Linking Wild and Captive Populations to Maximize Species Persistence: Optimal Translocation Strategies BRIGITTE TENHUMBERG, * § ANDREW J. TYRE,* KATRIONA SHEA,t AND HUGH E POSSINGHAMt *The University of Queensland, St. Lucia, QLD 4072, Australia tDepartment of Biology, 208 Mueller Laboratory, Pennsylvania State University, University Park, PA 16802, U.S.A. $The Ecology Centre, Department of Mathematics, and School of Life Sciences, The University of Queensland, St. Lucia, QLD 4072, Australia Abstract: Captive breeding of animals is widely used to manage endangered species, frequently with the ambition of future reintroduction into the wild. Because this conservation measure is very expensive, we need to optimize decisions, such as when to capture wild animals or release captive-bred individuals into the wild. It is unlikely that one particular strategy will always work best; instead, we expect the best decision to depend on the number of individuals in the wild and in captivity. We constructed a first-order Markov-chain population modelfor two populations, one captive and one wild, and we used stochastic dynamic programming to identify optimal state-dependent strategies. The model recommends unique sequences of optimal management actions over several years. A robust rule of thumb for species that can increase faster in captivity than in the wild is to capture the entire wild population whenever the wild population is below a threshold size of 20 females. This rule applies even if the wild population is growing and under a broad range of different parameter values. Once a captive population is established, it should be maintained as a safety net and animals should be released only if the captive population is close to its carrying capacity. We illustrate the utility of this model by applying it to the Arabian oryx (Oryx leucoryx^). The threshold for capturing the entire Arabian oryx population in the wild is 36females, and captive-bred individuals should not be released before the captive facilities are at least 85% full. Key Words: captive breeding, endangered species, optimal management strategies, stochastic dynamic programing, translocation Combinacion de Poblaciones Silvestres y Cautivas para Maximizar la Persistencia de Especies: Estrategias de Translo-cacion Optima Resumen: La reproduction de animates en cautiverio es utilizada ampliamente para manejar especies en peligro, frecuentemente con la ambition de reintroducirlos al medio natural. Debido a que esta medida de conservation es muy costosa necesitamos optimizar decisiones, tales como cuando capturar animates silvestres o liberar individuos criados en cautiverio. Es poco probable que una estrategia particular siempre funcione mejor; mas bien, esperamos que la mejor decision dependa del numero de individuos silvestres y en cautiverio. Construimos un modelo poblacional de cadena de Markov de primer orden para dos poblaciones, una en cautiverio y otra silvestre, y usamos programacion dindmica estocdstica para identificar estrategias estado-dependientes optimas. El modelo recomienda secuencias unicas de acciones de manejo Optimo durante varios anos. Una regla bdsica robusta para especies quepueden incrementar mas rdpidamente en cautiverio que en su medio natural es la captura de toda la poblacion silvestre, cuando esta se encuentre debajo del umbral de 20 hembras. Esta regla aplica aun si la poblacion silvestre esta creciendoy bajo una amplia gama de valores de diferentes pardmetros. Una vez que se establece una poblacion en cautiverio, debe ser mantenida ^Current address: School of Natural Resource Sciences, 302 Biochemistry Hall, University of Nebraska-Lincoln, Lincoln, NE 68583-0759, U.S.A., email btenhumberg2@unl.edu Paper submitted June 3, 2003; revised manuscript accepted January 22, 2004. 1304 Conservation Biology, Pages 1304-1314 Volume 18, No. 5, October 2004 Tenhumberg etal. Optimal Translocation Strategies 1305 como una red de seguridady los animales deben ser liberados solo si la población en cautiverio se aproxima a su capacidad de carga. Ilustramos la utilidad de este modelo aplicándolo al Oryx leucoryx. El umbralpara la captura de toda la población Silvestře de oryx es 36 hembras, y los individuos criados en cautiverio no deberán ser liberados antes de que las instalaciones de cautiverio estén llenaspor lo menos al 85%. Palabras Clave: especies en peligro, estrategias de manejo óptimo, programación dinámica estocástica, repro-ducción en cautiverio, translocación Introduction Extinction rates of populations or entire species have reached catastrophic levels (MacPhee 1999)- Conservation biologists aim to prevent species extinction in the wild where possible, usually by removing or mitigating probable threats such as habitat loss or fragmentation, invasive species, or poaching (Vitousek et al. 1996). In certain cases, however, in situ conservation efforts may be insufficient, and more extreme intervention is required to enhance the probability of species persistence. As a last resort, captive breeding may be advocated (Beck et al. 1994; Snyder et al. 1996), though it is very expensive (Balmford et al. 1996; Kleiman et al. 2000). Translocation is an inherent part of any captive breeding program. A translocation is the deliberate human-mediated movement of organisms between populations. Such translocations include movement between wild populations, movement from wild to captive populations (capture or collection), and movement from captive to wild populations (reintroduction or release). Captive breeding involves translocating individuals, either to remove them from the threats they face in the wild, or, if captive breeding is successful, to attempt their reintroduction (Ebenhard 1995). One of the key factors determining the success of reintroduction programs is the number of individuals released (Griffith et al. 1989; Veltman et al. 1996; Wolf et al. 1998). As a consequence, the guidelines of the World Conservation Union (IUCN) for translocations in general (IUCN 1987) and for reintroductions in particular (IUCN 1998) specifically call for the use of models "to specify the optimal number... of individuals to be released... to promote establishment of a viable population." Several surveys of success rates for reintroduction programs (largely for mammals and birds) have been carried out (Griffith et al. 1989; Wolf et al. 1996; Wolf et al. 1998; Fischer & Lindenmayer 2000). All indicate that success rates are poor (< 50%; Griffith et al. 1989; Beck et al. 1994) and search for factors that correlate with (and potentially cause) reintroduction success. These surveys suggest that major factors influencing success include the number of individuals released and the number of release attempts (Griffith et al. 1989; Veltman et al. 1996; Wolf et al. 1998). In situations where decision makers are faced with choices under uncertainty, methods of decision analysis can be a useful tool in evaluating different courses of action (Raiffa 1968). Models of reintroductions and captive breeding programs have been developed with a variety of methods and for a variety of systems (e.g., Hearne & Swart 1991; Akcakaya et al. 1995; Southgate & Possing-ham 1995; Sarrazin & Legendre 2000), but few use decision theory or can lay claim to being true optimization models (Lubow 1996). Exceptions include Lubow (1996), who examined translocations between two wild populations with similar demography; Haight et al. (2000), who focused on translocation strategies for scenarios when there are uncertainties in future biological and economic parameters; Maguire (1986), who used a decision tree to determine whether proponents and opponents of captive breeding recommended management consistent with their beliefs about the status of the population; and Kostreva et al. (1999), who developed one-period planning models for optimization of genetic variation (based on founder contributions) of relocated animals. Here we used an optimization algorithm, stochastic dynamic programing (SDP), to identify translocation strategies between wild and captive populations (e.g., in zoos, captive breeding programs, protected areas) that maximize overall species persistence. We were particularly interested in generating broadly applicable rules of thumb to guide conservation biologists in minimizing the probability of extinction of an endangered species. We first developed a stochastic population dynamic model for translocations between wild and captive populations that relies on demographic parameters and predicts the numbers of individuals in both populations. We then applied the model and algorithm to a case study of the Arabian oryx (Oryx leucoryx). Models Stochastic Population Model In our model we considered a captive population, Z, and a wild population, W. Each population was limited to a maximum size Kz or Kw. These limits were required for the numerical solution of the problem (see below). The Kz had a natural interpretation as a consequence of space restrictions in the captive facilities. It was tempting to associate Kw with "carrying capacity" of the wild population Conservation Biology Volume 18, No. 5, October 2004 1306 Optimal Translocation Strategies Tenhumbergetal. arising from limited resources or habitat through ceiling-type density dependence. A better interpretation, however, was that Kw — 1 is the largest population size explicitly considered. All larger population sizes were lumped into a single state, Kw. We discuss the accuracy of this approximation below. We assumed that females always have the opportunity to mate regardless of male abundance, so we only tracked the number of females. We also ignored age structure, so the dynamics of the populations can be modeled as a first-order Markov chain. Let the number of females in a population at any given time be the state of the population; the transition matrix describes the probability that the population moves from one state to another in a single year. The Markov-chain transition matrix describing the transition rates from population density time (f) from t to t+1 was A = LS, which is the matrix product of the recruitment matrix L and the survival matrix S. This means that only surviving individuals have the opportunity to reproduce. Each element of S, s,>j, is the probability of having i surviving individuals at t + 1, given j individuals at time t, with 0 otherwise, Ď, i — 0. (2) The probability that j females have i newborns can be obtained recursively as follows: hj = \Y^bkJ-\bi-k,\ for i < , k=o At high population densities, reproduction is truncated by K such that £ ( female newborns + adult females) < K. This is the only place where density dependence enters the basic population model. Given bij, one can calculate the elements of the recruitment matrix L, lm,„, as the probability that the population density changes from n to m due to reproduction as bm-n,n if H < Ťtl < K K-l 1 - bi-n^n if m— K (4) i=n 0 if m < n or m > K. Based on the Markov-chain transition matrices, we calculated an approximation of the per capita growth rate as the expected number of female replacements resulting from one female: 12iAi nt+i nt (5) This expected growth rate is a good approximation for n up to 90% of K. Above this point the actual expectation is slightly reduced because the population cannot grow above K. Stochastic Dynamic Programing (SDP) Algorithm The algorithm optimized management decisions involving captive breeding programs. We addressed the following general questions: (1) At what population size should a wildlife manager start breeding an endangered species in captivity? (2) How many individuals should we take out of the wild? (3) How many individuals should we release into the wild? The SDP model has three states: the number of individuals in captivity (;/: — 0,..., Kz}, the number of individuals in the wild (nw — 0,..., Kw}, and the time over which the management plan will be optimized (t — 0,..., T). The change in population size over time in both populations follows from Markov-chain population matrices for the wild population Aw and the zoo population Az. We assumed that the per capita growth rate of the captive population equals or exceeds that of the wild population. At each time step a wildlife manager can either do nothing or transfer n individuals from the wild into captivity (captures) or vice versa (releases). The maximum number of captures or releases depends on the current population sizes in captivity and in the wild. If we define releases as negative captures, the SDP model evaluates the consequences of all possible captures (decision variable d — ii....., 0,..., nw}. We set an objective function V that gives a reward to the manager at the end of the time horizon (t — T) that minimizes the probability that the wild population is extinct e years after the captive breeding programs ceases: otherwise, b, 0, where d is the number of captured or translocated individuals (releases being considered negative captures), and do nothing =££f(í+1,í, J^l^Kv t=0 j=0 h Kw 0 release = + ^ ^ ^ V(t + 1, i, j - k) t=0 j=0 k=d X ^nA-ifll^ and h Kw d capture = + X! X! X! V(t+l,i +k,j) t=0 j=0 k=0 w-h cap z aj,nw-dak,dai,nz- Superscripts indicate the transition matrix (e.g., d) H is the probability that nz females of the captive population in year t become i females in year t + 1). For some parameter combinations the optimization surface was very flat, resulting in virtually the same survival probabilities for a range of management strategies. If the benefit of transferring some individuals from captivity to the wild or vice versa is insignificant, it makes more sense to do nothing. Therefore, we introduced a small penalty, 0 (stop capturing) (boundaries between the gray and white areas in Fig. 1). If the population was growing faster in captivity than in the wild, the model suggested aiming for a large captive population, even if the wild population was growing. The particulars of the optimal strategy differed depending on the growth rates of the populations in the wild and in captivity. Changing the capturing mortality (cccapt), fixed mortality ((Xflxeci), or release mortality (ccrei) did not influence the optimal management strategy significantly (results not shown). These population boundaries are rather small, but running the model with larger values of Kw and Kz was not feasible because the size of the population in the wild and in captivity determined the state space, and in SDP models the running time increases exponentially with the state space. For example, running the model with slightly larger maximum populations of Kw = 150 and Kz — 30 took >9 days on a 700 MHz PHI. We carried out a small number of scenarios with larger state spaces. A larger value of Kz shifted the entire release state space to larger captive population sizes; the state space for capturing remained the same. If a population is threatened with extinction, the captive facilities should be filled as quickly as possible and maintained; thus, the larger the captive facilities the larger the number of animals captured. Increasing Kw changed neither the capturing nor the release state space. The results were independent of Kw because the transition probabilities are independent of Kw, given nw < Kw. However, the small value of Kw limited the applicability of this implementation of the model to the management of populations that had already declined to very low levels (nw < 50) because the calculated strategy did not cover wild populations larger than this. Influence of the Per Capita Growth Rate in Captivity, Rz As a baseline case, we assumed that the wild population was decreasing annually by 15% and that the captive population was increasing annually by 30% (Fig. 1). In general, the lower the population numbers in the wild and in captivity, the higher the proportion of wild animals captured. For example, if the wild population was <36 females and there was no captive population, our model suggested transferring the entire wild population into captivity. In some cases, the average number of captured animals exceeded the carrying capacity of the captive population. Although this may seem counterintuitive, it is better to guarantee filling up the captive facilities despite the high risk of losing some animals through lack of space in the captive facilities because the wild population is rapidly approaching extinction. With increasing growth rate in captivity, the region of the state space where capturing was optimal decreased (Fig. 2). Because the captive population serves as a safety net, it is best to maintain a large captive population. This is achieved more quickly with high breeding success in captivity; so the initiation of capturing should be delayed until lower abundances of the captive population are reached. The optimal release strategy was relatively independent of population numbers in the wild. Animals were only released if the captive population was close to its maximum size, and only relatively small numbers were Conservation Biology Volume 18, No. 5, October 2004 Tenhumberg etal. Optimal Translocation Strategies 1309 50 -i 40 - 30 - I 20- 10 - 5 10 15 Captive population 20 Figure 2. Influence of changing breeding success in captivity on the optimal captive breeding strategies, given thatrw — 0.85. Lines indicate the boundaries between d > 0 (capturing), d — 0 (do nothing), and d < 0 (releasing) (boundaries between the gray and white areas in Fig. 1). Dotted lines specify the "capturing" state space boundary and solid lines the "releasing" state space. Letters next to each line indicate the value for the per capita growth rate in captivity: a, rz — 1.3; b, rz — 1.2; c, rz — 1.1; d, rz — 1.0. Ifrz — 1.0, the model suggested that animals should never be released from captivity; consequently, there is no d in the "releasing" state space. released (between two and six females) (Fig. 1). With increasing growth rate in captivity, the state space that suggested releasing females increased (Fig. 2). If the population in captivity only replaced itself (rz — 1.0), no animals were released. The captive population was an important safety net as long as the population growth rate in captivity was higher than that in the wild, and only surplus females were released into the wild. If rz — 1.0, a surplus in captivity was unlikely. Hence, no animals were released. As long as the growth rate, rz, was the same, the exact combination of the recruitment rate, Xz, and the mortality rate, \iz, had little influence on the results. The relative values of recruitment and mortality were more important than the absolute values. The exception was in scenarios with rz — 1.2, where the "capturing" state space was larger for \iz — 0.2 (i.e., shifted toward the right) compared with \iz — 0.04. This was because the increase in mortality between the two scenarios needed to maintain a growth rate of 1.2 was much larger than for any of the other scenarios. 50 40 5 10 15 Captive population Figure 3. Optimal number of translocated animals as a function of population numbers in the wild and in captivity. The gray-scale intensity is proportional to the number of translocated animals: white, 0; dark gray, 50. Key: C, captures; R, releases; stripes, entire wild population should be captured (d — nw) (captive population: Xz — 1.0, [iz — 0.1, rz = 1.3; wild population: Xw — 0.8, ^w = 0.2, rw = 1.1). Arrow indicates the only combination of states where releases take place. Influence of the Per Capita Growth Rate in the Wild, Rm Next we assumed that the wild population was growing annually by 10% and, as before, that the captive population was increasing annually by 30% (Fig. 3). If the wild population was <29 females and the captive population was rather small, our model recommended capturing the entire wild population. In contrast to the scenario with a negative growth rate in the wild (Fig. 1), the state space where animals were captured was smaller, mainly because the wild population was left alone if the population exceeded 30 females. If the wild population was rather small, the risk of extinction was significant, even if the population was growing. Consequently, it was advantageous to maintain a viable captive population. With decreasing growth rates in the wild, the state space that suggested capturing >1 animal increased (Fig. 4). There was a trade-off between the risk of individuals dying in the wild and the risk of individuals dying in captivity as a result of the limited maximum size. The worse off the population was in the wild the more the balance shifted in favor of the captive population, resulting in an increasing "capturing" state space with decreasing per capita growth rate in the wild. Conservation Biology Volume 18, No. 5, October 2004 1310 Optimal Translocation Strategies Tenhumbergetal. ■ ■ ■ * ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ - •■ # ■ ■ J ; ■ mm ": M i b ...... e; ■ d. .. t ■ ■ ■ . . . I A -•: ■ ; i ■ c ..... ■ ■ ■ ■ ■ ■ ■ ■ .. t ■ ■ ■ ■ *. . . . ■ "■ .. r ■ ■ 1 1 ■ ■ 0 5 10 15 20 Captive population Figure 4. Influence of changing the per capita growth rate of the wild population on optimal captive breeding strategies, given rz = 1.3. Lines indicate the boundaries between d > 0 (capturing), d — 0 (do nothing), and d < 0 (releasing) (boundaries between the gray and white areas in Fig. 3). Dotted lines specify the "capturing" state space boundary and solid lines the "releasing" state space. Letters next to each line indicate the value for the per capita growth rate in the wild: a, rw = 1.1; b, rw = 0.9; c, rz = 0.85; d, rw a ,SV e, rw = 0.7. Small and capital letters indicate different recruitment rates in the wild: A and C, Xw — 0.8; b, d, and e, Xw — 0.5. The release strategy depended on whether the wild per capita growth rate, rw, was >1 or <1. If the population was decreasing in numbers (rw < 1), the "release" state space decreased with decreasing wild population growth rate, rw, until no animals were released at rw < 0.85. At this point the mortality risk in the wild was similar to the mortality risk of the captive population approaching its carrying capacity, and it was better not to release individuals. If the wild population was growing (rw > 1), animals were only released if the captive population had reached its carrying capacity and the wild population was extinct. Not to release excess animals from the zoo was a bit surprising, but if the wild per capita growth rate is > 1, increasing the number of wild animals does not increase their long-term survival probability because the population will most likely recover from small population sizes on its own, and if the population happens to go extinct, the captive population provides females to recolonize the wild population. Case Study: Arabian Oryx Arabian oryx populations once ranged throughout most of the desert plains of the Arabian Peninsula but became threatened by overhunting and poaching (Marshall & Spalton 2000). Several captive breeding programs were initiated with the intent of reestablishing oryx into native habitats (Stanley Price 1989; Ostrowski et al. 1998; Spalton et al. 1999). Reintroductions started in 1982, and the wild population increased to 400 animals in 1996. Unfortunately poaching began again and is threatening Arabian oryx with extinction in the wild a second time (Spalton et al. 1999). Oryx populations flourished so well in sanctuaries that Treydte et al. (2001) developed a population viability analysis (PVA) model to determine the optimal number of oryx to eliminate from a sanctuary to minimize the effect of overcrowding. We parameterized our model with data on Arabian oryx (Oryx leucoryx) from the literature. Here, we summarize the range of vital rates published for this species. Recruitment: Under optimal conditions females give birth to a single calf each year, which has a 75% (Mace 1988) to 92.5% (Vie 1996) chance of surviving the first year. Therefore the annual recruitment rate, X, is 0.75-0.925, and the sex ratio/ = 0.5 (Mace 1988; Vie 1996; Spalton et al. 1999). Mortality: Annual mortality of adult Arabian oryx in captivity ranges between 4% and 15% (Abu Jafar & Hays-Shahin 1988; Mace 1988). We assumed that the wild mortality rate increases up to 40% due to poaching (Spalton et al. 1999). Translocation costs: The losses due to capturing and transferring Arabian oryx into captivity and vice versa are small, with mortality ranging between 0 and 5% (S. Ostrowski, personal communication). As far as we know, fixed costs have not been documented for Arabian oryx. For the sake of parsimony, we assumed that the fixed costs are the same as the variable translocation costs (0.05). For the captive population, we assumed a best-case scenario with a per capita growth rate of 1.3 (Xz — 0.5; \iz — 0.13), and for the wild population we assumed a per capita growth rate of 0.85 (Xw — 0.4; \iw — 0.4). These per capita growth rates are consistent with population growth rates found in Arabian oryx sanctuaries (Abu Jafar & Hays-Shahin 1988; Ostrowski et al. 1998; Spalton et al. 1999; Marshall & Spalton 2000). These parameter combinations are identical to the ones used to calculate the optimal breeding strategies in our first scenario (Fig. 1). If the population of Arabian oryx in the wild drops below 36 females, the entire population should be transferred into captivity, and captive-bred individuals should not be released unless the captive facilities are at least 85% full. Discussion Reintroduction programs have been proposed or carried out for a wide taxonomie range of species. Although many taxonomie groups are suitable for translocations, the majority have been birds and large mammals (Griffith et al. Conservation Biology Volume 18, No. 5, October 2004 Tenhumberg etal. Optimal Translocation Strategies 1311 Table 1. Parameter combination for different scenarios in the model for translocations between wild and captive populations.* K M w ^capt 0Lrei T r2 Varying rz by keeping Xz 1.0 0.13 0.8 0.4 0.05 0.05 0.05 — — 1.3* 0.85 constant and changing \iz accordingly 1.0 0.20 0.8 0.4 0.05 0.05 0.05 — — 1.2 0.85 1.0 0.27 0.8 0.4 0.05 0.05 0.05 — — 1.1 0.85 1.0 0.33 0.8 0.4 0.05 0.05 0.05 — — 1.0 0.85 0.5 0.04 0.8 0.4 0.05 0.05 0.05 — — 1.2 0.85 0.5 0.12 0.8 0.4 0.05 0.05 0.05 — — 1.1 0.85 0.5 0.20 0.8 0.4 0.05 0.05 0.05 — — 1.0 0.85 Varying rw by keeping Xw 1.0 0.13 0.5 0.25 0.05 0.05 0.05 — — 1.3 0.9 constant and changing \iw accordingly 1.0 0.13 0.5 0.36 0.05 0.05 0.05 — — 1.3 0.8 1.0 0.13 0.5 0.44 0.05 0.05 0.05 — — 1.3 0.7 1.0 0.13 0.2 0.18 0.05 0.05 0.05 — — 1.3 0.9 1.0 0.13 0.2 0.27 0.05 0.05 0.05 — — 1.3 0.8 1.0 0.13 0.2 0.36 0.05 0.05 0.05 — — 1.3 0.7 Varying acapt 1.0 0.13 0.8 0.4 0.0 0.05 0.05 — — 1.3 0.85 1.0 0.13 0.8 0.4 0.05 0.05 0.05 — — 1.3 0.85 1.0 0.13 0.8 0.4 0.1 0.05 0.05 — — 1.3 0.85 Varying