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Quantifying Ecological Life Support: The Biological Efficacy of Alternative Supplementation Strategies for Imperiled Amphibian Populations


  • Editor Javier Simonetti


Global biodiversity loss has prompted diverse efforts to stem or reverse declines for many species. Such efforts are often implemented before the efficacy of alternative management actions is quantified. Here, we use matrix models to compare the effectiveness of two supplementation strategies, head-starting early life stages and captive breeding for reintroduction, at reducing extinction risk of declining amphibians. We use the imperiled Oregon spotted frog (Rana pretiosa) as a case study and find that when supplementation occurs after metamorphosis, captive breeding is more effective at reducing extinction risk than head-starting, but the difference declines with increasing supplementation effort. We also find that captive breeding with release as larvae yields similar reductions in extinction risk, and is two orders of magnitude more effective at reducing extinction probabilities than head-starting the same stage. Our results highlight that even basic demographic data can be leveraged to assess tradeoffs among alternative supplementation strategies.


Rates of biodiversity loss over the past century have prompted global concern (Loh et al. 2005; Hoffmann et al. 2010). While some species have declined to extinction (Stuart et al. 2004; Hoffmann et al. 2010), more commonly species exist at lower population densities or in fewer locations. As a consequence, an increasing number of species are conservation-reliant, persisting with the aid of continuous management (Scott et al. 2005). Management tools for such species depend on specific threats, but include habitat manipulation, invasive species removal, genetic assurance populations, and population supplementation (Fischer & Lindenmayer 2000; Scott et al. 2005). However, the effectiveness of management strategies is usually understood poorly prior to implementation, especially when knowledge of basic population dynamics and causes of decline are limited. As such, decisions to implement conservation actions to avert extinction often occur despite imperfect or unavailable information (Thorpe & Stanley 2011; Martin et al. 2012).

Unlike addressing habitat limitations or invasive species linked to decline, population supplementation is generally a proximal solution to an ultimate cause of decline, yet can be effective at maintaining populations while underlying mechanisms are better studied (Zippel & Mendelson 2008). Supplementation has been implemented for a wide range of taxa, including birds, mammals, fish, and herpetofauna (Fischer & Lindenmayer 2000), and is attributed to reducing extinction risk of Black-footed ferret (Mustela nigripes) and California condor (Gymnogyps californianus; Woods et al. 2007), among others. However, supplementation is highly contested for some species. For example, hatchery-raised Pacific salmon (Oncorhynchus spp.) often numerically and genetically dominate populations, resulting in reducedproductivity and maladaptive changes in feeding or predator-avoidance behavior (Lynch & O'Hely 2001; Araki et al. 2007; Araki et al. 2009).

While using captive-reared individuals to supplement wild populations has the potential for adverse effects, both captive head-start and captive breeding programs are commonly used to counterbalance declines in amphibian populations (Stuart et al. 2004; Gascon et al. 2007; Zippel & Mendelson 2008). Head-start programs remove individuals from the wild and rear them in captivity during life history stages with suspected low survival in the wild (Dodd & Seigel 1991; Dodd 2005; Adama and Beaucher 2006; Frostner et al. 2007). Life history schedules of many amphibians appear to be good candidates for head-starting, as high mortality rates in early life stages present an obvious target for improvement. Similarly, captive breeding programs are also widely employed for endangered amphibians (Gascon et al. 2007; Griffiths & Pavajeau 2008; Zippel & Mendelson 2008) and use the offspring of captive-reared adults to supplement wild populations. The efficacy of captive breeding to recover amphibians is still under debate (Dodd & Seigel 1991; Seigel & Dodd 2002; Griffiths & Pavajeau 2008), but has been suggested as one of only a few solutions for species experiencing sharp decline (Stuart et al. 2004).

Although resources are commonly devoted to establishing relatively robust supplementation programs, postrelease monitoring and quantifying effectiveness at stemming population declines is rare (Dodd & Seigel 1991; Fischer & Lindenmayer 2000). Understanding age structure, growth rate, and population size of focal species before and after supplementation can help increase the success of a program and guide decisions, such as the life stage and quantity of individuals to release (Sarrazin & Legendre 2000; Tenhumberg et al. 2004). To date, few resources exist to both evaluate tradeoffs between supplementation strategies and to determine the level of effort required to effect change in population demographics.

Here, we quantitatively compared two forms of population supplementation, head-starting and captive breeding, over a hypothetical 10-year timespan for an imperiled amphibian, Rana pretiosa, as a test case. We used field-collected demographic data and population dynamics models to determine how much supplementation would be required to reduce the R. pretiosa extinction probability below 50% over 10 years, the threshold criteria for downlisting from Critically Endangered to Endangered under the International Union for Conservation of Nature (IUCN) guidelines (extinction probability <50% but >20% over 20 years; IUCN 2013). We constructed a series of stochastic matrix models to compare the efficacy of each recovery strategy at reducing the 10-year extinction probability, and evaluated a range of efforts for the two strategies. We additionally explored supplementation scenarios that released animals as larvae or post-metamorphic frogs across a range of wild population sizes (i.e., the degree of imperilment). Finally, we estimated the elasticity of the population growth rate to variation in vital rates of the R. pretiosa life cycle to assess whether early life stages are likely to affect population-level dynamics. We present a blueprint for determining what supplementation type and level of effort will elicit the greatest reduction in decadal extinction probabilities. Although based on R. pretiosa, we propose that this framework can be modified for other species being considered for population supplementation if a moderate amount of demographic data exist.


Study species

R. pretiosa is an IUCN Vulnerable species, Endangered in Canada, British Columbia (BC), and Washington State, and a candidate for listing under the US Endangered Species Act. The species has been extirpated from up to 90% of its distribution, which ranged between southwestern BC and northern California (Hammerson & Pearl 2004). Three populations (<500 adults) of R. pretiosa persist in Canada, and although lack of genetic data preclude estimates of effective number of breeders (Nb), it has been demonstrated for some Ranid species, including one population of R. pretiosa in Oregon (Phillipsen et al. 2010), that Nb may be less than total adult population size. Additionally, population isolation and habitat patch size may limit population growth (Pearl and Hayes 2004). To stem declines, both head-start and captive breeding supplementation programs were implemented as part of the federal recovery strategy (Canadian Oregon Spotted Frog Recovery Team 2012; details in supplementary information).

Matrix models

We used stochastic, stage-based matrices with a 1-year time interval to model the dynamics of a declining R. pretiosa population. We constructed female-only models (Morris & Doak 2002) to simulate: (1) wild population dynamics, (2) wild population with head-start supplementation, and (3) wild population with captive breeding supplementation. We further modeled each strategy with captive individuals reared until (A) larvae (free-swimming tadpoles, 1–2 weeks old) or (B) post-metamorphic Young-of-Year (YOY) frogs (4–8 weeks post-metamorphosis), resulting in four supplementation scenarios (1. wild, 2A. head-start, larvae, 2B. head-start, YOY, 3A. captive, larvae, 3B. captive, YOY; Figure 1). We divided the life history of R. pretiosa into four annual stages, or matrix elements (aij, Fij; Figure 2) made up of one or more vital rates (Caswell 2001) that represent transition probabilities within a single year. Mean estimates of each vital rate were calculated from experiments, surveys, and literature values (see below), and we incorporated stochasticity into our models by using the variances (s2) around the means for each vital rate (Table S1). We ran 10,000 iterations of each simulation in MATLAB (R2012a) to calculate the cumulative 10-year probability of quasi-extinction (n ≤ 20 adult females, hereto extinction probability) for each scenario. In each forward simulation, we began the population at stable-stage distribution, drawing vital rates randomly in each time step. Finally, we calculated the stochastic growth rate (λs) for our wild model to determine the rate of population decline.

Figure 1.

Schematic diagram of the four-stage Oregon spotted frog matrix models and alternative supplementation scenarios (dashed lines). Solid arrows represent transition probabilities among stages. The top life cycle (white frogs) represents the wild population. Stage 1 (in box) includes embryos, larvae, and young of the year (YOY), individuals transition to the next stage after a 1-year time step. The arrow going from the adult and second juvenile stages back to stage one represents the reproductive contribution (fecundity) of the population. Under head-start scenarios (2A, 2B), a portion of the reproduction is removed from the wild and raised in captivity, represented by the arrow leading from the fecundity of wild individuals to light gray individuals, with release into wild at either the larval (Scenario 2A) or YOY (Scenario 2B) stage. Finally, the dark gray population shown at the bottom represents an independently regulated captive breeding population from which individuals are released into the wild at either the larval (Scenario 3A) or YOY (Scenario 3B) stage.

Figure 2.

Matrix model structure and vital rate definitions. Here, ni is the number of individuals in stage i at time t, Fij represents per capita fecundity, aij is the transition rate from one stage to the next and is made up of component vital rates shown in the Parameter Equation column. ϕ represents survival, YOY = young of the year, Prbreed is the probability of a second year juvenile breeding, HS = head-start, PHS is the proportion of the population removed from the wild for head-starting, CB = captive breeding, HB = the number of individuals held back to maintain the captive population, W = wild population.

We varied the degree of effort for each supplementation strategy based on practices of R. pretiosa head-start and captive breeding facilities in Canada (Table 1; Canadian Oregon Spotted Frog Recovery Team 2012). For head-start scenarios, we varied the proportion of annual breeding effort removed from the wild from 5% to 30%, in increments of 5%. For captive breeding scenarios, we varied the number of breeding females in captivity from 10 to 60 in increments of 10. We tracked the cumulative number of YOY added to the population for each scenario (see Supplementary information for details). To compare efficacy across scenarios and effort, we calculated the decrease in extinction probability (ΔE) when compared to the unsupplemented wild population (ΔE = EwildEscenario, herein effectiveness) for one example of low, medium, and high levels of effort for each scenario (Table 1).

Table 1. Comparison of effort for head-start (% wild reproduction removed to captivity) and captive breeding (number of captive breeding females) scenarios
Effort% Head-startedbNo. of captive breeding femalesc


  1. a

    Example scenarios referred to in analyses and text as low, medium, and high.

  2. b

    Percentage of wild reproduction removed per year for head-starting.

  3. c

    Number of breeding females in a separate captive population.


Demographic rates

We modeled survival (ϕ), fecundity (F), and transition probabilities between stages (Pr; Figure 2) primarily from our field studies of R. pretiosa in BC, with additional rates derived from published literature (Table S1). Field studies consisted of an in situ larval enclosure experiment in 2011 to estimate larval survival and a capture-mark-recapture study of adults in 2010 and 2011 to estimate adult female survival (see Supplementary information for details). We derived head-start and captive breeding vital rates from observations from captive facilities in BC (A. Gielens and D. Thoney, unpublished data; Table S1). Differences among the four supplementation scenarios were modeled within matrix element a21 (Figure 2), which is composed of three lower-level vital rates making up the first year of life (embryonic, larval, and post-metamorphic stages). For head-start models (Scenario 2A, 2B), we added vital rates for captive survival (ϕHSembryo, ϕHSlarvae), and for captive breeding models (Scenarios 3A, 3B), we generated embryos from a fixed captive population that survived in captivity at rates independent of those in the wild (ϕCBembryo, ϕCBlarvae), and held back a small subset of embryos each year to maintain the captive population (Figure 2, Table S1).

Wild population size

Extinction probability for a wild population is a function of population size and rate of decline. For our wild model, we explored how extinction probability changed with the degree of imperilment by running models with population sizes ranging from 50 to 300 breeding females. This range of population sizes reflects observed spatiotemporal variation in population size for R. pretiosa and includes population sizes for which urgent conservation actions, including supplementation, are generally warranted (Caughley 1994). We limited our evaluation of the effectiveness of supplementation to population sizes that resulted in a 10-year extinction probability >20% (IUCN criteria for Endangered listing).

Elasticity analysis

We calculated deterministic elasticity values, which give the proportional change in lambda given a proportional change in a vital rate, as a relative ranking of vital rate contributions to population dynamics using mean values of the wild population matrix. Declining populations often experience variation in multiple vital rates simultaneously and such changes violate the basic assumptions of deterministic elasticity analysis (Caswell 2010). To account for the possibility of multiple changing vital rates, we also conducted a simulation-based elasticity analysis in which 10,000 random matrices were constructed with vital rates drawn at random from uniform distributions between minimum and maximum values (2.5 and 97.5 quantiles of the probability density functions for each vital rate; Table S5) and calculated mean deterministic elasticities across the simulations (Wisdom et al. 2000).


Matrix models

Without supplementation, our wild R. pretiosa model (Scenario 1) predicts a stochastic growth rate (λs) of 0.86, equivalent to a 14% annual rate of decline, and a 10-year extinction probability between 3% and 92% at initial population sizes of 300 and 50 adult females, respectively (Figure 3). Only wild populations of ≤150 breeding females had an extinction probability >20%, coinciding with IUCN criteria for Endangered listing and warranting consideration for supplementation. We found that supplementation can strongly reduce extinction probability, but the degree of reduction varied with supplementation type, stage at release, effort, and initial population size (Figure 4). Head-start models with release at the larval stage (Scenario 2A) reduced extinction risk below 50% in 12 out of 18 cases we ran (when effort was ≥5% of eggs removed from the wild and populations were ≥100), but were ineffective at reducing extinction risk for smaller populations (Figure 4a). In contrast, head-start models with release at the YOY stage (Scenario 2B) reduced extinction risk below 50% in 16 out of 18 cases, and large populations (≥100), required only 5% of wild eggs be removed to captivity and raised to YOY stage. For small populations, ≥15% effort (i.e., 15% of wild eggs removed to captivity) was required to reduce extinction risk below 50% under Scenario 2B. Captive breeding models with release at the larval stage (Scenario 3A) were more effective than Scenario 2A at reducing extinction probability, and comparable to Scenario 2B (16/18 cases resulted in <50% extinction risk; Figure 3c); breeding ≥30 captive females and releasing as larvae reduced extinction risk to <50% for a population of 50 individuals, whereas breeding 10 captive females was enough to reduce extinction below this threshold for populations >50. Captive breeding models with release as YOY (Scenario 3B) were most effective at reducing extinction probability (<50% extinction in 17/18 cases), dropping below 50% at an effort of 20 breeding females for a population size of 50 individuals, and at a minimum effort for population sizes ≥100 (Figure 3d).

Figure 3.

The 10-year cumulative extinction probability for R. pretiosa with no supplementation as a function of initial wild population size (number of adult females).

Figure 4.

The 10-year extinction probability for a range of efforts (x-axis) for (a) Scenario 2A, head-start and larval release; (b) head-start and release as YOY (2B); (c) captive breeding, larval release (3A); and (d) captive breeding and YOY release (3B). Lines depict initial wild population sizes (solid = 50, dashed = 100, dotted = 150). Note an effort of zero corresponds to no supplementation (Scenario 1). The gray line shows 50% extinction risk (Critically Endangered threshold).

Effective strategies are those that maximize reduction in extinction risk over 10 years. We calculated the decrease in extinction probability relative to the unsupplemented wild population (effectiveness) for a subset of our scenarios (lowest, medium, and highest; Table 1) and found that captive breeding models maximized effectiveness with one exception (high effort, release as YOY; Figure 5). When reintroduction occurred at the larval stage, captive breeding scenarios were 23 to 33 times more effective than head-start scenarios. When individuals were released as YOY, captive breeding and head-start scenarios were virtually identical, except at low effort when captive breeding was 2.1× more effective.

Figure 5.

The decrease in the 10-year extinction probability under a given supplementation strategy for a low, medium, and high level of effort across a range of initial wild population sizes (number of adult females). Left panels depict supplementation with release at the larval stage and right panels release at the YOY stage. Solid lines indicate captive breeding and dashed lines indicate head-starting.

Elasticity analysis

The elasticity analysis revealed that vital rates contributed unequally to population growth. The most elastic parameter was adult survival for both the deterministic and simulated elasticity analysis. Larval and metamorphic elasticity ranked among the second most elastic parameters, ahead of adult and juvenile fecundity (Figure 6a). Our simulation-based elasticity results were highly correlated with the deterministic elasticity for all stages (Elastictysim = 1.098 · Elastictydet, r2 = 0.99; Figure 6b).

Figure 6.

Simulated mean elasticity values and 95% confidence intervals for wild R. pretiosa population vital rates (top panel, a). Correlation between the deterministic and simulated elasticity values of the component vital rates for R. pretiosa (Elastictysim = 1.098·Elastictydet, r2 = 0.9912; bottom panel, b).


Our analysis demonstrates the tradeoffs among supplementation strategies for a declining amphibian, and that effectiveness depends on when supplementation is initiated during a decline. When our simulated wild population was small (≤100), extinction probability (0.53–0.92) met the criteria of Critically Endangered by the IUCN (>50% extinction probability in 10 years or three generations, IUCN Standards and Petitions Subcommitee 2013). In contrast, our head-start and captive breeding scenarios illustrate pathways to reduce extinction probabilities below this threshold. We found that supplementation under all scenarios was most effective when the population was initially ≤100 individuals (Figure 5). These findings, if more general, imply that supplementation at the levels of effort we explored is likely to be most effective at very small population sizes, when the high degree of imperilment demands consideration of “last resort” options.

Although we have illustrated pathways to reduce extinction risk below IUCN Critically Endangered for imperiled amphibian populations, we also present a framework for identifying supplementation scenarios that maximize reduction in extinction probability while minimizing conservation effort. When we compared the reduction in 10-year extinction probabilities between a simulated wild population and our four supplementation strategies, we found lower levels of captive breeding effort reduced extinction risk more effectively than a head-start program, and that captive breeding and release as larvae can reduce extinction risk almost as effectively as release at the YOY stage (Figure 5). This suggests that captive breeding may help buffer a wide range of demographic and population-level variability. Because captive breeding and release occurs independently of fluctuations in wild populations, this strategy allows managers to consistently add individuals to the wild population (Figure S1).

Developing tools and metrics to evaluate conservation strategies to decrease extinction risk are critical for imperiled populations. Stage-based demographic models provide a unique opportunity to couple the complexities of species’ life histories with quantitative models to identify life stages with the highest potential to affect population dynamics (Sæther & Bakke 2000; Heppell et al. 2000). Later life stages have been demonstrated to contribute more to overall population growth rates than early stages in mammals (Heppel et al. 2000), reptiles (Crouse et al. 1987), birds (Stahl and Oli 2006), and amphibians (Biek et al. 2002; Vonesh & De la Cruz 2002; Govindarajulu et al. 2005). Yet our analysis suggests that despite lower elasticity for early life stages, with large enough efforts, population-level improvements are possible through early life-stage supplementation. Given that affecting survival at later life stages often requires elucidating and treating specific causes of low survival, it is important to know that targeting alternative stages can positively impact emergent population dynamics.

Our modeling approach assumes no genetic cost to the population and that individuals from captivity survive at rates equal to that of their wild counterparts following release. There is some evidence that releasing captive-bred individuals can result in a fitness reduction for other taxa (Lynch & O'Hely 2001; Araki et al. 2007; Araki et al. 2009), and that captive rearing wild individuals for release can negatively affect growth (Adama and Beaucher 2006). Although questions regarding the utility of supplementation remain for most species, there are few other options available when management is required to maintain critically imperiled populations (Stuart et al. 2004; Scott et al. 2010). Setting aside assumptions that captive breeding and rearing have negligible effects on survival and fitness in the wild, another conservation reality is the financial cost of recovery. Keeping individuals in captivity is expensive (Dodd 2005) and costs likely constrain recovery options. A holistic approach to decision making which incorporates both the biological and financial realities of recovery is therefore necessary to determine the best way to increase population numbers.

Here, we have shown that it is possible to improve the quantitative basis for decisions regarding alternative recovery actions when basic demographic data are available. The framework we used with R. pretiosa provides an example of the biological tradeoffs that exist among alternative supplementation strategies. Such tools are not commonly available to conservation decision makers, but we argue that adapting models for other species is relatively straightforward and can be used to guide management decisions. For species with limited data, a similar, but deterministic approach can be used to make relative comparisons of management options. Although supplementation alone is unlikely to sustain a population in the long term (but see Scott et al. 2005), we have shown that it has the potential to be an effective tool to reduce short-term (10-year) extinction probability while ultimate causes for decline are better understood.


We thank members of BC Oregon Spotted Frog Recovery Team, staff at the Vancouver Aquarium and the Greater Vancouver Zoo for help and support with project planning and providing data. We thank Rylee Murray, Hannah Gehrels, Michelle Segal, Morgan Stubbs, Isabell Eischeid, Jill Miners, and Monica Pearson for field assistance and Seabird Island Nations Band for their support and interest in this study conducted on their traditional territory. We also thank M. Hayes for comments on an earlier draft and two anonymous reviewers for their suggestions, which greatly improved the manuscript. Funding was provided by an Interdepartmental Recovery Funds Grant to C.B., a U.S. Fish and Wildlife Service Competitive State Wildlife Grant to the Washington Department of Fish and Wildlife (M. Hayes and P.G.), a Canadian Wildlife Federation Grant, an NSERC Discovery Grant, and the Canada Research Chairs Program to W.P.