Optimal release strategies for cost-effective reintroductions

Authors


Summary

  1. Ex situ programmes for endangered species commonly focus on two main objectives: insurance against immediate risk of extinction and reintroduction. Releases influence the size of captive and wild populations and may present managers with a trade-off between the two objectives. This can be further complicated when considering the costs of the captive population and the possible release of different life stages.

  2. We approached this decision problem by combining population models and decision-analytic methods, using the reintroduction programme for the southern corroboree frog Pseudophryne corroboree in Australia as an example. We identified the optimal release rates of eggs and subadults which maximized the size of the captive and reintroduced populations while meeting constraints. We explored two scenarios: a long-term programme for a stable age-distributed captive population and a short-term programme with non-stable age distribution and limited budget. We accounted for uncertainty in the estimated vital rates and demographic stochasticity.

  3. Assuming a stable age distribution, large proportions of individuals could be released without decreasing the captive population below its initial size. The optimal strategy was sensitive to the post-release survival of both life stages, but subadult releases were generally most cost-effective, producing a large wild population and requiring a cheaper captive population. Egg releases were optimal for high expected juvenile survival, whereas mixed releases of both life stages were never optimal.

  4. In the short-term realistic scenario, subadult releases also produced the largest wild population, but they required a large increase in the size and cost of the captive population that exceeded the available budget. Egg releases were cheaper but yielded smaller numbers in the wild, whereas joint releases of both life stages provided more wild individuals, meeting budget constraints without depleting the captive population.

  5. Synthesis and applications. Optimal release strategies for endangered species reflect the trade-offs between insurance and reintroduction objectives and depend on the vital rates of the released individuals. Although focusing on a single life stage may have practical advantages, mixed strategies can maximize cost-effectiveness by combining the relative advantages of releasing early and late life stages.

Introduction

Reintroductions from captive breeding programmes for endangered species have been criticized for their low success rates and high resource requirements (Snyder et al. 1996). However, they may be effective when species cannot be recovered by in situ conservation alone (Balmford, Mace & Leader-Williams 1996; Bowkett 2009). Captive programmes can have multiple objectives, including education and research (Converse et al. 2013): however, the main focus is usually the long-term viability of the target species (IUCN 2013). This is usually achieved by establishing captive insurance populations to minimize the short-term extinction risk and by reintroducing individuals into the wild to re-establish self-sustaining populations (Armstrong & Seddon 2008). In the short term, large captive populations can provide greater insurance value; in the long term, they will allow larger releases, which can improve the chances of a successful reintroduction (Griffith et al. 1989; Wolf et al. 1996; Fischer & Lindenmayer 2000).

However, releases deplete the captive population and can reduce its viability, generating a trade-off between the ‘insurance’ and ‘reintroduction’ objectives. Both aspects need to be considered, even though their relative importance can vary among programmes. Indeed, for several species, the decision to retain individuals in captivity after releases had started has ensured that eventual reintroduction failure did not result in their overall extinctions (Odum & Corn 2003; Winnard & Coulson 2008). Even for captive populations with no immediate prospect of reintroduction, releases can help in evaluating management actions and understanding threats (Rodriguez, Barrios & Delibes 1995; Letty et al. 2000). Here, larger releases can provide more information, but at the cost of reducing the viability of the captive population and negatively affecting eventual reintroductions. The biological aspects of the trade-off between reintroduction and insurance have previously been recognized (McCarthy 1994). However, the implications for cost-effectiveness have not been considered: larger captive populations can provide better insurance value, but can be more expensive to maintain. Given limited conservation resources, this aspect of the trade-off must be explicitly addressed.

The cost of the captive population can also vary depending on the length of time that individuals spend in captivity, which in turn may affect reintroduction success. Releasing early life stages may be cheaper because of reduced husbandry requirements per individual: however, younger animals generally have lower survival. Therefore, the survival and fecundity of the respective life stages will influence the trade-offs associated with the choice of actions (which life stage to release) and the importance of fundamental objectives (insurance and reintroduction). Longer periods in captivity may also imply a lack of exposure to natural selection, which can reduce survival following release, as observed for several taxa (hereon, we refer to such reductions simply as ‘post-release effects’; see for example Jule, Leaver & Lea 2008). Later life stages may incur greater post-release effects in species in which selection affects mainly early stages, such as amphibians (Wells 2007). Again, previous analyses of this trade-off have not included cost as an important decision-making criterion (Burgman, Ferson & Lindenmayer 1994; Sarrazin & Legendre 2000).

In this study, we use population models to assess the cost-effectiveness of alternative release strategies for species with complex life histories. For an ongoing programme for a critically endangered amphibian, we identified the optimal release rates for eggs or subadults, in regard to both insurance and reintroduction objectives and management costs. Under a long-term programme, assuming a captive population with a stable age distribution, large releases of subadults were the optimal choice. Conversely, for a short-term release plan, mixed releases of variable proportions of both eggs and subadults provided larger and cheaper wild and captive populations.

Materials and methods

Matrix population model

In a stage-structured population model, the vector N(t+1) of stage-specific abundance at time + 1 is the product of the abundance in the previous time step (N(t)) and the transition matrix L:

display math(1)

where fj is the reproductive output of individuals in age class j, and sij is the probability of transitioning (survival) from stage i to stage j (Caswell 1989). For a matrix Lc associated with a captive population, the transition rates apply to individuals that have not been released. Therefore, release rates can be interpreted as another matrix R of the same dimensions, whose elements are multiplied by the respective elements of Lc (Hadamard product):

display math(2)

where ri(t) is the proportion of individuals in age class i that are retained (not released) in the captive population in year t. Note that here we assume releases are carried out after reproduction: therefore, in captivity multipliers for fecundities are equal to 1, and the release rate of the first captive life stage changes the probability of transitioning to the second stage. The left eigenvector of L provides the stable age distribution, the proportion of individuals within each age class in the population when this is growing at the rate λ (the dominant eigenvalue of L: Caswell 1989).

The ‘insurance’ objective ultimately describes the viability of the captive population. Translating this to a target number of individuals can facilitate interpretation and measurement of this objective for management purposes. The exact target may depend, for example, on the population size required to retain genetic diversity (Lande & Barrowclough 1987). In a stable age-distributed population, the insurance objective can be expressed in terms of the growth rate for the captive population. For example, the objective of maintaining at least the initial population size can be stated as λ ≥ 1.

Similarly, the ‘reintroduction’ objective might reflect the size of the recipient population. Here, the vector W of age-structured abundances at time + 1 can also be represented as the product of the abundance at time t and the vital rates of that population (Lw), augmented at any given time by releases from the captive population:

display math(3)

where (1–R)(t) is the matrix of release rates (the proportion of individuals that are not retained in the captive population at year t) and Lr is the matrix that describes the vital rates of individuals post-release. These can correspond to the rates of the wild population if no post-release effects are assumed (Lr = Lw), or can be represented as another matrix of estimated vital rates that describe any post-release effects such as increased mortalities or decreased fecundities. The optimal release strategy corresponds to the values of R that maximize success for the chosen objectives.

Given a sufficiently long time frame (damping ratio of L: Caswell 1989) with constant vital rates, all populations will reach an asymptotic stable age distribution. However, in actual reintroduction programmes, initial numbers may deviate from the stable age distribution, which may not be achieved within short time frames. In this case, the discrete growth rate might be an unsuitable measure of success; however, the matrix framework (Eqs (1)-(3)) can still be used to identify the optimal release rates after adapting the objectives.

Study species

We applied our approach to the ongoing release programme for the southern corroboree frog Pseudophryne corroboree Moore (Anura: Myobatrachidae). This species, endemic to south-eastern Australia, has declined since the late 1980s (Osborne 1989) and is listed as critically endangered on the IUCN Red List (IUCN 2011). A captive breeding programme was advocated since the development of the initial recovery plan (Hunter et al. 1999; NSW National Parks & Wildlife Service 2001), particularly after the discovery of the fungal disease chytridiomycosis in wild populations (Hunter et al. 2010). P. corroboree is now being bred in captivity at several Australian institutions (McFadden et al. 2013). The project currently aims to maintain a presence of individuals in the wild to improve knowledge of the dynamics of disease spread and induced mortality, and to allow the possible development of tolerance to the pathogen. At the same time, it is necessary not to deplete the captive population to the extent of reducing its viability, to allow future full-scale reintroductions.

We represented the reintroduction programme for P. corroboree as a combination of two populations (one wild and one captive). We modelled only females, assuming equal sex ratio (as observed in the captive population: M. McFadden, unpublished data), and defined six age classes: eggs (N0), one-, two- and three-year-old juveniles (N1, N2, N3), four-year-old subadults (N4) and sexually mature adults (N5) five or more years old (Hunter 2000). We parameterized the transition matrices Lc and Lw, for the captive and wild population, respectively (eqns (1)-(3)), using values elicited from experts, relying on their knowledge and on published information (Hunter et al. 1999; Hunter 2000). We defined a most-likely, a worst-case and a best-case estimate for every parameter (Table 1). To fully characterize uncertainty, for each parameter we then fit a beta-PERT distribution to the estimates, a modified beta distribution specifically developed for the treatment of expert-elicited information (Vose 1996).

Table 1. Parameter estimates for the three considered scenarios (best-, worst- and most-likely case). Parameters: s0 indicates the survival of eggs to one-year-old froglets; s1 to s5 indicate survival for the corresponding age class post-metamorphosis; f indicates the fecundity of adult frogs; b indicates the proportion of individuals breeding in a given year
ParameterCaptive populationWild population
BestLikelyWorstBestLikelyWorst
s 0 0·820·70·650·20·150·1
s 1 0·850·850·80·40·40·35
s 2 0·90·850·80·450·450·4
s 3 0·950·90·850·50·450·4
s 4 0·950·90·850·550·450·4
s 5 0·950·90·850·60·50·4
f 15126151311
b 10·750·510·750·5

Stable age distribution

Initially, we assumed a stable age distribution and identified the maximum release rate of either eggs or subadults that could be sustained indefinitely without reducing the captive population below its initial size (λc ≥ 1). We used simulations to account for parametric uncertainty in the parameters of Lc and Lw. For each of 10 000 iterations, we parameterized Lc drawing the value of each parameter from its distribution and identified the maximum release rate (1–ri) of the chosen life stage, constraining for λc ≥ 1. We calculated mean and 95% confidence intervals of the maximum release rate across all iterations. We repeated the analysis three times, calculating the maximum release rate for either eggs or subadults when retaining all the other life stages, and the maximum rate for each stage when releasing both eggs and subadults. We carried out all optimizations and simulations using the Solver and MCSimSolver add-ins in MS Excel.

To evaluate the consequences of these release rates for the reintroduction objective, we simulated the trajectories of a system of two populations when the maximum rates were used to populate R (eqns (2), (3)). For the captive population, we assumed a stable age distribution from = 0, as inferred from the dominant eigenvector of the matrix LcR (eqn (3)). We also calculated the trajectory of a wild population, with initial size set to zero, which received the corresponding number of released individuals at every time step. We expanded the simulation to account for parametric uncertainty in the wild population. We expressed the result in terms of the ratio of individuals in the wild per individual in the captive population; assuming the captive population remains stable, its size can be easily translated into resource requirements for any given time step. We then repeated the analysis for a different objective function, the ratio between the wild population size and the yearly cost of maintaining the captive population. We estimated costs based on expert opinion, with yearly figures of A$ 58 for the first year (from egg to metamorphosis) and of A$ 50 for every year in the life of a post-metamorphic individual. These figures include all costs of food, housing, disease screening, equipment maintenance and staffing, based on records for the two main captive populations of P. corroboree. We did not include the cost of releases, assuming that they would be equal for different life stages. All costs were borne after breeding and before any reintroduction.

Initially, we ran all analyses assuming no post-release reduction in vital rates. We then assessed the sensitivity of outcomes to the post-release survival of released individuals in both life stages and to the fecundity of released subadults (we assumed no change in the fecundity of individuals released as eggs, after being exposed to 4 years of natural selection). For all possible combinations of tadpole and subadult survival (over the [0, 1] interval) and subadult fecundity (over the realistic estimated range [6, 15]: Table 1), we calculated the expected outcome of each strategy as the number of adults in the wild for every A$ 1000 spent. For clarity, we ignored parametric uncertainty by setting all remaining parameters equal to the mean values of their distributions, and applied the average optimal release rates identified for those values.

Variable initial values and demographic stochasticity

We then simulated a more realistic scenario in which the stable age assumption was violated and the time frame shortened. We set the initial values for the captive population as N0(0) = 300, N1(0) = 150, N2(0) = 250, N3(0) = 900, N4(0) = 300 and N5(0) = 340, based on actual numbers held in captivity at the beginning of this study. We identified the release rates that maximized the average number of adult individuals in the wild (W5) over a 10-year period. We compared the optimal release rates for eggs only, subadults only and a mixture of the two age classes. Again, we used simulations to represent parametric uncertainty, reporting means and confidence intervals of the optimal release rates. We set two constraints to the optimization. First, the number of captive breeding adults at any given time should not be smaller than that at the beginning of the programme (N5(t)N5(0)), again reflecting a simplified ‘insurance’ objective as previously discussed. Secondly, the total cost of the captive population at any time step should not exceed A$ 250 000, reflecting the actual yearly budget in the years 2008–2012.

Finally, we compared the outcomes of each strategy when incorporating demographic stochasticity. Using the mean values for Lc and Lw, we re-fitted the models in RAMAS Metapop (Akçakaya & Root 2002) assuming that fecundity and individual survival followed Poisson and binomial distributions, respectively (Akcakaya 1991). We ran 10 000 simulations for each strategy over 10 years, using the optimal release rates. We assumed no density dependence, allowing the populations to grow exponentially. We then compared the mean number of adults in the wild and the cost of the resulting captive population.

Results

Stable age distribution

Assuming a stable age distribution, the mean growth rate of the captive population was λc = 1·64 (95% CI: 1·57, 1·69). The maximum sustainable release rate of either eggs or subadults was on average = 0·98 (95% CI: 0·97, 0·99; Table 2). When releasing equal proportions of eggs and subadults, the maximum sustainable release rate for each stage averaged = 0·86 (95% CI: 0·85, 0·91; Table 2). The stable age distribution in the captive population was also influenced by the release strategy. For egg and joint releases, adults represented more than half of the population, whereas for subadult releases they were only 2% of all individuals (Table 2). On the other hand, subadult releases produced a more diverse stable age distribution, with similar proportions of the first four stages.

Table 2. Outcomes of applying the maximum release rates to a captive population with stable age distribution
 Release strategy
Eggs onlySubadults onlyJoint and equal releases
  1. a

    Maximum release rate for λc ≥1.

  2. b

    Calculated by multiplying the stable age proportion for each class by its respective cost (A$ 58 for eggs, A$ 51 for post-metamorphic individuals).

  3. c

    Number of wild individuals for every individual maintained in captivity.

Maximum release ratea0·980·980·86
Stable age distribution of captive population
Eggs0·140·300·13
1 year0·100·210·10
2 years0·080·180·09
3 years0·070·150·09
Subadults0·060·140·08
Adults0·560·020·50
Yearly cost of captive populationb51·157·151·1
Wild/captive ratioc0·412·411·80

The discrete growth rate for the wild population was λw = 0·75 (95% CI: 0·71, 0·80), suggesting that without continuous releases the population would not persist. When releasing 98% of eggs, the wild population became stable at a constant size equal to 41% of the stable captive population (31%, 54%; Table 2). When releasing subadults, the ratio increased to 249% (191%, 325%; Table 2). Finally, when releasing both eggs and subadults at = 86%, the stable wild population was 102% the size of the captive one (80%, 131%; Table 2). Population trajectories are described in Fig. 1. The cost of the captive population was slightly higher for subadult releases (A$ 57 per individual, compared to A$ 51 for egg and joint releases), since they implied retaining eggs. However, this difference was marginal and the cost of the captive population at stability was similar under all scenarios: therefore, the optimal choice did not change when including costs in the objective function.

Figure 1.

Outcomes of optimal release strategies under the stable age distribution assumption. Y-axis values correspond to the number of wild individuals for every individual existing in captivity at a given time. Maximum release rates calculated for a captive population with λ = 1, for each scenario (eggs or adults only: 98%; joint releases: 86% each). The shaded areas correspond to 95% confidence intervals over 10 000 simulations across the parametric uncertainty of vital rates.

Figure 2 shows the sensitivity of the optimal choice and its outcome to the post-release survival of tadpoles and subadults. For any combination of these rates, the joint release strategy was always worse than at least one of the single-stage ones. Egg releases were only optimal for low subadult survival rates and unrealistically high tadpole survival (s0 > 0·75; s4 < 0·2). Even where they were the optimal choice, their outcome was poor, yielding less than one wild adult every A$ 1000 spent (Fig. 2). Outcomes were largely insensitive to the fecundity of individuals in the year post-release: even assuming that released subadults would not breed in the first year (= 0), the wild/captive population ratio at stability varied by <0·01, and the optimal strategy did not change.

Figure 2.

Changes in the effectiveness of releasing either eggs or subadults, depending on the respective vital rates in the year after release. For every combination of tadpole and subadult post-release survival (x- and y-axes, respectively), the plot indicates which strategy is most effective (egg releases below the solid line, sub-adult releases above) and the outcome of the optimal strategy, indicated by the background colour, and expressed as the number of adult individuals in the wild for every A$ 1000 spent. For example, if the post-release survival is 0·2 for tadpoles and 0·4 for subadults, subadult releases are the optimal strategy, and they result in two wild adults every A$ 1000 spent. All outcomes were calculated assuming maximum release rates under a stable age distribution, with average vital rates for all other stages.

Variable initial values and demographic stochasticity

Under a more realistic scenario with different initial abundance in captivity, budget constraints and short-term objectives, the optimal release rates differed for every year. Over a 10-year period, a strategy focusing on egg releases required large releases (>98% in years 1–9 and 65% in year 10). This strategy was generally cheaper than the available budget, but it never produced more than 150 breeding adults in the wild (Fig. 3). A strategy focusing on subadult releases also required high release rates (>90% every year) and was expected to provide the highest number of wild individuals (Fig. 3). However, this strategy required a very large captive population, and it was not possible to satisfy both constraints: when aiming not to deplete the captive population, the yearly budget was exceeded (Fig. 3). The optimal strategy using joint releases of both stages required partial retention of eggs (averaging 20–70%) in the first 2 years, to reach capacity and maximize production in the following years, partial retention of subadults in years three and four (39% and 40%) to ensure that the desired number of adults was maintained, and finally large releases of both stages in years 5–9 (>80%). This strategy provided better outcomes than egg releases alone, and although in the last 5 years it produced fewer individuals than a subadult-only strategy, its total cost was 68% lower, without exceeding the yearly budget (Fig. 3).

Figure 3.

Outcomes of the optimal strategies for a 10-year programme with non-stable initial age distribution in the captive population. Plots represent the annual costs of maintaining the captive population (top) and numbers of adults in the wild population (bottom). The shaded areas represent demographic stochasticity (95% confidence intervals).

Discussion

The first objective of ex situ programmes for critically endangered species is often the establishment of a viable captive population as insurance in the event of extinction in the wild (Conway 2011). The growth rate of the captive population will determine whether this objective can be met, and how it can be balanced with future reintroduction efforts. Populations with high predicted growth are more likely to be able to sustain large release rates and still maintain viability. For P. corroboree, long-term persistence of the captive population could be ensured even when releasing a large proportion (0·98 on average) of either eggs or subadults, due to high survivorship and productivity in captivity.

Releasing different life stages will also change the stable age distribution of the captive population and may affect specific objectives regarding its structure (e.g. representation of genetic diversity). The cost of a stable and constant captive population depends on the maintenance requirements of different stages. In the stable age distribution scenario for P. corroboree, the difference between maintenance costs for eggs and other life stages was not sufficient to change the optimal strategy. However, if differences are significant (e.g. when breeding adults need large individual enclosures), different release strategies may have different costs, influencing the optimal decision when cost is an objective.

In the stable age distribution scenario, the insurance objective for the captive P. corroboree population was to maintain λc ≥ 1, as a simple approximation of viability. Managers may initially seek a higher growth rate, to increase the size of the captive population and release greater absolute numbers in the future: however, resource constraints are likely to impose an upper limit to the captive population size. Once this carrying capacity is reached, the ‘insurance’ objective may simply shift to λc = 1. Similarly, initial releases in excess of the maximum sustainable rate will result in a population reduction (λc < 1) until a lower bound is reached. In our case, we assumed that this bound was equal to the initial population size, although the exact relationship may differ among projects. In a theoretical study, Tenhumberg et al. (2004) suggested that it is generally optimal to increase the size of the captive population as rapidly as possible, and to start releases once this approaches its carrying capacity. In real programmes, the practical challenge for managers lies in estimating the optimal duration of this ‘build-up’ phase and the subsequent proportion of individuals to release. Framing population models in a clear decision-analytic framework can help in assessing the optimal decision.

In regard to the reintroduction objective, the trajectory of the wild population depends on its intrinsic growth rate. If λw > 1, then the population will grow accordingly after the initial releases, and assuming exponential growth, constant releases from a stable and constant captive population will become progressively less important in the long term. On the other hand, if λw < 1, as it was for P. corroboree in this study, continuous releases are needed to prevent the wild population from declining to extinction. Whether such an approach is justified depends on the objectives of the specific programme. In the case of P. corroboree, where the wild population depended on continuous releases, egg releases were less effective than subadult releases, yielding a smaller number of individuals in the wild for every individual maintained in captivity. If cost is an objective, it is therefore necessary to consider that when releasing eggs a greater population will need to be maintained to provide the same absolute numbers of individuals in the wild.

The effectiveness of releasing different life stages will depend on their expected vital rates. In general, individuals that are released later in life will have better survival than those released early and thus provide a greater wild-to-captive ratio. Within the matrix population model framework, the effects of this increase in survival can be summarized, for example, using reproductive values (the expected number of offspring an individual will produce over its lifetime: see for example Sarrazin & Legendre 2000). However, newly released individuals can suffer abnormally high mortality or low fecundity, reflecting a lack of natural selection during the captive phase or adaptation to captivity (McCarthy, Armstrong & Runge 2012). Reintroduced adults can also exhibit abnormally high dispersal, a behavioural aspect observed in several taxa (Le Gouar, Mihoub & Sarrazin 2012). The use of environmental cues for dispersal has been demonstrated for amphibians, particularly for juveniles learning dispersal routes post-metamorphosis (Ferguson 1971). In this case, the effects of post-release dispersal on the establishment of a reintroduced population may be higher for late-age-class release strategies, in which individuals have had no opportunity to learn dispersal routes. Although no information is available in this sense for P. corroboree, post-release dispersal could be considered as additional mortality.

Although such post-release effects can reduce the relative benefit of releasing later life stages, these may still be advantageous where the better survival of older individuals compensates the incidence of post-release effects. For example, Sarrazin & Legendre (2000) modelled releases of Griffon vultures Gyps fulvus in Europe, suggesting that where post-release effects remain small, releases of adults should indeed prove more effective for long-lived species. In this sense, the average longevity of P. corroboree (6–10 years in the wild: Hunter 2007) makes it a comparable case study for several amphibians, mammals and birds targeted by captive breeding efforts (see for example the species listed in Short et al. 1992; Griffiths & Pavajeau 2008; Graham et al. 2013). Additionally, for amphibians and other r-selected taxa, mortality in early life stages can naturally be an order of magnitude higher than for adults, potentially offsetting post-release mortality of older individuals. Amphibians are also less reliant on learnt behaviour than mammals or birds, further reducing the potential for adaptation to captivity (Griffiths & Pavajeau 2008). Finally, for many amphibian species, it might be possible to compensate mortality by releasing thousands of individuals, especially for juvenile stages, as shown, for example, by our results for P. corroboree. Such numbers may not be practical for other taxa, reducing the scope for a solution of the trade-offs in vital rates.

In our case study, results were also generally insensitive to the short-term fecundity of released subadults. This was a result of the longevity of adults and our assumption of no long-term variation in fecundity (from the second year after release all individuals would have the same reproductive output). Greater sensitivity might be expected in the case of long-term variations in fecundity that differed between life stages (e.g. if early-age releases achieved full reproductive potential, and late-age releases never did). In this sense, our results are consistent with those of Sarrazin & Legendre (2000), who found greater sensitivity of reintroduction success to post-release survival than to fecundity for Gyps fulvus in Europe (for reductions both in the short and in the long term).

Environmental stochasticity can also have life stage-specific effects that will influence the relative effectiveness of release strategies (Sarrazin & Legendre 2000). In P. corroboree, egg survival can be affected by environmental stochasticity: since eggs are laid in nests on the ground, they need sufficient precipitation to be flushed to a water body that must retain water throughout the period of tadpole development (Hunter et al. 2009). High mortality of eggs and low recruitment have been observed in drought years (Osborne 1989). On the other hand, wet years can facilitate the spread and virulence of chytrid fungus, again with potential age-specific effects (Kriger 2009). In the light of this complexity, currently not entirely understood for P. corroboree, we chose not to explicitly model environmental stochasticity in our study; however, it may affect the efficiency of egg releases in particular, and monitoring is being carried out to evaluate this possibility.

When the size of the captive population is not constant, retaining individuals in captivity for a longer period will increase the overall financial cost of a programme and may generate conflicts where limited resources are available (such as space or human resources at zoo institutions). In this case, strategies that envisage releases of a single life stage releases inevitably bear the consequences of this trade-off. Focusing only on releases of early life stages might be appealing to risk-seeking managers with strict budget constraints. This was clearly reflected in our realistic, short-term example for P. corroboree with multiple objectives (insurance, reintroduction and costs). Across the full range of parametric uncertainty, mixed strategies including joint releases of eggs and subadults provided the most cost-effective solution. Although egg releases allowed the lowest costs, they were also less effective towards the reintroduction objective. The reduction of age-class diversity in the captive population might be another concern. Conversely, releasing subadults was predicted to produce a greater presence in the wild. This potential risk-averse solution, however, led to high and increasing costs, making it impossible to meet both cost and insurance objectives. In this sense, mixed strategies allow managers to combine the advantages of releasing different life stages, for example releasing subadults to improve viability and managing egg releases to control the size and cost of the captive population.

Ultimately, the evaluation of the trade-off between additional costs and the predicted improvements in viability associated with releasing later life stages must be solved on the basis of the importance given to each objective. For example, Martínez-Abraín et al. (2011) used population viability analysis to assess translocation options for crested coots Fulica atra in Spain: they found that releasing adults improved viability, but this remained generally poor. They concluded that a 160% increase in costs ‘outweighed’ the marginal conservation benefits of releasing adults rather than juveniles. However, the definition of the threshold above which benefits are outweighed by costs will differ among programmes. Adopting an explicit decision-analytic approach may help define priorities and consequently inform the optimal decision.

The definition of clear objectives is the key to a rigorous approach to decision-making (Possingham et al. 2001). In our realistic scenario, we chose a short time frame to reflect the current requirement of the release programme for P. corroboree and used the number of breeding adults as a metric of success; longer programmes may focus on growth rates or probability of extinction. Our choices are influenced by the current difficulty in mitigating threats for this species, reflected by the expected negative growth rate of the wild population. Reintroduction programmes aimed at establishing self-sustaining populations, or involving species with longer generation times, may need to consider longer time frames, which can be easily accommodated in our approach. Finally, we recognize that legislative or funding constraints can create additional objectives, for example requiring managers to report some metric of success within a given deadline. If such additional objectives can be stated explicitly, the decision framework can be modified to accommodate them.

Additional aspects would also need to be considered in a more realistic analysis. For example, our assumption of exponential growth may be violated by small-population dysfunctions such as Allee effects. We did not model the genetic viability of the species either in captivity or in the wild, although the management of captive populations to minimize inbreeding is recognized as a key component of recovery efforts for P. corroboree (Lees, McFadden & Hunter 2013). Again, different components of the decision process for this problem could be modified to account for these aspects.

The ex situ conservation programme for P. corroboree shows characteristics common to most similar efforts world-wide: the rapid and seemingly irreversible decline of the target species, the unknown feasibility and time frame of threat abatement, the need to minimize time in captivity and maximize production of release candidates, while containing costs. Population models can provide useful information for managing a captive insurance population, while life stage-specific release plans can help in addressing trade-offs between numbers of releases, the probability of establishing a wild population and management costs. Framing models in an explicit decision-analytic framework can assist in evaluating key objectives, uncertainty and trade-offs.

Acknowledgements

Manuscript preparation was supported by the ARC Centre of Excellence for Environmental Decisions and the University of Melbourne. The study was initiated by the Corroboree Frog Recovery Team, through a grant to MMC funded by the NSW Government and Australian Government through a National Heritage Trust grant to the Murray Catchment Management Authority, whose support is gratefully acknowledged. Comments by two referees greatly improved an earlier version of this manuscript.

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