A Stand Density Management Diagram for mixed stands of Pinus sylvestris and Pinus pinaster in the Sierra de la Demanda (Spain)

Master Erasmus Mundus in Mediterranean Forestry and Natural Resources (MEDFOR) A Stand Density Management Diagram for mixed stands of Pinus sylvestris and Pinus pinaster in the Sierra de la Demanda (Spain) Student: Ali Askarieh Co-advisors: Dr. Irene Ruano Benito, & Prof. Dr. Felipe Bravo Oviedo July, 2019 A Stand Density Management Diagram for mixed stands of Pinus sylvestris and Pinus pinaster in the Sierra de la Demanda (Spain) Ali Askarieh Master Erasmus Mundus in Mediterranean Forestry and Natural Resources (MEDFOR) 2 A Stand Density Management Diagram for mixed stands of Pinus sylvestris and Pinus pinaster in the Sierra de la Demanda (Spain) Ali Askarieh Master Erasmus Mundus in Mediterranean Forestry and Natural Resources (MEDFOR) 3 A Stand Density Management Diagram for mixed stands of Pinus sylvestris and Pinus pinaster in the Sierra de la Demanda (Spain) Ali Askarieh Master Erasmus Mundus in Mediterranean Forestry and Natural Resources (MEDFOR) 4 INDEX RESUMEN ..................................................................................................................................... 5 ABSTRACT .................................................................................................................................... 5 1.- INTRODUCTION ..................................................................................................................... 7 2.-OBJECTIVES .......................................................................................................................... 10 3.- MATERIAL AND METHODS ............................................................................................... 10 3.1. Study site .......................................................................................................................... 10 3.2. Data ................................................................................................................................... 12 3.3. Model structure and statistical methods ...................................................................... 17 4.- RESULTS ............................................................................................................................... 18 4.1. Models fitting and statistical analysis: .......................................................................... 18 4.2. SDMD for Pinus sylvestris-Pinus pinaster mixed stands: ......................................... 21 5.- DISCUSSION ......................................................................................................................... 21 6. - CONCLUSIONS ................................................................................................................... 25 7.- ACKNOWLEDGMENTS ....................................................................................................... 26 8-. REFERENCES ...................................................................................................................... 27 ANNEX 1 STATSTICAL SCRIPT ............................................................................................. 32 A Stand Density Management Diagram for mixed stands of Pinus sylvestris and Pinus pinaster in the Sierra de la Demanda (Spain) Ali Askarieh Master Erasmus Mundus in Mediterranean Forestry and Natural Resources (MEDFOR) 5 RESUMEN Los diagramas de manejo de la densidad son herramientas de decisión robustas disponibles para los gestores forestales que disponen de información limitada. Los diagramas son modelos empíricos a nivel de masa, gráficamente representan las relaciones temporales entre la densidad de masa y diferentes variables como el diámetro medio cuadrático, la altura dominante o el volumen. Son usados para definir espaciamiento inicial de una plantación o para organizar las claras. En la actualidad hay un interés creciente en los bosques mixtos como una opción de la gestión forestal adaptativa ya que se consideran cada vez más como una garantía para salvaguardar una amplia variedad de servicios ecosistémicos dentro de la sostenibilidad. Pero hay todavía una falta de conocimiento, herramientas eficientes y modelos para las masas mixtas, como pueden ser los diagramas de densidad. El objetivo de este estudio es desarrollar un diagrama de densidad para las masas mixtas de Pinus sylvestris y Pinus pinaster en la Sierra de la Demanda usando los datos del tercer Inventario Forestal Nacional ya que son dos de las coníferas más importantes en Europa y en la cuenca mediterránea, sobre todo en España. Se pueden usar diferentes variables para desarrollar un diagrama de densidad. En este caso se usaron el diámetro medio cuadrático, la altura dominante, el volumen de la masa, la densidad y el índice de Reineke. Además se realizó un ajuste simultáneo de dos ecuaciones. Estas ecuaciones se ajustaron incluyendo una nueva variable representando la proporción de ambas especies para tener en cuenta la mezcla de la masa. Todos los análisis estadísticos y la construcción del diagrama se realizaron usando el software estadístico R. Los resultados del ajuste simultáneo mostraron que la nueva variable representando la proporción de ambas especies no fue significativo. Basado en esto se construyó un diagrama sin el grado de mezcla de las especies. Este diagrama podrá ser usado por los gestores forestales como una eficiente herramienta para la gestión de la selvicultura de estas masas. Palabras clave: Índice de Reineke, altura dominante, selvicultura, clara, grado de mezcla ABSTRACT Stand density management diagrams (SDMDs) are robust decision-support tools available to forest managers under limited information. SDMDs which are empirical models at stand level, graphically represent the temporal relationships among stand density, and different stand variables such as quadratic mean diameter, dominant height and mean tree volume. They are used to define initial planting spacing or thinning interventions, in order to meet various management objectives. Nowadays, there is a growing interest in mixed-species forests as an option of adaptive forest management, where they are considered a guarantor to safeguarding a wide variety of ecosystem services within the framework of sustainability. But there is still a lack of knowledge and efficient tools and models for mixed stands such as SDMDs. The aim of this study is to develop an SDMD for Pinus sylvestris and Pinus pinaster mixed stands in the Sierra de la Demanda using data from the third Spanish National Forest Inventory, as they are two of the important coniferous species in Europe and in the Mediterranean basin zone especially in Spain. A Stand Density Management Diagram for mixed stands of Pinus sylvestris and Pinus pinaster in the Sierra de la Demanda (Spain) Ali Askarieh Master Erasmus Mundus in Mediterranean Forestry and Natural Resources (MEDFOR) 6 Different variables can be used to develop an SDMD. In this case quadratic mean diameter, dominant height, total stand volume, number of trees per hectare and stand density index (Reineke index) were estimated. Moreover a simultaneous fitting was developed. These equations were fit including a new variable representing the proportion of both species to take into account the mixed stand. All statistical analysis and the construction of the SDMD were developed using the software R. The results of the simultaneous fitting showed the new variable representing the proportion of both species was not significant. Based on that, the SDMD was constructed without including mixture degree. This SDMD can be used by forest managers as an efficient tool to plan thinning practices. Key words: Reineke index, dominant height, silviculture, thinning, mixture degree. A Stand Density Management Diagram for mixed stands of Pinus sylvestris and Pinus pinaster in the Sierra de la Demanda (Spain) Ali Askarieh Master Erasmus Mundus in Mediterranean Forestry and Natural Resources (MEDFOR) 7 1.- INTRODUCTION Stand density has a considerable effect on both tree size and stand yield (Drew and Flewelling 1979), thus it impacts how a stand develops over a rotation period, Long et al (2004) defined a stand development as the increase of mean tree size with decreasing number of trees per unit area. In silviculture, forest density regulation or in other words, density management, can be seen as one of the most robust and effective tools available to foresters, in order to achieve desired conditions of the managed stands, consequently a wide range of stand management objectives can be acquired. Hence it may help in overcoming some of the harmful effects of climate change and site degradation. From a conceptual point of view, stand density management is defined as a procedure to control tree competition through density manipulation to meet various management objectives (Newton, 1997; Newton et al. , 2005). At the operational level, this manipulation of density can be achieved by controlling the level of growing stock through initial spacing and/or a sequence of thinning interventions (Barrio-Anta and ÁlvarezGonzález 2005). Hence the responses to such practices, are the results of their influence on the availability of resources necessary for growth, the ability of trees to utilize available resources and finally the distribution of those resources within the site (Long et al., 2004). Determining proper levels of growing stock is critical for planning a stand density regime and should be done precisely. This determination of levels is a complicated process as it involves biological, technological, economic and operational factors fixed to a specific management case (Castedo-Dorado et al. 2009). The process needs selecting the upper and lower limits of growing stock, considering that the upper limit of growing stock is selected to ensure acceptable stand-level growth and tree vitality, while the lower limit of growing stock is selected to ensure maintaining adequate site-occupancy (Dean and Baldwin, 1996). Thus the optimal exploitation of site resources by individual trees and ensuring a sound stand growth are a matter of the proper timing and intensity of thinning treatments, which are strongly dictated by both limits of the growing stock (Kimsey et at., 2019). The implication of thinning treatments at stand level have a major favorable impact on its productivity and yield. This is due to two main reasons, on one hand, making profits from the removed trees (commercial thinning) that would die as a result of stand self-thinning, while on the other hand, these treatments decrease competition among trees, consequently accelerating and improving individual tree growth (Dean and Baldwin, 1993). As mentioned before, thinning interventions have to be scheduled precisely as much as possible, if we are aiming to fulfill maximum benefits out of a given stand. Dean and Baldwin (1993) stated that by overly soon thinning, a stand will negatively be affected in terms of its growing stock and gross yield, as a result of slow tree response. In spite of the fact that thinning experiment plots are the best and most competent method to set the proper timing of thinning and to define density targets (Valbuena et al., 2008; Schnell et al., 2012). They have some critical restrictions, they are timeconsuming as they need too many years to get the results, which cannot be accurately applied on sites have different conditions (site quality and management objectives) from those experienced in field trials (Dean and Baldwin, 1993; Schnell et al., 2012). Moreover, stand densities can occur in an almost infinite array of combinations, consequently, it is unreasonable to expect that all possible combinations could be tested in field trial before applying it in operational forestry (Valbuena et al., 2008). In this regards, stand density management diagrams (SDMDs), also known as ‘stand density control diagrams’ and ‘yield-density diagrams’ have emerged as a time-saving A Stand Density Management Diagram for mixed stands of Pinus sylvestris and Pinus pinaster in the Sierra de la Demanda (Spain) Ali Askarieh Master Erasmus Mundus in Mediterranean Forestry and Natural Resources (MEDFOR) 8 and cost-effective approach, Jack and Long (1996) concluded that SDMDs have a robust conceptual principle in describing even-aged stand dynamics. On the contrary to thinning trials, SDMDs are simple decision-support tools found to help forest managers in the decision-making process under limited information, they are flexible and adaptable to different site conditions and management goals (Schnell et al., 2012). They are efficient in quantitative silviculture as they help forest managers to design, display and evaluate various density management regimes (Jack and Long, 1996; Newton, 2003), in order to predict what stand post-thinning density would be. In terms of operating costs, SDMDs are an inexpensive tool especially for certain areas like the Mediterranean region where the silvicultural practice has to be enacted under critical budget constraints (Valbuena et al., 2008). The main principle of any SDMD based on the stand self-thinning rule, SDMDs are defined as empirical models at stand level which graphically represent the temporal relationships among stand density, and different stand variables such as quadratic mean diameter, dominant height and mean tree volume (Farnden, 1996; Newton, 1997). This size-density relationship is a cornerstone for the establishment of those diagrams by characterizing the growing stock, using indices that relate the average tree size (e.g. diameter, volume, or height) to the number of trees per hectare(Barrio-Anta & AlvarezGonzález 2005). Among these density indices which based on size-density relationships, Reineke’s stand density index (SDI) (Reineke, 1933) was used the most (e.g. Shaw and Long, 2007; Valbuena et al., 2008; Vanderschaaf and Burkhart, 2012; Quiñonez-barraza et al., 2018). Moreover Reineke index is more accurate in Mediterranean pine forests than Hart index (Rodríguez et al. 2008). SDI can be computed based on number of trees per unit area and one of the following stand attributes: quadratic mean diameter, mean stem volume, mean stand height or stand basal area. However, Burkhart (2013) reported that SDI calculated using quadratic mean diameter performed best in comparison with the other stand attributes. Practically, SDMDs are used to defined initial planting spacing or thinning interventions, consequently to meet various management objectives, which include but not be limited to, increasing stand stability and decreasing crown fire risk (López-Sánchez and Rodríguez-Soalleiro, 2009), creating and conserving habitat for wildlife endangered species (Shaw and Long 2007). reducing vulnerability to beetles attacks (Anhold et al. 1996; Long and Shaw, 2005), optimizing stand density for timber production purposes at rotation age (Cabrera-Pérez et al., 2019). SDMDs have been developed worldwide for a broad set of species, which varied between broad-leaved and conifer species. However most of them were focused monoculture stands: Quercus robur (Barrio Anta and Álvarez González, 2005), Pinus banksiana (Sharma and Zhang, 2007), Pinus palustris (Shaw and Long 2007), Pinus halepensis and Pinus pinaster (Valbuena et al., 2008), Pinus radiata (Castedo-Dorado et al., 2009), Picea abies (Vacchiano et al., 2013), Cunninghamia lanceolata (Tang et al., 2015), Eucalyptus grandis (Marangon et al., 2017), Castanea sativa (Patrício and Nunes 2017). While there are very few SDMDs for mixed-species forests: Abies balsamea, Picea rubens, Picea mariana and Picea glauca forests in northeastern North America (Swift et al., 2007), Juniperus procera and Podocarpus falcatus natural mixed forest in Ethiopia (Tesfaye et al., 2016) or Pinus-Quercus natural mixed forests in Mexico (Cabrera-Pérez et al., 2018). According to the State of Europe's Forests 2015 Report, the forested lands with a single tree species dropped over the last 15 years at a rate of about 0.6% annually, while mixed stands cover is estimated to be about 19% of European forest area. In Spain about 19% of the forested areas are mixed forests which are around 3.5 million hectares, in the form of broadleaf-broadleaf or broadleaf-conifer species, which is mostly composed of Pinus-Fagus sylvatica or Pinus-Quercus species (MAGRAMA, 2012). A Stand Density Management Diagram for mixed stands of Pinus sylvestris and Pinus pinaster in the Sierra de la Demanda (Spain) Ali Askarieh Master Erasmus Mundus in Mediterranean Forestry and Natural Resources (MEDFOR) 9 For the time being, forest management is paying more attention to have measures and strategies aimed at increasing the resistance, resilience, and adaptability against disturbances to forest ecosystems (Puettmann et al., 2015). This new tendency gives priority to safeguarding a wide variety of ecosystem services within the framework of sustainability by adopting the species mixing principle as an option of adaptive forest management (Ammer, 2016). In this context, it is becoming increasingly worthwhile for mixed-species forests to play a significant role in reinforcing ecosystem functions and services, consequently enhancing the contribution to climate change mitigation and adaptation, and the conservation of biodiversity. Mixed forests in comparison with monoculture forests have favorable effects on various ecosystem services at higher levels, including production (Gamfeldt et al., 2013). Moreover, they have more resistance to natural disturbance factors (Jactel et al., 2017), and species mixing can positively influence the stability of productivity (del Río et al 2017). All these demonstrate the widely-known multifunctionality of the mixed forests (Van Der Plas et al., 2016). While there is a growing interest in mixed-species forests, there is still a lot of room for research in this area. Specifically, studies which focus on comparing mixed stands and monoculture stands in similar stands, making these discussions mostly theoretical (Pretzsch 2009a). In the Mediterranean basin, it is known that forests are characterized by low productivity. While there are studies that analyse intraand interspecific interactions from a productivity stance (Piotto et. al 2004; Kuehne et al. 2013; Vanclay et al. 2013), there is a dearth of information about different ecosystems like Mediterranean forests or species in terms of a low productivity standpoint. This gives rise to the important endeavour of producing additional data and information for forest managers using evidence-based silivicultural procedures (Coll et al., 2018). Scots pine(Pinus sylvestris L.) and Maritime pine (Pinus pinaster Ait.) are two of the important coniferous species in Europe and in the Mediterranean basin. Where P. sylvestris is widely distributed over the Eurasian continent (Mátyás and Samuel 2004), while P. pinaster occurs in the western Mediterranean Basin, and the Atlantic coast in Spain, Portugal, and France, and currently it is used for forestation even outside its natural distributions (EUFORGEN 2011). The wood of P. sylvestris, with its good mechanical properties, is commercially significant due to its industrial use as timber for construction and pulpwood (Mátyás and Samuel 2004). On the other hand P. pinaster has a traditional use in resin tapping in addition to its uses in afforestation programs for wood production or soil protection, due to its high drought tolerance for long periods and its capability to grow in poor soil (EUFORGEN 2011). In Spain, P. sylvestris has an area of 1.20 million hectares, and it grows mostly in montane climates: 800-2000 m.a.s.l., 600-1200 mm mean annual precipitation and summer precipitation above 100 mm. While P. pinaster has 0.68 million hectares and it grows in sub-humid and continental Mediterranean climates: 600-1300 m.a.s.l., 400-800 mm mean annual precipitation and 20-125 mm summer precipitation. P. sylvestris and P. pinaster occur in natural and afforested stands, either mixed or pure stands (Serrada et al., 2008). Co-existing pine species occur as well in Spain, with a forest cover of 0.5 million ha (Montero and Serrada, 2013), where both of these species are co-existing in mixed stands, distributed in an area of around 120000 hectares of moderate slopes, mainly in the Iberian and Central Mountain Range (Riofrío et al., 2018). These mixed stands occur at different altitude levels ranging from less than 400 m up to 2000 m, where the largest areas are at 1000-1200 m, 800-1000 m, and 200-1400 m, representing 44.3%, 22.6%, and 16.3% respectively of the total area of P.sylvestrisP.pinaster mixed stands (Cañellas et al. 2000). In terms of productivity, Pinus pinaster A Stand Density Management Diagram for mixed stands of Pinus sylvestris and Pinus pinaster in the Sierra de la Demanda (Spain) Ali Askarieh Master Erasmus Mundus in Mediterranean Forestry and Natural Resources (MEDFOR) 16 Cumulative sum of the expansion factors (exp.fact) Estadillo dbh H exp.fact 2188 26.4 11.5 14.14711 2188 34.4 12.5 14.14711 2188 25.3 10.5 14.14711 2188 29.55 12 14.14711 2188 28.45 11.5 14.14711 2188 37.05 14.5 14.14711 2188 28 11 14.14711 2188 32.45 13 14.14711 2188 30.2 8.5 14.14711 2188 33.65 10.5 14.14711 2188 30.45 12.5 14.14711 2188 33.05 11 14.14711 2188 13.3 5.5 31.83099 2188 25 11.5 14.14711 2188 29.2 11 14.14711 2188 22.65 9 14.14711 2188 25.1 11.5 14.14711 2188 19.05 8.5 31.83099 2188 30.3 10 14.14711 2188 30.55 9.5 14.14711 2188 23.65 10.5 14.14711 2188 20.6 11 31.83099 2188 20.6 10.5 31.83099 Ordering the trees based on DBH from the greater to the smaller c_sum_exp.fact 14.14710605 28.29421211 42.44131816 56.58842421 70.73553026 84.88263632 99.02974237 113.1768484 127.3239545 141.4710605 155.6181666 169.7652726 183.9123787 198.0594847 212.2065908 226.3536968 240.5008029 254.6479089 268.795015 300.6260036 332.4569922 364.2879809 396.1189695 Choose the trees until the first value of c_sum_exp.fact >= 100 c_sum_exp.fact 14.14710605 28.29421211 42.44131816 56.58842421 70.73553026 84.88263632 99.02974237 113.1768484 127.3239545 141.4710605 155.6181666 169.7652726 183.9123787 198.0594847 212.2065908 226.3536968 240.5008029 254.6479089 268.795015 300.6260036 332.4569922 364.2879809 396.1189695 DBH H exp.fact 37.05 14.5 14.14711 34.4 12.5 14.14711 33.65 10.5 14.14711 33.05 11 14.14711 32.45 13 14.14711 30.55 9.5 14.14711 30.45 12.5 14.14711 30.3 10 14.14711 30.2 8.5 14.14711 29.55 12 14.14711 29.2 11 14.14711 28.45 11.5 14.14711 28 11 14.14711 26.4 11.5 14.14711 25.3 10.5 14.14711 25.1 11.5 14.14711 25 11.5 14.14711 23.65 10.5 14.14711 22.65 9 14.14711 20.6 11 31.83099 20.6 10.5 31.83099 19.05 8.5 31.83099 13.3 5.5 31.83099 Change the chosen value of c_sum_exp.fact to 100 by changing the corresponding value of exp.fact And in this case we meet the method of (Assmann, 1970) to choose the100 thickest trees per hectare exp.fact c_sum_exp.fact 14.14711 14.14710605 14.14711 28.29421211 14.14711 42.44131816 14.14711 56.58842421 14.14711 70.73553026 14.14711 84.88263632 14.14711 99.02974237 0.970258 100 14.14711 114.1471061 14.14711 128.2942121 14.14711 142.4413182 14.14711 156.5884242 14.14711 170.7355303 14.14711 184.8826363 14.14711 199.0297424 14.14711 213.1768484 14.14711 227.3239545 14.14711 241.4710605 14.14711 255.6181666 31.83099 287.4491552 31.83099 319.2801438 31.83099 351.1111324 31.83099 382.9421211 Multiply the c_sum_exp.fact by corresponding H just until c_sum_fact=100 H*exp.fact 205.1330378 176.8388257 148.5446136 155.6181666 183.9123787 134.3975075 176.8388257 9.702576317 Sum the H*exp.fact ∑H*exp.fact = 1190.986 Dominant height for plot number (2188) Ho = 11.910 m exp.fac: Expansion factor represents the number of trees per hectare, and as trees are considered in different subplots depending on their DBH we have the following expansion factors: exp.fac = 5.092958: subplot of 25 m radius, trees with a DBH ≥ 42.5 cm are measured exp.fac = 14.14711: subplot of 15 m radius, trees with a DBH ≥ 22.5 cm are measured exp.fac = 31.83099: subplot of 10 m radius, trees with a DBH ≥ 12.5 cm are measured exp.fac = 127.324: subplot of 5 m radius, trees with a DBH ≥ 7.5 cm are measured Figure 4: Dominant height calculation process Plot DBH DBH A Stand Density Management Diagram for mixed stands of Pinus sylvestris and Pinus pinaster in the Sierra de la Demanda (Spain) Ali Askarieh Master Erasmus Mundus in Mediterranean Forestry and Natural Resources (MEDFOR) 17 Table 1: Summary of the data set used to develop SDMD for Pinus sylvestris and Pinus pinaster mixed stands in the Sierra de la Demanda Attributes (Variable) Mean Minimum Maximum Standard desviation (SD) n = 210 DBH 24.92 9.13 45.28 8.00 QMD 26.43 9.19 48.22 8.00 H 12.95 4.70 22.88 4.00 Ho 15.78 6.50 26.17 3.84 N 741.30 101.29 3338.72 493.85 V 301.47 12.27 977.69 162.43 G 34.32 2.53 81.98 15.49 SDI 669.19 74.66 1712.22 289.47 n: total number of plots, DBH: average diameter at breast height (cm), QMD: quadratic mean diameter (cm), H: average tree height (m), Ho = dominant height (m), N: the number of trees per hectare, V: the over bark volume (m3 ha-1), G: basal area (m2 ha-1), SDI: Reineke’s stand density index. 3.3. Model structure and statistical methods The aimed SDMD model has the following fundamental components: - Reineke’s stand density index - An allometric system of two linear equations [1] and [2] ln𝑄𝑀𝐷 =𝛽0+𝛽1.ln𝑁+𝛽2.ln𝐻𝑜 [1] ln𝑉 =𝛽3+𝛽4.ln𝑄𝑀𝐷+𝛽5.ln𝐻𝑜+𝛽6.ln𝑁 [2] where: QMD: quadratic stem diameter (cm) N: stand density (tree ha-1) Ho: dominant height (m) V: stand total volume (m3 ha-1) βi: regression coefficients Equation [1] relates the quadratic mean diameter with stand density, and dominant height, while equation [2] relates the over bark volume with the quadratic mean diameter, dominant height, and stand density. Ln QMD and Ln V are instrumental and dependent endogenous variables, while Ln Ho and Ln N are independent exogenous variables, but as Ln QMD is defined independently of the system in equation [2], so it is considered as an independent exogenous variable. As a consequence, the two equations were fit simultaneously to prevent error correlation. A Stand Density Management Diagram for mixed stands of Pinus sylvestris and Pinus pinaster in the Sierra de la Demanda (Spain) Ali Askarieh Master Erasmus Mundus in Mediterranean Forestry and Natural Resources (MEDFOR) 18 In order to test mixing effect on QMD and V two models were developed from [1] and [2] by taking mixture proportions into account, in this regard a new variable (mixfrac) represents mixing degree was introduced into both equations [3] and [4] (Swift et al., 2007). ln𝑄𝑀𝐷 =𝛽0+𝛽1.𝑚𝑖𝑥𝑓𝑟𝑎𝑐+(𝛽2+𝛽3.𝑚𝑖𝑥𝑓𝑟𝑎𝑐).ln𝑁+(𝛽4+𝛽5.𝑚𝑖𝑥𝑓𝑟𝑎𝑐).ln𝐻𝑜 [3] ln𝑉 = 𝛽6+𝛽7.𝑚𝑖𝑥𝑓𝑟𝑎𝑐+(𝛽8+𝛽9.𝑚𝑖𝑥𝑓𝑟𝑎𝑐).ln𝑄𝑀𝐷+(𝛽10+𝛽11.𝑚𝑖𝑥𝑓𝑟𝑎𝑐).ln𝐻𝑜+(𝛽12+ 𝛽13.𝑚𝑖𝑥𝑓𝑟𝑎𝑐).ln𝑁 [4] Where: 𝑚𝑖𝑥𝑓𝑟𝑎𝑐=0.5−|(𝑠𝑦𝑙𝑓𝑟𝑎𝑐−0.5)| 𝑠𝑦𝑙𝑓𝑟𝑎𝑐= 𝑃.𝑠𝑦𝑙𝑣𝑒𝑠𝑡𝑟𝑖𝑠 𝑏𝑎𝑠𝑎𝑙 𝑎𝑟𝑒𝑎 𝑇𝑜𝑡𝑎𝑙 𝑏𝑎𝑠𝑎𝑙 𝑎𝑟𝑒𝑎 The simultaneous fitting of the equations and the statistical analyses were done using the R (R Development Core Team 2019) (Annex 1). SDMD was constructed using the format described by Barrio-Anta and Álvarez González (2005), with quadratic mean diameter (QMD) and density (N) on the major axes. QMD was represented on the (x) axis as a logarithmic scale, while N was represented on the (y) axis as a logarithmic scale too. Then isolines representing dominant height (Ho), over bark volume (V), and Reineke’s stand density index (SDI) were superimposed on the bivariate graph. 4.- RESULTS 4.1. Models fitting and statistical analysis: The results from the simultaneous fitting of equations [3] and [4] to estimate quadratic mean diameter and total stand volume, show that the coefficients of the mixture degree variable (mixfrac) were not significant at a 0.05 significance level, the coefficients estimated are presented in Table 2. Validation statistics of simultaneous fitting of the two equations system are shown in Table 3, where Rsquared (R2) was 0.8376 for ln QMD equation, while it was quite high 0.9504 for ln V equation. A Stand Density Management Diagram for mixed stands of Pinus sylvestris and Pinus pinaster in the Sierra de la Demanda (Spain) Ali Askarieh Master Erasmus Mundus in Mediterranean Forestry and Natural Resources (MEDFOR) 19 Table 2: Coefficients resulted from the simultaneous fitting of the equations [3] and [4] to estimate QMD and V for Pinus sylvestris and Pinus pinaster mixed stands. Coefficients of regression Parameter Estimate Pr(>|t|) QMD equation [3] β0 (Intercept) 2.66935 < 2e-16 β1 0.61017 0.5484 β2 -0.23221 2.4e-16 β3 -0.23966 0.0239 β4 0.76750 < 2e-16 β5 0.24811 0.3356 V equation [4] β6 (Intercept) -7.96060 < 2e-16 β7 -1.13565 0.559 β8 1.85251 < 2e-16 β9 0.47175 0.374 Β1 0.77648 1.05e-08 β11 -0.64931 0.217 β12 0.84664 < 2e-16 β13 0.19217 0.341 Table 3: Validation statistics of simultaneous fitting of the equations [3] and [4] to estimate QMD and V for Pinus sylvestris and Pinus pinaster mixed stands. Equation Value QMD equation [3] RSE on 204 degrees of freedom 0.133 R2 0.8376 Adjusted R2 0.8336 p-value < 2.2e-16 V equation [4] RSE on 202 degrees of freedom 0.1536 R2 0.9504 Adjusted R2 0.9487 p-value < 2.2e-16 The mixture degree variable (mixfrac) was eliminated and another run of simultaneous fitting of the initial system of equation represented by equation [1] and [2] was done to estimate quadratic mean diameter and total stand volume, the results show that all the coefficients were quite significant at a 0.05 significance level, the coefficients estimated are presented in Table 4. Validation statistics of simultaneous fitting of the two equations system are shown in Table 5, where Rsquared (R2) was 0.8376 for ln QMD equation, while it was quite high 0.9504 for ln V equation. A Stand Density Management Diagram for mixed stands of Pinus sylvestris and Pinus pinaster in the Sierra de la Demanda (Spain) Ali Askarieh Master Erasmus Mundus in Mediterranean Forestry and Natural Resources (MEDFOR) 20 Table 4: Coefficients resulted from the simultaneous fitting of the equations [3] and [4] to estimate QMD and V for Pinus sylvestris and Pinus pinaster mixed stands. Coefficients of regression Parameter Estimate Pr(>|t|) QMD equation [1] β0 (Intercept) 2.73396 <2e-16 β1 -0.27044 <2e-16 β2 0.81594 <2e-16 V equation [2] β3 (Intercept) -8.28660 < 2e-16 β4 1.98235 < 2e-16 β5 0.62759 9.69e-15 β6 0.89051 < 2e-16 Table 5: Validation statistics of simultaneous fitting of the equations [1] and [2] to estimate QMD and V for Pinus sylvestris and Pinus pinaster mixed stands. Equation Value QMD equation [1] RSE on 207 degrees of freedom 0.1393 R2 0.8191 Adjusted R2 0.8173 p-value < 2.2e-16 V equation [2] RSE on 206 degrees of freedom 0.1546 R2 0.9488 Adjusted R2 0.948 p-value < 2.2e-16 Thus, the two linear models [1] and [2] exhibit efficient goodness-of-fit statistics, as R2 values were high, making it the appropriate choice to develop the aimed Stand Density Management Diagram. Eventually, the two adjusted linear models to estimate quadratic mean diameter and total stand volume for Pinus sylvestris-Pinus pinaster mixtures in the Sierra de la Demanda were: ln𝑄𝑀𝐷 =2.73396−0.27044.ln𝑁+0.81594.ln𝐻𝑜 [5] ln𝑉 =−8.28660+1.98235.ln𝑄𝑀𝐷+0.62759.ln𝐻𝑜+0.89051.ln𝑁 [6] where: QMD: quadratic stem diameter (cm) N: stand density (tree ha-1) Ho: dominant height (m) V: stand total volume (m3 ha-1) A Stand Density Management Diagram for mixed stands of Pinus sylvestris and Pinus pinaster in the Sierra de la Demanda (Spain) Ali Askarieh Master Erasmus Mundus in Mediterranean Forestry and Natural Resources (MEDFOR) 21 4.2. SDMD for Pinus sylvestris-Pinus pinaster mixed stands: An SDMD for the mixed stands of Pinus sylvestris and Pinus pinaster in the Sierra de la Demanda was constructed using the data extracted from the Spanish national forest inventory, equation [5], equation [6] and the formula of Reineke’s stand density index (Figure 5). Where quadratic mean diameter (QMD) and density (N) were plotted on (x) axis and (y) axis respectively as logarithmic scales. QMD ranged between 9 and 48 cm, and N ranged between 100 and 3500 tree per hectare, minimum and maximum values of data range. While the isolines of: dominant height (Ho) (in red), total volume (V) (in blue), and Reineke’s index (SDI) (in green) were superimposed on the bivariate graph. The islolines in bold green represent the upper and lower growing stock limits and they are 60% of maximum SDI for the upper limits (Dean and Baldwin, 1993) and 35% of maximum SDI for the lower limit (Long, 1985). Optimal density levels should be found between these limits, it means, both bold green lines. Values above the maximum limit means silvicultural treatments like a thinning should be done and values below the minimum limit means density is inadequate. 5.- DISCUSSION The value of the stand density management diagram developed in this study for P.sylvestris–P.pinaster mixed stands, emerges from the new current orientation of moving further in developing efficient tools and models in quantitative silviculture for mixed stands in order to enhance forest wood and non-wood production and ecosystem functions and services quantitatively and qualitatively, especially in light of lack information about mixed forests combined with raised interest in such forest systems. Table 6: Silvicultural management alternative showed in Figure 6. N: density (trees ha-1), QMD: quadratic mean diameter (cm), SDI: Reineke’s stand density index,V: the over bark volume (m3 ha-1). Entry N (tree ha-1) QMD (cm) SDI V (m3) Before After Before After Before After Before After I-II 1700 814.2 21 21 1252.7 600 472.9 210.6 III-IV 814.2 488.5 28.9 28.9 1000 600 505.7 288.5 V (Final cut) 488.5 ــــــــ 39.7 ــــــــ 1000 ــــــــ 692.6 ــــــــ A Stand Density Management Diagram for mixed stands of Pinus sylvestris and Pinus pinaster in the Sierra de la Demanda (Spain) Ali Askarieh Master Erasmus Mundus in Mediterranean Forestry and Natural Resources (MEDFOR) 22 Figure 5: Stand Density Management Diagram for mixed stands of Pinus sylvestris and Pinus pinaster in the Sierra de la Demanda A Stand Density Management Diagram for mixed stands of Pinus sylvestris and Pinus pinaster in the Sierra de la Demanda (Spain) Ali Askarieh Master Erasmus Mundus in Mediterranean Forestry and Natural Resources (MEDFOR) 23 Figure 6: Silvicultural management alternative for mixed stands of Pinus sylvestris and Pinus pinaster in the Sierra de la Demanda I II III IV V A Stand Density Management Diagram for mixed stands of Pinus sylvestris and Pinus pinaster in the Sierra de la Demanda (Spain) Ali Askarieh Master Erasmus Mundus in Mediterranean Forestry and Natural Resources (MEDFOR) 24 An example of a management alternative in this type of forest is showed in Table 6 and Figure 6. In this case a set of systematic thinning interventions were applied in two times and different intensities (I-II and II-III) and a final cut. The initial density was 1700 trees ha-1 and a quadratic mean diameter of 21 cm. The first systematic thinning was applied to obtain a density of 814.2 tree ha-1. Then the stand grew considering no natural mortality until a quadratic mean diameter of 28.9 cm, when the second systematic thinning should be applied. The density decrease from 814.2 trees ha-1 to 488.5 trees ha1 after this second thinning. Again the stand grew until a quadratic mean diameter of approximately 40 cm, when the final cut should be applied. Mixed-species stands as diverse systems: show a greater increment in above-ground woody biomass than pure-species stands (Vilà et al. 2007 ; Paquette and Messier 2011), for example, the annual woody biomass production of mixed stands in the Alto Tajo region in Spain, which consist of two pine species (Pinus sylvestris and Pinus nigra) and two oak species (Quercus ilex and Quercus faginea), exceed the production of monocultures stands by more than 48% (Jucker et al., 2014). Moreover, mixed stands have a higher level of carbon storage in root system (Brassard et al., 2011), in addition to their role in enriching wildlife taxa (Castagneyrol and Jactel 2012), Our results showed that introducing a new variable reflects species mixing effects into the system of equations was not significant, while it was significant in other studies and was retained in the models to formulate SDMD (Swift et al., 2007; Tesfaye et al., 2016), indicating that there was no impact of species mixing on stand yield represented by quadratic mean diameter and over bark volume. That is contrary to what Riofrío et al (2018) concluded that at stand level for the two species in mixture stands, there was a shared gain in productivity with respect to varying tree growth responses to inter-specific competition for each species. In another study of mixed stands, but this time the mixture is a combination between Pinus sylvestris and Fagus sylvatica species, the results were similar to the previous one, where it showed increased productivity in the stands with superior growth of Pinus sylvestris than Fagus sylvatica growth which was reduced (Pretzsch et al., 2015). Meaning that the behavior of our two species in mixed stands could be quite similar in term of productivity. Based on that, we led to only fit the system of models that uses stand density and dominant height, and quadratic mean diameter as independent endogenous variables. These result should not be generalized about various site conditions because of differing productivity relationships on-site. Moreover there is a lack of knowledge for mixed stands although it is increasing during the last years: Pretzsch and Schütze, 2016; Riofrío et al., 2019... Different cases of site–growth relationships in mixed stands can be observed based on different site conditions: In the first case, when the interactions between the two species are absent, the stand mutual gain in productivity would result in a proportional increase of each species, it means the total productivity summarize the productivity of each species individually as in pure stands. In other cases, when there are interactions between both species, the total productivity is not the same than the sum of the individual productivities in pure stands, facilitative or competitive effects affect final productivity (Pretzsch, 2009b). In the present work the interaction between both species is not clear because mixture degree was not significant in the quadratic mean diameter and volume models. Dominant height is one of the main variables to characterize a forest stand at forest mensuration level. Assmann definition is widely used in Spain to estimate this variable but its estimation presents some inconveniences. One of them is the plot size. Dominant height is defined as the height corresponding to the tree that presents the average height of the 100 thickest trees per hectare. If your plot size is 100 m2, only one tree is considered to define dominant height (Bengoa 1999). In the case of national forest A Stand Density Management Diagram for mixed stands of Pinus sylvestris and Pinus pinaster in the Sierra de la Demanda (Spain) Ali Askarieh Master Erasmus Mundus in Mediterranean Forestry and Natural Resources (MEDFOR) 25 inventory, plots consist of four circular subplots and minimum measured diameter at breast height is increasing along with subplots. Therefore expansion factors are necessary to know how many trees are representing each tree of NFI plots at hectare level. The number of trees to estimate the Assmann dominant height varies for each plot which complicates its estimation. 6. - CONCLUSIONS - In the present master thesis a stand density management diagram for Pinus sylvestris and Pinus pinaster mixed forests from Sierra de la Demanda (Spain) has been developed. This diagram could be an easy tool for owners and managers of this region to manage mixed stands using simple variables like dominant height or density. - Despite the increasing interest in mixed-species forests, due to its recognized role in reinforcing ecosystem functions and services. But as it is a complex system in terms of different mixing effects at different levels, there is still a lack of knowledge and a room for more studies in this area. This complexity of mixing effects is reflected in our results which showed that the interaction between both species is not clear, thus no effects on stand yield. Eventually, to examine the behavior and influences on productivity, further studies should be done by taking into account different levels and scales. A Stand Density Management Diagram for mixed stands of Pinus sylvestris and Pinus pinaster in the Sierra de la Demanda (Spain) Ali Askarieh Master Erasmus Mundus in Mediterranean Forestry and Natural Resources (MEDFOR) 32 ANNEX 1 STATSTICAL SCRIPT ####################################################################### #### SDMD for mixed stands of Pinus sylvestris and Pinus pinaster ##### ####################### in Demandas mountains ######################### ####################################################################### ### work directory ### setwd('E:/MScThesis_MEDFOR_UVa/Data/Processed') ################################################ ################ Data selection ################ ################################################ ### Packages and libraries: install.packages("Hmisc") install.packages(pkgs='E:/MScThesis_MEDFOR_UVa/Data/ Processed/Rbasifor/Rbasifor_0.1.tar.gz', repos = NULL) library(measurements) library(Hmisc) library(RODBC) # package to extrac and compute variables from Spanish National Forest Inventory: library(Rbasifor) # help(Rbasifor) library(foreign) ## read tree data from url using Rbasifor: bu.tree <- readNFI('https://www.mapama.gob.es/es/biodiversidad/ servicios/banco-datos-naturaleza/ifn3p09_tcm30-29392 3.zip') so.tree <- readNFI('https://www.mapama.gob.es/es/biodiversidad/ servicios/banco-datos-naturaleza/ifn3p42_tcm30-29398 9.zip') ####################################################################### ######################### volume calculation ########################## ####################################################################### ### First calculate dendrometric variables to use metics2Vol function: ## Burgos provinces: bu.de.met <- nfiMetrics(bu.tree) #(Burgos_dendrometric variables) burgos <- metrics2Vol(bu.de.met) head(burgos) # Dendrometrics at plot level: burgos.p <- dendroMetrics(burgos) head(burgos.p) A Stand Density Management Diagram for mixed stands of Pinus sylvestris and Pinus pinaster in the Sierra de la Demanda (Spain) Ali Askarieh Master Erasmus Mundus in Mediterranean Forestry and Natural Resources (MEDFOR) 33 ####################################################################### ### A new coefficient represent the proportions of the species in ##### ### the mixed stands (Pinus sylvestris as a reference)(Burgos): ####### ####################################################################### ## P.sylvestris basal area (tree level)(m^2/tree) bu.bas.P.syl<- burgos[burgos$Especie=="21",] # P.sylvestris basal area per ha (tree level)(m^2/ha) bu.bas.P.syl <- dendroMetrics(bu.bas.P.syl) names(bu.bas.P.syl)[names(bu.bas.P.syl) == "ba"] <- "p.syl_ba" bu.bas.P.syl$prv_plot <- with(bu.bas.P.syl, paste(pr, Estadillo, sep=' _')) head(bu.bas.P.syl) ####################################################################### ## Soria provinces: so.de.met<- nfiMetrics(so.tree) #(Soria_dendrometric variables) soria <- metrics2Vol(so.de.met) head(soria) # Dendrometrics at plot level: soria.p <- dendroMetrics(soria) head(soria.p) ####################################################################### ### A new coefficient represent the proportions of the species in ##### ### the mixed stand (Pinus sylvestris as a reference)(Soria): ######### ####################################################################### ## P.sylvestris basal area (tree level)(m^2/tree) so.bas.P.syl<- soria[soria$Especie=="21",] # P.sylvestris basal area per ha (tree level)(m^2/ha) so.bas.P.syl <- dendroMetrics(so.bas.P.syl) names(so.bas.P.syl)[names(so.bas.P.syl) == "ba"] <- "p.syl_ba" so.bas.P.syl$prv_plot <- with(so.bas.P.syl, paste(pr, Estadillo, sep=' _')) head(so.bas.P.syl) ########################################################### ###### Dominant height calculation ######################## ########################################################### ### Burgos: bu.test<- nfiMetrics(bu.tree) #(Burgos_dendrometric variables) head(bu.test) bu.syl<- bu.test[bu.test$Especie==21,] bu.pin<- bu.test[bu.test$Especie==26,] bu.pinus <- rbind (bu.syl,bu.pin) bu.pinus <- na.omit(bu.pinus) A Stand Density Management Diagram for mixed stands of Pinus sylvestris and Pinus pinaster in the Sierra de la Demanda (Spain) Ali Askarieh Master Erasmus Mundus in Mediterranean Forestry and Natural Resources (MEDFOR) 34 head(bu.pinus) bu.pinus$d <-(bu.pinus$d/10) bu.pinus$h<-(bu.pinus$h/10) max(bu.pinus$Especie) ## loop to calculate the dominante height (Burgos) : plots<-bu.pinus$Estadillo bu.domH<-data.frame() for (i in plots){ # i<-45 # Plots selection: plot.i<-bu.pinus[bu.pinus$Estadillo==i,] # if (plot.i$Estadillo>0) # Order plot i according to DBH (bigger to smaller) ordering<-plot.i[order(plot.i$d,decreasing=TRUE),] # Calculate cumulative sums of the expansion factor: ordering$sum.exp.fact <- cumsum(ordering$n) # Select rows until 100 of cumulative sum of expansion factor: select.Pi <- ordering[0:(nrow(ordering[ordering$sum.exp.fact<100,]))+ 1,] if (nrow(select.Pi)>1) { ## we are going to change expansion factor of the last tree to # obtain exactly 100 trees per hectare: new.exp.fact <- replace(select.Pi$n,select.Pi$sum.exp.fact>=100,100 -select.Pi [nrow(select.Pi)-1,'sum.exp.fact']) select.Pi<-as.data.frame(select.Pi) # select.Pi is a list, not a da taframe select.Pi <-cbind(select.Pi,new.exp.fact) select.Pi$sum.exp.fact2 <- cumsum(select.Pi$new.exp.fact) # dominant height Ho<-sum(select.Pi$h*select.Pi$new.exp.fact)/100 }else{ if (select.Pi$n>100){ Ho<- select.Pi$h }else{ Ho<- 0 } } A Stand Density Management Diagram for mixed stands of Pinus sylvestris and Pinus pinaster in the Sierra de la Demanda (Spain) Ali Askarieh Master Erasmus Mundus in Mediterranean Forestry and Natural Resources (MEDFOR) 35 Estadillo <-i domH<-cbind(Estadillo,Ho) bu.domH<-rbind(bu.domH,domH) } bu.domH <- na.omit(bu.domH) bu.domH<-unique(bu.domH) max(bu.domH$Ho) bu.domH$prv_plot <- with(bu.domH, paste("9", Estadillo, sep='_')) head(bu.domH) write.csv(bu.domH,file="bu.domH.csv") ############################################################### ############################################################### ### Soria: so.test<- nfiMetrics(so.tree) #(Soria_dendrometric variables) head(so.test) so.syl<- so.test[so.test$Especie==21,] so.pin<- so.test[so.test$Especie==26,] so.pinus <- rbind (so.syl,so.pin) so.pinus <- na.omit(so.pinus) head(so.pinus) so.pinus$d <-(so.pinus$d/10) so.pinus$h<-(so.pinus$h/10) max(so.pinus$Especie) ###loop to calculate the dominante height (Soria) : plots<-so.pinus$Estadillo so.domH<-data.frame() for (i in plots){ # i<-45 # Plots selection: plot.i<-so.pinus[so.pinus$Estadillo==i,] # if (plot.i$Estadillo>0) # Order plot i according to DBH (bigger to smaller) ordering<-plot.i[order(plot.i$d,decreasing=TRUE),] # Calculate cumulative sums of the expansion factor: ordering$sum.exp.fact <- cumsum(ordering$n) # Select rows until 100 of cumulative sum of expansion factor: select.Pi <- ordering[0:(nrow(ordering[ordering$sum.exp.fact<100,]))+ 1,] A Stand Density Management Diagram for mixed stands of Pinus sylvestris and Pinus pinaster in the Sierra de la Demanda (Spain) Ali Askarieh Master Erasmus Mundus in Mediterranean Forestry and Natural Resources (MEDFOR) 36 if (nrow(select.Pi)>1) { ## we are going to change expansion factor of the last tree to # obtain exactly 100 trees per hectare: new.exp.fact <- replace(select.Pi$n,select.Pi$sum.exp.fact>=100,100 -select.Pi [nrow(select.Pi)-1,'sum.exp.fact']) select.Pi<-as.data.frame(select.Pi) # select.Pi is a list, not a da taframe select.Pi <-cbind(select.Pi,new.exp.fact) select.Pi$sum.exp.fact2 <- cumsum(select.Pi$new.exp.fact) # dominant height Ho<-sum(select.Pi$h*select.Pi$new.exp.fact)/100 }else{ if (select.Pi$n>100){ Ho<- select.Pi$h }else{ Ho<- 0 } } Estadillo <-i domH<-cbind(Estadillo,Ho) so.domH<-rbind(so.domH,domH) } so.domH <- na.omit(so.domH) so.domH<-unique(so.domH) max(so.domH$Ho) so.domH$prv_plot <- with(so.domH, paste("42", Estadillo, sep='_')) head(so.domH) write.csv(so.domH,file="so.domH.csv") ################################################# ## join data frames of "bu.domH" and "so.domH":## ################################################# bu.so.domH <- rbind (bu.domH,so.domH) ############################################################ ###### selecting mixed plots in Demandas mountains ######### ############################################################ ## Makeing a new variable joins "Provincia" and "Estadillo" # in both data frames of Bugros and Soria (estadillo is plot: burgos.p$prv_plot <- with(burgos.p, paste(pr, Estadillo, sep='_')) A Stand Density Management Diagram for mixed stands of Pinus sylvestris and Pinus pinaster in the Sierra de la Demanda (Spain) Ali Askarieh Master Erasmus Mundus in Mediterranean Forestry and Natural Resources (MEDFOR) 37 head(burgos.p) soria.p$prv_plot <- with(soria.p, paste(pr, Estadillo, sep='_')) head(soria.p) ## join data frames of "burgos.p" and "soria.p": bu.so.p <- rbind (burgos.p,soria.p) head(bu.so.p) ## join data frames of "bu.bas.P.syl" and "so.bas.P.syl": bu.so.bas.P.syl <- rbind (bu.bas.P.syl,so.bas.P.syl) head(bu.so.bas.P.syl) ### selecting the mixed plots in Demandas mountains: #################################################### library("foreign", lib.loc="C:/Program Files/R/R-3.4.0/library") demanda <- read.dbf("IFN-PsPt-Demanda.dbf") head(demanda) ## Makeing a new variable joins "Provincia" and "Estadillo" # in the data frame of Demandas mountains: demanda$prv_plot <- with(demanda, paste(Provincia, Estadillo, sep='_') ) head(demanda) ## selecting the mixed plots: demanda.mix <- demanda[demanda$Type=="M",] head(demanda.mix) ####################################################################### # selecting the common mixed plots between "demanda.mix" and "bu.so.p": data.de <- bu.so.p[which(bu.so.p$prv_plot %in% demanda.mix$prv_plot),] head (data.de) # Merging and selecting common mixed plots between "data.de" and "bu.so .bas.P.syl" data.de.2<- merge(data.de,bu.so.bas.P.syl ,by="prv_plot") head(data.de.2) data.de.3<-data.de.2[,c("prv_plot","pr.x","Especie.x","X.x","Estadillo. x","ba", "p.syl_ba","d.x","dg.x","h.x","n.x","v.x")] head(data.de.3) names(data.de.3)[names(data.de.3) == "pr.x"] <- "pr" names(data.de.3)[names(data.de.3) == "Especie.x"] <- "Especie" names(data.de.3)[names(data.de.3) == "X.x"] <- "X" names(data.de.3)[names(data.de.3) == "Estadillo.x"] <- "Estadillo" names(data.de.3)[names(data.de.3) == "d.x"] <- "d" names(data.de.3)[names(data.de.3) == "dg.x"] <- "dg" names(data.de.3)[names(data.de.3) == "h.x"] <- "h" names(data.de.3)[names(data.de.3) == "n.x"] <- "n" names(data.de.3)[names(data.de.3) == "v.x"] <- "v" A Stand Density Management Diagram for mixed stands of Pinus sylvestris and Pinus pinaster in the Sierra de la Demanda (Spain) Ali Askarieh Master Erasmus Mundus in Mediterranean Forestry and Natural Resources (MEDFOR) 38 ####################################################################### ## join data frames of "data.de.3" and "bu.so.domH" to get the final da ta # of the mixed plots in Demanda mountains with the needed variables: Final.De <- merge(data.de.3,bu.so.domH,by="prv_plot") Final.Demanda <- na.omit(Final.De) Final.Demanda$syl.frac<-(Final.Demanda$p.syl_ba/Final.Demanda$ba) Final.Demanda$mix.frac<-(0.5-abs(Final.Demanda$syl.frac-0.5)) Final.Demanda$SDI<- Final.Demanda$n*(Final.Demanda$dg/25.4)^1.605 max(Final.Demanda$Ho) summary(Final.Demanda) write.csv(Final.Demanda,file="Final.Demanda.csv") ################################################ ############### Summary statistics ############# ################################################ ## install.packages pkgs <- c("dplyr", "tidyr", "broom") install.packages(pkgs) #install sapply(pkgs, require, character.only = T) #load ### summary of plots characteristics head(Final.Demanda) sumstat <- Final.Demanda %>% # Select and rename five variables select( `DBH` = d, `QMD` = dg, `H` = h, `Ho` = Ho, `N` = n, `V` = v, `G` = ba, `SDI` = SDI) %>% # Find the mean, min, max and st.dev.for each variable summarise_each(funs(mean, min, max, sd)) %>% # Move summary to columns gather(key, value, everything()) %>% separate(key, into = c("variable", "stat"), sep = "_") %>% spread(stat, value) %>% # Set order of summary statistics select(variable, mean, min, max, sd) %>% A Stand Density Management Diagram for mixed stands of Pinus sylvestris and Pinus pinaster in the Sierra de la Demanda (Spain) Ali Askarieh Master Erasmus Mundus in Mediterranean Forestry and Natural Resources (MEDFOR) 39 # Round all numeric variables to one decimal point mutate_each(funs(round(., 2)), -variable) # Write to .txt write.table(sumstat, file = "sumstats.txt", sep = ",", quote = FALSE, row.names = F) summary(Final.Demanda) ####################################################################### ###### Simultaneous fitting of a system of two linear equations ####### ####################################################################### # logarithm of the variables (linearizing the two equations QMD and V): head(Final.Demanda) Final.Demanda$logdg <- log(Final.Demanda$dg) Final.Demanda$logN <- log(Final.Demanda$n) Final.Demanda$logHo <- log(Final.Demanda$Ho) Final.Demanda$logV <- log(Final.Demanda$v) pairs(~logdg+logN+logHo+logV, data=Final.Demanda, main="Matrix scatter chart") Final.Demanda$mixfrac.logdg <- (Final.Demanda$logdg*Final.Demanda$mix.f rac) Final.Demanda$mixfrac.logN <- (Final.Demanda$logN*Final.Demanda$mix.fra c) Final.Demanda$mixfrac.logHo <- (Final.Demanda$logHo*Final.Demanda$mix.f rac) Final.Demanda$mixfrac.logV <- (Final.Demanda$logV*Final.Demanda$mix.fra c) Final.Demanda$syl.frac.logdg <- (Final.Demanda$logdg*Final.Demanda$syl. frac) Final.Demanda$syl.frac.logN <- (Final.Demanda$logN*Final.Demanda$syl.fr ac) Final.Demanda$syl.frac.logHo <- (Final.Demanda$logHo*Final.Demanda$syl. frac) Final.Demanda$syl.frac.logV <- (Final.Demanda$logV*Final.Demanda$syl.fr ac) head(Final.Demanda) write.csv(Final.Demanda,file="Final.Demanda.csv") ##(1) Simultaneous fitting of the two non-linear models (lnQMD) and (ln V) # with (mix.frac) variable: # Adjustment of the linearized allometric model QMD: model01l<- lm(logdg~mix.frac+logN+mixfrac.logN+logHo+mixfrac.logHo, Final.Demanda) A Stand Density Management Diagram for mixed stands of Pinus sylvestris and Pinus pinaster in the Sierra de la Demanda (Spain) Ali Askarieh Master Erasmus Mundus in Mediterranean Forestry and Natural Resources (MEDFOR) 40 #Summary of the linear adjustment QMD: summary(model01l) # Adjustment of the linearized allometric model V: model02l<- lm(logV~mix.frac+logdg+mixfrac.logdg+logHo+mixfrac.logHo+ logN+mixfrac.logN,Final.Demanda) # Summary of the linear adjustment V: summary(model02l) ####################################################################### # Fitting without introducing the (mix.frac) variable into the models # ####################################################################### ##(2) Simultaneous fitting of the two non-linear models (lnQMD) and (ln V) # without (mix.frac) variable: ## Adjustment of the linearized allometric model QMD: model01lmod<- lm(logdg~logN+logHo,data=Final.Demanda) # Summary of the linear adjustment QMD: summary(model01lmod) ## MODIFICATION Adjustment of the linearized allometric model V: model02lmod<- lm(logV~logdg+logHo+logN,data=Final.Demanda) # Summary of the linear adjustment V: summary(model02lmod) ########################################################### ################## The Diagram (SDMD) ##################### ########################################################### modlm1<-lm(logdg~logN+logH0,Final.Demanda) summary(modlm1) modlm2<-lm(logV~logdg+logH0+logN,Final.Demanda) summary(modlm2) modnls1 <- nls(dg~b0*N^b1*H0^b2, data=Final.Demanda, start=list(b0=2.73 396, b1=-0.27044, b2=0.81594)) summary(modnls1) modnls2 <- nls(V~b3*dg^b4*H0^b5*N^b6, data=Final.Demanda, start=list(b3 =-8.28660 , b4=1.98235 , b5=0.62759, b6=0.89051)) summary(modnls2) deviance(modnls1) A Stand Density Management Diagram for mixed stands of Pinus sylvestris and Pinus pinaster in the Sierra de la Demanda (Spain) Ali Askarieh Master Erasmus Mundus in Mediterranean Forestry and Natural Resources (MEDFOR) 41 deviance(modnls2) require(sqldf) f01 <-sqldf("select Avg(dg) as AvgOfDg, Avg(V) as AvgOfV from Final.Dem anda") f02 <-sqldf("select Sum(power(dg a sAvgOfDg, 2)) as SCTdg, Sum(power(Vâ € AvgOfV, 2)) as SCTV from Final.Demanda, f01") f02 <-sqldf("select Sum(power(dg???AvgOfDg, 2)) as SCTdg, Sum(power(V?? ?AvgOfV, 2)) as SCTV from Final.Demanda, f01") f02$R2dg <-1-deviance(modnls1)/f02$SCTdg # R² of the first model f02$R2V <-1-deviance(modnls2)/f02$SCTV # R² of the second model f02 H0 <-seq(5, 35, 2) SDI<-seq(10, 54, 4) Final.Demanda<-merge(H0,SDI) names(Final.Demanda) <-c("H0", "SDI") Final.Demanda$valor.ih<-(10000/(Final.Demanda$H0*Final.Demanda$SDI) )^2 N <-c(seq(50, 100, 10), seq(125, 400, 25), seq(450, 950, 50), seq(1000, 2000, 100), seq(2250, 3000, 250)) Nn <- c(100, 200, 300, 400, 500, 600, 700, 800, 1000, 2000, 3000) parm <- data.frame(b0=2.73396 , b1=-0.27044, b2=0.81594, b3=-8.28660, b4=1.98235, b5=0.62759, b6=0.89051) parm$b304 <- parm$b3*parm$b0^parm$b4 parm$b245 <- parm$b2*parm$b4+parm$b5 parm$b146 <- parm$b1*parm$b4+parm$b6 library(lattice) win.graph() library(lattice) win.graph() xyplot(log10(valor.ih)~H0, data=Final.Demanda, groups=SDI , type="l", col=1, lwd=2, xlim=c(5, 35), ylim=c(min(log10(N)), max( log10(N)))) scales=list(y=list( at=log10(c(seq(50, 80, 10), seq(100, 200, 25), seq(250, 450, 50), seq (500, 900, 100), seq(1000, 1800, 200), seq(2000, 3000, 50 0))), labels= c(seq(50, 80, 10), seq(100, 200, 25), seq(250, 450, 50), seq( 500, 900, 100), seq(1000, 1800, 200), seq(2000, 3000, 50 0))) )