mean point density In this study The 𝐿 – function was applied at whole stand level, quadrant level and species level (within and between interactions of species) in each quadrant. Point patterns can vary from complete random patterns (𝐿(𝑟)=0) by being either aggregated (𝐿(𝑟)>0) or regular (𝐿(𝑟)<0) (Butt, 2010). Therefore, if 𝐿(𝑟) falls on the expected values (dotted diagonal lines), the trees have a random distribution; if 𝐿(𝑟) r falls above the expected values (dotted diagonal lines), the trees have a clumpy distribution; if 𝐿(𝑟) r falls below the expected values (dotted diagonal lines), the trees have a uniform distribution. The Aggregation index (𝑅) (Clark & Evans, 1954) is a crude measure of clustering or order of a point pattern. Aggregation index (𝑅) is the ratio of the observed mean nearest neighbor distance in the pattern to that expected mean distance in a random tree distribution. 𝑅= 𝑟𝑜𝑏𝑠𝑒𝑟𝑣𝑒𝑟 𝐸(𝑟) ,𝑤𝑖𝑡ℎ 𝐸(𝑟)=0.5×√𝐴 𝑁 Where: Aboveground tree biomass, carbon stocks and tree diversity in a mixed forest plantation in Northern Vietnam Thi Nhat Minh Doan Máster en Gestión Forestal basada en Ciencia de Datos - Master on Forest Management based on Data Science (DATAFOREST) 21  𝑟𝑜𝑏𝑠𝑒𝑟𝑣𝑒𝑟 is mean of distance between reference tres and neighbours  𝐸(𝑟) is the average distance to be expected when tres are randomly distributed  𝑁 is the number of trees in the plot  𝐴 is the size of the plot Aggregation index (𝑅) range between 0 (greatest clumping, all objects occur at the same point) and 2.1491 (strictly regular hexagonal pattern), and indicates wherther the trees are distributed regularly, randomly or in clumps across an area. 𝑅>1 describe a tendency towards regular distribution, 𝑅<1 indicates a tendency towards clustering and Value around 1 shows random distribution. In this study Aggregation index (R) was calculated in R-studio softwear at whole stand level, quadrant level and species level (within and between interactions of species) in each quadrant. In R-studio, correction for edge effects is necessary. Aggregation index R will be positively biased without correction for edge effects because edge effects arise due to a case for a point of X located close to the edge of the plot, its nearest neighbour can be outside the plot. Therefore, the observed distances to nearest neighbour tend to be larger than the distances to the true nearest neighbour. The nearest neighbour distance distribution function G(r) of the stationary point process is estimated by Gest using the Kaplan-Meier type edge correction. Then the mean of the distribution is calculated from the cumulative distribution function. The Uniform Angle Index (𝑊) developed by (Klaus v. Gadow, 1993) describes the degree of regularity in the spatial distribution of individuals tree. This index is based on the classification of angles between nearest neighbours tree of the reference tree (K von Gadow et al., 2002) 𝑊𝑖=1 𝑛∑𝑣𝑗 𝑛 𝑗=1 𝑤ℎ𝑒𝑟𝑒 𝑣𝑗={1,𝛼𝑗<𝛼0 0,𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒 Where:  𝑛 is number of nearest neighbours around the reference tree i  𝛼0=360𝑜 /𝑛 is the expected standard angle between reference tree and its neighbour The Uniform Angle Index (𝑊) range from 0 to 1:  𝑊<0.5 shows regular tree distribution pattern.  0.5≤𝑊≤0.6 illustrate random distribution  𝑊>0.6 can be considered as clumpled. 𝑊𝑖=0 4=0 𝑊𝑖=1 4 =0.25 𝑊𝑖=2 4=0.5 𝑊𝑖=3 4=0.75 𝑊𝑖=4 4=1 Aboveground tree biomass, carbon stocks and tree diversity in a mixed forest plantation in Northern Vietnam Thi Nhat Minh Doan Máster en Gestión Forestal basada en Ciencia de Datos - Master on Forest Management based on Data Science (DATAFOREST) 22 Very regular Regular Random Irregular Very irregular Figure 5: Calculation of uniform angle index W and possible values for structural group of 4 neighbours around the reference 𝒊-tree (adapted from (K von Gadow et al., 2002)) 3.2.2. Stand level Derived from the diameter at breast height is the basal area. The basal area of a tree is defined as the cross-sectional area of a stem measured at breast height. The basal area of each tree (𝐺𝑖) in the Marteloscope was calculated using the following equation: 𝐺𝑖=𝜋×(𝐷𝐵𝐻𝑖 2)2 The Number of tree per hectare (N) is calculated by multiply the number of tree in the area (n) with the expansion factor which is defined by taking the size of 1 hectare in adequate mensuration unit dividing by the area of the plot (A). The number of tree per hectare is computed as follow: 𝑁=𝑛 × 10000 𝐴 3.3. Statistical Ananlysis Pearson’s correlation coefficient is a statistical measure of the strength of a linear relationship between paired data. In order to insight into the strength of the linear relationship betweet paired date, the correlation coefficient was defined as follows: −1≤𝑟≤1 Furthermore:  Positive values denote positive linear correlation;  Negative values denote negative linear correlation;  A value of 0 denotes no linear correlation;  The closer the value is to 1 or –1, the stronger the linear correlation. In this study, in order to avoid correlation between parameters when fitting different models, we test the maxtrix correlation coefficient in R-studio. Although the significance of parameters does not only be effected by the correlation between parameters, the pairs of variables which have the correlation coefficient (r) out of the range of −0.5≤𝑟≤0.5 will not be included together in the fit models to avoid insignificant results in parameters t-test. Regression analyses are conducted using the R-open software in order to explain the relationships between tree above ground biomass and trees density, species richness & diversity, species intermingling and tree distribution pattern. Therefore, in each equation, the dependent variable is tree above ground biomass when the independent varibles include basal area of each quadrant, number of tree per hectar of each quadrant and the calculated indices. 3 forms of equations in Table… were used to develop various model for the two most abundant species which are Acacia mangium and Acacia auriculiformis. The log transformation homogenized the variance about the regression surface and linearized the parameters of the equation to meet the assumptions of linear regression techniques. Aboveground tree biomass, carbon stocks and tree diversity in a mixed forest plantation in Northern Vietnam Thi Nhat Minh Doan Máster en Gestión Forestal basada en Ciencia de Datos - Master on Forest Management based on Data Science (DATAFOREST) 23 Table 4: Model forms for statistical annalysis Linear form 𝐴𝐵𝐺=𝛽0+∑𝛽𝑖𝑋𝑖 𝑛 𝑖=1 + 𝜀 (𝐼) Non-linear form Original form Log-tranformed form 𝐴𝐺𝐵=exp(𝛽0+∑𝛽𝑖𝑋𝑖 𝑛 𝑖=1 +𝜀) (𝐼𝐼) 𝑙𝑛𝐴𝐺𝐵=𝛽0+𝛽1𝐺+𝛽2𝑁 𝐴𝐺𝐵=𝛽0×𝑋1𝛽1×…×𝑋𝑛𝛽𝑛+ 𝜀 (𝐼𝐼𝐼) 𝑙𝑛𝐴𝐺𝐵=𝑙𝑛𝛽0+𝛽1𝑙𝑛𝑋1+⋯+𝛽𝑛𝑙𝑛𝑋𝑛 The p-value of the coefficients (Pr(>|t|)) indicates whether the independent variable has statistically significant predictive capability. It essentially shows the probability of the coefficient being attributed to random variation. The lower the probability, the more significant the impact of the coefficient. In R–studio, the p-value is automatically calculated by comparing the t-value against the Student's T distribution table. A p-value of less than 5% (p-value<0.05) indicates the significance of the indepentdent variables. It is important to select the optimum model because under-fitting a model might not capture the true nature of the variability in the outcome variable. On the other hand, an over-fitted model loses generality. Optimal equation selection was based on the following criteria: Akaike’s information criterion (AIC) was first developed by (Akaike, 1973) as a way to compare different models on a given outcome. AIC compares the quality of a set of statistical models to each other. tries to formulate the bias variance trade off that every statistical modeler faces when fitting a model to finite set of data. In other words, while fitting a model if the number of parameters is increased, the log likelihood would be improved but might run into the danger of over fitting. The AIC penalizes for increasing the number of parameters thus minimizing the AIC selects the model where the improvement in log likelihood is not worth the penalty for increasing the number of parameters. 𝐴𝐼𝐶=−2log (𝐿(𝜃))+2𝑘 Where:  k is the number of estimated parameters included in the model.  𝜃 represents the maximum likelihood estimates of the model parameters  log (𝐿(𝜃)) is the log-likelihood of the model given the data AIC is computed for every candidate model and the optimum model is the candidate model which has the smallest AIC. The −2log (𝐿(𝜃)) is the first component in calculating AIC which indicates the value of the likelihood function. Because the value of the likelihood function is multiplied by –2, the model with the minimum AIC is the one with the highest value for the likelihood function when we ignore the second component, However, we add an adjustment based on the number of estimated parameters to the first component, therefore, parameters lead to the greater amount added to the first component, hence the value for the AIC increased. Thus, there is a trade-off: the better fit, created by making a Aboveground tree biomass, carbon stocks and tree diversity in a mixed forest plantation in Northern Vietnam Thi Nhat Minh Doan Máster en Gestión Forestal basada en Ciencia de Datos - Master on Forest Management based on Data Science (DATAFOREST) 24 more complex model by adding more parameters, must be considered in light of the penalty imposed by adding more parameters. This is the reason why the second component of the AIC is thought of in terms of a penalty Bayesian information criterion (BIC) proposed by (Schwarz, 1978) is a criterion for model selection. When fitting models, overfitting might occur if the likelihood is increased by adding parameters, but doing so may result in. The BIC can solve this problem by bringing a penalty term for the number of parameters in the model. The best model is the one that provides the minimum BIC 𝐵𝐼𝐶=2𝑙𝑜𝑔 (𝐿(𝜃))+𝑘𝑙𝑜𝑔(𝑁) The coefficient of determination (denoted by R2) is a key output of regression analysis. It is interpreted as the proportionate amount of variation in the response variable 𝑦 explained by the independent variables 𝑋 in the linear regression model. R2 range from 0 to 1, the larger the R2 is, the more variability is explained by the linear regression model. Aboveground tree biomass, carbon stocks and tree diversity in a mixed forest plantation in Northern Vietnam Thi Nhat Minh Doan Máster en Gestión Forestal basada en Ciencia de Datos - Master on Forest Management based on Data Science (DATAFOREST) 25 Ordinary — Ordinary (unadjusted) 𝑅2 𝑅2=𝑆𝑆𝑅 𝑆𝑆𝑇=1−𝑆𝑆𝐸 𝑆𝑆𝑇 Adjusted — R-squared adjusted for the number of coefficients 𝑅2=1−(𝑛−1 𝑛−𝑝)×𝑆𝑆𝐸 𝑆𝑆𝑇=1−(𝑛−1 𝑛−𝑝)×(1−𝑅2) Where:  SSE is the sum of squared error: 𝑆𝑆𝐸=∑(𝑦𝑖−𝑦𝑖)2 𝑛 𝑖=1  SSR is the sum of squared regression: 𝑆𝑆𝑅=∑(𝑦𝑖−𝑦)2 𝑛 𝑖=1  SST is the sum of squared total: 𝑆𝑆𝐸=∑(𝑦𝑖−𝑦)2 𝑛 𝑖=1 =𝑆𝑆𝑅+𝑆𝑆𝐸  n is the number of observations  p is the number of regression coefficients. Note that p includes the intercept, so for example, p is 2 for a linear fit. Because R-squared increases with added predictor variables in the regression model, the adjusted R-squared adjusts for the number of predictor variables in the model. This makes it more useful for comparing models with a different number of predictors.  𝑦𝑖 represents observed values  𝑦𝑖 represents predicted values Mean square error (MSE) is the average of the squares of the deviations which is also the gap between the observation and fitted value. Due to the randomness or the lack of information which could give a more accurate estimation, there exist differences between actual values and expected values. The mean square error supports in determinating the quality of a predictor with a non-negative value. If the value of the MSE is close to 0, then it indicates that the quality of the predictor is better. The value of MSE is used to compare the two or more than two models of statistics. The result indicates how well the observations are explained by candidate models is provided afterward. In the regression analysis, the MSE is measured to analyse variance and to determine the significance of the predictor or estimator. MSE is calculated for every candidate model and the optimum model is the candidate model which has the smallest MSE. 𝑀𝑆𝐸=1 𝑛×∑(𝑦𝑖−𝑦𝑖)2 𝑛 𝑖=1 Where:  n is the number of observations  𝑦𝑖 represents observed values  𝑦𝑖 represents predicted values Once the best model is selected, the sensitivity analysis of the model is carried out. Sensitivity analysis includes a series of procedures to quantify how the variability in the output of a model is related to that in its inputs. In this study, the sensitivity analysis of the optimal model was done in order to assess how sensitive the tree above ground biomass is to the fluctuations of parameters and data on which the model is built. The results of Aboveground tree biomass, carbon stocks and tree diversity in a mixed forest plantation in Northern Vietnam Thi Nhat Minh Doan Máster en Gestión Forestal basada en Ciencia de Datos - Master on Forest Management based on Data Science (DATAFOREST) 32 Figure 11: Above ground biomass vs stand density and stand diversity 4.3. Tree distribution pattern 4.3.1. Species Intermingling From Figure 12, It can be observed that most of the species in the Marteloscope has a trend toward segration since the value of mostly greater than 0. For Senna siamea only located in quadrant 16 and distributed close to eachother, hence the Segregation index of this species close to one means that the reference tree is surrounded by the same species. Aboveground tree biomass, carbon stocks and tree diversity in a mixed forest plantation in Northern Vietnam Thi Nhat Minh Doan Máster en Gestión Forestal basada en Ciencia de Datos - Master on Forest Management based on Data Science (DATAFOREST) 33 Figure 12: Segregation index for each species Figure 13: Percentage frequency distribution of Mingling Index (Mi) in each quadrants Aboveground tree biomass, carbon stocks and tree diversity in a mixed forest plantation in Northern Vietnam Thi Nhat Minh Doan Máster en Gestión Forestal basada en Ciencia de Datos - Master on Forest Management based on Data Science (DATAFOREST) 34 The tree distribution situations depicted by Mingling index seem to have a considerable variability throughout the 16 quadrants (Figure 13). In quadrant: 2, 7, 13, 14, 16 we can see a higher component in 0.25-value class in which only two of four nearest neighbours j belongs to different species compared to the reference tree i; in other words it is indicated by a higher presence of weak mingling; or a low mixture measured at small scale. On the other hand, in some other cases (quadrants 8 and 12) small monospecific groups are more present in which the mingling index has 0-value. Generally, considering quadrant, we can notice a trend of the mingling values distribution towards monospecific groups such as quadrants in 2, 7, 8, 11, 12, 13, 14, 16; towards mean mingling such as quadrants in 1, 4, 6, 10, 15 or towards multi-specific groups such as quadrants 3, 5, 9. Figure 14: Spatial Diversity Index (MSi) of each quadrant The Spatial Diversity Index (MSi) measures the tree species richness as well as an important spatial characteristic of each quadrant. As can be seen from Figure 14 that the reference trees in quadrant 7, 11, 13, 14 and 16 are more likely to have neighbors of the same species, which is reflected by low MS value. On the other hand, quadrant 3, 6, 9 and 10 seems to have high MS value, indicates a high diversity and as the reference trees are observed to be more likely to have neighbours of the different species. 4.3.2. Vertical Spatial Pattern The Vertical Species profile A for 3 height zones (100-80%, 80-50%, 50-0% of the maximu height) in each quadrant were illustrated in Figure 15. It is clear that for most of the quadrant, Zone 2 which range from 80-50% of the maximum height has the highest value of A, indicates that for all quadrant, the vertical profile in zone 2 is more heterogeneous than other zones. For quadrant 9, there was no value of A in zone 1 because all trees this quadrant has the total height above 50% of the maximum height Aboveground tree biomass, carbon stocks and tree diversity in a mixed forest plantation in Northern Vietnam Thi Nhat Minh Doan Máster en Gestión Forestal basada en Ciencia de Datos - Master on Forest Management based on Data Science (DATAFOREST) 35 Figure 15: Vertical Species profile A for each zone in each quadrants Figure 16: Height Differentiation Index (TH) in each quandrant Aboveground tree biomass, carbon stocks and tree diversity in a mixed forest plantation in Northern Vietnam Thi Nhat Minh Doan Máster en Gestión Forestal basada en Ciencia de Datos - Master on Forest Management based on Data Science (DATAFOREST) 36 Figure 17: TH class by two most abundant species As can be seen from Figure 16, the value of Height Differentiation Index is relatively low, although in some quadrants, the outliers with high value were observed. TH class by two most abundant species which are Acacia auriculiformis (108 observations) and Acacia mangium (300 observations) is presented in Figure 17. As can be observed for both species, more than 40% of the TH value fall between 0 to 0.2 and 0.2 to 0.4. This means that only limited height differences between neighboring trees were be observed. 4.3.3. Horizontal Spatial Pattern According to the results presented in Figure 18, for the whole Marteloscope with clumply distributions, the L-function line slightly deviates from the expected values, which is inevident and almost invisible, and thus it is very easy to wrongly consider this L-function line as a random distribution or uniform distribution. Therefore, it is needed to have closer look at the L-funtion line in quadrant level. Figure 18: L – function for the whole Marteloscope Aboveground tree biomass, carbon stocks and tree diversity in a mixed forest plantation in Northern Vietnam Thi Nhat Minh Doan Máster en Gestión Forestal basada en Ciencia de Datos - Master on Forest Management based on Data Science (DATAFOREST) 37 Figure 19 presents results of the 16 quadrants in the Marteloscope. The L-function line very slightly deviates from the expected values (dotted diagonal lines); for small r, the actual values are very slightly below the expected values. Althought this might indicate a uniform distribution, I would rather say that this is reflecting a random distribution since the deviation are not are not big enough to be considered as uniform distribution. For bigger r, the actual values mostly fall on the expected values, indicating random distribution. This can be observed in almost all quadrant, except for quadrants 1 and 9 which will need for a closer evaluation in Figure 19. However, the extent of the deviations is very small, so the probability of being wrongly determined distribution pattern is very high. Therefore, an extra test for distribution pattern is inneed Figure 19: L – function for quandrants 1 to 16 The result from the distribution pattern test of quadrant 1 and 9 which showing random distribution in both quadrants (Figure 20). For small r around 1𝑒−05, althought the actual values falls below the expected values (dotted diagonal lines) but the deviation is still very small, it was not clearly wheather this indicate random or uniform distribution. Aboveground tree biomass, carbon stocks and tree diversity in a mixed forest plantation in Northern Vietnam Thi Nhat Minh Doan Máster en Gestión Forestal basada en Ciencia de Datos - Master on Forest Management based on Data Science (DATAFOREST) 38 For incresing r, the actual values in the two quadrants performed differently. While the actual line in quadrant 1 tend to fall below the expected values, the actual line in quadrant 9 falls above the expected values. However, as the deviation from the expected value is small, thus it is very easy to wrongly consider this L-function line as whether a random, uniform or clumpy distribution. Figure 20: L – function for quandrants 1 and 9 The Clark and Evans aggregation index of the whole Marteloscope was done in R (R Core Team, 2019) and the result (Figure21) shows that the aggregation index is R=1.110826 indicates a Random distribution for the whole stand. For each quadrant, the Agrregation index range from 0.8248 to 1.199 as showed in Figure 20 which indicates that all quadrant and species in the Marteloscope has a tendency toward random distribution. The full results of Aggregation index calculated for each quadrant and species is presented in Annex 2. Although the study site is said to be a plantation acoording to the staff in Campus Hoa Lac of Vietnam National University, the result of L-function and Aggregation index indicates randon distribution for the whole Marteloscope. . Figure 21: Agregation index calculated for each quadrant and species Aboveground tree biomass, carbon stocks and tree diversity in a mixed forest plantation in Northern Vietnam Thi Nhat Minh Doan Máster en Gestión Forestal basada en Ciencia de Datos - Master on Forest Management based on Data Science (DATAFOREST) 39 Figure 22: Percentage frequency distribution of Uniform Angle Index (W) in each quadrants As presented in Figure 22 the percentage frequency distribution of Uniform Angle Index (W) values in each quadrant displayed in order to describe and characterize the horizontal structure and to evaluate differences in 16 quadrants in the stand. According to (Klaus v. Gadow, 1993), the random distribution (0.5 value) represents the more frequent value for most of the quadrant, except for quadrant 4 and quadrant 7. Moreover, in most quadrants, the distribution of W usually resembles a symmetric distribution. The frequency of random distribution (0.5 value) registered in each quadrant can vary, in some quadrant the amount of this distribution can have higher values (>50%) such as quadrant 1, 5, 6, 9 with values respectively of: 53%, 65%, 58%, 72%, or lower values like quadrant 10 with value of 36%, resulting in higher values for the other components. In some cases, we can appreciate the skewness of the distribution, such as the regular distribution represented in quadrant 11 the irregular distribution represented in quadrant 4. Furthermore, some quadrant can be oriented towards a regular distribution for examples quadrants 2, 10, 13, 14, 15 or towards an irregular or clumped distribution such as quadrants 3, 8, 16. Aboveground tree biomass, carbon stocks and tree diversity in a mixed forest plantation in Northern Vietnam Thi Nhat Minh Doan Máster en Gestión Forestal basada en Ciencia de Datos - Master on Forest Management based on Data Science (DATAFOREST) 40 4.4. Statistical Analysis 4.4.1. Statistical analysis for Acacia mangium As presented in the Figure, the value of the correlation and the bivariate scatter plots with a fitted line indicates the high correlation pairs in which the value of r is significantly and −0.5 < 𝑟 < 0.5. Thus, the pairs which need to be avoided adding together when developing models are N-Sh, N-Sm, N-E, N-R, N-A, Sh-Sm, Sh-E, Sh-R, Sh-A, Sm-E, Sm-R, E-D, E-R, D-R and Mi-MS (Figure 23) Various model were explored and tested, but only those that meet regression assumption such as homogeneity of variance, normality, linearity and non-autocorrelation with high goodness of fit were retained. The list 10 best fitted models is presented in Table 7, the full list of fitted equation is presented in Annex 3 For all model, the 𝑅2 is low, indicates a weak relationship between Above ground biomass and the predictor variables. This is acceptable because these models were built in order to explain the relationship between the above-ground biomass and the species diversity, not to predict that. On comparing AIC, BIC, 𝑅2 and MSE, model (1.1) is selected as the optimal model for explaining the relationship between tree above ground biomass and species diversity. 𝐴𝐺𝐵=exp (6.098+0.001×𝐺2−0.113×𝑆ℎ2−1.555×𝑇𝐻2) Model (1.1) Model (1.1) requires basal area of each quadrant, Shannon index and Height differentiation index. To have an insight on model (1.1), regression diagnostic plots of model (1.1) are presented in Figure 23 In which indicates that Residuals are almost horizontal and well spread, the spread is almost uniform and no point has excess the leverage, residuals have passed the test of Normality since it follows a Normal distribution. Figure 23: Regression diagnostic plots of Model (1.1) Aboveground tree biomass, carbon stocks and tree diversity in a mixed forest plantation in Northern Vietnam Thi Nhat Minh Doan Máster en Gestión Forestal basada en Ciencia de Datos - Master on Forest Management based on Data Science (DATAFOREST) 41 Figure 24: Pearson’s correlation matrix between tree above ground biomass and input variables for Acacia mangium ( G is basal area of each quadrant (m2/ha); N is number of tree per hectare, Sh is Shannon index; Sm is Simpson index; E is Evenness index; D is Berger-Parker index; R is Aggregation index; Mi is Mingling index; MS is Spatial diversity status; W is Uniform Angle index; S is segregation index; A is Vertical species profile; TH is Height differentiation index; p-values(0, 0.001, 0.01, 0.05, 0.1, 1) associated with symbols(“***”, “**”, “*”, “.”, " “) respectively Aboveground tree biomass, carbon stocks and tree diversity in a mixed forest plantation in Northern Vietnam Thi Nhat Minh Doan Máster en Gestión Forestal basada en Ciencia de Datos - Master on Forest Management based on Data Science (DATAFOREST) 48 5.- DISCUSSION Figure 29: Distribution of Acacia species Although the Marteloscope is confirmed to be a plantation by the staffs and managers of the Hoa Lac Campus of Vietnam National University, the value of aggregation index together with L-function calculated for the whole Marteloscope and for each quadrants indicates that, the trees distribution in the Marteloscope has a trend towards random (Poisson) distribution. It is hardly to see any clear pattern of trees distribution wheather in terms of species or quandrants or at whole stand level (Figure 28). There a possibility in consideering the historical status of the stand that some trees in the plantation died from natural events, overmature or harvested in the past which leads to the random Aboveground tree biomass, carbon stocks and tree diversity in a mixed forest plantation in Northern Vietnam Thi Nhat Minh Doan Máster en Gestión Forestal basada en Ciencia de Datos - Master on Forest Management based on Data Science (DATAFOREST) 49 distribution observed from this Figure 29 and also proven from the calculated trees distrbution pattern indices. The result of Biomass calculation indicates that the total tree above ground biomass calculated by above ground biomass equations is not equal to the total above groud biomass calculated by the sum of biomass in compartments (Figure 30). This lack of additivity is a common issue in many studies due to the method used in developing biomass allometric equations. Figure 30: Relation between tree above ground calculated by biomass equations and by sum of biomass in compartments In general, in order to estimate total biomass and compartments biomass, most studies usually regress the total tree biomass and compartments biomass such as stem, branches, leaves, and bark biomass against basic mensuration of tree attributes such as diameter at breast height (DBH) and tree total height using linear and nonlinear regression. This method was also used in (Đ. H. Nguyễn et al., 2012; Ounban et al., 2016; Phạm, 2014; Traoré et al., 2018) where the tree above ground biomass equations by compartments was adopted to calculate tree above ground biomass for Acacia mangium, Acacia auriculiformis, Eucalyptus camadulensis, and Litsea glutinosa. However, this method does not ensure that the sum of the total above ground biomass calculated from models for compartments biomass is equal to the biomass calculated from the total aboveground biomass model. This issue is called additivity which is a common issue found in many biomass or carbon allometric equations. The problem of additivity can be solved by fitting compartments models and total biomass models as a simultaneous system. Such Aboveground tree biomass, carbon stocks and tree diversity in a mixed forest plantation in Northern Vietnam Thi Nhat Minh Doan Máster en Gestión Forestal basada en Ciencia de Datos - Master on Forest Management based on Data Science (DATAFOREST) 50 methods ignore the inherent correlations among the component models if fitted with the ordinary least squares approach (Parresol, 1999). Hence, another method to estimate total biomass and compartments biomass is a regression-based approach in which a system of equations should be used in order to deal with the issue of non-additivity. In recent years, the popularity of the seemingly unrelated regression (SUR) and non-linear seemingly unrelated regression (NSUR) have been increasing immensely, in which various estimation methods have been proposed in order to ensure the additivity in a system of biomass equations for both linear and nonlinear models (Parresol, 2001; RuizPeinado et al., 2012, 2011). Shannon Weaver index, Simpson diversity index, Evenness index, and BergerParker index resulting from indices calculation indicate that the study area has high species diversity and high species evenness. For the past 10 years, various studies were carried out to insight into the effect of species richness and species diversity on productivity in the forests using data from different sources in different regions of the world (Scherer-Lorenzen et al., 2007; Vila et al., 2005; Vilà et al., 2007; Woodroffe et al., 2014) Figure 31: Tree above groud biomass and Shannon index of each quadrants The negative relationships between species diversity and the tree above ground biomass as well as carbon sequestration in Acacia mangium and Acacia auriculiformis were indicated from the results of statistical analysis. While the statistical analysis for Acacia mangium was carried out with 300 observations, the number of observation for Aboveground tree biomass, carbon stocks and tree diversity in a mixed forest plantation in Northern Vietnam Thi Nhat Minh Doan Máster en Gestión Forestal basada en Ciencia de Datos - Master on Forest Management based on Data Science (DATAFOREST) 51 Acacia auriculiformis was only 107. Due to the differences in the dataset for the two different species, the model forms fitted for these two species also have dissimilarities. For both species, 3 model forms were fitted using linear regression in R (R Core Team, 2019). However, only model form II 𝐴𝐺𝐵=𝑒𝑥𝑝(𝛽0+∑𝛽𝑖𝑋𝑖 𝑛 𝑖=1 +𝜀) shows the good result in terms of regression assumption such as homogeneity of variance, normality, linearity, and non-autocorrelation with a high goodness of fit. The other two forms mostly show the none-significant relationship between fitted variables in different forms (power of 2; -1; -0.5 and 0.5). The optimal models for both species contain similar independent variables which are TH2 and Sh2 (power of two of Height differentiation index and Shannon index). Propaly due to the distribution of each species, the Basal area of each quadrant was inly well fitted for Acacia mangium. While our results of sensitivity analysis for both models fitted for Acacia mangium and Acacia auriculiformis show that the species richness and diversity had a negative efect on tree above ground biomass and carbon sequestration, the study of (Li et al., 2018) on the relationship between species richness and aboveground biomass in a primary Pinus kesiya forest indicated a reverse result across forest strata, and widely exists in all forest vegetation strata in primary Pinus kesiya forests. Another interesting finding compares to the results of this study can be seen from (Day et al., 2013) in which the outcomes illustrate a complex and highly variable relationship between species diversity and above ground biomass in Central African rainforests. In this study, the effect trend of species diversity to above ground biomass varied in different locations within the study area. While some plots with high diversity had relatively low biomass, other plots with low diversity had high biomass since the study areas located in different forest types, and the conditions of the plots were also different in terms of management designations, altitudinal and climate conditions. However, despite this variability, the author claimed that, in general, there was evidence of a positive relationship between biomass and species diversity. This is similar with the general relation ship observed from Figure 30. The similar results were found for a positive correlation between above ground biomass and species richness/ diversity in (Liang et al., 2016; Zhang et al., 2015, 2017). The differencies in outcomes of our study compare to others might be cecause of the effect from the covariation of the number of tree species with other variables such as stand age, environmental factors, species complementary and so on The result from the calculation of species Evenness index indicates that the species have equal abundance in the study area. Although Evenness index was included in the model development process, the results show that it was not able to address the clearer the relationship between Evenness and tree above ground biomass. Despite this fact, the Shannon index which accounts for both abundance and evenness of the species were successfully showed the negative correlations with tree above ground biomass. On the other hand, in the study of (Zhang et al., 2012), species evenness together with species richness was found to be able to explain the productivity of forest. Carbon sequestration in forests has been acknowledged to perform the main role to reduce the effect of global climates changes. It has been studied that, depending on different conditions of the forest stand, forest structure, species composition, stand age, etc., the unmanaged forest may store a larger amount of carbon than a forest under management (Krug et al., 2012; Pukkala, 2017). However, carbon sequestration is usually not the only objective in forest management designation. Additionally, the managers also Aboveground tree biomass, carbon stocks and tree diversity in a mixed forest plantation in Northern Vietnam Thi Nhat Minh Doan Máster en Gestión Forestal basada en Ciencia de Datos - Master on Forest Management based on Data Science (DATAFOREST) 52 take into account biodiversity conservation, possible ecosystem services and other products provided by the forest systems when considering adequate the management regimes. (Bellassen & Luyssaert, 2014; Ruiz-peinado et al., 2017) indicates that wellmanaged forests are able to hold as much carbon as unmanaged forests. The study area embraces 110.66 tons/ha of tree aboveground biomass and 55.33 tons/ha of carbon which is considered as a large amount of carbon sequestration. In Vietnam, it is obvious that positive relationship between species diversity and tree above ground biomass/ carbon concentration will have an important impact on management policy designations and implementation since it would support the assertion in which the REDD+ schemes can provide extraordinary co-benefits for biodiversity conservation. However, for the cases of negative correlation, there would be many trade-offs between biodiversity conservation and biomass accumulation/ carbon sequestration. 6. - CONCLUSION 1 Tree above ground biomass by compartments was calculated using different developed biomass equations and the carbon sequestration was derived from tree above ground biomass. The results show that the study area embraces 110.66 tons/ha of tree aboveground biomass and 55.33 tons/ha of carbon. 2 For each tree, different measures of tree diversity and mixture around it were computed to estimate species richness & diversity, species intermingling, and tree distribution pattern (vertical and horizontal). The result shows that the study area has high species diversity with relatively high evenness. Although the study area is confirmed to be a plantation the results from functions and indices for depicting the horizontal spatial patterns indicate that the distribution of trees in the Marteloscope follows a trend towards random (Poisson) distribution. 3 The relationship between above ground tree biomass and species diversity were examined by regression analysis using a set of parameters for the characterization of mixed stand structure include stand density and diversity, species intermingling, horizontal and vertical tree distribution pattern. As a result, a negative relationship between above ground tree biomass and species diversity was obtained from the outcomes of optimum model sensitivity analysis. Such relationship was not common when compared to other studies and would lead to many trade-offs between biodiversity conservation and biomass accumulation/ carbon sequestration. Aboveground tree biomass, carbon stocks and tree diversity in a mixed forest plantation in Northern Vietnam Thi Nhat Minh Doan Máster en Gestión Forestal basada en Ciencia de Datos - Master on Forest Management based on Data Science (DATAFOREST) 53 7.- AKNOWLEDGES I would like to extend thanks to the many people who so generously contributed to the work presented in this thesis. Firstly, I would like to express my sincere gratitude to my supervisors Professor Felipe Bravo Oviedo from University of Valladolid and Professor Vu Van Manh from Vietnam National University - University of Sciences for their patience and the continuous support of my study. Besides my supervisors, I would like to express my thanks and sincere to Irene Ruano, Cristóbal Ordóñez, Narangarav Dugarsuren, people and other students in ETS Agricultural Engineering University of Valladolid for their assistance and supports in many aspects of the study. A special thank goes to the professors, staffs and students in Vietnam National University - University of Sciences who have been involved in the planning, establishment, and measurement of the Marteloscope in the framework of the BioEcoN project. The study has been made possible through the BioEcoN project financed by the Erasmus+, Capacity Building in the Field of Higher Education. Finally, but by no means least, my deep appreciation to my family and friends for providing me with unconditionally support and continuous encouragement throughout my years of study. 8.- REFERENCES AEBIOM. (2017). European Biomass Association. Statistical report. European bioenergy outlook. 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The Annals of Statistics, 6(2), Aboveground tree biomass, carbon stocks and tree diversity in a mixed forest plantation in Northern Vietnam Thi Nhat Minh Doan Máster en Gestión Forestal basada en Ciencia de Datos - Master on Forest Management based on Data Science (DATAFOREST) 64 No. Model 𝜷𝟎 𝜷𝟏 𝜷𝟐 𝜷𝟑 𝑹𝟐 𝒑−𝒗𝒂𝒍𝒖𝒆 MSE AIC BIC 55 𝐴𝐺𝐵=exp (𝛽0+𝛽1𝐺2+𝛽2𝑆−1+𝛽3𝑆ℎ) 6.9181 0.0010 0.0411 -0.7272 0.0844 <0.0001 0.5830 695.6768 713.9916 56 𝐴𝐺𝐵=exp (𝛽0+𝛽1𝐺2+𝛽2𝑆−1+𝛽3𝑆ℎ2) 5.7754 0.0010 0.0411 -0.1132 0.0854 <0.0001 0.5824 695.3526 713.6674 57 𝐴𝐺𝐵=exp (𝛽0+𝛽1𝐺2+𝛽2𝑆−1+𝛽3𝑆ℎ−1) 2.2963 0.0011 0.0410 7.1867 0.0815 <0.0001 0.5849 696.6217 714.9366 58 𝐴𝐺𝐵=exp (𝛽0+𝛽1𝐺2+𝛽2𝑆−1+𝛽3𝑆ℎ−0.5) -0.0026*** 0.0011 0.0411 8.1512 0.0824 <0.0001 0.5843 696.3494 714.6642 59 𝐴𝐺𝐵=exp (𝛽0+𝛽1𝐺2+𝛽2𝑆−1+𝛽3𝑆ℎ0.5) 9.2166 0.0010 0.0411 -2.5927 0.0838 <0.0001 0.5834 695.8762 714.1911 60 𝐴𝐺𝐵=exp (𝛽0+𝛽1𝐺2+𝛽2𝑆−1+𝛽3𝑆𝑚) 17.1570 0.0011 0.0410 -13.2659 0.0787 <0.0001 0.5867 697.5447 715.8596 61 𝐴𝐺𝐵=exp (𝛽0+𝛽1𝐺2+𝛽2𝑆−1+𝛽3𝑆𝑚2) 10.9139 0.0011 0.0410 -7.0419 0.0791 <0.0001 0.5864 697.4252 715.7400 62 𝐴𝐺𝐵=exp (𝛽0+𝛽1𝐺2+𝛽2𝑆−1+𝛽3𝑆𝑚−0.5) -20.3068 0.0011 0.0409 24.2259 0.0781 <0.0001 0.5870 697.7313 716.0461 63 𝐴𝐺𝐵=exp (𝛽0+𝛽1𝐺2+𝛽2𝑆−1+𝛽3𝑆𝑚0.5) 29.6443 0.0011 0.0410 -25.7437 0.0785 <0.0001 0.5868 697.6060 715.9208 64 𝐴𝐺𝐵=exp (𝛽0+𝛽1𝐺2+𝛽2𝑆−1+𝛽3𝑅) 6.9775 0.0008 0.0480 -2.2594 0.0852 <0.0001 0.5825 695.4151 713.7299 65 𝐴𝐺𝐵=exp (𝛽0+𝛽1𝐺2+𝛽2𝑆−1+𝛽3𝑅2) 5.8000 0.0008 0.0482 -1.0742 0.0857 <0.0001 0.5822 695.2735 713.5883 66 𝐴𝐺𝐵=exp (𝛽0+𝛽1𝐺2+𝛽2𝑆−1+𝛽3𝑅−1) 2.2780 0.0008 0.0473 2.4205 0.0835 <0.0001 0.5836 695.9809 714.2957 67 𝐴𝐺𝐵=exp (𝛽0+𝛽1𝐺2+𝛽2𝑆−1+𝛽3𝑅−0.5) -0.0753*** 0.0008 0.0475 4.7792 0.0840 <0.0001 0.5833 695.7997 714.1146 68 𝐴𝐺𝐵=exp (𝛽0+𝛽1𝐺2+𝛽2𝑆−1+𝛽3𝑅0.5) 9.3305 0.0008 0.0479 -4.6167 0.0849 <0.0001 0.5827 695.5186 713.8334 69 𝐴𝐺𝐵=exp (𝛽0+𝛽1𝐺2+𝛽2𝑆−0.5+𝛽3𝑁) 5.1113 0.0009 0.2349 -0.0266 0.0856 <0.0001 0.5823 695.2859 713.6008 70 𝐴𝐺𝐵=exp (𝛽0+𝛽1𝐺2+𝛽2𝑆−0.5+𝛽3𝑁−1) 3.4650 0.0011 0.2318 21.2774 0.0780 <0.0001 0.5871 697.7722 716.0870 71 𝐴𝐺𝐵=exp (𝛽0+𝛽1𝐺2+𝛽2𝑆−0.5+𝛽3𝑁−0.5) 2.6893 0.0010 0.2340 8.2981 0.0805 <0.0001 0.5855 696.9694 715.2843 72 𝐴𝐺𝐵=exp (𝛽0+𝛽1𝐺2+𝛽2𝑆−0.5+𝛽3𝑁0.5) 5.8811 0.0010 0.2356 -0.2930 0.0844 <0.0001 0.5831 695.7008 714.0156 73 𝐴𝐺𝐵=exp (𝛽0+𝛽1𝐺2+𝛽2𝑆−0.5+𝛽3𝑆ℎ) 6.6213 0.0010 0.2329 -0.7326 0.0827 <0.0001 0.5841 696.2557 714.5705 74 𝐴𝐺𝐵=exp (𝛽0+𝛽1𝐺2+𝛽2𝑆−0.5+𝛽3𝑆ℎ2) 5.4705 0.0010 0.2327 -0.1141 0.0837 <0.0001 0.5835 695.9266 714.2414 75 𝐴𝐺𝐵=exp (𝛽0+𝛽1𝐺2+𝛽2𝑆−0.5+𝛽3𝑆ℎ−1) 1.9676 0.0011 0.2318 7.2387 0.0797 <0.0001 0.5860 697.2119 715.5268 76 𝐴𝐺𝐵=exp (𝛽0+𝛽1𝐺2+𝛽2𝑆−0.5+𝛽3𝑆ℎ−0.5) -0.3489*** 0.0011 0.2323 8.2106 0.0806 <0.0001 0.5855 696.9366 715.2514 77 𝐴𝐺𝐵=exp (𝛽0+𝛽1𝐺2+𝛽2𝑆−0.5+𝛽3𝑆ℎ0.5) 8.9368 0.0010 0.2329 -2.6118 0.0820 <0.0001 0.5845 696.4578 714.7726 78 𝐴𝐺𝐵=exp (𝛽0+𝛽1𝐺2+𝛽2𝑆−0.5+𝛽3𝑅) 6.6253 0.0008 0.2779 -2.2857 0.0835 <0.0001 0.5836 695.9650 714.2798 79 𝐴𝐺𝐵=exp (𝛽0+𝛽1𝐺2+𝛽2𝑆−0.5+𝛽3𝑅2) 5.4321 0.0008 0.2792 -1.0866 0.0840 <0.0001 0.5833 695.8272 714.1420 80 𝐴𝐺𝐵=exp (𝛽0+𝛽1𝐺2+𝛽2𝑆−0.5+𝛽3𝑅−1) 1.8770 0.0008 0.2736 2.4489 0.0818 <0.0001 0.5847 696.5271 714.8419 81 𝐴𝐺𝐵=exp (𝛽0+𝛽1𝐺2+𝛽2𝑆−0.5+𝛽3𝑅−0.5) -0.5058*** 0.0008 0.2749 4.8353 0.0824 <0.0001 0.5843 696.3462 714.6611 82 𝐴𝐺𝐵=exp (𝛽0+𝛽1𝐺2+𝛽2𝑆−0.5+𝛽3𝑅0.5) 9.0070 0.0008 0.2771 -4.6707 0.0832 <0.0001 0.5838 696.0670 714.3818 Aboveground tree biomass, carbon stocks and tree diversity in a mixed forest plantation in Northern Vietnam Thi Nhat Minh Doan Máster en Gestión Forestal basada en Ciencia de Datos - Master on Forest Management based on Data Science (DATAFOREST) 65 No. Model 𝜷𝟎 𝜷𝟏 𝜷𝟐 𝜷𝟑 𝑹𝟐 𝒑−𝒗𝒂𝒍𝒖𝒆 MSE AIC BIC 83 𝐴𝐺𝐵=exp (𝛽0+𝛽1𝐺2+𝛽2𝑆−0.5+𝛽3𝑊0.5) 4.5269 0.0008 0.1547*** -0.1629*** 0.0260 0.0503 0.6202 714.2445 732.5594 84 𝐴𝐺𝐵=exp (𝛽0+𝛽1𝐺2+𝛽2𝑆0.5+𝛽3𝑁) 6.2233 0.0009 -1.3010*** -0.0265 0.0807 <0.0001 0.5854 696.9102 715.2251 85 𝐴𝐺𝐵=exp (𝛽0+𝛽1𝐺2+𝛽2𝑆0.5+𝛽3𝑁2) 5.8520 0.0008 -1.2800*** -0.0004 0.0820 <0.0001 0.5846 696.4775 714.7923 86 𝐴𝐺𝐵=exp (𝛽0+𝛽1𝐺2+𝛽2𝑆0.5+𝛽3𝑁0.5) 6.9897 0.0010 -1.3005*** -0.2915 0.0793 <0.0001 0.5863 697.3516 715.6664 87 𝐴𝐺𝐵=exp (𝛽0+𝛽1𝐺2+𝛽2𝑆0.5+𝛽3𝑆ℎ) 7.7106 0.0010 -1.2800*** -0.7286 0.0776 <0.0001 0.5873 697.8910 716.2058 88 𝐴𝐺𝐵=exp (𝛽0+𝛽1𝐺2+𝛽2𝑆0.5+𝛽3𝑆ℎ2) 6.5665 0.0010 -1.2811*** -0.1135 0.0787 <0.0001 0.5867 697.5502 715.8651 89 𝐴𝐺𝐵=exp (𝛽0+𝛽1𝐺2+𝛽2𝑆0.5+𝛽3𝑆ℎ0.5) 10.0113 0.0010 -1.2779*** -2.5970 0.0770 <0.0001 0.5877 698.0975 716.4123 90 𝐴𝐺𝐵=exp (𝛽0+𝛽1𝐺2+𝛽2𝑆0.5+𝛽3𝑅) 7.9374 0.0008 -1.5861 -2.2596 0.0775 <0.0001 0.5874 697.9394 716.2542 91 𝐴𝐺𝐵=exp (𝛽0+𝛽1𝐺2+𝛽2𝑆0.5+𝛽3𝑅2) 6.7635 0.0008 -1.5933 -1.0738 0.0779 <0.0001 0.5872 697.8191 716.1339 92 𝐴𝐺𝐵=exp (𝛽0+𝛽1𝐺2+𝛽2𝑆0.5+𝛽3𝑅−1) 3.2197 0.0008 -1.5583*** 2.4226 0.0759 <0.0001 0.5884 698.4557 716.7706 93 𝐴𝐺𝐵=exp (𝛽0+𝛽1𝐺2+𝛽2𝑆0.5+𝛽3𝑅−0.5) 0.8701*** 0.0008 -1.5671*** 4.7826 0.0764 <0.0001 0.5881 698.2877 716.6026 94 𝐴𝐺𝐵=exp (𝛽0+𝛽1𝐺2+𝛽2𝑆0.5+𝛽3𝑅0.5) 10.2886 0.0008 -1.5810 -4.6182 0.0772 <0.0001 0.5876 698.0313 716.3462 95 𝐴𝐺𝐵=exp (𝛽0+𝛽1𝐺2+𝛽2𝐸2+𝛽3𝑇𝐻2) 8.7756 0.0010 -4.3151 -1.3031 0.0579 0.0005 0.5999 704.2526 722.5675 96 𝐴𝐺𝐵=exp (𝛽0+𝛽1𝐺2+𝛽2𝐸−1+𝛽3𝑇𝐻2) -2.9025*** 0.0010 7.3909 -1.2988 0.0578 0.0005 0.6000 704.2863 722.6012 97 𝐴𝐺𝐵=exp (𝛽0+𝛽1𝐺2+𝛽2𝐸+𝛽3𝑇𝐻2) 12.6732 0.0010 -8.2034 -1.3017 0.0579 0.0005 0.5999 704.2597 722.5746 98 𝐴𝐺𝐵=𝛽0+𝛽1𝐺2 111.2538 0.2704 - - 0.0285 0.0033 53980.7767 4124.3525 4135.3828 99 𝐴𝐺𝐵=𝛽0+𝛽1𝐺2+𝛽2𝑆ℎ+𝛽3𝑀𝑖 572.0256 0.3456 -152.8159 90.8462*** 0.0721 0.0001 51905.6872 4114.6954 4133.0102 100 𝐴𝐺𝐵=𝛽0+𝛽1𝐺2+𝛽2𝑆ℎ+𝛽3𝑀𝑖2 539.9327 0.3368 -141.0055 139.5531 0.0804 <0.0001 51442.9412 4112.0089 4130.3237 101 𝐴𝐺𝐵=𝛽0+𝛽1𝐺2+𝛽2𝑆ℎ+𝛽3𝑀𝑆2 589.5807 0.3393 -152.6341 477.4073*** 0.0717 0.0001 51930.7666 4114.8403 4133.1551 102 𝐴𝐺𝐵=𝛽0+𝛽1𝐺2+𝛽2𝑆ℎ2+𝛽3𝑀𝑖 332.5423 0.3395 -23.8261 89.7512*** 0.0727 0.0001 51876.7194 4114.5279 4132.8427 103 𝐴𝐺𝐵=𝛽0+𝛽1𝐺2+𝛽2𝑆ℎ2+𝛽3𝑀𝑖2 318.7797 0.3312 -21.9799 138.2643 0.0808 <0.0001 51420.7839 4111.8796 4130.1944 104 𝐴𝐺𝐵=𝛽0+𝛽1𝐺2+𝛽2𝑆ℎ2+𝛽3𝑀𝑆2 350.3588 0.3333 -23.8198 472.7873*** 0.0723 0.0001 51898.3246 4114.6528 4132.9677 105 𝐴𝐺𝐵=𝛽0+𝛽1𝐺2+𝛽2𝑆ℎ−1+𝛽3𝑀𝑖2 -354.5409 0.3463 1385.7435 142.2634*** 0.0790 <0.0001 51520.2270 4112.4592 4130.7741 106 𝐴𝐺𝐵=𝛽0+𝛽1𝐺2+𝛽2𝑆ℎ−0.5+𝛽3𝑀𝑖 -879.8592 0.3538 1707.2342 92.4724*** 0.0710 0.0001 51971.4281 4115.0751 4133.3899 107 𝐴𝐺𝐵=𝛽0+𝛽1𝐺2+𝛽2𝑆ℎ−0.5+𝛽3𝑀𝑖2 -799.2580 0.3442 1574.7164 141.5787 0.0794 <0.0001 51496.8729 4112.3232 4130.6380 108 𝐴𝐺𝐵=𝛽0+𝛽1𝐺2+𝛽2𝑆ℎ0.5+𝛽3𝑀𝑖 1053.9582 0.3485 -544.3562 91.3939*** 0.0718 0.0001 51924.6429 4114.8049 4133.1198 109 𝐴𝐺𝐵=𝛽0+𝛽1𝐺2+𝛽2𝑆ℎ0.5+𝛽3𝑀𝑖2 984.6544 0.3394 -502.2726 140.2196 0.0801 <0.0001 51458.1630 4112.0976 4130.4124 110 𝐴𝐺𝐵=𝛽0+𝛽1𝐺2+𝛽2𝑆ℎ0.5+𝛽3𝑀𝑆2 1070.5672 0.3421 -543.4282 479.6880*** 0.0713 0.0001 51951.5602 4114.9604 4133.2752 Aboveground tree biomass, carbon stocks and tree diversity in a mixed forest plantation in Northern Vietnam Thi Nhat Minh Doan Máster en Gestión Forestal basada en Ciencia de Datos - Master on Forest Management based on Data Science (DATAFOREST) 66 No. Model 𝜷𝟎 𝜷𝟏 𝜷𝟐 𝜷𝟑 𝑹𝟐 𝒑−𝒗𝒂𝒍𝒖𝒆 MSE AIC BIC 111 𝐴𝐺𝐵=𝛽0+𝛽1𝐺2+𝛽2𝑆𝑚+𝛽3𝑀𝑖2 2423.7656 0.3436 -2465.7444 140.1278 0.0761 <0.0001 51682.1758 4113.4008 4131.7156 112 𝐴𝐺𝐵=𝛽0+𝛽1𝐺2+𝛽2𝑆𝑚2+𝛽3𝑀𝑖2 1265.4259 0.3432 -1311.0766 139.8578 0.0763 <0.0001 51670.7236 4113.3343 4131.6491 113 𝐴𝐺𝐵=𝛽0+𝛽1𝐺2+𝛽2𝑆𝑚−1+𝛽3𝑀𝑖2 -2210.8547 0.3443 2175.9214 140.6728 0.0757 <0.0001 51706.1088 4113.5397 4131.8545 114 𝐴𝐺𝐵=𝛽0+𝛽1𝐺2+𝛽2𝑆𝑚−0.5+𝛽3𝑀𝑖2 -4527.8443 0.3441 4491.1863 140.5360 0.0758 <0.0001 51699.9997 4113.5042 4131.8190 115 𝐴𝐺𝐵=𝛽0+𝛽1𝐺2+𝛽2𝑆𝑚0.5+𝛽3𝑀𝑖2 4740.7572 0.3438 -4780.9377 140.2635 0.0760 <0.0001 51688.0321 4113.4348 4131.7496 116 𝐴𝐺𝐵=𝛽0+𝛽1𝐺2+𝛽2𝑅+𝛽3𝑀𝑖 612.0602 0.2944 -494.8133 96.6393 0.0763 <0.0001 51673.8089 4113.3522 4131.6670 117 𝐴𝐺𝐵=𝛽0+𝛽1𝐺2+𝛽2𝑅+𝛽3𝑀𝑖2 589.8170 0.2895 -468.0241 147.3425 0.0856 <0.0001 51152.9359 4110.3128 4128.6277 118 𝐴𝐺𝐵=𝛽0+𝛽1𝐺2+𝛽2𝑅+𝛽3(𝑀𝑖+1)−1 764.2193 0.2944 -506.2785 -137.5924*** 0.0719 0.0001 51917.5119 4114.7637 4133.0786 119 𝐴𝐺𝐵=𝛽0+𝛽1𝐺2+𝛽2𝑅+𝛽3(𝑀𝑖+1)−0.5 878.5821 0.2945 -503.9158 -255.2357*** 0.0728 0.0001 51867.7028 4114.4758 4132.7906 120 𝐴𝐺𝐵=𝛽0+𝛽1𝐺2+𝛽2𝑅+𝛽3𝑀𝑖0.5 629.8858 0.2954 -511.1425 65.6077*** 0.0715 0.0001 51940.1676 4114.8946 4133.2094 121 𝐴𝐺𝐵=𝛽0+𝛽1𝐺2+𝛽2𝑅+𝛽3𝑀𝑆 630.3659 0.2951 -506.7116 203.4404*** 0.0742 <0.0001 51788.7944 4114.0190 4132.3339 122 𝐴𝐺𝐵=𝛽0+𝛽1𝐺2+𝛽2𝑅+𝛽3𝑀𝑆2 634.8697 0.2881 -498.5333 522.3695 0.0765 <0.0001 51663.3592 4113.2915 4131.6064 123 𝐴𝐺𝐵=𝛽0+𝛽1𝐺2+𝛽2𝑅+𝛽3(𝑀𝑆+1)−1 889.1875 0.2957 -509.8489 -256.4631*** 0.0727 0.0001 51875.3379 4114.5199 4132.8348 124 𝐴𝐺𝐵=𝛽0+𝛽1𝐺2+𝛽2𝑅+𝛽3(𝑀𝑆+1)−0.5 1119.5123 0.2956 -509.0726 -487.5323*** 0.0731 0.0001 51853.3233 4114.3926 4132.7074 125 𝐴𝐺𝐵=𝛽0+𝛽1𝐺2+𝛽2𝑅2+𝛽3𝑀𝑖 354.0280 0.2936 -234.7952 96.3161*** 0.0764 <0.0001 51666.1757 4113.3079 4131.6227 126 𝐴𝐺𝐵=𝛽0+𝛽1𝐺2+𝛽2𝑅2+𝛽3𝑀𝑖2 346.0359 0.2887 -222.4186 147.3346 0.0858 <0.0001 51140.6807 4110.2410 4128.5558 127 𝐴𝐺𝐵=𝛽0+𝛽1𝐺2+𝛽2𝑅2+𝛽3(𝑀𝑖+1)2 499.3140 0.2935 -240.1425 -136.7070 0.0720 0.0001 51910.8371 4114.7252 4133.0400 128 𝐴𝐺𝐵=𝛽0+𝛽1𝐺2+𝛽2𝑅2+𝛽3(𝑀𝑖+1)−0.5 614.3543 0.2936 -239.0379 -253.8009*** 0.0729 0.0001 51860.9062 4114.4365 4132.7513 129 𝐴𝐺𝐵=𝛽0+𝛽1𝐺2+𝛽2𝑅2+𝛽3𝑀𝑖0.5 363.3159 0.2945 -242.3958 65.1171*** 0.0716 0.0001 51934.0030 4114.8590 4133.1738 130 𝐴𝐺𝐵=𝛽0+𝛽1𝐺2+𝛽2𝑅2+𝛽3𝑀𝑆 366.1669 0.2942 -240.5168 202.9551*** 0.0744 <0.0001 51779.1996 4113.9634 4132.2783 131 𝐴𝐺𝐵=𝛽0+𝛽1𝐺2+𝛽2𝑅2+𝛽3𝑀𝑆2 375.1126 0.2873 -236.8561 522.6159 0.0767 <0.0001 51650.3901 4113.2162 4131.5310 132 𝐴𝐺𝐵=𝛽0+𝛽1𝐺2+𝛽2𝑅2+𝛽3(𝑀𝑆+1)−1 622.3858 0.2948 -241.9470 -255.5205*** 0.0728 0.0001 51866.5425 4114.4691 4132.7839 133 𝐴𝐺𝐵=𝛽0+𝛽1𝐺2+𝛽2𝑅2+𝛽3(𝑀𝑆+1)−0.5 852.4364 0.2948 -241.5919 -485.9069*** 0.0732 0.0001 51844.3548 4114.3407 4132.6555 134 𝐴𝐺𝐵=𝛽0+𝛽1𝐺2+𝛽2𝑅2+𝛽3𝑀𝑆0.5 368.2703 0.2954 -244.8714 97.1280*** 0.0710 0.0001 51967.4510 4115.0522 4133.3670 135 𝐴𝐺𝐵=𝛽0+𝛽1𝐺2+𝛽2𝑅2+𝛽3𝑊2 425.2118 0.2890 -244.2001 -84.9516*** 0.0710 0.0001 51966.4684 4115.0465 4133.3613 136 𝐴𝐺𝐵=𝛽0+𝛽1𝐺2+𝛽2𝑅−1+𝛽3𝑀𝑖 -418.9905 0.2963 530.9160 97.1903 0.0753 <0.0001 51727.1053 4113.6615 4131.9763 137 𝐴𝐺𝐵=𝛽0+𝛽1𝐺2+𝛽2𝑅−1+𝛽3𝑀𝑖2 -383.2320 0.2911 500.0452 147.3247 0.0845 <0.0001 51215.0065 4110.6767 4128.9915 138 𝐴𝐺𝐵=𝛽0+𝛽1𝐺2+𝛽2𝑅−1+𝛽3(𝑀𝑖+1)−1 -289.9981*** 0.2964 543.9073 -139.1393*** 0.0710 0.0001 51968.8620 4115.0603 4133.3751 Aboveground tree biomass, carbon stocks and tree diversity in a mixed forest plantation in Northern Vietnam Thi Nhat Minh Doan Máster en Gestión Forestal basada en Ciencia de Datos - Master on Forest Management based on Data Science (DATAFOREST) 67 No. Model 𝜷𝟎 𝜷𝟏 𝜷𝟐 𝜷𝟑 𝑹𝟐 𝒑−𝒗𝒂𝒍𝒖𝒆 MSE AIC BIC 139 𝐴𝐺𝐵=𝛽0+𝛽1𝐺2+𝛽2𝑅−1+𝛽3(𝑀𝑖+1)−0.5 -169.5955*** 0.2965 541.2426 -257.7341*** 0.0719 0.0001 51919.3106 4114.7741 4133.0889 140 𝐴𝐺𝐵=𝛽0+𝛽1𝐺2+𝛽2𝑅−1+𝛽3𝑀𝑖0.5 -436.3972 0.2975 549.4483 66.4554*** 0.0706 0.0001 51990.7297 4115.1865 4133.5013 141 𝐴𝐺𝐵=𝛽0+𝛽1𝐺2+𝛽2𝑅−1+𝛽3𝑀𝑆 -424.9545 0.2969 543.2963 203.8034*** 0.0732 0.0001 51848.0139 4114.3619 4132.6767 142 𝐴𝐺𝐵=𝛽0+𝛽1𝐺2+𝛽2𝑅−1+𝛽3𝑀𝑆2 -402.1960 0.2898 533.3399 520.6724 0.0753 <0.0001 51729.2142 4113.6737 4131.9885 143 𝐴𝐺𝐵=𝛽0+𝛽1𝐺2+𝛽2𝑅−0.5+𝛽3𝑀𝑖2 -870.2518 0.2907 988.4786 147.3297 0.0848 <0.0001 51194.3491 4110.5556 4128.8705 144 𝐴𝐺𝐵=𝛽0+𝛽1𝐺2+𝛽2𝑅−0.5+𝛽3(𝑀𝑖+1)−1 -818.3283 0.2958 1073.4493 -138.7864*** 0.0713 0.0001 51950.7328 4114.9556 4133.2705 145 𝐴𝐺𝐵=𝛽0+𝛽1𝐺2+𝛽2𝑅−0.5+𝛽3(𝑀𝑖+1)−0.5 -695.6395 0.2960 1068.2667 -257.1645*** 0.0722 0.0001 51901.1198 4114.6690 4132.9838 146 𝐴𝐺𝐵=𝛽0+𝛽1𝐺2+𝛽2𝑅−0.5+𝛽3𝑀𝑖0.5 -969.5684 0.2969 1084.2109 66.2642*** 0.0709 0.0001 51972.7545 4115.0828 4133.3976 147 𝐴𝐺𝐵=𝛽0+𝛽1𝐺2+𝛽2𝑅−0.5+𝛽3(𝑀𝑆+1)−1 -703.6709 0.2971 1080.0198 -257.3553*** 0.0720 0.0001 51912.8631 4114.7369 4133.0517 148 𝐴𝐺𝐵=𝛽0+𝛽1𝐺2+𝛽2𝑅−0.5+𝛽3(𝑀𝑆+1)−0.5 -470.2086*** 0.2970 1078.2543 -489.0033*** 0.0724 0.0001 51891.1526 4114.6114 4132.9262 149 𝐴𝐺𝐵=𝛽0+𝛽1𝐺2+𝛽2𝑅0.5+𝛽3𝑀𝑖 1127.8547 0.2949 -1011.7672 96.7897 0.0761 <0.0001 51682.0655 4113.4001 4131.7150 150 𝐴𝐺𝐵=𝛽0+𝛽1𝐺2+𝛽2𝑅0.5+𝛽3𝑀𝑖0.5 1163.0420 0.2959 -1045.5530 65.8387*** 0.0714 0.0001 51947.6940 4114.9381 4133.2529 151 𝐴𝐺𝐵=𝛽0+𝛽1𝐺2+𝛽2𝑅0.5+𝛽3𝑀𝑆 1158.4149 0.2955 -1035.9217 203.6097*** 0.0741 <0.0001 51798.2773 4114.0739 4132.3888 152 𝐴𝐺𝐵=𝛽0+𝛽1𝐺2+𝛽2𝑅0.5+𝛽3𝑀𝑆2 1153.8916 0.2885 -1018.6822 522.0933 0.0763 <0.0001 51674.5368 4113.3564 4131.6713 153 𝐴𝐺𝐵=𝛽0+𝛽1𝐺2+𝛽2𝑅0.5+𝛽3(𝑀𝑆+1)−1 1421.0125 0.2962 -1042.4866 -256.8337*** 0.0725 0.0001 51884.3847 4114.5722 4132.8871 154 𝐴𝐺𝐵=𝛽0+𝛽1𝐺2+𝛽2𝑅0.5+𝛽3(𝑀𝑆+1)−0.5 1650.7525 0.2961 -1040.8648 -488.1579*** 0.0729 0.0001 51862.4663 4114.4455 4132.7603 155 𝐴𝐺𝐵=𝛽0+𝛽1𝐺2+𝛽2𝑆+𝛽3𝑁 386.9866 0.3117 -336.8901*** -6.3800 0.0689 0.0001 52086.4654 4115.7384 4134.0532 156 𝐴𝐺𝐵=𝛽0+𝛽1𝐺2+𝛽2𝑆+𝛽3𝑁2 297.1966 0.2877 -330.4407*** -0.0975 0.0690 0.0001 52082.6214 4115.7163 4134.0311 157 𝐴𝐺𝐵=𝛽0+𝛽1𝐺2+𝛽2𝑆+𝛽3𝑅 823.1657 0.2829 -433.7118 -576.2434 0.0712 0.0001 51955.6716 4114.9841 4133.2990 158 𝐴𝐺𝐵=𝛽0+𝛽1𝐺2+𝛽2𝑆+𝛽3𝑅2 523.4011 0.2820 -435.7339*** -273.8443 0.0715 0.0001 51939.8825 4114.8930 4133.2078 159 𝐴𝐺𝐵=𝛽0+𝛽1𝐺2+𝛽2𝑆+𝛽3𝑅−1 -377.2639 0.2849 -424.8738*** 616.3951 0.0699 0.0001 52032.1125 4115.4252 4133.7400 160 𝐴𝐺𝐵=𝛽0+𝛽1𝐺2+𝛽2𝑆+𝛽3𝑅−0.5 -976.5124 0.2844 -427.7444*** 1217.9208 0.0703 0.0001 52006.8054 4115.2793 4133.5941 161 𝐴𝐺𝐵=𝛽0+𝛽1𝐺2+𝛽2𝑆+𝛽3𝑅0.5 1422.6781 0.2834 -432.1385*** -1177.3788 0.0710 0.0001 51968.8171 4115.0600 4133.3749 162 𝐴𝐺𝐵=𝛽0+𝛽1𝐺2+𝛽2𝑆2+𝛽3𝑁 346.8661 0.3111 -703.7564*** -6.2957 0.0673 0.0001 52177.2809 4116.2610 4134.5759 163 𝐴𝐺𝐵=𝛽0+𝛽1𝐺2+𝛽2𝑆2+𝛽3𝑁2 259.4547 0.2875 -696.6044*** -0.0964 0.0675 0.0001 52167.6026 4116.2054 4134.5202 164 𝐴𝐺𝐵=𝛽0+𝛽1𝐺2+𝛽2𝑆2+𝛽3𝑅 762.8839 0.2827 -936.3257*** -563.9398 0.0690 0.0001 52082.1923 4115.7138 4134.0286 165 𝐴𝐺𝐵=𝛽0+𝛽1𝐺2+𝛽2𝑆2+𝛽3𝑅2 469.2446 0.2818 -940.5999*** -267.9460 0.0692 0.0001 52067.5223 4115.6293 4133.9441 166 𝐴𝐺𝐵=𝛽0+𝛽1𝐺2+𝛽2𝑆2+𝛽3𝑅0−1 -411.2575 0.2846 -915.6041*** 603.4464 0.0677 0.0001 52154.8145 4116.1318 4134.4467 Aboveground tree biomass, carbon stocks and tree diversity in a mixed forest plantation in Northern Vietnam Thi Nhat Minh Doan Máster en Gestión Forestal basada en Ciencia de Datos - Master on Forest Management based on Data Science (DATAFOREST) 68 No. Model 𝜷𝟎 𝜷𝟏 𝜷𝟐 𝜷𝟑 𝑹𝟐 𝒑−𝒗𝒂𝒍𝒖𝒆 MSE AIC BIC 167 𝐴𝐺𝐵=𝛽0+𝛽1𝐺2+𝛽2𝑆2+𝛽3𝑅−0.5 -998.0954 0.2841 -922.4699*** 1192.2378 0.0681 0.0001 52130.6747 4115.9929 4134.3078 168 𝐴𝐺𝐵=𝛽0+𝛽1𝐺2+𝛽2𝑆2+𝛽3𝑅0.5 1349.8645 0.2832 -932.7647*** -1152.3471 0.0688 0.0001 52094.5897 4115.7852 4134.1000 169 𝐴𝐺𝐵=𝛽0+𝛽1𝐺2+𝛽2𝑆−1+𝛽3𝑁 274.1192 0.3090 8.1857*** -6.3154 0.0712 0.0001 51955.2646 4114.9818 4133.2966 170 𝐴𝐺𝐵=𝛽0+𝛽1𝐺2+𝛽2𝑆−1+𝛽3𝑁2 187.3738 0.2854 7.9754*** -0.0963 0.0711 0.0001 51960.8829 4115.0142 4133.3291 171 𝐴𝐺𝐵=𝛽0+𝛽1𝐺2+𝛽2𝑆−1+𝛽3𝑁0.5 458.3938 0.3212 8.2344*** -69.8699 0.0706 0.0001 51988.9401 4115.1762 4133.4910 172 𝐴𝐺𝐵=𝛽0+𝛽1𝐺2+𝛽2𝑆−1+𝛽3𝑅 676.8613 0.2800 10.0184*** -570.1519 0.0740 <0.0001 51798.9938 4114.0781 4132.3929 173 𝐴𝐺𝐵=𝛽0+𝛽1𝐺2+𝛽2𝑆−1+𝛽3𝑅2 379.7481 0.2791 10.0735*** -271.0967 0.0744 <0.0001 51781.0371 4113.9741 4132.2889 174 𝐴𝐺𝐵=𝛽0+𝛽1𝐺2+𝛽2𝑆−1+𝛽3𝑅−1 -507.6997 0.2820 9.8311*** 609.3986 0.0726 0.0001 51879.4976 4114.5440 4132.8588 175 𝐴𝐺𝐵=𝛽0+𝛽1𝐺2+𝛽2𝑆−1+𝛽3𝑅−0.5 -1101.1888 0.2815 9.8883*** 1204.2787 0.0731 0.0001 51853.2313 4114.3921 4132.7069 176 𝐴𝐺𝐵=𝛽0+𝛽1𝐺2+𝛽2𝑆−1+𝛽3𝑅0.5 1270.2509 0.2805 9.9816*** -1164.6539 0.0738 <0.0001 51813.2023 4114.1604 4132.4752 177 𝐴𝐺𝐵=𝛽0+𝛽1𝐺2+𝛽2𝑆−0.5+𝛽3𝑁 209.3312 0.3101 48.0941*** -6.3706 0.0709 0.0001 51974.2189 4115.0912 4133.4061 178 𝐴𝐺𝐵=𝛽0+𝛽1𝐺2+𝛽2𝑆−0.5+𝛽3𝑁2 123.5679*** 0.2861 46.8398*** -0.0972 0.0708 0.0001 51979.0419 4115.1191 4133.4339 179 𝐴𝐺𝐵=𝛽0+𝛽1𝐺2+𝛽2𝑆−0.5+𝛽3𝑁0.5 394.8919 0.3223 48.3340*** -70.4734 0.0703 0.0001 52008.8330 4115.2910 4133.6058 180 𝐴𝐺𝐵=𝛽0+𝛽1𝐺2+𝛽2𝑆−0.5+𝛽3𝑅 601.1183 0.2810 60.0430*** -577.9815 0.0739 <0.0001 51808.9004 4114.1355 4132.4503 181 𝐴𝐺𝐵=𝛽0+𝛽1𝐺2+𝛽2𝑆−0.5+𝛽3𝑅2 299.4492 0.2801 60.3712*** -274.8018 0.0742 <0.0001 51791.1005 4114.0324 4132.3472 182 𝐴𝐺𝐵=𝛽0+𝛽1𝐺2+𝛽2𝑆−0.5+𝛽3𝑅−1 -598.0083 0.2830 58.8632*** 617.7604 0.0724 0.0001 51889.9603 4114.6045 4132.9193 183 𝐴𝐺𝐵=𝛽0+𝛽1𝐺2+𝛽2𝑆−0.5+𝛽3𝑅−0.5 -1200.1985 0.2824 59.2293*** 1220.8308 0.0729 0.0001 51863.4330 4114.4511 4132.7659 184 𝐴𝐺𝐵=𝛽0+𝛽1𝐺2+𝛽2𝑆−0.5+𝛽3𝑅0.5 1202.9967 0.2815 59.8169*** -1180.6666 0.0736 <0.0001 51823.1311 4114.2179 4132.5327 185 𝐴𝐺𝐵=𝛽0+𝛽1𝐺2+𝛽2𝑆−0.5+𝛽3𝑇𝐻 41.2647*** 0.2688 23.6780*** 63.8102*** 0.0319 0.0221 54155.2727 4127.4235 4145.7383 186 𝐴𝐺𝐵=𝛽0+𝛽1𝐺2+𝛽2𝑆−0.5+𝛽3𝑇𝐻2 43.4152*** 0.2716 29.8742*** -31.4520*** 0.0310 0.0251 54206.6113 4127.7077 4146.0226 187 𝐴𝐺𝐵=𝛽0+𝛽1𝐺2+𝛽2𝑆−0.5+𝛽3𝑇𝐻0.5 17.4941*** 0.2692 20.3958*** 98.0652*** 0.0333 0.0182 54078.2511 4126.9965 4145.3113 188 𝐴𝐺𝐵=𝛽0+𝛽1𝐺2+𝛽2𝑆−0.5+𝛽3𝑀𝑖2 98.2250 0.2828*** -10.2062 172.1548*** 0.0561 0.0007 52800.3845 4119.8224 4138.1373 189 𝐴𝐺𝐵=𝛽0+𝛽1𝐺2+𝛽2𝑆−0.5+𝛽3𝑀𝑆2 66.2694*** 0.2793 10.6751*** 531.7566*** 0.0427 0.0047 53550.1243 4124.0523 4142.3671 190 𝐴𝐺𝐵=𝛽0+𝛽1𝐺2+𝛽2𝑆−0.5+𝛽3𝑊0.5 85.5245*** 0.2769 28.9852*** -64.8295*** 0.0335 0.0176 54064.5403 4126.9204 4145.2353 191 𝐴𝐺𝐵=𝛽0+𝛽1𝐺2+𝛽2𝑆0.5+𝛽3𝑁 453.0672 0.3114 -299.4290*** -6.3966 0.0696 0.0001 52046.4034 4115.5076 4133.8224 192 𝐴𝐺𝐵=𝛽0+𝛽1𝐺2+𝛽2𝑆0.5+𝛽3𝑁2 361.2387 0.2874 -292.6967*** -0.0977 0.0696 0.0001 52045.7470 4115.5038 4133.8186 193 𝐴𝐺𝐵=𝛽0+𝛽1𝐺2+𝛽2𝑆0.5+𝛽3𝑅 909.7418 0.2826 -382.2239*** -579.5761 0.0722 0.0001 51899.8085 4114.6614 4132.9762 194 𝐴𝐺𝐵=𝛽0+𝛽1𝐺2+𝛽2𝑆0.5+𝛽3𝑅2 608.7247 0.2817 -384.1110*** -275.4705 0.0725 0.0001 51883.3305 4114.5661 4132.8810 Aboveground tree biomass, carbon stocks and tree diversity in a mixed forest plantation in Northern Vietnam Thi Nhat Minh Doan Máster en Gestión Forestal basada en Ciencia de Datos - Master on Forest Management based on Data Science (DATAFOREST) 69 No. Model 𝜷𝟎 𝜷𝟏 𝜷𝟐 𝜷𝟑 𝑹𝟐 𝒑−𝒗𝒂𝒍𝒖𝒆 MSE AIC BIC 195 𝐴𝐺𝐵=𝛽0+𝛽1𝐺2+𝛽2𝑆0.5+𝛽3𝑅−1 -299.1193*** 0.2845 -374.5010*** 619.7842 0.0708 0.0001 51978.1387 4115.1138 4133.4287 196 𝐴𝐺𝐵=𝛽0+𝛽1𝐺2+𝛽2𝑆0.5+𝛽3𝑅−0.5 -901.2194 0.2840 -376.9741*** 1224.6984 0.0713 0.0001 51952.2939 4114.9646 4133.2795 197 𝐴𝐺𝐵=𝛽0+𝛽1𝐺2+𝛽2𝑆0.5+𝛽3𝑅0.5 1512.3204 0.2830 -380.8160*** -1184.0994 0.0720 0.0001 51913.3614 4114.7397 4133.0546 198 𝐴𝐺𝐵=𝛽0×(𝐺2)𝛽1 3.8184 0.2122 - - 0.0091 0.0996 0.6268 715.2793 726.3096 199 𝐴𝐺𝐵=𝛽0×(𝐺2)𝛽1×(𝑆ℎ)𝛽2 5.4650 0.4284 -2.3930 - 0.0655 <0.0001 0.5930 699.7364 714.4159 200 𝐴𝐺𝐵=𝛽0×(𝐺2)𝛽1×(𝑆𝑚)𝛽2 1.9111 0.4437 -13.1461 - 0.0611 0.0001 0.5958 701.1442 715.8238 201 𝐴𝐺𝐵=𝛽0×(𝐺2)𝛽1×(𝐸)𝛽2 2.9005 0.3168 -7.7992 - 0.0291 0.0124 0.6161 711.1950 725.8746 202 𝐴𝐺𝐵=𝛽0×(𝐺2)𝛽1×(𝐷)𝛽2 3.5519 0.2246*** 0.4451 - 0.0220 0.0365 0.6206 713.3836 728.0631 203 𝐴𝐺𝐵=𝛽0×(𝐺2)𝛽1×(𝑅)𝛽2 3.5576 0.2892 -2.1943 - 0.0608 0.0001 0.5961 701.2630 715.9425 204 𝐴𝐺𝐵=𝛽0×(𝐺2)𝛽1×(𝑇𝐻)𝛽2 3.7416 0.2115*** -0.0519*** - 0.0103 0.2136 0.6281 716.9507 731.6303 205 𝐴𝐺𝐵=𝛽0×(𝐺2)𝛽1×(𝑇𝐻2)𝛽2 3.7416 0.2115*** -0.0260*** - 0.0103 0.2136 0.6281 716.9507 731.6303 206 𝐴𝐺𝐵=𝛽0×(𝐺2)𝛽1×((𝑀𝑖+1)2)𝛽2 3.6852 0.2233*** 0.1250*** - 0.0129 0.1444 0.6264 716.1588 730.8384 207 𝐴𝐺𝐵=𝛽0×(𝐺2)𝛽1×(𝑆ℎ)𝛽2×(𝑇𝐻)𝛽3 5.3882 0.4390 -2.5265 -0.1140*** 0.0715 0.0001 0.5913 699.8963 718.2111 208 𝐴𝐺𝐵=𝛽0×(𝐺2)𝛽1×(𝑆ℎ)𝛽2×(𝑀𝑖+1)𝛽3 5.3407 0.4347 -2.3656 0.1979*** 0.0679 0.0001 0.5935 701.0269 719.3417 209 𝐴𝐺𝐵=𝛽0×(𝐺2)𝛽1×(𝑆ℎ)𝛽2×(𝑀𝑆+1)𝛽3 5.3378 0.4376 -2.3751 0.4265*** 0.0683 0.0001 0.5933 700.9041 719.2189 210 𝐴𝐺𝐵=𝛽0×(𝐺2)𝛽1×(𝑆ℎ)𝛽2×((𝑊+1)−0.5)𝛽3 5.5801 0.4382 -2.4342 0.6165*** 0.0688 0.0001 0.5930 700.7571 719.0720 211 𝐴𝐺𝐵=𝛽0×(𝐺2)𝛽1×(𝑆ℎ)𝛽2×((𝑊+1)0.5)𝛽3 5.5801 0.4382 -2.4342 -0.6165*** 0.0688 0.0001 0.5930 700.7571 719.0720 212 𝐴𝐺𝐵=𝛽0×(𝐺2)𝛽1×(𝑆ℎ)𝛽2×(𝐴)𝛽3 5.7214 0.4432 -3.0153 0.4587 0.0809 <0.0001 0.5852 696.8254 715.1402 213 𝐴𝐺𝐵=𝛽0×(𝐺2)𝛽1×(𝑆ℎ2)𝛽2×(𝑇𝐻)𝛽3 5.3882 0.4390 -1.2632 -0.1140*** 0.0715 0.0001 0.5913 699.8963 718.2111 214 𝐴𝐺𝐵=𝛽0×(𝐺2)𝛽1×(𝑆ℎ2)𝛽2×(𝑀𝑖+1)𝛽3 5.3407 0.4347 -1.1828 0.1979*** 0.0679 0.0001 0.5935 701.0269 719.3417 215 𝐴𝐺𝐵=𝛽0×(𝐺2)𝛽1×(𝑆ℎ2)𝛽2×(𝑊+1)𝛽3 5.5801 0.4382 -1.2171 -0.3083*** 0.0688 0.0001 0.5930 700.7571 719.0720 216 𝐴𝐺𝐵=𝛽0×(𝐺2)𝛽1×(𝑆ℎ2)𝛽2×(𝐴)𝛽3 5.7214 0.4432 -1.5076 0.4587 0.0809 <0.0001 0.5852 696.8254 715.1402 217 𝐴𝐺𝐵=𝛽0×(𝐺2)𝛽1×(𝑆ℎ2)𝛽2×(𝐴2)𝛽3 5.7214 0.4432 -1.5076 0.2294 0.0809 <0.0001 0.5852 696.8254 715.1402 218 𝐴𝐺𝐵=𝛽0×(𝐺2)𝛽1×(𝑆ℎ−1)𝛽2×(𝑇𝐻2)𝛽3 5.3882 0.4390 2.5265 -0.0570*** 0.0715 0.0001 0.5913 699.8963 718.2111 219 𝐴𝐺𝐵=𝛽0×(𝐺2)𝛽1×(𝑆ℎ−1)𝛽2×(𝑀𝑖+1)𝛽3 5.3407 0.4347 2.3656*** 0.1979 0.0679 0.0001 0.5935 701.0269 719.3417 220 𝐴𝐺𝐵=𝛽0×(𝐺2)𝛽1×(𝑆ℎ−1)𝛽2×(𝑀𝑆+1)𝛽3 5.3378 0.4376 2.3751*** 0.4265 0.0683 0.0001 0.5933 700.9041 719.2189 221 𝐴𝐺𝐵=𝛽0×(𝐺2)𝛽1×(𝑆ℎ−1)𝛽2×((𝑊+1)0.5)𝛽3 5.5801 0.4382 2.4342*** -0.6165 0.0688 0.0001 0.5930 700.7571 719.0720 222 𝐴𝐺𝐵=𝛽0×(𝐺2)𝛽1×(𝑆ℎ−1)𝛽2×(𝐴0.5)𝛽3 5.7214 0.4432 3.0153 -0.9175 0.0809 <0.0001 0.5852 696.8254 715.1402 Aboveground tree biomass, carbon stocks and tree diversity in a mixed forest plantation in Northern Vietnam Thi Nhat Minh Doan Máster en Gestión Forestal basada en Ciencia de Datos - Master on Forest Management based on Data Science (DATAFOREST) 70 No. Model 𝜷𝟎 𝜷𝟏 𝜷𝟐 𝜷𝟑 𝑹𝟐 𝒑−𝒗𝒂𝒍𝒖𝒆 MSE AIC BIC 223 𝐴𝐺𝐵=𝛽0×(𝐺2)𝛽1×(𝑆ℎ−0.5)𝛽2×(𝑇𝐻−1)𝛽3 5.3882 0.4390 5.0529 0.1140*** 0.0715 0.0001 0.5913 699.8963 718.2111 224 𝐴𝐺𝐵=𝛽0×(𝐺2)𝛽1×(𝑆ℎ−0.5)𝛽2×((𝑀𝑖+1)2)𝛽3 5.3407 0.4347 4.7312 0.0990*** 0.0679 0.0001 0.5935 701.0269 719.3417 225 𝐴𝐺𝐵=𝛽0×(𝐺2)𝛽1×(𝑆ℎ−0.5)𝛽2×((𝑀𝑆+1)0.5)𝛽3 5.3378 0.4376 4.7502 0.8530*** 0.0683 0.0001 0.5933 700.9041 719.2189 226 𝐴𝐺𝐵=𝛽0×(𝐺2)𝛽1×(𝑆ℎ−0.5)𝛽2×(𝑊+1)𝛽3 5.5801 0.4382 4.8685 -0.3083*** 0.0688 0.0001 0.5930 700.7571 719.0720 227 𝐴𝐺𝐵=𝛽0×(𝐺2)𝛽1×(𝑆ℎ−0.5)𝛽2×(𝐴)𝛽3 5.7214 0.4432 6.0305 0.4587 0.0809 <0.0001 0.5852 696.8254 715.1402 228 𝐴𝐺𝐵=𝛽0×(𝐺2)𝛽1×(𝑆ℎ0.5)𝛽2×(𝑇𝐻)𝛽3 5.3882 0.4390 -5.0529 -0.1140*** 0.0715 0.0001 0.5913 699.8963 718.2111 229 𝐴𝐺𝐵=𝛽0×(𝐺2)𝛽1×(𝑆ℎ0.5)𝛽2×((𝑀𝑖+1)2)𝛽3 5.3407 0.4347 -4.7312 0.0990*** 0.0679 0.0001 0.5935 701.0269 719.3417 230 𝐴𝐺𝐵=𝛽0×(𝐺2)𝛽1×(𝑆ℎ0.5)𝛽2×((𝑀𝑆+1)2)𝛽3 5.3378 0.4376 -4.7502 0.2132*** 0.0683 0.0001 0.5933 700.9041 719.2189 231 𝐴𝐺𝐵=𝛽0×(𝐺2)𝛽1×(𝑆ℎ0.5)𝛽2×((𝑊+1)−0.5)𝛽3 5.5801 0.4382 -4.8685 0.6165*** 0.0688 0.0001 0.5930 700.7571 719.0720 232 𝐴𝐺𝐵=𝛽0×(𝐺2)𝛽1×(𝑆ℎ0.5)𝛽2×(𝐴0.5)𝛽3 5.7214 0.4432 -6.0305 0.9175 0.0809 <0.0001 0.5852 696.8254 715.1402 233 𝐴𝐺𝐵=𝛽0×(𝐺2)𝛽1×(𝑆𝑚)𝛽2×(𝑇𝐻0.5)𝛽3 1.6876*** 0.4518 -13.6775 -0.1980*** 0.0657 0.0002 0.5950 701.7658 720.0807 234 𝐴𝐺𝐵=𝛽0×(𝐺2)𝛽1×(𝑆𝑚)𝛽2×(𝑀𝑖+1)𝛽3 1.8418 0.4484 -12.9514 0.1831*** 0.0632 0.0002 0.5965 702.5518 720.8667 235 𝐴𝐺𝐵=𝛽0×(𝐺2)𝛽1×(𝑆𝑚)𝛽2×((𝑀𝑆+1)0.5)𝛽3 1.8291 0.4508 -12.9903 0.7771*** 0.0635 0.0002 0.5964 702.4702 720.7850 236 𝐴𝐺𝐵=𝛽0×(𝐺2)𝛽1×(𝑆𝑚)𝛽2×(𝑊+1)𝛽3 1.9675 0.4519 -13.2979 -0.2785*** 0.0638 0.0002 0.5961 702.3597 720.6745 237 𝐴𝐺𝐵=𝛽0×(𝐺2)𝛽1×(𝑆𝑚)𝛽2×(𝐴2)𝛽3 1.3477*** 0.4582 -16.0049 0.1986*** 0.0731 0.0001 0.5902 699.3764 717.6913 238 𝐴𝐺𝐵=𝛽0×(𝐺2)𝛽1×(𝑆𝑚2)𝛽2×(𝑇𝐻0.5)𝛽3 1.6876*** 0.4518 -6.8388 -0.1980*** 0.0657 0.0002 0.5950 701.7658 720.0807 239 𝐴𝐺𝐵=𝛽0×(𝐺2)𝛽1×(𝑆𝑚2)𝛽2×((𝑀𝑖+1)−1)𝛽3 1.8418 0.4484 -6.4757 -0.1831*** 0.0632 0.0002 0.5965 702.5518 720.8667 240 𝐴𝐺𝐵=𝛽0×(𝐺2)𝛽1×(𝑆𝑚2)𝛽2×((𝑀𝑆+1)0.5)𝛽3 1.8291 0.4508 -6.4951 0.7771*** 0.0635 0.0002 0.5964 702.4702 720.7850 241 𝐴𝐺𝐵=𝛽0×(𝐺2)𝛽1×(𝑆𝑚2)𝛽2×(𝑊+1)𝛽3 1.9675 0.4519 -6.6490 -0.2785*** 0.0638 0.0002 0.5961 702.3597 720.6745 242 𝐴𝐺𝐵=𝛽0×(𝐺2)𝛽1×(𝑆𝑚2)𝛽2×((𝑊+1)2)𝛽3 1.9675 0.4519 -6.6490 -0.1393*** 0.0638 0.0002 0.5961 702.3597 720.6745 243 𝐴𝐺𝐵=𝛽0×(𝐺2)𝛽1×(𝑆𝑚2)𝛽2×((𝑊+1)−1)𝛽3 1.9675 0.4519 -6.6490 0.2785*** 0.0638 0.0002 0.5961 702.3597 720.6745 244 𝐴𝐺𝐵=𝛽0×(𝐺2)𝛽1×(𝑆𝑚2)𝛽2×((𝑊+1)−0.5)𝛽3 1.9675 0.4519 -6.6490 0.5570*** 0.0638 0.0002 0.5961 702.3597 720.6745 245 𝐴𝐺𝐵=𝛽0×(𝐺2)𝛽1×(𝑆𝑚2)𝛽2×((𝑊+1)0.5)𝛽3 1.9675 0.4519 -6.6490 -0.5570*** 0.0638 0.0002 0.5961 702.3597 720.6745 246 𝐴𝐺𝐵=𝛽0×(𝐺2)𝛽1×(𝑆𝑚2)𝛽2×(𝐴)𝛽3 1.3477*** 0.4582 -8.0024 0.3972*** 0.0731 0.0001 0.5902 699.3764 717.6913 247 𝐴𝐺𝐵=𝛽0×(𝐺2)𝛽1×(𝑆𝑚2)𝛽2×(𝐴2)𝛽3 1.3477*** 0.4582 -8.0024 0.1986*** 0.0731 0.0001 0.5902 699.3764 717.6913 248 𝐴𝐺𝐵=𝛽0×(𝐺2)𝛽1×(𝑆𝑚2)𝛽2×(𝐴−1)𝛽3 1.3477*** 0.4582 -8.0024 -0.3972*** 0.0731 0.0001 0.5902 699.3764 717.6913 249 𝐴𝐺𝐵=𝛽0×(𝐺2)𝛽1×(𝑆𝑚2)𝛽2×(𝐴−0.5)𝛽3 1.3477*** 0.4582 -8.0024 -0.7943*** 0.0731 0.0001 0.5902 699.3764 717.6913 250 𝐴𝐺𝐵=𝛽0×(𝐺2)𝛽1×(𝑆𝑚2)𝛽2×(𝐴0.5)𝛽3 1.3477*** 0.4582 -8.0024 0.7943*** 0.0731 0.0001 0.5902 699.3764 717.6913 Aboveground tree biomass, carbon stocks and tree diversity in a mixed forest plantation in Northern Vietnam Thi Nhat Minh Doan Máster en Gestión Forestal basada en Ciencia de Datos - Master on Forest Management based on Data Science (DATAFOREST) 71 No. Model 𝜷𝟎 𝜷𝟏 𝜷𝟐 𝜷𝟑 𝑹𝟐 𝒑−𝒗𝒂𝒍𝒖𝒆 MSE AIC BIC 251 𝐴𝐺𝐵=𝛽0×(𝐺2)𝛽1×(𝑆𝑚−1)𝛽2×(𝑇𝐻)𝛽3 1.6876*** 0.4518 13.6775 -0.0990*** 0.0657 0.0002 0.5950 701.7658 720.0807 252 𝐴𝐺𝐵=𝛽0×(𝐺2)𝛽1×(𝑆𝑚−1)𝛽2×((𝑀𝑖+1)0.5)𝛽3 1.8418 0.4484 12.9514 0.3662*** 0.0632 0.0002 0.5965 702.5518 720.8667 253 𝐴𝐺𝐵=𝛽0×(𝐺2)𝛽1×(𝑆𝑚−1)𝛽2×((𝑀𝑆+1)0.5)𝛽3 1.8291 0.4508 12.9903 0.3885*** 0.0635 0.0002 0.5964 702.4702 720.7850 254 𝐴𝐺𝐵=𝛽0×(𝐺2)𝛽1×(𝑆𝑚−1)𝛽2×((𝑊+1)0.5)𝛽3 1.9675 0.4519 13.2979 0.2785*** 0.0638 0.0002 0.5961 702.3597 720.6745 255 𝐴𝐺𝐵=𝛽0×(𝐺2)𝛽1×(𝑆𝑚−1)𝛽2×(𝐴2)𝛽3 1.3477*** 0.4582 16.0049 0.1986*** 0.0731 0.0001 0.5902 699.3764 717.6913 256 𝐴𝐺𝐵=𝛽0×(𝐺2)𝛽1×(𝑆𝑚−0.5)𝛽2×(𝑇𝐻)𝛽3 1.6876*** 0.4518 27.3551 -0.0990*** 0.0657 0.0002 0.5950 701.7658 720.0807 257 𝐴𝐺𝐵=𝛽0×(𝐺2)𝛽1×(𝑆𝑚−0.5)𝛽2×((𝑀𝑖+1)2)𝛽3 1.8418 0.4484 25.9029 0.0916*** 0.0632 0.0002 0.5965 702.5518 720.8667 258 𝐴𝐺𝐵=𝛽0×(𝐺2)𝛽1×(𝑆𝑚−0.5)𝛽2×((𝑀𝑆+1)0.5)𝛽3 1.8291 0.4508 25.9806 0.7771*** 0.0635 0.0002 0.5964 702.4702 720.7850 259 𝐴𝐺𝐵=𝛽0×(𝐺2)𝛽1×(𝑆𝑚−0.5)𝛽2×((𝑊+1)−1)𝛽3 1.9675 0.4519 26.5958 0.2785*** 0.0638 0.0002 0.5961 702.3597 720.6745 260 𝐴𝐺𝐵=𝛽0×(𝐺2)𝛽1×(𝑆𝑚−0.5)𝛽2×(𝐴2)𝛽3 1.3477*** 0.4582 32.0097 0.1986*** 0.0731 0.0001 0.5902 699.3764 717.6913 261 𝐴𝐺𝐵=𝛽0×(𝐺2)𝛽1×(𝑆𝑚0.5)𝛽2×(𝑇𝐻−0.5)𝛽3 1.6876*** 0.4518 -27.3551 0.1980*** 0.0657 0.0002 0.5950 701.7658 720.0807 262 𝐴𝐺𝐵=𝛽0×(𝐺2)𝛽1×(𝐸)𝛽2×(𝐴−1)𝛽3 2.7828 0.3118 -8.3583 -0.1387*** 0.0308 0.0259 0.6172 712.7528 731.0676 263 𝐴𝐺𝐵=𝛽0×(𝐺2)𝛽1×(𝐸2)𝛽2×(𝑊+1)𝛽3 2.9615 0.3205 -3.8867 -0.2058*** 0.0306 0.0266 0.6173 712.8124 731.1272 264 𝐴𝐺𝐵=𝛽0×(𝐺2)𝛽1×(𝐸−1)𝛽2×((𝑀𝑖+1)2)𝛽3 2.8994 0.3157 7.4689 0.0375*** 0.0295 0.0311 0.6180 713.1666 731.4815 265 𝐴𝐺𝐵=𝛽0×(𝐺2)𝛽1×(𝐸−0.5)𝛽2×(𝑇𝐻2)𝛽3 2.7541 0.3199 16.2037 -0.0375*** 0.0318 0.0226 0.6166 712.4577 730.7726 266 𝐴𝐺𝐵=𝛽0×(𝐺2)𝛽1×(𝐸0.5)𝛽2×(𝑀𝑖+1)𝛽3 2.8994 0.3157 -14.9379 0.0751*** 0.0295 0.0311 0.6180 713.1666 731.4815 267 𝐴𝐺𝐵=𝛽0×(𝐺2)𝛽1×(𝐸0.5)𝛽2×((𝑀𝑖+1)2)𝛽3 2.8994 0.3157 -14.9379 0.0375*** 0.0295 0.0311 0.6180 713.1666 731.4815 268 𝐴𝐺𝐵=𝛽0×(𝐺2)𝛽1×(𝐷)𝛽2×(𝐴−1)𝛽3 3.5011 0.2165*** 0.4687 -0.0978*** 0.0229 0.0765 0.6222 715.1952 733.5100 269 𝐴𝐺𝐵=𝛽0×(𝐺2)𝛽1×(𝐷)𝛽2×(𝐴−0.5)𝛽3 3.5011 0.2165*** 0.4687 -0.1957*** 0.0229 0.0765 0.6222 715.1952 733.5100 270 𝐴𝐺𝐵=𝛽0×(𝐺2)𝛽1×(𝐷2)𝛽2×(𝑇𝐻)𝛽3 3.4063 0.2247*** 0.2417 -0.0829*** 0.0252 0.0561 0.6207 714.4894 732.8042 271 𝐴𝐺𝐵=𝛽0×(𝐺2)𝛽1×(𝐷2)𝛽2×(𝑇𝐻2)𝛽3 3.4063 0.2247*** 0.2417 -0.0415*** 0.0252 0.0561 0.6207 714.4894 732.8042 272 𝐴𝐺𝐵=𝛽0×(𝐺2)𝛽1×(𝐷2)𝛽2×(𝑇𝐻−0.5)𝛽3 3.4063 0.2247*** 0.2417 0.1659*** 0.0252 0.0561 0.6207 714.4894 732.8042 273 𝐴𝐺𝐵=𝛽0×(𝐺2)𝛽1×(𝐷2)𝛽2×(𝑇𝐻0.5)𝛽3 3.4063 0.2247*** 0.2417 -0.1659*** 0.0252 0.0561 0.6207 714.4894 732.8042 274 𝐴𝐺𝐵=𝛽0×(𝐺2)𝛽1×(𝐷2)𝛽2×(𝑀𝑖+1)𝛽3 3.5219 0.2279*** 0.2057*** 0.0943*** 0.0225 0.0803 0.6224 715.3060 733.6208 275 𝐴𝐺𝐵=𝛽0×(𝐺2)𝛽1×(𝐷−1)𝛽2×(𝐴2)𝛽3 3.5011 0.2165*** -0.4687 0.0489*** 0.0229 0.0765 0.6222 715.1952 733.5100 276 𝐴𝐺𝐵=𝛽0×(𝐺2)𝛽1×(𝐷−0.5)𝛽2×((𝑀𝑖+1)0.5)𝛽3 3.5219 0.2279*** -0.8226*** 0.1886*** 0.0225 0.0803 0.6224 715.3060 733.6208 277 𝐴𝐺𝐵=𝛽0×(𝐺2)𝛽1×(𝐷−0.5)𝛽2×(𝑀𝑆+1)𝛽3 3.5177 0.2288*** -0.8237*** 0.2006*** 0.0226 0.0795 0.6224 715.2838 733.5986 278 𝐴𝐺𝐵=𝛽0×(𝐺2)𝛽1×(𝐷−0.5)𝛽2×((𝑀𝑆+1)2)𝛽3 3.5177 0.2288*** -0.8237*** 0.1003*** 0.0226 0.0795 0.6224 715.2838 733.5986 Aboveground tree biomass, carbon stocks and tree diversity in a mixed forest plantation in Northern Vietnam Thi Nhat Minh Doan Máster en Gestión Forestal basada en Ciencia de Datos - Master on Forest Management based on Data Science (DATAFOREST) 72 No. Model 𝜷𝟎 𝜷𝟏 𝜷𝟐 𝜷𝟑 𝑹𝟐 𝒑−𝒗𝒂𝒍𝒖𝒆 MSE AIC BIC 279 𝐴𝐺𝐵=𝛽0×(𝐺2)𝛽1×(𝐷−0.5)𝛽2×((𝑀𝑆+1)−1)𝛽3 3.5177 0.2288*** -0.8237 -0.2006*** 0.0226 0.0795 0.6224 715.2838 733.5986 280 𝐴𝐺𝐵=𝛽0×(𝐺2)𝛽1×(𝐷−0.5)𝛽2×((𝑀𝑆+1)−0.5)𝛽3 3.5177 0.2288*** -0.8237 -0.4012*** 0.0226 0.0795 0.6224 715.2838 733.5986 281 𝐴𝐺𝐵=𝛽0×(𝐺2)𝛽1×(𝑅2)𝛽2×(𝐴)𝛽3 3.3753 0.2709 -1.2984 0.3592*** 0.0708 0.0001 0.5917 700.1107 718.4256 282 𝐴𝐺𝐵=𝛽0×(𝐺2)𝛽1×(𝑅−1)𝛽2×(𝑀𝑖+1)𝛽3 3.4359 0.2991 2.1826 0.2309*** 0.0641 0.0002 0.5960 702.2752 720.5900 283 𝐴𝐺𝐵=𝛽0×(𝐺2)𝛽1×(𝑅−1)𝛽2×((𝑀𝑖+1)2)𝛽3 3.4359 0.2991 2.1826 0.1154*** 0.0641 0.0002 0.5960 702.2752 720.5900 284 𝐴𝐺𝐵=𝛽0×(𝐺2)𝛽1×(𝑅−1)𝛽2×((𝑀𝑖+1)−1)𝛽3 3.4359 0.2991 2.1826 -0.2309*** 0.0641 0.0002 0.5960 702.2752 720.5900 285 𝐴𝐺𝐵=𝛽0×(𝐺2)𝛽1×(𝑅−1)𝛽2×((𝑀𝑖+1)−0.5)𝛽3 3.4359 0.2991 2.1826 -0.4617*** 0.0641 0.0002 0.5960 702.2752 720.5900 286 𝐴𝐺𝐵=𝛽0×(𝐺2)𝛽1×(𝑅−1)𝛽2×((𝑀𝑖+1)0.5)𝛽3 3.4359 0.2991 2.1826 0.4617*** 0.0641 0.0002 0.5960 702.2752 720.5900 287 𝐴𝐺𝐵=𝛽0×(𝐺2)𝛽1×(𝑅−1)𝛽2×(𝑀𝑆+1)𝛽3 3.4222 0.3021 2.1979 0.5011*** 0.0646 0.0002 0.5956 702.0921 720.4069 288 𝐴𝐺𝐵=𝛽0×(𝐺2)𝛽1×(𝑅−1)𝛽2×((𝑀𝑆+1)2)𝛽3 3.4222 0.3021 2.1979 0.2506*** 0.0646 0.0002 0.5956 702.0921 720.4069 289 𝐴𝐺𝐵=𝛽0×(𝐺2)𝛽1×(𝑅−1)𝛽2×((𝑀𝑆+1)−1)𝛽3 3.4222 0.3021 2.1979 -0.5011*** 0.0646 0.0002 0.5956 702.0921 720.4069 290 𝐴𝐺𝐵=𝛽0×(𝐺2)𝛽1×(𝑅−1)𝛽2×((𝑀𝑆+1)−0.5)𝛽3 3.4222 0.3021 2.1979 -1.0022*** 0.0646 0.0002 0.5956 702.0921 720.4069 291 𝐴𝐺𝐵=𝛽0×(𝐺2)𝛽1×(𝑅−1)𝛽2×((𝑀𝑆+1)0.5)𝛽3 3.4222 0.3021 2.1979 1.0022*** 0.0646 0.0002 0.5956 702.0921 720.4069 292 𝐴𝐺𝐵=𝛽0×(𝐺2)𝛽1×(𝑅−1)𝛽2×(𝑊+1)𝛽3 3.6222 0.2940 2.2000 -0.2319*** 0.0626 0.0003 0.5969 702.7389 721.0537 293 𝐴𝐺𝐵=𝛽0×(𝐺2)𝛽1×(𝑅−1)𝛽2×((𝑊+1)2)𝛽3 3.6222 0.2940 2.2000 -0.1160*** 0.0626 0.0003 0.5969 702.7389 721.0537 294 𝐴𝐺𝐵=𝛽0×(𝐺2)𝛽1×(𝑅−1)𝛽2×((𝑊+1)−1)𝛽3 3.6222 0.2940 2.2000 0.2319*** 0.0626 0.0003 0.5969 702.7389 721.0537 295 𝐴𝐺𝐵=𝛽0×(𝐺2)𝛽1×(𝑅−1)𝛽2×((𝑊+1)−0.5)𝛽3 3.6222 0.2940 2.2000 0.4639*** 0.0626 0.0003 0.5969 702.7389 721.0537 296 𝐴𝐺𝐵=𝛽0×(𝐺2)𝛽1×(𝑅−1)𝛽2×((𝑊+1)0.5)𝛽3 3.6222 0.2940 2.2000 -0.4639*** 0.0626 0.0003 0.5969 702.7389 721.0537 297 𝐴𝐺𝐵=𝛽0×(𝐺2)𝛽1×(𝑅−1)𝛽2×(𝐴)𝛽3 3.3753 0.2709 2.5967 0.3592*** 0.0708 0.0001 0.5917 700.1107 718.4256 298 𝐴𝐺𝐵=𝛽0×(𝐺2)𝛽1×(𝑅−1)𝛽2×(𝐴2)𝛽3 3.3753 0.2709 2.5967 0.1796*** 0.0708 0.0001 0.5917 700.1107 718.4256 Aboveground tree biomass, carbon stocks and tree diversity in a mixed forest plantation in Northern Vietnam Thi Nhat Minh Doan Máster en Gestión Forestal basada en Ciencia de Datos - Master on Forest Management based on Data Science (DATAFOREST) 73 Annex 4: Model fitted for Acacia auriculiformis (*** indicates p-value>0.05) No. Model 𝜷𝟎 𝜷𝟏 𝜷𝟐 𝜷𝟑 𝑹𝟐 𝒑−𝒗𝒂𝒍𝒖𝒆 MSE AIC BIC 1 𝐴𝐺𝐵=exp (𝛽0+𝛽1𝑇𝐻2) 5.3644 -4.1514 - - 0.1073 0.0005 0.7378 277.8661 285.6817 2 𝐴𝐺𝐵=exp (𝛽0+𝛽1𝑇𝐻2+𝛽2𝑁0.5) 7.1477 -4.2258 -0.3151 - 0.1658 0.0001 0.6961 272.7099 283.0501 3 𝐴𝐺𝐵=exp (𝛽0+𝛽1𝑇𝐻2+𝛽2𝑆ℎ2) 6.7131 -4.1277 -0.1248 - 0.1697 0.0001 0.6928 272.1988 282.5390 4 𝐴𝐺𝐵=exp (𝛽0+𝛽1𝑇𝐻2+𝛽2𝑆ℎ−1) 3.2154 -4.0410 6.9505 - 0.1672 0.0001 0.6949 272.5302 282.8704 5 𝐴𝐺𝐵=exp (𝛽0+𝛽1𝑇𝐻2+𝛽2𝑆ℎ) 7.8752 -4.0985 -0.7675 - 0.1693 0.0001 0.6932 272.2584 282.5985 6 𝐴𝐺𝐵=exp (𝛽0+𝛽1𝑇𝐻2+𝛽2𝑆𝑚) 16.9614 -3.9665 -12.1873 - 0.1653 0.0001 0.6965 272.7778 283.1180 7 𝐴𝐺𝐵=exp (𝛽0+𝛽1𝑇𝐻2+𝛽2𝑆𝑚2) 11.2770 -3.9718 -6.5268 - 0.1656 0.0001 0.6962 272.7349 283.0751 8 𝐴𝐺𝐵=exp (𝛽0+𝛽1𝑇𝐻2+𝛽2𝐸) 16.1278 -3.6734 -11.3612 - 0.1541 0.0002 0.7058 274.2122 284.5524 9 𝐴𝐺𝐵=exp (𝛽0+𝛽1𝑇𝐻2+𝛽2𝐸2) 10.8051 -3.6752 -6.0591 - 0.1540 0.0002 0.7059 274.2263 284.5665 10 𝐴𝐺𝐵=exp (𝛽0+𝛽1𝑇𝐻2+𝛽2𝐸0.5) 26.7711 -3.6725 -21.9943 - 0.1541 0.0002 0.7058 274.2061 284.5463 11 𝐴𝐺𝐵=exp (𝛽0+𝛽1𝑇𝐻2+𝛽2𝑁2) 5.9042 -4.2948 -0.0005 - 0.1616 0.0001 0.6996 273.2468 283.5870 12 𝐴𝐺𝐵=exp (𝛽0+𝛽1𝑇𝐻2+𝛽2𝐷−1) 5.7929 -4.0398 -0.8047*** - 0.1143 0.0017 0.7391 279.1825 289.5227 13 𝐴𝐺𝐵=exp (𝛽0+𝛽1𝑇𝐻2+𝛽2𝐷0.5) 4.3419 -4.0357 0.7396*** - 0.1150 0.0016 0.7385 279.0981 289.4383 14 𝐴𝐺𝐵=exp (𝛽0+𝛽1𝑇𝐻2+𝐺) 5.2864 -4.1876 0.0041*** - 0.1076 0.0025 0.7446 279.9890 290.3292 15 𝐴𝐺𝐵=exp (𝛽0+𝛽1𝑇𝐻2+𝛽2𝐺2) 5.3229 -4.1952 0.0001*** - 0.1077 0.0025 0.7445 279.9784 290.3186 16 𝐴𝐺𝐵=exp (𝛽0+𝛽1𝑇𝐻2+𝛽2𝑀𝑖2) 5.3512 -4.1580 0.0288*** - 0.1075 0.0026 0.7448 280.0089 290.3491 17 𝐴𝐺𝐵=exp (𝛽0+𝛽1𝑇𝐻2+𝛽2𝑆−0.5) 6.1592 -4.0616 -0.3813*** - 0.1112 0.0021 0.7417 279.5594 289.8996 18 𝐴𝐺𝐵=exp (𝛽0+𝛽1𝑇𝐻2+𝛽2𝑀𝑆2) 5.2888 -4.1405 0.8267*** - 0.1165 0.0015 0.7372 278.9054 289.2455 19 𝐴𝐺𝐵=exp (𝛽0+𝛽1𝑇𝐻2+𝛽2𝑆ℎ+𝛽3𝑊) 7.9057 -4.1197 -0.7685 -0.0539*** 0.1694 0.0002 0.6997 274.4360 287.2585 20 𝐴𝐺𝐵=𝑒𝑥𝑝 (𝛽0+𝛽1𝑇𝐻2+𝛽2𝑆ℎ+𝛽3𝑊2) 7.9071 -4.1417 -0.7687 -0.0898*** 0.1697 0.0002 0.6995 274.4026 287.2251 21 𝐴𝐺𝐵=𝑒𝑥𝑝 (𝛽0+𝛽1𝑇𝐻2+𝛽2𝑆ℎ+𝛽3(𝑊+1)−0.5) 7.8124 -4.1059 -0.7680 0.0783*** 0.1693 0.0002 0.6998 274.4541 287.2765 22 𝐴𝐺𝐵=𝑒𝑥𝑝 (𝛽0+𝛽1𝑇𝐻2+𝛽2𝑆ℎ+𝛽3𝑊0.5) 7.8284 -4.0868 -0.7662 0.0633*** 0.1695 0.0002 0.6997 274.4320 287.2544 23 𝐴𝐺𝐵=exp (𝛽0+𝛽1𝑇𝐻2+𝛽2𝑆ℎ−1+𝛽3𝑊) 3.2433 -4.0668 6.9677 -0.0660*** 0.1674 0.0003 0.7014 274.6970 287.5194 Aboveground tree biomass, carbon stocks and tree diversity in a mixed forest plantation in Northern Vietnam Thi Nhat Minh Doan Máster en Gestión Forestal basada en Ciencia de Datos - Master on Forest Management based on Data Science (DATAFOREST) 80 No. Model 𝜷𝟎 𝜷𝟏 𝜷𝟐 𝜷𝟑 𝑹𝟐 𝒑−𝒗𝒂𝒍𝒖𝒆 MSE AIC BIC 173 𝐴𝐺𝐵=𝛽0×(𝑇𝐻2)𝛽1×(𝑆ℎ)𝛽2×(𝑀𝑖+1)𝛽3 6.9719 -0.2024 -2.2579 0.3013*** 0.1150 0.0052 0.7456 281.2943 294.1167 174 𝐴𝐺𝐵=𝛽0×(𝑇𝐻2)𝛽1×(𝑆ℎ)𝛽2×(𝑀𝑆+1)𝛽3 6.9790 -0.1981 -2.2258 0.5012*** 0.1159 0.0049 0.7448 281.1768 293.9992 175 𝐴𝐺𝐵=𝛽0×(𝑇𝐻2)𝛽1×(𝑆ℎ)𝛽2×((𝑊+1)−0.5)𝛽3 7.1640 -0.1976 -2.2929 -0.0342*** 0.1114 0.0063 0.7486 281.7274 294.5498 176 𝐴𝐺𝐵=𝛽0×(𝑇𝐻2)𝛽1×(𝑆ℎ)𝛽2×((𝑊+1)0.5)𝛽3 7.1640 -0.1976 -2.2929 0.0342*** 0.1114 0.0063 0.7486 281.7274 294.5498 177 𝐴𝐺𝐵=𝛽0×(𝑇𝐻2)𝛽1×(𝑆ℎ)𝛽2×(𝐴)𝛽3 7.8877 -0.1371 -3.1427 0.5559*** 0.1283 0.0025 0.7344 279.6561 292.4785 178 𝐴𝐺𝐵=𝛽0×(𝑇𝐻2)𝛽1×(𝑆ℎ2)𝛽2×(𝐺)𝛽3 5.9574 -0.2133 -1.3864 0.5836*** 0.1238 0.0032 0.7382 280.2180 293.0404 179 𝐴𝐺𝐵=𝛽0×(𝑇𝐻2)𝛽1×(𝑆ℎ2)𝛽2×(𝑀𝑖+1)𝛽3 6.9719 -0.2024 -1.1290 0.3013*** 0.1150 0.0052 0.7456 281.2943 294.1167 180 𝐴𝐺𝐵=𝛽0×(𝑇𝐻2)𝛽1×(𝑆ℎ2)𝛽2×(𝑊+1)𝛽3 7.1640 -0.1976 -1.1465 0.0171*** 0.1114 0.0063 0.7486 281.7274 294.5498 181 𝐴𝐺𝐵=𝛽0×(𝑇𝐻2)𝛽1×(𝑆ℎ2)𝛽2×(𝐴)𝛽3 7.8877 -0.1371 -1.5714 0.5559*** 0.1283 0.0025 0.7344 279.6561 292.4785 182 𝐴𝐺𝐵=𝛽0×(𝑇𝐻2)𝛽1×(𝑆ℎ2)𝛽2×(𝐴2)𝛽3 7.8877 -0.1371 -1.5714 0.2779*** 0.1283 0.0025 0.7344 279.6561 292.4785 183 𝐴𝐺𝐵=𝛽0×(𝑇𝐻2)𝛽1×(𝑆ℎ−1)𝛽2×(𝐺2)𝛽3 5.9574 -0.2133 2.7728 0.2918*** 0.1238 0.0032 0.7382 280.2180 293.0404 184 𝐴𝐺𝐵=𝛽0×(𝑇𝐻2)𝛽1×(𝑆ℎ−1)𝛽2×(𝑀𝑖+1)𝛽3 6.9719 -0.2024 2.2579 0.3013*** 0.1150 0.0052 0.7456 281.2943 294.1167 185 𝐴𝐺𝐵=𝛽0×(𝑇𝐻2)𝛽1×(𝑆ℎ−1)𝛽2×(𝑀𝑆+1)𝛽3 6.9790 -0.1981 2.2258 0.5012*** 0.1159 0.0049 0.7448 281.1768 293.9992 186 𝐴𝐺𝐵=𝛽0×(𝑇𝐻2)𝛽1×(𝑆ℎ−1)𝛽2×((𝑊+1)0.5)𝛽3 7.1640 -0.1976 2.2929 0.0342*** 0.1114 0.0063 0.7486 281.7274 294.5498 187 𝐴𝐺𝐵=𝛽0×(𝑇𝐻2)𝛽1×(𝑆ℎ−1)𝛽2×(𝐴−0.5)𝛽3 7.8877 -0.1371 3.1427 -1.1118*** 0.1283 0.0025 0.7344 279.6561 292.4785 188 𝐴𝐺𝐵=𝛽0×(𝑇𝐻2)𝛽1×(𝑆ℎ−0.5)𝛽2×(𝐺−1)𝛽3 5.9574 -0.2133 5.5455 -0.5836*** 0.1238 0.0032 0.7382 280.2180 293.0404 189 𝐴𝐺𝐵=𝛽0×(𝑇𝐻2)𝛽1×(𝑆ℎ−0.5)𝛽2×((𝑀𝑖+1)2)𝛽3 6.9719 -0.2024 4.5159 0.1506*** 0.1150 0.0052 0.7456 281.2943 294.1167 190 𝐴𝐺𝐵=𝛽0×(𝑇𝐻2)𝛽1×(𝑆ℎ−0.5)𝛽2 ×((𝑀𝑆+1)0.5)𝛽3 6.9790 -0.1981 4.4517 1.0023*** 0.1159 0.0049 0.7448 281.1768 293.9992 191 𝐴𝐺𝐵=𝛽0×(𝑇𝐻2)𝛽1×(𝑆ℎ−0.5)𝛽2×(𝑊)𝛽3 7.1640 -0.1976 4.5859 0.0171*** 0.1114 0.0063 0.7486 281.7274 294.5498 192 𝐴𝐺𝐵=𝛽0×(𝑇𝐻2)𝛽1×(𝑆ℎ−0.5)𝛽2×(𝐴)𝛽3 7.8877 -0.1371 6.2855 0.5559*** 0.1283 0.0025 0.7344 279.6561 292.4785 193 𝐴𝐺𝐵=𝛽0×(𝑇𝐻2)𝛽1×(𝑆ℎ0.5)𝛽2×(𝐺)𝛽3 5.9574 -0.2133 -5.5455 0.5836*** 0.1238 0.0032 0.7382 280.2180 293.0404 194 𝐴𝐺𝐵=𝛽0×(𝑇𝐻2)𝛽1×(𝑆ℎ0.5)𝛽2×((𝑀𝑖+1)2)𝛽3 6.9719 -0.2024 -4.5159 0.1506*** 0.1150 0.0052 0.7456 281.2943 294.1167 195 𝐴𝐺𝐵=𝛽0×(𝑇𝐻2)𝛽1×(𝑆ℎ0.5)𝛽2×((𝑀𝑆+1)2)𝛽3 6.9790 -0.1981 -4.4517 0.2506*** 0.1159 0.0049 0.7448 281.1768 293.9992 Aboveground tree biomass, carbon stocks and tree diversity in a mixed forest plantation in Northern Vietnam Thi Nhat Minh Doan Máster en Gestión Forestal basada en Ciencia de Datos - Master on Forest Management based on Data Science (DATAFOREST) 81 No. Model 𝜷𝟎 𝜷𝟏 𝜷𝟐 𝜷𝟑 𝑹𝟐 𝒑−𝒗𝒂𝒍𝒖𝒆 MSE AIC BIC 196 𝐴𝐺𝐵=𝛽0×(𝑇𝐻2)𝛽1×(𝑆ℎ0.5)𝛽2 ×((𝑊+1)−0.5)𝛽3 7.1640 -0.1976 -4.5859 -0.0342*** 0.1114 0.0063 0.7486 281.7274 294.5498 197 𝐴𝐺𝐵=𝛽0×(𝑇𝐻2)𝛽1×(𝑆ℎ0.5)𝛽2×(𝐴0.5)𝛽3 7.8877 -0.1371 -6.2855 1.1118*** 0.1283 0.0025 0.7344 279.6561 292.4785 198 𝐴𝐺𝐵=𝛽0×(𝑇𝐻2)𝛽1×(𝑆𝑚)𝛽2×(𝐺0.5)𝛽3 2.0977 -0.2028 -13.7015 1.1310*** 0.1213 0.0037 0.7403 280.5231 293.3455 199 𝐴𝐺𝐵=𝛽0×(𝑇𝐻2)𝛽1×(𝑆𝑚)𝛽2×(𝑀𝑖+1)𝛽3 3.7809 -0.1943 -11.2073 0.3027*** 0.1132 0.0057 0.7470 281.5074 294.3298 200 𝐴𝐺𝐵=𝛽0×(𝑇𝐻2)𝛽1×(𝑆𝑚)𝛽2×((𝑀𝑆+1)0.5)𝛽3 3.8477 -0.1902 -10.9887 0.9015*** 0.1133 0.0057 0.7470 281.5029 294.3253 201 𝐴𝐺𝐵=𝛽0×(𝑇𝐻2)𝛽1×(𝑆𝑚)𝛽2×(𝑊+1)𝛽3 3.9219 -0.1892 -11.3832 0.0240*** 0.1097 0.0069 0.7501 281.9426 294.7650 202 𝐴𝐺𝐵=𝛽0×(𝑇𝐻2)𝛽1×(𝑆𝑚)𝛽2×(𝐴2)𝛽3 3.4888 -0.1310 -15.2057 0.2553*** 0.1243 0.0031 0.7378 280.1548 292.9772 203 𝐴𝐺𝐵=𝛽0×(𝑇𝐻2)𝛽1×(𝑆𝑚2)𝛽2×(𝐺0.5)𝛽3 2.0977 -0.2028 -6.8508 1.1310*** 0.1213 0.0037 0.7403 280.5231 293.3455 204 𝐴𝐺𝐵=𝛽0×(𝑇𝐻2)𝛽1×(𝑆𝑚2)𝛽2×((𝑀𝑖+1)−1)𝛽3 3.7809 -0.1943 -5.6036 -0.3027*** 0.1132 0.0057 0.7470 281.5074 294.3298 205 𝐴𝐺𝐵=𝛽0×(𝑇𝐻2)𝛽1×(𝑆𝑚2)𝛽2×((𝑀𝑆+1)0.5)𝛽3 3.8477 -0.1902 -5.4944 0.9015*** 0.1133 0.0057 0.7470 281.5029 294.3253 206 𝐴𝐺𝐵=𝛽0×(𝑇𝐻2)𝛽1×(𝑆𝑚2)𝛽2×(𝑊+1)𝛽3 3.9219 -0.1892 -5.6916 0.0240*** 0.1097 0.0069 0.7501 281.9426 294.7650 207 𝐴𝐺𝐵=𝛽0×(𝑇𝐻2)𝛽1×(𝑆𝑚2)𝛽2×((𝑊+1)2)𝛽3 3.9219 -0.1892 -5.6916 0.0120*** 0.1097 0.0069 0.7501 281.9426 294.7650 208 𝐴𝐺𝐵=𝛽0×(𝑇𝐻2)𝛽1×(𝑆𝑚2)𝛽2×((𝑊+1)−1)𝛽3 3.9219 -0.1892 -5.6916 -0.0240*** 0.1097 0.0069 0.7501 281.9426 294.7650 209 𝐴𝐺𝐵=𝛽0×(𝑇𝐻2)𝛽1×(𝑆𝑚2)𝛽2×((𝑊+1)−0.5)𝛽3 3.9219 -0.1892 -5.6916 -0.0480*** 0.1097 0.0069 0.7501 281.9426 294.7650 210 𝐴𝐺𝐵=𝛽0×(𝑇𝐻2)𝛽1×(𝑆𝑚2)𝛽2×((𝑊+1)0.5)𝛽3 3.9219 -0.1892 -5.6916 0.0480*** 0.1097 0.0069 0.7501 281.9426 294.7650 211 𝐴𝐺𝐵=𝛽0×(𝑇𝐻2)𝛽1×(𝑆𝑚2)𝛽2×(𝐴)𝛽3 3.4888 -0.1310 -7.6028 0.5105*** 0.1243 0.0031 0.7378 280.1548 292.9772 212 𝐴𝐺𝐵=𝛽0×(𝑇𝐻2)𝛽1×(𝑆𝑚2)𝛽2×(𝐴2)𝛽3 3.4888 -0.1310 -7.6028 0.2553*** 0.1243 0.0031 0.7378 280.1548 292.9772 213 𝐴𝐺𝐵=𝛽0×(𝑇𝐻2)𝛽1×(𝑆𝑚2)𝛽2×(𝐴−1)𝛽3 3.4888 -0.1310 -7.6028 -0.5105*** 0.1243 0.0031 0.7378 280.1548 292.9772 214 𝐴𝐺𝐵=𝛽0×(𝑇𝐻2)𝛽1×(𝑆𝑚2)𝛽2×(𝐴−0.5)𝛽3 3.4888 -0.1310 -7.6028 -1.0211*** 0.1243 0.0031 0.7378 280.1548 292.9772 215 𝐴𝐺𝐵=𝛽0×(𝑇𝐻2)𝛽1×(𝑆𝑚2)𝛽2×(𝐴0.5)𝛽3 3.4888 -0.1310 -7.6028 1.0211*** 0.1243 0.0031 0.7378 280.1548 292.9772 216 𝐴𝐺𝐵=𝛽0×(𝑇𝐻2)𝛽1×(𝑆𝑚−1)𝛽2×(𝐺)𝛽3 2.0977 -0.2028 13.7015 0.5655*** 0.1213 0.0037 0.7403 280.5231 293.3455 217 𝐴𝐺𝐵=𝛽0×(𝑇𝐻2)𝛽1×(𝑆𝑚−1)𝛽2×((𝑀𝑖+1)0.5)𝛽3 3.7809 -0.1943 11.2073 0.6053*** 0.1132 0.0057 0.7470 281.5074 294.3298 218 𝐴𝐺𝐵=𝛽0×(𝑇𝐻2)𝛽1×(𝑆𝑚−1)𝛽2×(𝑀𝑆+1)𝛽3 3.8477 -0.1902 10.9887 0.4508*** 0.1133 0.0057 0.7470 281.5029 294.3253 219 𝐴𝐺𝐵=𝛽0×(𝑇𝐻2)𝛽1×(𝑆𝑚−1)𝛽2×((𝑊+1)−1)𝛽3 3.9219 -0.1892 11.3832 -0.0240*** 0.1097 0.0069 0.7501 281.9426 294.7650 Aboveground tree biomass, carbon stocks and tree diversity in a mixed forest plantation in Northern Vietnam Thi Nhat Minh Doan Máster en Gestión Forestal basada en Ciencia de Datos - Master on Forest Management based on Data Science (DATAFOREST) 82 No. Model 𝜷𝟎 𝜷𝟏 𝜷𝟐 𝜷𝟑 𝑹𝟐 𝒑−𝒗𝒂𝒍𝒖𝒆 MSE AIC BIC 220 𝐴𝐺𝐵=𝛽0×(𝑇𝐻2)𝛽1×(𝑆𝑚−1)𝛽2×(𝐴2)𝛽3 3.4888 -0.1310 15.2057 0.2553*** 0.1243 0.0031 0.7378 280.1548 292.9772 221 𝐴𝐺𝐵=𝛽0×(𝑇𝐻2)𝛽1×(𝑆𝑚−0.5)𝛽2×(𝐺)𝛽3 2.0977 -0.2028 27.4031 0.5655*** 0.1213 0.0037 0.7403 280.5231 293.3455 222 𝐴𝐺𝐵=𝛽0×(𝑇𝐻2)𝛽1×(𝑆𝑚−0.5)𝛽2×((𝑀𝑖+1)2)𝛽3 3.7809 -0.1943 22.4145 0.1513*** 0.1132 0.0057 0.7470 281.5074 294.3298 223 𝐴𝐺𝐵=𝛽0×(𝑇𝐻2)𝛽1×(𝑆𝑚−0.5)𝛽2 ×((𝑀𝑆+1)0.5)𝛽3 3.8477 -0.1902 21.9775 0.9015*** 0.1133 0.0057 0.7470 281.5029 294.3253 224 𝐴𝐺𝐵=𝛽0×(𝑇𝐻2)𝛽1×(𝑆𝑚−0.5)𝛽2 ×((𝑊+1)−1)𝛽3 3.9219 -0.1892 22.7665 -0.0240*** 0.1097 0.0069 0.7501 281.9426 294.7650 225 𝐴𝐺𝐵=𝛽0×(𝑇𝐻2)𝛽1×(𝑆𝑚−0.5)𝛽2×(𝐴2)𝛽3 3.4888 -0.1310 30.4113 0.2553*** 0.1243 0.0031 0.7378 280.1548 292.9772 226 𝐴𝐺𝐵=𝛽0×(𝑇𝐻2)𝛽1×(𝑆𝑚0.5)𝛽2×(𝐺−0.5)𝛽3 2.0977 -0.2028 -27.4031 -1.1310*** 0.1213 0.0037 0.7403 280.5231 293.3455 Aboveground tree biomass, carbon stocks and tree diversity in a mixed forest plantation in Northern Vietnam Thi Nhat Minh Doan Máster en Gestión Forestal basada en Ciencia de Datos - Master on Forest Management based on Data Science (DATAFOREST) 83 Annex 5: R-script for tree above gorund biomass and índices calcutation ################################################################################### ################################ MASTER THESIS #################################### ####################### DOAN THI NHAT MINH _ DATAFOREST ########################### ######################## BIOMASS & INDICES CALCULATION ############################ #---------------------------------------------------------------------------------- ################## Data from Marterloscope core 43 in VNU_Vietnam ################# #---------------------------------------------------------------------------------- # Set working directory setwd("C:/Users/DELL/Desktop/MScThesis_DATAFOREST_UVa/data/processed") getwd() # Import data of Marteloscope A43 in VNU_Vietnam data<-read.csv("data_Marteloscope1_MSc_Minh_DATAFOREST.csv", header=TRUE) names(data) #check data names(data)[5]<-paste("Tree_form") data <- subset( data, select = -c( 8 : 12 )) names(data) # CONTENTS of the script: ##### BIOMASS CALCULATION # > Total Above ground biomass # > By compartment: Stems/ Braches/ Leaves ##### CHARACTERISTICS # > At Individual tree level # > - Basal area (gi) # > - Species proportion (Pi) defined in terms of basal area # > - Density of the stand (Density) # > - Relative density (Re_density) # > - Relative density index (RDI) # > - Slenderness (h/d ratio) # > - Crown indices # > At quadrant level # > - Basal area (G) # > - Above ground bimomass of each quadrant # > - Number of tree per hectare for each quadrant (N) ##### DIVERSITY INDICES (stand level indices) # > Simpson index (D) # > Shannon index (H) # > Evennes index (E) # > Berker-Parker index (D) ##### SPATIAL POINT PATTERN ANALYZES (stand level indices) # > L function (L) # > - at whole stand level # > - at quadrat level # > - at species level (within and between interactions of species) within each quadrat # > Aggregation index (R) # > - at whole stand level # > - at quadrat level # > - at species level (within and between interactions of species) within each quadrat ##### SPECIES INTERMINGLING INDICES (tree level indices) # > Mingling index (Mi) # > Spatial diversity Status (MS) # > Uniform angle index (W) # > Segregation index (S) ##### VERTICAL SPATIAL PATTERN INDICES (stand level indices) Aboveground tree biomass, carbon stocks and tree diversity in a mixed forest plantation in Northern Vietnam Thi Nhat Minh Doan Máster en Gestión Forestal basada en Ciencia de Datos - Master on Forest Management based on Data Science (DATAFOREST) 84 # > Vertical species profile (A) # > Height differentiation index (TH) ################################################################### ####################### BIOMASS CALCULATION ####################### #------------------------------------------------------------------ # Requiring the packages #if(!require("dplyr"))install.packages("dplyr") # cif(!require("lattice"))install.packages("lattice") library(dplyr) library(lattice) ## Calculate of each species # > AGB =Total above ground biomass # > Ws = STEM biomass of different species # > Wl = LEAVES biomass of different species # > Wb = Brances biomass of different species ## 7 Species # > Acacia auriculiformis #full equations # > Acacia mangium #full equations # > Eucalyptus camaldulensis #full equations # > Senna siamea #no compartments equation # > Litsea glutinosa #full equations # > Averrhoa carambola #no compartments equation # > Aporosa villosa #no compartments equation # Using ifelse() function to calculate AGB and biomass in compartments of each species # ifelse(test, yes, no) where # test: an object which can be coerced to logical mode -> defining each species # yes: return values for true elements of test -> the equation # no: return values for false elements of test -> Test of another specie # defining parameters for biomass calculation # DBH (cm), H(m), biomass(kg) d<-data$Diameter_cm h<-data$Total_height_m species<-data$Specie # AGB = Total above ground biomass of different species data$AGB_kg <- ifelse(species == "Acacia auriculiformis", - 2.1737+0.5109*(0.1911*(d^1.9710)*(h^0.5391)), #Thanh, 2014_Vietnam ifelse(species == "Acacia mangium", exp(-1.073+2.081*log(d)), #Traore, 2018_Cote d'Ivoire ifelse(species == "Senna siamea",exp(-3.1141+0.9719*log((d^2)*h)), #Brown, 1989_Tropical Forest ifelse(species == "Eucalyptus camaldulensis",0.035*((d^2)*h)^0.953, #Ounban, 2016_Thailand ifelse(species == "Litsea glutinosa", 0.1142*(d^2.4451), #UN-REDD, 2012_Vietnam ifelse(species=="Averrhoa carambola", exp(-3.1141+0.9719*log((d^2)*h)), #Brown, 1989_Tropical Forest ifelse(species == "Aporosa villosa", exp(-3.1141+0.9719*log((d^2)*h)), #Brown, 1989_Tropical Forest ifelse(species == "Died", exp(-3.1141+0.9719*log((d^2)*h)), NA)))))))) #Brown, 1989_Tropical Forest # Ws = Stem biomass of different species data$Ws_kg <- ifelse(species == "Acacia auriculiformis", -1.4322+0.5072*(0.0984*(d^1.8862)*(h^0.7628)), #Thanh, 2014_Vietnam ifelse(species == "Acacia mangium", exp(-3.228+1.681*log(d)+1.056*log(h)), #Traore, 2018_Cote d'Ivoire Aboveground tree biomass, carbon stocks and tree diversity in a mixed forest plantation in Northern Vietnam Thi Nhat Minh Doan Máster en Gestión Forestal basada en Ciencia de Datos - Master on Forest Management based on Data Science (DATAFOREST) 85 ifelse(species == "Senna siamea",0, #No compartments equations ifelse(species == "Eucalyptus camaldulensis",0.019*((d^2)*h)^1.005, #Ounban, 2016_Thailand ifelse(species == "Litsea glutinosa", 0.1274*(d^2.3655), #UN-REDD, 2012_Vietnam ifelse(species=="Averrhoa carambola", 0, #No compartments equations ifelse(species == "Aporosa villosa", 0, 0))))))) #No compartments equations # Wl = Leaves biomass of different species data$Wl_kg <- ifelse(species == "Acacia auriculiformis", -0.1051+0.5135*(0.0434*(d^1.9294)*(h^0.2828)), #Thanh, 2014_Vietnam ifelse(species == "Acacia mangium", exp(-0.882+1.399*log(d)), #Traore, 2018_Cote d'Ivoire ifelse(species == "Senna siamea",0, #No compartments equations ifelse(species == "Eucalyptus camaldulensis",0.013*((d^2)*h)^0.721, #Ounban, 2016_Thailand ifelse(species == "Litsea glutinosa", 0.0785*(d^1.4696), #UN-REDD, 2012_Vietnam ifelse(species=="Averrhoa carambola", 0, #No compartments equations ifelse(species == "Aporosa villosa", 0, 0))))))) #No compartments equations # Wb = Brances biomass of different species data$Wb_kg <- ifelse(species == "Acacia auriculiformis", 0.0840+0.4973*((0.1911*(d^1.9710)*(h^0.5391))- (0.0984*(d^1.8862)*(h^0.7628)+0.0434*(d^1.9294)*(h^0.2828))), #Thanh, 2014_Vietnam ifelse(species == "Acacia mangium", exp(-0.865+0.498*log((d^2)*h)), #Traore, 2018_Cote d'Ivoire ifelse(species == "Senna siamea",0, #No compartments equations ifelse(species == "Eucalyptus camaldulensis",0.015*((d^2)*h)^0.697, #Ounban, 2016_Thailand ifelse(species == "Litsea glutinosa", 0.0102*(d^2.5848), #UN-REDD, 2012_Vietnam ifelse(species=="Averrhoa carambola", 0, #No compartments equations ifelse(species == "Aporosa villosa", 0, 0))))))) #No compartments equations # View data to check result #View(data) sum(data$AGB_kg) mean(data$Diameter_cm) mean(data$Total_height_m) # CALCULATE CARBON STOCK data$C <- (data$AGB_kg)*0.5 data$CO2 <-(data$C)*3.666 # write csv file as the result of biomass calculation write.csv(data, file="C:/Users/DELL/Desktop/MScThesis_DATAFOREST_UVa/outputs/Biomass_Carbon_A83.csv") ############################################################################ ############################# CHARACTERISTICS ############################## #--------------------------------------------------------------------------- #####----------------- AT INDIVIDUAL TREE LEVEL ----------------- # > At Individual tree level # > - Basal area (gi) # > - Species proportion (Pi) defined in terms of basal area # > - Relative density (Re_density) # > - Relative density index (RDI) # > - Slenderness (h/d ratio) # > - Crown indices ### Tree Basal area # the cross-sectional area of a stem, usually measured at breast height # Gi=(pi/4)*d^2 Aboveground tree biomass, carbon stocks and tree diversity in a mixed forest plantation in Northern Vietnam Thi Nhat Minh Doan Máster en Gestión Forestal basada en Ciencia de Datos - Master on Forest Management based on Data Science (DATAFOREST) 86 # Gi(m2) d(m) data$Gi_m2 <- (pi/4)*(data$Diameter_cm*0.01)^2 ### Species proportion (Pi) defined in terms of basal area data$Pi <- data$Gi_m2/sum(data$Gi_m2) ### Density of the Marteloscope D_marte<-sum(data$Gi_m2)/max(data$Gi_m2) D_marte ### Height diameter ratio or Slenderness (h/d ratio) # (Mitchell, 2000). The more growing space a tree is granted, # the longer its crown and the smaller its height diameter ratio # Slenderness = h/d where h(m), d(m) # data$h_d_ratio_m <- ifelse(species != "Died", (data$Total_height_m)/(data$Diameter_cm*0.01),"Died") ### Crown indices or ratios # Crown ratio = crown length/tree height # data$Crown_ratio <- ifelse(species != "Died", (data$Total_height_mdata$H_to_canop_m)/(data$Total_height_m),"Died") # Crown form index = crown length/crown width # data$Crown_form_index <- ifelse(species != "Died", (data$Total_height_mdata$H_to_canop_m)/((data$Canopy_W1_m+data$Canopy_W2_m)/2),"Died") # Linear crown index # data$Linear_crown_index <- ifelse(species != "Died", ((data$Canopy_W1_m+data$Canopy_W2_m)/2)/(data$Diameter_cm*0.01),"Died") # Crown spread ratio # data$Crown_spread_ratio <- ifelse(species != "Died", ((data$Canopy_W1_m+data$Canopy_W2_m)/2)/(data$Total_height_m),"Died") #####------------------- AT QUADRANT LEVEL --------------------- # > Propotion of each species # > Basal area (G) # > Above ground bimomass of each quadrant # convert name of species (column) in letter into numerical value data$spNum <-as.numeric(data$Specie) head(data) # subset each quadrant separately q1 <- subset(data, Cell==1) q2 <- subset(data, Cell==2) q3 <- subset(data, Cell==3) q4 <- subset(data, Cell==4) q5 <- subset(data, Cell==5) q6 <- subset(data, Cell==6) q7 <- subset(data, Cell==7) q8 <- subset(data, Cell==8) q9 <- subset(data, Cell==9) q10 <- subset(data, Cell==10) q11 <- subset(data, Cell==11) q12 <- subset(data, Cell==12) q13 <- subset(data, Cell==13) q14 <- subset(data, Cell==14) q15 <- subset(data, Cell==15) q16 <- subset(data, Cell==16) # create list of all the data data.list <- list(q1,q2,q3,q4,q5,q6,q7,q8,q9,q10,q11,q12,q13,q14,q15,q16) # function to calculate carbon stocks C <- function(x){ AGB <- sum(x) C <- AGB*0.5*3.67 return(C) Aboveground tree biomass, carbon stocks and tree diversity in a mixed forest plantation in Northern Vietnam Thi Nhat Minh Doan Máster en Gestión Forestal basada en Ciencia de Datos - Master on Forest Management based on Data Science (DATAFOREST) 87 } # function to calculate basal area G <- function(x){ G <- sum(x)/(1/16) # G=sum(gi)/S (of the quadrant return(G) } # function to calculate ABG of a quadrant AGB<- function(x){ AGB<- sum(x) return(AGB) } # funtion to calculate number of tree per hectare N<- function(x){ N<-length(x)*(10000/625) # N = no of tree in a quadrant*(1ha/S of the quadrant) return(N) } #apply all the functions for all quadrants simultineously: Character <- lapply(data.list, function(x){ for(i in 1:nrow(x)){ x$TotalAGB_Kg <-AGB(x$AGB_kg) x$Basal_area <-G(x$Gi_m2) x$Treeperha <- N(x$Cell) x$Carbon <- C(x$AGB_kg) } x }) #View(Character[[3]]) #to check the result of quadrant 3 # reconstruct initial dataframe back Characteristic<- bind_rows(Character) # Propotion of each species # count the number of trees in each species type (n) data1 <- Characteristic %>% group_by(Cell, Specie) %>% mutate(n = n()) # count the total number of trees in each quadrant (N) Characteristic <- data1 %>% group_by(Cell) %>% mutate(N = n(), # get total number of trees in each quadrant sp.prop = n/N) # calculate proportion of each species in each quadrant # reconstruct initial dataframe back data <- merge(data, Characteristic, all.x = FALSE) names(data) ####################################################### ################## DIVERISTY INDICES ################## #------------------------------------------------------ # > Evennes index (E) # > Berker-Parker index (D) # > Simpson index (D) # > Shannon index (H) # Requiring the packages #if(!require("vegan"))install.packages("vegan") #if(!require("spatstat"))install.packages("spatstat") library(vegan) library(spatstat) ### first thing that we need to prepare our data for the analyzes Aboveground tree biomass, carbon stocks and tree diversity in a mixed forest plantation in Northern Vietnam Thi Nhat Minh Doan Máster en Gestión Forestal basada en Ciencia de Datos - Master on Forest Management based on Data Science (DATAFOREST) 88 # we already converted name of species (column) in letter into # numerical value because of vegan requirement. ### define functions that are going to be applied for each quadrant: # functions of some indices have already been developed in vegan package, Some are not # we should write function for those that don't have pre-defined function. # function for Evenness index: E <-function(x){ H <- diversity(x) # shannon S <- specnumber(x) # number of species, rowSums(BCI > 0) does the same... E <- H/log(S) # equation of Evennes index return(E) } # function for Berger-Parker index: D <-function(x){ N <- length(x) # total number of individuals in the quadrants n <- table(x) # number of individuals of each species Nmax <-max(n) # number of individuals in the most abundant species D <- Nmax/N # equation of Berker parker index recip.D <- 1/D # reciprocal of the index return(recip.D) } ### apply all the functions for all quadrants simultineously: result <- lapply(data.list, function(x){ for(i in 1:nrow(x)){ x$simpson <-diversity(x$spNum, "simpson") #get simmpson diversity index x$shannon <-diversity(x$spNum, "shannon") #get shannon index x$E <- E(x$spNum) #Evenness index x$D <- D(x$spNum) #Berger-Parker index } x # x is argument of the function, not variable }) #View(result[[16]]) #check if the result is okay # reconstruct initial dataframe back Diver <- bind_rows(result) write.csv(Diver, file="C:/Users/DELL/Desktop/MScThesis_DATAFOREST_UVa/outputs/Diversity_Indices.csv") # combine result into original data data <- merge(data, Diver, all.x = FALSE) names(data) write.csv(data, file="C:/Users/DELL/Desktop/MScThesis_DATAFOREST_UVa/outputs/AGB_C_indices.csv") ######### SPATIAL POINT PATTERN ANALYZES (stand level indices) ######## #---------------------------------------------------------------------- #####----------------------- L function (L) -------------------------- # > - at whole stand level # > - at quadrat level # > - at species level (within and between interactions of species) within each quadrat # L function is used to analyze spatial point pattern. # Spatial point pattern analysis (SPP) --> used to study the distribution of discrete points, # analyze and obtain information about spatial structure of individuals dispersed within a study area. # The idea is to distinguish between point patterns which tend toward complete spatial randomness (CSR), # clumping or regularity and at which scale these characterics occur. # Main question of our analyze here is distribution of points in our study are differs from CSR. Aboveground tree biomass, carbon stocks and tree diversity in a mixed forest plantation in Northern Vietnam Thi Nhat Minh Doan Máster en Gestión Forestal basada en Ciencia de Datos - Master on Forest Management based on Data Science (DATAFOREST) 89 # Therefore, for each level: # > 1st L function is calculated # > 2nd randomization test (Poisson null: CSR) is used to check if points different from CSR. ##### L for a whole marteloscope ---------------- ### Create spatial point pattern object from xy coordinates of the points (trees). # Use ppp()to create spatial point pattern object. # Syntax: name <- ppp(X, Y, rangeX, rangeY) OR name=ppp(X, Y, window=window). # --> need find ranges of x & y (define observation window). # create observation window from our data (xy coordinates of points) using ripras() function. # ripras() is used to determine observation window that fit/correspond to our points. window_marte <- ripras(data$Long, data$Lat) # create a point-pattern object that contains both the points and the observation window. point_patt <- ppp(data$Long, data$Lat, window= window_marte) plot(point_patt) # compute L function L_marteloscope <- Lest(point_patt, correction="Ripley") L_marteloscope plot(L_marteloscope, main = "L-function at whole stand level") # As we can see the result, analyzing SPP for a while plot don't provide much information for us. # so lets analyze SPP for each quadrants. ##### L for each quadrat --------------------- # apply L funcion for a list of datasets: L_quadrant <- lapply(data.list, function(x) { # apply function to a list of datasets window_qd <- ripras(x$Long, x$Lat) # create observation plot that fits to points point_patt <- ppp(x$Long, x$Lat, window=window_qd) # create point patterns from coordinates of trees return( Lest(point_patt, correction="Ripley")) # calculate L function }) plot.anylist(L_quadrant[1:8], main="L-function for quadrants 1 to 8") plot.anylist(L_quadrant[9:16], main="L-function for quadrants 9 to 16") plot.anylist(L_quadrant[1]) plot.anylist(L_quadrant[9]) #export immages ##### L for each species in each quadrat ----------------- # In this section, we analyze within & between interactions of different species in each quadrants. # Main steps for this analzye: # 1. group species by their type with factor() function. # 2. create observation window # 3. create point pattern object within observation window # 4. split each species type # 5. compute L function # 6. check CSR by randomisation test using envelope() function. # Combined the steps from 1 to 5 are in a single function and applied this function to # the list of datasets (quadrants) as below. L_specie <- lapply(data.list, function(x) { # apply function to a list of datasets group <- factor(x$Specie) # group species that belong to the same species together window_sp <- ripras(x$Long, x$Lat) # create observation window pp.group <- ppp(x$Long, x$Lat, window= window_sp, marks=group) # create point pattern within window split.group <- split(pp.group) # split species by their group return(alltypes(pp.group, "L")) # compute L function for all types of species Aboveground tree biomass, carbon stocks and tree diversity in a mixed forest plantation in Northern Vietnam Thi Nhat Minh Doan Máster en Gestión Forestal basada en Ciencia de Datos - Master on Forest Management based on Data Science (DATAFOREST) 96 # folows: # S=1-Pij/E(pij) # where: pij is observed probability, E(pij) is expected probability. # the range of values for S is -1 to 1. # if S < 0, we observe tendency towards an association of the 2 examined species. # If S > 0, it indicates a tendency towards a spatial segregation of the tree species. ##### Prepare datasets ---------------------------------------- # Prepare dataset for S index calculation in 2 by 2 contingency table. It # means we will separate (subset) the 2 species pairs of data from original dataset # because segregation index is used to analyze regularity of only 2 species. # That is why we need to subset species 2 by 2. # write a function to subset a pair of species based on conditions if 2 species # after defining pairs for every species, remove the pair with all 0 observations sub_fun <- function(data, i, j){ subs <- subset(data, sp_i %in% c(i, j) & sp_j %in% c(i, j)) rem <- droplevels(subs) # remove unused levels (0) from df return(rem) } # apply this function to subset species Aa.Am <- sub_fun(dist.m, "Acacia auriculiformis", "Acacia mangium"); table(Aa.Am$sp_i, Aa.Am$sp_j) Aa.Se <- sub_fun(dist.m, "Acacia auriculiformis", "Senna siamea"); table(Aa.Se$sp_i, Aa.Se$sp_j) Aa.Lg <- sub_fun(dist.m, "Acacia auriculiformis", "Litsea glutinosa"); table(Aa.Lg$sp_i, Aa.Lg$sp_j) Aa.Eu <- sub_fun(dist.m, "Acacia auriculiformis", "Eucalyptus camaldulensis"); table(Aa.Eu$sp_i, Aa.Eu$sp_j) Aa.Di <- sub_fun(dist.m, "Acacia auriculiformis", "Died"); table(Aa.Di$sp_i, Aa.Di$sp_j) Aa.Ap <- sub_fun(dist.m, "Acacia auriculiformis", "Aporosa villosa"); table(Aa.Ap$sp_i, Aa.Ap$sp_j) Aa.Av <- sub_fun(dist.m, "Acacia auriculiformis", "Averrhoa carambola"); table(Aa.Av$sp_i, Aa.Av$sp_j) Am.Se <- sub_fun(dist.m, "Acacia mangium", "Senna siamea"); table(Am.Se$sp_i, Am.Se$sp_j) Am.Lg <- sub_fun(dist.m, "Acacia mangium", "Litsea glutinosa"); table(Am.Lg$sp_i, Am.Lg$sp_j) Am.Eu <- sub_fun(dist.m, "Acacia mangium", "Eucalyptus camaldulensis"); table(Am.Eu$sp_i, Am.Eu$sp_j) Am.Di <- sub_fun(dist.m, "Acacia mangium", "Died"); table(Am.Di$sp_i, Am.Di$sp_j) Am.Ap <- sub_fun(dist.m, "Acacia mangium", "Aporosa villosa"); table(Am.Ap$sp_i, Am.Ap$sp_j) Am.Av <- sub_fun(dist.m, "Acacia mangium", "Averrhoa carambola"); table(Am.Av$sp_i, Am.Av$sp_j) Se.Lg <- sub_fun(dist.m, "Senna siamea", "Litsea glutinosa"); table(Se.Lg$sp_i, Se.Lg$sp_j) Se.Eu <- sub_fun(dist.m, "Senna siamea", "Eucalyptus cSealdulensis"); table(Se.Eu$sp_i, Se.Eu$sp_j) Se.Di <- sub_fun(dist.m, "Senna siamea", "Died"); table(Se.Di$sp_i, Se.Di$sp_j) Se.Ap <- sub_fun(dist.m, "Senna siamea", "Aporosa villosa"); table(Se.Ap$sp_i, Se.Ap$sp_j) Se.Av <- sub_fun(dist.m, "Senna siamea", "Averrhoa carSebola"); table(Se.Av$sp_i, Se.Av$sp_j) Li.Di <- sub_fun(dist.m, "Litsea glutinosa", "Died"); table(Li.Di$sp_i, Li.Di$sp_j) Eu.Di <- sub_fun(dist.m, "Eucalyptus camaldulensis", "Died"); table(Eu.Di$sp_i, Eu.Di$sp_j) Eu.Ap <- sub_fun(dist.m, "Eucalyptus camaldulensis", "Aporosa villosa"); table(Eu.Ap$sp_i, Eu.Ap$sp_j) Eu.Av <- sub_fun(dist.m, "Eucalyptus camaldulensis", "Averrhoa carEubola"); table(Eu.Av$sp_i, Eu.Av$sp_j) Di.Ap <- sub_fun(dist.m, "Died", "Aporosa villosa"); table(Di.Ap$sp_i, Di.Ap$sp_j) Di.Av <- sub_fun(dist.m, "Died", "Averrhoa carDibola"); table(Di.Av$sp_i, Di.Av$sp_j) ##### Calculating S index --------------------------------- ##### Aa.Am step by step calculation of S to check if the result is right. n <- table(Aa.Am$sp_i, Aa.Am$sp_j); n # for create contingency table by ref & neigh trees Nrow <- rowSums(n); Nrow # for total number of reference tree by species Ncol <- colSums(n); Ncol # for total number of neighbouring tree by species Ndissim <- length(which(Aa.Am$sp_j!=Aa.Am$sp_i)) # number of mixture species (diff sp) N <- length(Aa.Am$sp_i); N # for total number of plants in whole data obsProb <- N * Ndissim; obsProb # for observed probability expProb <- Nrow[1]*Ncol[2]+Nrow[2]*Ncol[1]; expProb # expected probability Aboveground tree biomass, carbon stocks and tree diversity in a mixed forest plantation in Northern Vietnam Thi Nhat Minh Doan Máster en Gestión Forestal basada en Ciencia de Datos - Master on Forest Management based on Data Science (DATAFOREST) 97 Aa.Am$S.ind <- 1-obsProb/expProb;Saaam<-Aa.Am$S.ind[1] # the result is ok ##### Aa.Se step by step calculation of S to check if the result is right. n <- table(Aa.Se$sp_i, Aa.Se$sp_j); n # for create contingency table by ref & neigh trees Nrow <- rowSums(n); Nrow # for total number of reference tree by species Ncol <- colSums(n); Ncol # for total number of neighbouring tree by species Ndissim <- length(which(Aa.Se$sp_j!=Aa.Se$sp_i)) # number of mixture species (diff sp) N <- length(Aa.Se$sp_i); N # for total number of plants in whole data obsProb <- N * Ndissim; obsProb # for observed probability expProb <- Nrow[1]*Ncol[2]+Nrow[2]*Ncol[1]; expProb # expected probability Aa.Se$S.ind <- 1-obsProb/expProb;Saase<-Aa.Se$S.ind[1] # the result is ok ##### Aa.Lg step by step calculation of S to check if the result is right. n <- table(Aa.Lg$sp_i, Aa.Lg$sp_j); n # for create contingency table by ref & neigh trees Nrow <- rowSums(n); Nrow # for total number of reference tree by species Ncol <- colSums(n); Ncol # for total number of neighbouring tree by species Ndissim <- length(which(Aa.Lg$sp_j!=Aa.Lg$sp_i)) # number of mixture species (diff sp) N <- length(Aa.Lg$sp_i); N # for total number of plants in whole data obsProb <- N * Ndissim; obsProb # for observed probability expProb <- Nrow[1]*Ncol[2]+Nrow[2]*Ncol[1]; expProb # expected probability Aa.Lg$S.ind <- 1-obsProb/expProb;Saalg<-Aa.Lg$S.ind[1] # the result is ok ##### Aa.Eu step by step calculation of S to check if the result is right. n <- table(Aa.Eu$sp_i, Aa.Eu$sp_j); n # for create contingency table by ref & neigh trees Nrow <- rowSums(n); Nrow # for total number of reference tree by species Ncol <- colSums(n); Ncol # for total number of neighbouring tree by species Ndissim <- length(which(Aa.Eu$sp_j!=Aa.Eu$sp_i)) # number of mixture species (diff sp) N <- length(Aa.Eu$sp_i); N # for total number of plants in whole data obsProb <- N * Ndissim; obsProb # for observed probability expProb <- Nrow[1]*Ncol[2]+Nrow[2]*Ncol[1]; expProb # expected probability Aa.Eu$S.ind <- 1-obsProb/expProb;Saaeu<-Aa.Eu$S.ind[1] # the result is ok ##### Aa.Di step by step calculation of S to check if the result is right. n <- table(Aa.Di$sp_i, Aa.Di$sp_j); n # for create contingency table by ref & neigh trees Nrow <- rowSums(n); Nrow # for total number of reference tree by species Ncol <- colSums(n); Ncol # for total number of neighbouring tree by species Ndissim <- length(which(Aa.Di$sp_j!=Aa.Di$sp_i)) # number of mixture species (diff sp) N <- length(Aa.Di$sp_i); N # for total number of plants in whole data obsProb <- N * Ndissim; obsProb # for observed probability expProb <- Nrow[1]*Ncol[2]+Nrow[2]*Ncol[1]; expProb # expected probability Aa.Di$S.ind <- 1-obsProb/expProb;Saadi<-Aa.Di$S.ind[1] # the result is ok ##### Aa.Ap step by step calculation of S to check if the result is right. n <- table(Aa.Ap$sp_i, Aa.Ap$sp_j); n # for create contingency table by ref & neigh trees Nrow <- rowSums(n); Nrow # for total number of reference tree by species Ncol <- colSums(n); Ncol # for total number of neighbouring tree by species Ndissim <- length(which(Aa.Ap$sp_j!=Aa.Ap$sp_i)) # number of mixture species (diff sp) N <- length(Aa.Ap$sp_i); N # for total number of plants in whole data obsProb <- N * Ndissim; obsProb # for observed probability expProb <- Nrow[1]*Ncol[2]+Nrow[2]*Ncol[1]; expProb # expected probability Aa.Ap$S.ind <- 1-obsProb/expProb;Saaap<-Aa.Ap$S.ind[1] # the result is ok ##### Aa.Av step by step calculation of S to check if the result is right. n <- table(Aa.Av$sp_i, Aa.Av$sp_j); n # for create contingency table by ref & neigh trees Nrow <- rowSums(n); Nrow # for total number of reference tree by species Ncol <- colSums(n); Ncol # for total number of neighbouring tree by species Aboveground tree biomass, carbon stocks and tree diversity in a mixed forest plantation in Northern Vietnam Thi Nhat Minh Doan Máster en Gestión Forestal basada en Ciencia de Datos - Master on Forest Management based on Data Science (DATAFOREST) 98 Ndissim <- length(which(Aa.Av$sp_j!=Aa.Av$sp_i)) # number of mixture species (diff sp) N <- length(Aa.Av$sp_i); N # for total number of plants in whole data obsProb <- N * Ndissim; obsProb # for observed probability expProb <- Nrow*Ncol+Nrow*Ncol; expProb # expected probability Aa.Av$S.ind <- 1-obsProb/expProb;Saaav<-Aa.Av$S.ind[1] # the result is ok ##### Am.Se step by step calculation of S to check if the result is right. n <- table(Am.Se$sp_i, Am.Se$sp_j); n # for create contingency table by ref & neigh trees Nrow <- rowSums(n); Nrow # for total number of reference tree by species Ncol <- colSums(n); Ncol # for total number of neighbouring tree by species Ndissim <- length(which(Am.Se$sp_j!=Am.Se$sp_i)) # number of mixture species (diff sp) N <- length(Am.Se$sp_i); N # for total number of plants in whole data obsProb <- N * Ndissim; obsProb # for observed probability expProb <- Nrow[1]*Ncol[2]+Nrow[2]*Ncol[1]; expProb # expected probability Am.Se$S.ind <- 1-obsProb/expProb;Samse<-Am.Se$S.ind[1] # the result is ok ##### Am.Lg step by step calculation of S to check if the result is right. n <- table(Am.Lg$sp_i, Am.Lg$sp_j); n # for create contingency table by ref & neigh trees Nrow <- rowSums(n); Nrow # for total number of reference tree by species Ncol <- colSums(n); Ncol # for total number of neighbouring tree by species Ndissim <- length(which(Am.Lg$sp_j!=Am.Lg$sp_i)) # number of mixture species (diff sp) N <- length(Am.Lg$sp_i); N # for total number of plants in whole data obsProb <- N * Ndissim; obsProb # for observed probability expProb <- Nrow[1]*Ncol[2]+Nrow[2]*Ncol[1]; expProb # expected probability Am.Lg$S.ind <- 1-obsProb/expProb;Samlg<-Am.Lg$S.ind[1] # the result is ok ##### Am.Eu step by step calculation of S to check if the result is right. n <- table(Am.Eu$sp_i, Am.Eu$sp_j); n # for create contingency table by ref & neigh trees Nrow <- rowSums(n); Nrow # for total number of reference tree by species Ncol <- colSums(n); Ncol # for total number of neighbouring tree by species Ndissim <- length(which(Am.Eu$sp_j!=Am.Eu$sp_i)) # number of mixture species (diff sp) N <- length(Am.Eu$sp_i); N # for total number of plants in whole data obsProb <- N * Ndissim; obsProb # for observed probability expProb <- Nrow[1]*Ncol[2]+Nrow[2]*Ncol[1]; expProb # expected probability Am.Eu$S.ind <- 1-obsProb/expProb;Sameu<-Am.Eu$S.ind[1] # the result is ok ##### Am.Di step by step calculation of S to check if the result is right. n <- table(Am.Di$sp_i, Am.Di$sp_j); n # for create contingency table by ref & neigh trees Nrow <- rowSums(n); Nrow # for total number of reference tree by species Ncol <- colSums(n); Ncol # for total number of neighbouring tree by species Ndissim <- length(which(Am.Di$sp_j!=Am.Di$sp_i)) # number of mixture species (diff sp) N <- length(Am.Di$sp_i); N # for total number of plants in whole data obsProb <- N * Ndissim; obsProb # for observed probability expProb <- Nrow[1]*Ncol[2]+Nrow[2]*Ncol[1]; expProb # expected probability Am.Di$S.ind <- 1-obsProb/expProb;Samdi<-Am.Di$S.ind[1] # the result is ok ##### Am.Ap step by step calculation of S to check if the result is right. n <- table(Am.Ap$sp_i, Am.Ap$sp_j); n # for create contingency table by ref & neigh trees Nrow <- rowSums(n); Nrow # for total number of reference tree by species Ncol <- colSums(n); Ncol # for total number of neighbouring tree by species Ndissim <- length(which(Am.Ap$sp_j!=Am.Ap$sp_i)) # number of mixture species (diff sp) N <- length(Am.Ap$sp_i); N # for total number of plants in whole data obsProb <- N * Ndissim; obsProb # for observed probability expProb <- Nrow[1]*Ncol[2]+Nrow[2]*Ncol[1]; expProb # expected probability Am.Ap$S.ind <- 1-obsProb/expProb;Samap<-Am.Ap$S.ind[1] # the result is ok Aboveground tree biomass, carbon stocks and tree diversity in a mixed forest plantation in Northern Vietnam Thi Nhat Minh Doan Máster en Gestión Forestal basada en Ciencia de Datos - Master on Forest Management based on Data Science (DATAFOREST) 99 ##### Am.Av step by step calculation of S to check if the result is right. n <- table(Am.Av$sp_i, Am.Av$sp_j); n # for create contingency table by ref & neigh trees Nrow <- rowSums(n); Nrow # for total number of reference tree by species Ncol <- colSums(n); Ncol # for total number of neighbouring tree by species Ndissim <- length(which(Am.Av$sp_j!=Am.Av$sp_i)) # number of mixture species (diff sp) N <- length(Am.Av$sp_i); N # for total number of plants in whole data obsProb <- N * Ndissim; obsProb # for observed probability expProb <- Nrow*Ncol+Nrow*Ncol; expProb # expected probability Am.Av$S.ind <- 1-obsProb/expProb;Samav<-Am.Av$S.ind[1] # the result is ok ##### Se.Lg step by step calculation of S to check if the result is right. n <- table(Se.Lg$sp_i, Se.Lg$sp_j); n # for create contingency table by ref & neigh trees Nrow <- rowSums(n); Nrow # for total number of reference tree by species Ncol <- colSums(n); Ncol # for total number of neighbouring tree by species Ndissim <- length(which(Se.Lg$sp_j!=Se.Lg$sp_i)) # number of mixture species (diff sp) N <- length(Se.Lg$sp_i); N # for total number of plants in whole data obsProb <- N * Ndissim; obsProb # for observed probability expProb <- Nrow*Ncol+Nrow*Ncol; expProb # expected probability Se.Lg$S.ind <- 1-obsProb/expProb;Sselg<-Se.Lg$S.ind[1] # the result is ok ##### Se.Eu step by step calculation of S to check if the result is right. n <- table(Se.Eu$sp_i, Se.Eu$sp_j); n # for create contingency table by ref & neigh trees Nrow <- rowSums(n); Nrow # for total number of reference tree by species Ncol <- colSums(n); Ncol # for total number of neighbouring tree by species Ndissim <- length(which(Se.Eu$sp_j!=Se.Eu$sp_i)) # number of mixture species (diff sp) N <- length(Se.Eu$sp_i); N # for total number of plants in whole data obsProb <- N * Ndissim; obsProb # for observed probability expProb <- Nrow*Ncol+Nrow*Ncol; expProb # expected probability Se.Eu$S.ind <- 1-obsProb/expProb;Sseeu<-Se.Eu$S.ind[1] # the result is ok ##### Se.Di step by step calculation of S to check if the result is right. n <- table(Se.Di$sp_i, Se.Di$sp_j); n # for create contingency table by ref & neigh trees Nrow <- rowSums(n); Nrow # for total number of reference tree by species Ncol <- colSums(n); Ncol # for total number of neighbouring tree by species Ndissim <- length(which(Se.Di$sp_j!=Se.Di$sp_i)) # number of mixture species (diff sp) N <- length(Se.Di$sp_i); N # for total number of plants in whole data obsProb <- N * Ndissim; obsProb # for observed probability expProb <- Nrow[1]*Ncol[2]+Nrow[2]*Ncol[1]; expProb # expected probability Se.Di$S.ind <- 1-obsProb/expProb;Ssedi<-Se.Di$S.ind[1] # the result is ok ##### Se.Ap step by step calculation of S to check if the result is right. n <- table(Se.Ap$sp_i, Se.Ap$sp_j); n # for create contingency table by ref & neigh trees Nrow <- rowSums(n); Nrow # for total number of reference tree by species Ncol <- colSums(n); Ncol # for total number of neighbouring tree by species Ndissim <- length(which(Se.Ap$sp_j!=Se.Ap$sp_i)) # number of mixture species (diff sp) N <- length(Se.Ap$sp_i); N # for total number of plants in whole data obsProb <- N * Ndissim; obsProb # for observed probability expProb <- Nrow*Ncol+Nrow*Ncol; expProb # expected probability Se.Ap$S.ind <- 1-obsProb/expProb;Sseap<-Se.Ap$S.ind[1] # the result is ok ##### Se.Av step by step calculation of S to check if the result is right. n <- table(Se.Av$sp_i, Se.Av$sp_j); n # for create contingency table by ref & neigh trees Nrow <- rowSums(n); Nrow # for total number of reference tree by species Ncol <- colSums(n); Ncol # for total number of neighbouring tree by species Ndissim <- length(which(Se.Av$sp_j!=Se.Av$sp_i)) # number of mixture species (diff sp) Aboveground tree biomass, carbon stocks and tree diversity in a mixed forest plantation in Northern Vietnam Thi Nhat Minh Doan Máster en Gestión Forestal basada en Ciencia de Datos - Master on Forest Management based on Data Science (DATAFOREST) 100 N <- length(Se.Av$sp_i); N # for total number of plants in whole data obsProb <- N * Ndissim; obsProb # for observed probability expProb <- Nrow*Ncol+Nrow*Ncol; expProb # expected probability Se.Av$S.ind <- 1-obsProb/expProb;Sseav<-Se.Av$S.ind[1] # the result is ok ##### Li.Di step by step calculation of S to check if the result is right. n <- table(Li.Di$sp_i, Li.Di$sp_j); n # for create contingency table by ref & neigh trees Nrow <- rowSums(n); Nrow # for total number of reference tree by species Ncol <- colSums(n); Ncol # for total number of neighbouring tree by species Ndissim <- length(which(Li.Di$sp_j!=Li.Di$sp_i)) # number of mixture species (diff sp) N <- length(Li.Di$sp_i); N # for total number of plants in whole data obsProb <- N * Ndissim; obsProb # for observed probability expProb <- Nrow[1]*Ncol[2]+Nrow[2]*Ncol[1]; expProb # expected probability Li.Di$S.ind <- 1-obsProb/expProb;Slidi<-Li.Di$S.ind[1] # the result is ok ##### Eu.Di step by step calculation of S to check if the result is right. n <- table(Eu.Di$sp_i, Eu.Di$sp_j); n # for create contingency table by ref & neigh trees Nrow <- rowSums(n); Nrow # for total number of reference tree by species Ncol <- colSums(n); Ncol # for total number of neighbouring tree by species Ndissim <- length(which(Eu.Di$sp_j!=Eu.Di$sp_i)) # number of mixture species (diff sp) N <- length(Eu.Di$sp_i); N # for total number of plants in whole data obsProb <- N * Ndissim; obsProb # for observed probability expProb <- Nrow[1]*Ncol[2]+Nrow[2]*Ncol[1]; expProb # expected probability Eu.Di$S.ind <- 1-obsProb/expProb;Seudi<-Eu.Di$S.ind[1] # the result is ok ##### Eu.Ap step by step calculation of S to check if the result is right. n <- table(Eu.Ap$sp_i, Eu.Ap$sp_j); n # for create contingency table by ref & neigh trees Nrow <- rowSums(n); Nrow # for total number of reference tree by species Ncol <- colSums(n); Ncol # for total number of neighbouring tree by species Ndissim <- length(which(Eu.Ap$sp_j!=Eu.Ap$sp_i)) # number of mixture species (diff sp) N <- length(Eu.Ap$sp_i); N # for total number of plants in whole data obsProb <- N * Ndissim; obsProb # for observed probability expProb <- Nrow[1]*Ncol[2]+Nrow[2]*Ncol[1]; expProb # expected probability Eu.Ap$S.ind <- 1-obsProb/expProb;Seuap<-Eu.Ap$S.ind[1] # the result is ok ##### Eu.Av step by step calculation of S to check if the result is right. n <- table(Eu.Av$sp_i, Eu.Av$sp_j); n # for create contingency table by ref & neigh trees Nrow <- rowSums(n); Nrow # for total number of reference tree by species Ncol <- colSums(n); Ncol # for total number of neighbouring tree by species Ndissim <- length(which(Eu.Av$sp_j!=Eu.Av$sp_i)) # number of mixture species (diff sp) N <- length(Eu.Av$sp_i); N # for total number of plants in whole data obsProb <- N * Ndissim; obsProb # for observed probability expProb <- Nrow*Ncol+Nrow*Ncol; expProb # expected probability Eu.Av$S.ind <- 1-obsProb/expProb;Seuap<-Eu.Av$S.ind[1] # the result is ok ##### Di.Ap step by step calculation of S to check if the result is right. n <- table(Di.Ap$sp_i, Di.Ap$sp_j); n # for create contingency table by ref & neigh trees Nrow <- rowSums(n); Nrow # for total number of reference tree by species Ncol <- colSums(n); Ncol # for total number of neighbouring tree by species Ndissim <- length(which(Di.Ap$sp_j!=Di.Ap$sp_i)) # number of mixture species (diff sp) N <- length(Di.Ap$sp_i); N # for total number of plants in whole data obsProb <- N * Ndissim; obsProb # for observed probability expProb <- Nrow*Ncol+Nrow*Ncol; expProb # expected probability Aboveground tree biomass, carbon stocks and tree diversity in a mixed forest plantation in Northern Vietnam Thi Nhat Minh Doan Máster en Gestión Forestal basada en Ciencia de Datos - Master on Forest Management based on Data Science (DATAFOREST) 101 Di.Ap$S.ind <- 1-obsProb/expProb;Sdiap<-Di.Ap$S.ind[1] # the result is ok ##### Di.Av step by step calculation of S to check if the result is right. n <- table(Di.Av$sp_i, Di.Av$sp_j); n # for create contingency table by ref & neigh trees Nrow <- rowSums(n); Nrow # for total number of reference tree by species Ncol <- colSums(n); Ncol # for total number of neighbouring tree by species Ndissim <- length(which(Di.Av$sp_j!=Di.Av$sp_i)) # number of mixture species (diff sp) N <- length(Di.Av$sp_i); N # for total number of plants in whole data obsProb <- N * Ndissim; obsProb # for observed probability expProb <- Nrow*Ncol+Nrow*Ncol; expProb # expected probability Di.Av$S.ind <- 1-obsProb/expProb;Sdiav<-Di.Av$S.ind[1] # the result is ok # reconstruct dataframe of dist.m using the result of S # if_else() is very strict, so you'll need to careful match the types of true and false. # This is most likely to bite you when you're using missing values, and you'll need to # use a specific NA: NA_integer_, NA_real_, or NA_character_: dist.m$Seg <- if_else(dist.m$sp_i %in% c("Acacia auriculiformis", "Acacia mangium") & dist.m$sp_j %in% c("Acacia auriculiformis", "Acacia mangium"), Saaam, if_else(dist.m$sp_i %in% c("Acacia auriculiformis", "Senna siamea") & dist.m$sp_j %in% c("Acacia auriculiformis", "Senna siamea"), Saase, if_else(dist.m$sp_i %in% c("Acacia auriculiformis", "Litsea glutinosa") & dist.m$sp_j %in% c("Acacia auriculiformis", "Litsea glutinosa"), Saalg, if_else(dist.m$sp_i %in% c("Acacia auriculiformis", "Eucalyptus camaldulensis") & dist.m$sp_j %in% c("Acacia auriculiformis", "Eucalyptus camaldulensis"), Saaeu, if_else(dist.m$sp_i %in% c("Acacia auriculiformis", "Died") & dist.m$sp_j %in% c("Acacia auriculiformis", "Died"), Saadi, if_else(dist.m$sp_i %in% c("Acacia auriculiformis", "Aporosa villosa") & dist.m$sp_j %in% c("Acacia auriculiformis", "Aporosa villosa"), Saaap, if_else(dist.m$sp_i %in% c("Acacia auriculiformis", "Averrhoa carambola") & dist.m$sp_j %in% c("Acacia auriculiformis", "Averrhoa carambola"), Saaav, if_else(dist.m$sp_i %in% c("Acacia mangium", "Senna siamea") & dist.m$sp_j %in% c("Acacia mangium", "Senna siamea"), Samse, if_else(dist.m$sp_i %in% c("Acacia mangium", "Litsea glutinosa") & dist.m$sp_j %in% c("Acacia mangium", "Litsea glutinosa"), Samlg, if_else(dist.m$sp_i %in% c("Acacia mangium", "Eucalyptus camaldulensis") & dist.m$sp_j %in% c("Acacia mangium", "Eucalyptus camaldulensis"), Sameu, if_else(dist.m$sp_i %in% c("Acacia mangium", "Died") & dist.m$sp_j %in% c("Acacia mangium", "Died"), Samdi, if_else(dist.m$sp_i %in% c("Acacia mangium", "Aporosa villosa") & dist.m$sp_j %in% c("Acacia mangium", "Aporosa villosa"), Samap, if_else(dist.m$sp_i %in% c("Acacia mangium", "Averrhoa carambola") & dist.m$sp_j %in% c("Acacia mangium", "Averrhoa carambola"), Samav, if_else(dist.m$sp_i %in% c("Senna siamea", "Litsea glutinosa") & dist.m$sp_j %in% c("Senna siamea", "Litsea glutinosa"), Sselg, if_else(dist.m$sp_i %in% c("Senna siamea", "Eucalyptus camaldulensis") & dist.m$sp_j %in% c("Senna siamea", "Eucalyptus camaldulensis"), Sseeu, if_else(dist.m$sp_i %in% c("Senna siamea", "Died") & dist.m$sp_j %in% c("Senna siamea", "Died"), Ssedi, if_else(dist.m$sp_i %in% c("Senna siamea", "Aporosa villosa") & dist.m$sp_j %in% c("Senna siamea", "Aporosa villosa"), Sseap, if_else(dist.m$sp_i %in% c("Senna siamea", "Averrhoa carambola") & dist.m$sp_j %in% c("Senna siamea", "Averrhoa carambola"), Sseav, if_else(dist.m$sp_i %in% c("Litsea glutinosa", "Died") & dist.m$sp_j %in% c("Litsea glutinosa", "Died"), Slidi, if_else(dist.m$sp_i %in% c("Eucalyptus camaldulensis", "Died") & Aboveground tree biomass, carbon stocks and tree diversity in a mixed forest plantation in Northern Vietnam Thi Nhat Minh Doan Máster en Gestión Forestal basada en Ciencia de Datos - Master on Forest Management based on Data Science (DATAFOREST) 102 dist.m$sp_j %in% c("Eucalyptus camaldulensis", "Died"), Seudi, if_else(dist.m$sp_i %in% c("Eucalyptus camaldulensis", "Aporosa villosa") & dist.m$sp_j %in% c("Eucalyptus camaldulensis", "Aporosa villosa"), Seuap, if_else(dist.m$sp_i %in% c("Died", "Aporosa villosa") & dist.m$sp_j %in% c("Died", "Aporosa villosa"), Sdiap, if_else(dist.m$sp_i %in% c("Died", "Averrhoa carambola") & dist.m$sp_j %in% c("Died", "Averrhoa carambola"), Sdiav,NA_real_))))))))))))))))))))))) # select reference tree informations outputS <- dist.m %>% select(target_tree_i, sp_i, dbh_i, H_i, x_i, y_i, distij, Seg) %>% group_by(tree1 = gl(n()/4, 4), sp_i) %>% mutate(S = mean(Seg), dbh_i = dbh_i[1], H_i = H_i[1], x_i = x_i[1], y_i = y_i[1], distij = distij[1]) %>% slice(1) head(outputS) ### merge all outputs into one single data names(outputS) names(outputS)[1]<-paste("Tree_ID") names(outputS)[5]<-paste("Long") # combine result into original data and clean it by deleting unesscesary column data <- merge(data, outputS, by=c("Tree_ID","Long") ,all.x = FALSE) names(data) data <- subset( data, select = -c( 34: 40 )) names(data) range(data$S) names(outputS)[1]<-paste("target_tree_i") names(outputS)[5]<-paste("x_i") ################################################################################################### #################### VERTICAL SPATIAL PATTERN INDICES (stand level indices) ####################### #-------------------------------------------------------------------------------------------------- #--------------------------------- Vertical Species profile (A) ----------------------------------- packages <-c("dplyr", "vegan", "tidyverse") lapply(packages, require, character.only=TRUE) # A index is based on Shannon index and proposed the differentation of tree species within each # height layer. It takes into account proportion of species and number of layers in a stand. # Its value is greater than 0. 0 is for a single-layered pure stand. The more heterogeneous # the vertical profile, the higher the A value. # convert name of species (column) in letter into numerical value because of vegan requirement. # Species types must be in numeric type for shannon indices calculation using vegan package. # There are 2 main steps to calculate A index # > classify height zones # > compute A index ##### classify height zones: # divide Height into 3 zones: If we assume the height of the highest tree in the stand # to be 100%, zone I extends from 100% down to 80%, zone 2 from 80% down to 50% and zone 3 from 50% # down to the forest ground. If the top of a tree is located in one of these zones, we # consider the tree belonging to this zone. # Zones: # zone1 = 0-50% of total height # zone2 = 50-80% of total height # zone3 = 80-100% of total height Aboveground tree biomass, carbon stocks and tree diversity in a mixed forest plantation in Northern Vietnam Thi Nhat Minh Doan Máster en Gestión Forestal basada en Ciencia de Datos - Master on Forest Management based on Data Science (DATAFOREST) 103 # write a function that divide height of the stand into 3 zones zones.fun <- function(H){ # determine break points that are going to be 50%, 80%, 100% values of max height H100 <- max(H) H80 <- H100 * 0.8 H50 <- H100 * 0.5 # divide the stand into 3 zones accordint to their height zones <- cut(H, breaks = c(0, H50, H80, H100), labels = c("zone1", "zone2", "zone3"), right=TRUE) return(zones) } ##### A index for a whole stand ---------------------------- data$Hzones.st <- zones.fun(data$Total_height_m) data <- data %>% group_by(Hzones.st) %>% mutate(Atmp = diversity(spNum, "shannon")) # Standardization of A which can be done by dividing A by max value of A. Amax=log(S*Z). Z <- 3 # number of height zones in the stand S <- length(unique(data$Specie)); S # number of species in a stand data$Arel <- data$Atmp/log(S*Z) ##### A index for each quadrants ----------------------------- # define zones in each quadrant data <- data %>% group_by(Cell) %>% mutate(Hzones.qd = zones.fun(Total_height_m)) # subset each quadrant separately q1 <- subset(data, Cell==1) q2 <- subset(data, Cell==2) q3 <- subset(data, Cell==3) q4 <- subset(data, Cell==4) q5 <- subset(data, Cell==5) q6 <- subset(data, Cell==6) q7 <- subset(data, Cell==7) q8 <- subset(data, Cell==8) q9 <- subset(data, Cell==9) q10 <- subset(data, Cell==10) q11 <- subset(data, Cell==11) q12 <- subset(data, Cell==12) q13 <- subset(data, Cell==13) q14 <- subset(data, Cell==14) q15 <- subset(data, Cell==15) q16 <- subset(data, Cell==16) # create list of all the data data.list <- list(q1,q2,q3,q4,q5,q6,q7,q8,q9,q10,q11,q12,q13,q14,q15,q16) # write a function to compute A for each quadrant A.fun <- function(data, Hzones.qd, spNum) { data %>% group_by_at(Hzones.qd) %>% mutate(A = diversity(!! rlang::sym(spNum), "shannon")) } # apply it to the datalist outA <- map(data.list, A.fun, Hzones.qd = "Hzones.qd", spNum = "spNum") Aboveground tree biomass, carbon stocks and tree diversity in a mixed forest plantation in Northern Vietnam Thi Nhat Minh Doan Máster en Gestión Forestal basada en Ciencia de Datos - Master on Forest Management based on Data Science (DATAFOREST) 104 # combine data of quadrants into a single data outA <- bind_rows(outA) # the more heterogenious the vertical profile, A become higher. # merge the result with data data <- merge(data, outA, all.x = FALSE) names(data) data$Arel2 <- data$A/log(S*Z) # export result as a csv file write.csv(data, file="C:/Users/DELL/Desktop/MScThesis_DATAFOREST_UVa/outputs/Vertical_profile.csv") #-------------------------------- Height difference index (TH) --------------------------------------- packages <- c("dplyr") lapply(packages, require, character.only =TRUE) # it is a single tree variable and be calulated for each pair of neighbours trees and reference/t. # also it can be calculated at a whole stand level (subpopulation) & at species level by # summing up TH values & divided it by the number of trees or individuals of the subpopulation. # Formula is: Th = 1-min(Hi, Hj)/max(Hi, Hj); where Hi is height of reference tree # Hj is height of neighbour tree. For each pair the one with min value is divided by the one # with max value. # 0 < TH < 1: # if TH=1, neighbour trees have high differentiation in height, # if TH=0, neightbour trees have equal height. # Procedures: # > define nearest neighbour trees # > calculate TH index # we have already calculated distances between reference tree and nearest neighbour trees. # using that, lets calculate TH ##### Calculate height differ index TH: ---------------------------- ### compute TH for each pairs of reference tree and nearest neighbors. For example: # if we choose 3 neihgbour trees, it will be calculated like Ti1, Ti2, Ti3 which mean that # i is reference tree to 1st neighbour # i reference tree to 2nd, # i reference tree to 3rd neighbour dist.m$THij <- 1 - (pmin(dist.m$H_i, dist.m$H_j)/pmax(dist.m$H_i, dist.m$H_j)) head(dist.m) # pmin () and pmax() returns parallel min or max of two or more input vectors names(dist.m) outputTH <- dist.m %>% select(target_tree_i, sp_i, dbh_i, H_i, x_i, y_i, distij, THij) %>% group_by(tree1 = gl(n()/4, 4), sp_i) %>% mutate(TH = mean(THij), dbh_i = dbh_i[1], H_i = H_i[1], x_i=x_i[1], y_i = y_i[1], distij = distij[1]) %>% slice(1) ### the average of T by species TH.sp <- outputTH %>% select(sp_i, TH) %>% group_by(sp_i) %>% summarise(TH.sp = mean(TH)); TH.sp ### merge all outputs into one single data #out.list <- list(data, outputS, outputTH) Aboveground tree biomass, carbon stocks and tree diversity in a mixed forest plantation in Northern Vietnam Thi Nhat Minh Doan Máster en Gestión Forestal basada en Ciencia de Datos - Master on Forest Management based on Data Science (DATAFOREST) 105 #data <- Reduce(function(x, y) merge(x, y, all=TRUE), out.list) names(outputTH) names(outputTH)[1]<-paste("Tree_ID") names(outputTH)[5]<-paste("Long") # combine result into original data and clean it by deleting unesscesary column data <- merge(data, outputTH, by=c("Tree_ID","Long") ,all.x = FALSE) names(data) data <- subset( data, select = -c( 41: 47 )) names(data) names(outputTH)[1]<-paste("target_tree_i") names(outputTH)[5]<-paste("x_i") write.csv(data, file="C:/Users/DELL/Desktop/MScThesis_DATAFOREST_UVa/outputs/MSc_Minh_Calculations.csv") Aboveground tree biomass, carbon stocks and tree diversity in a mixed forest plantation in Northern Vietnam Thi Nhat Minh Doan Máster en Gestión Forestal basada en Ciencia de Datos - Master on Forest Management based on Data Science (DATAFOREST) 112 ## Selection of the best model of the significant models # function to determine R2, SSE, RES, MSE, AIC and BIC stats<-function(model){ mse<-rev(anova(model)$"Mean Sq")[1] r2<-summary(model)$r.squared B0<- summary(model)$coefficients[1] B1<- summary(model)$coefficients[2] B2<- summary(model)$coefficients[3] B3<- summary(model)$coefficients[4] rse<-summary(model)$sigma pvalue <- glance(model)$p.value aic<-AICc(model) bic<-BIC(model) c(b0=B0, b1=B1, b2=B2, b3=B3, R2=r2, P=pvalue, MSE=mse, AIC=aic, BIC=bic) } List<-data.frame(rbind(stats(MD1), stats(MD2), stats(MD3),…,stats(MD226)) #model list presented in annex 4 #Rank the models rankAIC <- List[order(List$AIC),] ; View(rankAIC) rankBIC <- List[order(List$BIC),] ; View(rankBIC) rankR2 <- List[order(-(List$R2)),] ; View(rankR2) rankMSE <- List[order(List$MSE),] ; View(rankMSE) write.csv(rankAIC, file="C:/Users/DELL/Desktop/MScThesis_DATAFOREST_UVa/outputs/rankAIC_auri.csv") ##====>>> Best model is model 3 ##### ------------------------ Sensitivity analysis ----------------------------- ### In this step, we will explain the relation between Sh and AGB of Acacia auriculiformis using the optimum model MD3 <- lm(log(AGB_kg) ~ I(TH^2) + I(Sh^2),data=Aca_au) summary(MD3) B0<- summary(MD3)$coefficients[1];B0 B1<- summary(MD3)$coefficients[2];B1 B2<- summary(MD3)$coefficients[3];B2 ##### Fix TH at 0.05 0.15 0.25 0.35 0.45 0.55 Aca_au$AGB.TH05<-exp(B0 + B1*(0.05)^2 + B2*(Aca_au$Sh)^2) Aca_au$AGB.TH15<-exp(B0 + B1*(0.15)^2 + B2*(Aca_au$Sh)^2) Aca_au$AGB.TH25<-exp(B0 + B1*(0.25)^2 + B2*(Aca_au$Sh)^2) Aca_au$AGB.TH35<-exp(B0 + B1*(0.35)^2 + B2*(Aca_au$Sh)^2) Aca_au$AGB.TH45<-exp(B0 + B1*(0.45)^2 + B2*(Aca_au$Sh)^2) Aca_au$AGB.TH55<-exp(B0 + B1*(0.55)^2 + B2*(Aca_au$Sh)^2) f <- list( family = "Arial", size = 18, color = "#fffff") a1 <- list( a2 <- list( title = "Shannon index", titlefont = f, showline = TRUE, linewidth = 1) b2 <- list( title = "AGB (kg)", titlefont = f, showline = TRUE, linewidth = 1) p <- plot_ly(Aca_au, x = ~Sh) %>% add_trace(y = ~AGB.TH05, type='scatter', name = 'fix TH at 0.05', mode = 'markers') %>% Aboveground tree biomass, carbon stocks and tree diversity in a mixed forest plantation in Northern Vietnam Thi Nhat Minh Doan Máster en Gestión Forestal basada en Ciencia de Datos - Master on Forest Management based on Data Science (DATAFOREST) 113 add_trace(y = ~AGB.TH15, type='scatter', name = 'fix TH at 0.15', mode = 'markers') %>% add_trace(y = ~AGB.TH25, type='scatter', name = 'fix TH at 0.25', mode = 'markers') %>% add_trace(y = ~AGB.TH35, type='scatter', name = 'fix TH at 0.35', mode = 'markers') %>% add_trace(y = ~AGB.TH45, type='scatter', name = 'fix TH at 0.45', mode = 'markers') %>% add_trace(y = ~AGB.TH55, type='scatter', name = 'fix TH at 0.55', mode = 'markers') %>% layout(xaxis = a2, yaxis = b2, showlegend = TRUE);p #Sys.setenv("plotly_username" = "YOUR USER NAME") #Sys.setenv("plotly_api_key" = "YOUR API KEY") Sys.setenv("plotly_username" = "dtnmahbu") Sys.setenv("plotly_api_key" = "9X09RgPxK6LKLqdCZF3C") ## save image plotly_IMAGE(p, format = "png", out_file = "AGB_auri.png") Aboveground tree biomass, carbon stocks and tree diversity in a mixed forest plantation in Northern Vietnam Thi Nhat Minh Doan Máster en Gestión Forestal basada en Ciencia de Datos - Master on Forest Management based on Data Science (DATAFOREST) 114 Annex 8: Forms for data collection Aboveground tree biomass, carbon stocks and tree diversity in a mixed forest plantation in Northern Vietnam Thi Nhat Minh Doan Máster en Gestión Forestal basada en Ciencia de Datos - Master on Forest Management based on Data Science (DATAFOREST) 115 Aboveground tree biomass, carbon stocks and tree diversity in a mixed forest plantation in Northern Vietnam Thi Nhat Minh Doan Máster en Gestión Forestal basada en Ciencia de Datos - Master on Forest Management based on Data Science (DATAFOREST) 116 Annex 9: Picture from field measurements Determining the coordinates of each tree Setting up the grid line Trees measuring Measuring tree height Discussion before the field work Tree lable