Modeling Ecosystems Using P Systems: The Bearded Vulture, a Case Study

Modeling Ecosystems Using P Systems: The Bearded Vulture, a Case Study M´onica Cardona1, M. Angels Colomer1,MarioJ.P´erez-Jim´enez2, Delf´ıSanuy 3, and Antoni Margalida4 1Dept. of Mathematics, University of Lleida Av. Alcalde Rovira Roure, 191. 25198 Lleida, Spain {mcardona,colomer}@matematica.udl.es 2Research Group on Natural Computing Dept. of Computer Science and Artificial Intelligence, University of Sevilla Avda. Reina Mercedes s/n, 41012 Sevilla, Spain [email protected] 3Dept. of Animal Production, University of Lleida Av. Alcalde Rovira Roure, 191. 25198 Lleida, Spain [email protected] 4Bearded Vulture Study & Protection Group Adpo. 43 E-25520 El Pont de Suert (Lleida), Spain [email protected] Abstract. The Bearded Vulture (Gypaetus barbatus) is an endangered species in Europe that feeds almost exclusively on bone remains of wild and domestic ungulates. In this paper, we present a model of an ecosystem related to the Bearded Vulture in the Pyrenees (NE Spain), by using P systems. The evolution of six species is studied: the Bearded Vulture and five subfamilies of domestic and wild ungulates upon which the vulture feeds. P systems provide a high level computational modeling framework which integrates the structural and dynamic aspects of ecosystems in a comprehensive and relevant way. P systems explicitly represent the discrete character of the components of an ecosystem by using rewriting rules on multisets of objects which represent individuals of the population and bones. The inherent stochasticity and uncertainty in ecosystems is captured by using probabilistic strategies. In order to experimentally validate the P system designed, we have constructed a simulator that allows us to analyze the evolution of the ecosystem under different initial conditions. 1 Introduction Animal species are interconnected in a network in which some species depend on others in terms of feeding [10], [26]. Variations in biomass affect the composition of the population structures [24]. In mountain ecosystems, the presence of domestic animals has disrupted the traditional relationships between wild ungulates and their predators[6]. Animals located at the top of the ecological pyramid are susceptible to the presence and number of these domestic animals. The abandonment of dead animals in the mountains is a major source of food for necrophagous species [15]. This is the case for the Bearded Vulture (Gypaetus barbatus), a threatened species which feeds on bone remains of domestic and wild ungulates. The study of population ecology and how species interact with the environment [13] is one aspect of conservation biology of great interest to managers and conservationists [2]. A widespread tool used in this area is the ecological model, which uses mathematical representations of ecological processes [21]. In this study, we design a model that studies the evolution of an ecosystem located in the Pyrenees, taking advantage of the capacity the P systems to work in parallel. P systems provide a high level computational modeling framework which integrates the structural and dynamic aspects of ecosystems in a comprehensive and relevant way. P systems explicitly represent the discrete character of the components of an ecosystem by using rewriting rules on multisets of objects which represent individuals of the population and biomass available. The inherent stochasticity and uncertainty in ecosystems is captured by using probabilistic strategies. The ecosystem included six species: Bearded Vulture as a scavenger (predator) species and the Pyrenean Chamois (Rupicapra pyrenaica), Red Deer (Cervus elaphus), Fallow Deer (Dama dama), Roe Deer (Capreolus capreolus) and Sheep (Ovis capra) as carrion (prey) species. In order to experimentally validate of the P system designed we have constructed a simulator that allows us to analyze the evolution of the ecosystem under different initial conditions. The Bearded Vulture is an endangered species and so there are many projects that study its behavior and how it is affected by its environment. Thanks to these studies there is a large amount of information available which is required to define the P system and to validate the results obtained. The paper is structured as follows. In the next section, basic concepts of the ecosystem to be modeled are introduced. The most outstanding aspects of each species are detailed as well as the interactions among them. In Section 3, a dynamic probabilistic P system to describe the ecosystem is presented. In order to study the dynamics of the ecosystem, a simulator of that probabilistic P system is designed in Section 4. The following section is devoted to the analysis of the results produced by the simulator. Finally, conclusions are presented in the last section. 2 Modeling the Ecosystem The ecosystem to be modeled is located in the Catalan Pyrenees, in the Northeast of Spain. This area contains a total of 35 breeding territories that constitutes 34.3% of the Bearded Vulture’s Spanish population in 2007 (n = 102). See Figure 1 [15]. The ecosystem to be modeled is composed of six species: the Bearded Vulture (predator species) and the Pyrenean Chamois, Red Deer, Fallow Deer, Roe Deer, and Sheep (prey species). Prey species belong to the bovid family, they are herbivores and their bone remains form the basic source of nourishment for the Bearded Vulture in the Pyrenees. Fig. 1. Regional distribution of the Bearded Vulture in the Catalan Pyrenees The Bearded Vulture is a cliff-nesting and territorial large scavenger distributed in mountains ranges in Eurasia and Africa. This is one of the rarest raptors in Europe (150 breeding pairs in 2007). This species has a mean lifespan in wild birds of 21.4 years [4]. The mean age of first breeding is 8.1 years, whereas the mean age of first successful breeding was 11.4 years [1]. Egg-laying takes place from December to February and after 52-54 days of incubation and after about 120 days of chick-rearing, the chick abandons the nest between June and August [19]. Clutch size in this species is usually two eggs, but only one chick survives as a consequence of sibling aggression [18]. The female’s annual fertility rate in Catalonia during the last five years is estimated around 38%. The Bearded Vulture is the only vertebrate that feeds almost exclusively on bone remains. Its main food source is bone remains of dead small and mediumsized animals. In the Pyrenees, the remains of Pyrenean Chamois, Red Deer, Fallow Deer, Roe Deer, and Sheep form 67% of the vulture’s food resources, and the remaining 33% includes the remains of small sized mammals (e.g., dogs, cats), large mammals (cows, horses), medium sized mammals (e.g., wild boars) and birds [15]. A pair of Bearded Vultures needs an average of 341 Kg of bones per year [17],[16]. During the dispersal period (from fledgling until the birds become territorial at 6 or 7 years), non-adult Bearded Vultures cover large distances surveying different areas. For example, the average surface covered by four young vultures monitored after fledging was 4932 km2(range 950-10294 km2, [23]). Breeding birds are territorial and the approximate home ranges obtained for eight pairs studied varied between 250 km2and 650 km2. The average annual growth in the population of the Bearded Vultures in the Pyrenees has been estimated at 4-5%. The floating population principally remains in feeding stations situated in the central Pyrenees (Aragon). The natural behavior of the five bovid species is similar because they are all herbivores and they all reach adult size at one year of age. In general, they reach sexual maturity within two years of birth. Pyrenean Chamois and the Red Deer have a longer life expectancy than Fallow Deer and Roe Deer (for a review of population parameters see [7], [8], [3], [9] and [20]). The natural mortality rates are similar in all five species in the first year of life it is calculated to be 50% and 6% during their remaining years. In spite of the great degree of similarity between these five species, important differences exist. For example, some are naturally occurring while others have been introduced by human populations0. It is essential to bear these differences in mind while defining a P system that can simulate the ecosystem in a reliable way. Red Deer are appreciated by hunters, not for their meat but as a trophy and so only the males are hunted. This causes the natural evolution of the population to be modified. The hunter only takes the head as a trophy leaving the animal’s body in the field. Hence the carcass is eaten by other species and the bone remains may then be eaten by the Bearded Vulture. Fallow Deer and Roe Deer live in areas that are difficult to reach and for this reason, the Bearded Vulture cannot take advantage of the remains of all of the dead animals of these species. As sheep [25] are domestic animals, humans exert a high level of control over their populations. The size and growth of the sheep population is limited by the owners of the flocks. The natural average life expectancy of sheep is longer than their actual life expectancy in the field because upon a decrease in fertility rate at the age of eight, they are removed from the habitat. Most of the lambs are sold to market and so they are removed from the habitat in the first year of life. Only 20% to 30% of the lambs, mostly females, are left in the field and these are used to replace sheep that have died naturally and those older sheep that have been removed from the flock. The number of animals in the Catalan Pyrenees during the years 1994 and 2008 is shown in Table 1 (see Appendix). In this study, the feeding of the Bearded Vulture is dependent on the evolution of the P system. However the P system does not consider the fact that the availability of food limits the feeding of the herbivores, and so the growth of vegetation is not modeled. Taking all of this background information into consideration, the following data was required for each species: –I1: Age at which adult size is reached. Age at which the animal consumes as much as an adult. At this age the animal will have surpassed the critical early phase during which mortality rate is high; –I2: Age at which it begins to be fertile; –I3: Age at which it stops being fertile; –I4: Average life expectancy; –I5: Fertility ratio (number of descendants by 100 fertile females); –I6: Mortality ratio in first years, age < I1(this quantity is expressed in terms of percentage); –I7: Mortality ratio in adult animals, age ≥I1(this quantity is expressed in terms of percentage); –I8: Ratio of females in the population (this quantity is expressed in terms of percentage). The required information about each species is shown in Table 2 (see the Appendix). When an animal dies, the weight of the bones that it leaves behind is around 20% of its total weight. Table 3 (see Appendix) shows the average weight of each animal as well as the weight of bones left behind. In the case of Fallow Deer and Roe Deer, the value of the weight of bones is then multiplied by 0,2 (20%) which is the portion of bones from which the Bearded Vulture may benefit. In the P system only Bearded Vultures older than 8 are considered, because younger ones are floating birds. There are seven feeding stations in Catalonia which provide around 10500 kg of bone remains annually. These artificial feeding sites have not been considered in the study and most of the floating birds feed at these sites. 3 A P System Based Model of the Ecosystem Membrane computing is a branch of Natural Computing that was initiated at the end of 1998 by Gh. P˘aun (by a paper circulated at that time on the web and published in 2000 [22]). Since then it has received important attention from the scientific community. Details can be found on the web page http://ppage.psystems.eu/ In short, one abstracts computing models from the structure and the functioning of living cells, as well as from the organization of cells in tissues, organs, and other higher order structures. The main components of such a model are a cell-like membrane structure,inthecompartments of which one places multisets of symbol-objects which evolve in a synchronous maximally parallel manner according to given evolution rules, also associated with the membranes. The semantic of the P systems is defined as follows: a configuration of a P system consists of a membrane structure and a family of multisets of objects associated with each region of the structure. At the beginning, there is a configuration called the initial configuration of the system. In each time unit we can transform a given configuration to another one by applying the evolution rules to the objects placed inside the regions of the configurations, in a non–deterministic, and maximally parallel manner (the rules are chosen in a non–deterministic way, and in each region all objects that can evolve must do so). In this way, we obtain transitions from one configuration of the system to the next. Acomputation of the system is a (finite or infinite) sequence of configurations such that each is obtained from the previous by a transition, and shows how the system is evolving. A computation that reaches a configuration in which no more rules can be applied to the existing objects is called a halting computation.The result of a halting computation is usually encoded by the multiset associated with a specific output membrane (or the environment) in the final configuration. In this section, we present a model of the ecosystem described in Section 2 by means of probabilistic P systems. We will study the behavior of this ecosystem under diverse initial conditions. First, we define the P systems based framework (probabilistic P systems), where additional features such as two electrical charges which describe specific properties in a better way, are used. Definition 1. A probabilistic P system of degree nis a tuple Π=(Γ,μ,w1,...,w n,R,{cr}r∈R), where: –Γis the alphabet (finite and nonempty) of objects (the working alphabet); –μis a membrane structure, consisting of nmembranes, labeled 1,2,...,n. The skin membrane is labeled by 1. We also associate electrical charges with membranes from the set {0,+}, neutral and positive; –w1,...,w nare strings over Γ, describing the multisets of objects initially placed in the nregions of μ; –Ris a finite set of evolution rules. An evolution rule associated with the membrane labeled by iis of the form r:u[v]i cr −→ u[v]i,whereu, v, u,v are a multiset over Γand crisarealnumberbetween0and1associated with the rule. We assume that a global clock exists, marking the time for the whole system (for all compartments of the system); that is, all membranes and the application of all rules are synchronized. The n-tuple of multisets of objects present at any moment in the nregions of the system constitutes the configuration of the system at that moment. The tuple (w1,...,w n) is the initial configuration of the system. The P system can pass from one configuration to another by using the rules from Ras follows: at each transition step, the rules to be applied are selected according to the probabilities assigned to them, and all applicable rules are simultaneously applied and all occurrences of the left–hand side of the rules are consumed, as usual. 3.1 The Model Our model consists of the following probabilistic P system of degree 2 with two electrical charges (neutral and positive): Π=(Γ,μ, w1,w 2,R,{cr}r∈R), where: –In the alphabet Γ, we represent the six species of the ecosystem (index iis associated with the species and index jis associated with their age, and the symbols X,Yand Zrepresent the same animal but in different states); it also contains the auxiliary symbol B, which represents 0.5kgofbones,and C, which allows a change in the polarization of the membrane labeled by 2 at a specific stage. Γ={Xij,Y ij,Z ij :1≤i≤7,0≤j≤ki,4}∪{B, C} –In the membrane structure, we consider two regions, μ=[[] 2]1(neutral polarization will be omitted): •the skin region where the objects that represent animals evolve according to the rules of reproduction and mortality. •an inner membrane where the objects associated with animals evolve according to the feeding rules. –In w1and w2, we specify the initial number of objects present in each region (encoding the initial population and the initial food); •w1={Xqij ij |1≤i≤7,0≤j≤ki,4}, where the multiplicity qij indicates the number of animals, of species iwhose age is jthat are initially present in the ecosystem; •w2={CB α},whereαis defined as follows: α= 21  j=1 q1j·1.10 ·682 Value αrepresents an external contribution of food which is added during the first year of study so that the Bearded Vulture survives. In the formula, q1jrepresents the number of jyears of age of Bearded Vultures, the finality of constant factor 1.10 is to guarantee enough food for 10% population growth. At present, the population growth is estimated an average 4%, but this value can reach higher values. Thus, to avoid problems related with the underestimation of this value the first year we estimated the population growth (overestimated) at 10%. The constant value 682 represents the amount of food needed per year for a Bearded Vulture pair to survive. –The set Rof evolution rules consists of: •Reproduction-rules. Adult males: ∗r0≡[Xij (1−ki,13)·(1−ki,15) −−−→ Yij]1,1≤i≤7,k i,2≤j≤ki,4. Adult females that reproduce: ∗r1≡[Xij ki,5·ki,13·(1−ki,15) −−−→ YijYi0]1,1≤i≤7,k i,2≤j<k i,3. Fertile adult females that do not reproduce: ∗r2≡[Xij (1−ki,5)·ki,13·(1−ki,15) −−−→ Yij]1,1≤i≤7,k i,2≤j<k i,3. Not fertile adult females: ∗r3≡[Xij ki,13·(1−ki,15) −−−→ Yij ]1,1≤i≤7,k i,3≤j≤ki,4. Young animals that do not reproduce: ∗r4≡[Xij 1−ki,15 −−−→ Yij ]1,1≤i≤7,0≤j<k i,2. •Growth rules. ∗r5≡[Xij (ki,6+ki,10)·ki,15 −−−→ Yiki,2Yij]1,1≤i≤7,k i,2≤j<k i,4. ∗r6≡[Xij (1−ki,6−ki,10)·ki,15 −−−→ Yij ]1,1≤i≤7,k i,2≤j<k i,4. ∗r7≡[Xij ki,6·ki,15 −−−→ Yiki,2Yij]1,1≤i≤7,j=ki,4. ∗r8≡[Xij (1−ki,6)·ki,15 −−−→ Yij ]1,1≤i≤7,j=ki,4. •Mortality rules. - Young animals Those which survive: ∗r9≡Yij[] 2 1−ki,7−ki,8 −−−→ [Zij]2,1≤i≤7,0≤j<k i,1. Those which die: ∗r10 ≡Yij[] 2 ki,8 −−−→[Bki,11 ]2,1≤i≤7,0≤j<k i,1. Those which are retired from the ecosystem: ∗r11 ≡[Yij ki,7 −−−→ λ]1,1≤i≤7,0≤j<k i,1. - Adult animals that don’t arrive at an average life expectancy . Those which survive: ∗r12 ≡Yij[] 2 1−ki,10 −−−→[Zij]2,1≤i≤7,k i,1≤j<k i,4. Those which die: ∗r13 ≡Yij[] 2 ki,10 −−−→[Bki,12 ]2,1≤i≤7,k i,1≤j<k i,4. - Animals that arrive at an average life expectancy: Those which growth population depend on the fertility ratio and die in the ecosystem: ∗r14 ≡Yij[] 2 (1−ki,15)·(ki,9+(1−ki,9)·ki,10) −−−→ [Bki,12 ]2,1≤i≤7,j=ki,4. Those which growth population depend on the fertility ratio and are retired of the ecosystem: ∗r15 ≡[Yij (1−ki,15)·(1−ki,9)·(1−ki,10) −−−→ λ]1,1≤i≤7,j=ki,4. Those which growth population not depend on the fertility ratio: ∗r16 ≡Yij[] 2 ki,15 −−−→[Ziki,2]2,1≤i≤7,j=ki,4. •Feeding rules. ∗r17 ≡[ZijBki,14 ]2→Xij+1[] + 2,1≤i≤7,0≤j≤ki,4. •Balance rules. The propose of this rules is to make a balance at the end of the year. It is to say the leftover food not served for the next year, so it is necessary eliminate, and if the amount of food not is enough some animals die. Elimination of remaining bones: ∗r18 ≡[B]+ 2→[] 2. Adult animals that die because they have not enough food: ∗r19 ≡[Zij]+ 2→[Bki,12 ]2,1≤i≤7,k i,1≤j≤ki,4 Young animals that die because they have not enough food: ∗r20 ≡[Zij]+ 2→[Bki,11 ]2,1≤i≤7,j<k i,1 If the food is equal to the necessary the object C allow to change the polarization. ∗r21 ≡[C]+ 2→[C]2. The constants associated with the rules have the following meaning: –ki,1: Age at which adult size is reached. This is the age at which the animal consumes food as an adult does, and at which, if the animal dies, the amount of biomass it leaves behind is similar to the total left by an adult. Moreover, at this age it will have surpassed the critical early phase during which the mortality rate is high. –ki,2: Age at which it begins to be fertile. –ki,3: Age at which it stops being fertile. –ki,4: Average life expectancy in the ecosystem. –ki,5: Fertility ratio (number of descendants by fertile females). –ki,6: Population growth (this quantity is expressed in terms of 1). –ki,7: Animals retired from the ecosystem in the first years, age < ki,1(this quantity is expressed in terms of 1). –ki,8: Natural mortality ratio in first years, age < ki,1(this quantity is expressed in terms of 1). –ki,9:0 if the live animals are retired at age ki,4, in other cases, the value is 1. –ki,10: Mortality ratio in adult animals, age ≥ki,1(this quantity is expressed in terms of 1). –ki,11: Amount of bones from young animals, age < ki,1. –ki,12: Amount of bones from adult animals, age ≥ki,1. –ki,13: Proportion of females in the population (this quantity is expressed in terms of 1). –ki,14: Amount of food necessary per year and breeding pair (1 unit is equal to0.5kgofbones). –ki,15: Equal to 0 when the species experience natural growth (animals that remain in the same territory throughout their lives) and is equal to 1 when animals are nomadic (the Bearded Vulture moves from one place to another until it is 6–7 years old, at which point it remains in one location). Values for each species are shown in Table 4 (see Appendix). Most values in that table are equal to those in Table 2 (see Appendix), but it is necessary to Mortality by lack of food Elimination of leftover food Feeding Natural / hunter mortality Reproduction- Growth 1 2 0 C B X ij 0 1 2 0 C B Y ij Y i0 0 1 2 0 C B Z ij 0 1 2 + C B Z 1j 0 Reproduction- Growth X ij Fig. 2. Structure of the P system running In order to obtain a model which allows us to study the evolution of an ecosystem in the long–term, it is necessary to take into account certain biological factors such as the following: –Maximum population density for each species. –Available feeding in the area in which the ungulates may feed. –Amount of food eaten daily by each of the ungulate species considering their age. Moreover, under adequate environmental conditions, the species exhibits a certain behavior such that some values of the biological parameters can be accepted. When essential environmental conditions such as temperature and rainfall are not ideal, biological constants change as a reaction to the environment. A model based on Markov chains in order to model temperature and rainfall can be accepted. P systems modeling Markov chains were previously presented in [5] and they should be considered in order to improve some results. In future work, we will also try to model interactions between neighboring ecosystems. Acknowledgements. M.J. P´erez–Jim´enez acknowledges the support of the project TIN2006-13425 of the Ministerio de Educaci´on y Ciencia of Spain, co– financed by FEDER funds, and of the Project of Excellence TIC 581 of the Junta de Andalucia. Financial support for A. Margalida was obtained from the Departament de Medi Ambient i Habitatge of Generalitat de Catalunya. References 1. 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Blackwell Scientific Publications, Oxford (1970) Appendix Table 1. Number of animals presents in the Catalan Pyrenees between 1994–1998 Species 1994 2008 Bearded Vulture pairs 20 37 Pyrenean Chamois 9000 12000 Red deer 1000 5500 Fallow deer 600 1500 Roe deer 1000 10000 Sheep 15000 200000 Table 2. Natural constants used in the model Species I1I2I3I4I5I6I7I8 Bearded Vulture 1 8 20 21 38 612 50 Pyrenean Chamois 1 2 18 18 75 60 655 Red Deer 1 2 17 17-20 75 34 650 Fallow Deer 1 2 12 12 55 50 675 Roe Deer 1 1 10 10 100 58 667 Sheep 1 2 8 8 75 15 396 Table 3. Descriptive variables used to model the ecosystem Species Weigh Weigh Percentage Average Biomass: Biomass: Kg accessible Male Female Female weigh bone bone by B. Vulture adult young kg kg kg kg kg (adult/young) Bearded Vulture 56.5 50 5.75 - - - Pyrenean Chamois 28 32 50 30 6 3 6/3 Red Deer Female -75 -75 15 7.5 15/7.5 Red Deer Male 120 - - 120 24 12 24/12 Fallow Deer 63 42 80 46 94.5 2/1 Roe Deer 27 23 66 24 52.5 1/0.5 Sheep 42 35 97 35.2 73.5 7/3.5 Table 4. Constants used in the P system based model Species i ki,1ki,2ki,3ki,4ki,5ki,6ki,7ki,8ki,9ki,10 ki,11 ki,12 ki,13 ki,14 ki,15 Bearded Vulture 1 1 8 20 21 0.38 0.04 00.06 10.12 0 0 0.50 460 1 Pyrenean Chamois 2 1 2 18 18 0.75 - 0 0.60 10.06 612 0.55 - 0 Red Deer Female 3 1 2 17 17 0.75 - 0 0.34 10.06 15 30 1.00 - 0 Red Deer Male 4 1 2 - 20 - - 0 0.34 10.36 24 48 0 - 0 Fallow Deer 5 1 2 12 12 0.55 - 0 0.50 10.06 2 4 0.75 - 0 Roe Deer 6 1 1 10 10 1.00 - 0 0.58 10.06 1 2 0.67 - 0 Sheep 7 1 2 8 8 0.75 -0.57 0.15 00.03 714 0.96 - 0 Table 5. Estimation of number of animals per age in 1994 Age Bearded V. Chamois Red d. female Red d. male Fallow deer Roe deer Sheep 1 0 741 167 58 83 121 20832 2 0 740 133 44 73 121 20208 3 0 668 107 35 69 121 19601 4 0 667 85 28 63 121 19014 5 0 667 68 23 59 109 18443 6 0 596 41 14 55 108 17890 7 0 594 33 11 51 108 17353 8 2 518 26 947 96 16659 9 2 517 21 735 96 0 10 2444 17 533 0 0 11 2444 13 530 0 0 12 2444 11 4 0 0 0 13 2373 9 3 0 0 0 14 1373 7 2 0 0 0 15 1372 5 2 0 0 0 16 1296 4 1 0 0 0 17 1296 3 1 0 0 0 18 1252 0 0 0 0 0 19 1 0 0 0 0 0 0 20 1 0 0 0 0 0 0 21 1 0 0 0 0 0 0 Table 6. Estimation of number of animals per age in 2008 Age Bearded V. Chamois Red d. female Red d. male Fallow deer Roe deer Sheep 1 0 988 978 254 125 1210 27776 2 0 987 780 192 110 1207 26944 3 0 890 625 154 103 1207 26135 4 0 889 500 124 95 1207 25352 5 0 889 400 99 89 1085 24591 6 0 795 240 60 83 1083 23854 7 0 792 195 48 77 1083 23137 8 6 690 155 38 71 959 22212 9 6 689 123 30 52 959 0 10 6592 97 24 50 0 0 11 6592 78 20 45 0 0 12 5592 62 16 0 0 0 13 5497 50 12 0 0 0 14 5497 40 10 0 0 0 15 5496 32 8 0 0 0 16 5395 25 6 0 0 0 17 5394 20 5 0 0 0 18 5336 0 0 0 0 0 19 5 0 0 0 0 0 0 20 5 0 0 0 0 0 0 21 5 0 0 0 0 0 0 Table 7. Number of animals produced by the simulator Year Bearded Pyrenean Pyrenean Red Fallow Roe Sheep Vulture Chamois Chamois Deer Deer Deer 1994 20 9000 1000 600 1000 150000 1995 21 9541 1115 667 1213 152074 1996 21 10023 1263 710 1371 153951 1997 22 10590 1432 758 1568 156183 1998 23 11121 1617 808 1812 158571 1999 24 11718 1834 859 2106 161318 2000 25 12366 2087 908 2469 164391 2001 27 13032 2368 967 2906 167914 2002 28 13767 2705 1032 3459 171940 2003 29 14597 3067 1111 4132 174713 2004 31 15488 10000 3470 1202 4969 177973 2005 33 16468 10594 3917 1297 5883 181300 2006 35 17508 11133 4437 1399 6974 184790 2007 36 18647 11709 5004 1495 8272 188357 2008 38 19866 12297 5631 1602 9774 192097