Digging the pupfish out of its hole: risk analyses to guide harvest of Devils Hole pupfish for captive breeding

Modeling risk and harvest strategies for captive breeding using DHP counts

Visual counts of pupfish from 1972 to 2013, made by SCUBA divers in the pool and by observers on the shallow shelf, were obtained from Death Valley National Park personnel (Fig. 1). See Dzul et al. (2012) for survey details and sources of error. Counts of pupfish did not distinguish between adults and detectable early life stage individuals, and were conducted on about a monthly basis from 1972–1983. By 1985 counts were mainly done biannually, in the spring (March–April) during the main breeding season of the pupfish and in the fall (Sept.–Oct.) during a second but reduced pulse of breeding. Only one count per season was conducted in most years, which precluded the use of N-mixture models of population estimation that require repeated sampling (Royle & Dorazio, 2008). In the absence of survey-level covariates of effort, I was unable to use a single visit conditional likelihood approach to estimate abundance (Lele, Moreno & Bayne, 2012; Solymos, Lele & Bayne, 2012). Thus, I choose to use the maximum count for each season in each year as an estimate of the population size, creating two time series of counts. Treating counts separately provided independently derived estimates of population trends and permitted seasonal evaluation of harvest options.

I calculated the rate of population growth (r = ln(N_t+1/N_t)) from pairs of counts of population size (N) from consecutive years (t). I then fit one density-independent and two density-dependent models of population growth to the period when pupfish numbers grew (1972–1995) and the period of population decline (1996–2013) following Morris & Doak (2002):

Exponential (density-independent): (1)${\displaystyle ln\left(N_{t+1}/N_t\right)=r+{\epsilon }_i}$ Logistic (density-dependent): (2)${\displaystyle ln\left(N_{t+1}/N_t\right)=r\left[1-\left(\frac{N_t}{K}\right)+{\epsilon }_i\right]}$ Theta-logistic (density-dependent): (3)${\displaystyle ln\left(N_{t+1}/N_t\right)=r\left[1-{\left(\frac{N_t}{K}\right)}^{\theta }+{\epsilon }_i\right]}$ where r = growth rate, K = carrying capacity, θ adjusts how population growth changes with N, and ε_i = is the variance or deviation in the natural logarithm of population growth (lnr) centered around zero. Akaike’s Information Criterion (AIC) corrected for small sample size (AICc) was used to quantify model fit (Burnham & Anderson, 2002).

To model extinction risk in the wild, the pupfish population in Devils Hole was projected forward in time for 100 years with separate models for spring and fall using each season’s fitted values for average population growth rate, carrying capacity (when appropriate), and annual deviations from mean growth rates (ε_i) estimated from 1996–2013 to yield the median time (years) to extinction and probability of extinction. Starting population size was set to the number of pupfish counted in 2013 for spring (35) and fall (68), and 10,000 iterations were run. Fractional numbers of individuals were rounded down each year. Projections were done using the program @Risk (@Risk 6.2; Palisade Software, Ithaca, New York) in Microsoft Excel, as were all simulations presented below.

Using ε_i to model annual variation among counts has contrasting effects on the resulting estimate of extinction risk. The ε_i term incorporates implicit effects captured in DHP count fluctuations including: (1) demographic, environmental, and genetic stochasticity; (2) catastrophes; and (3) sampling variation. Nevertheless, these processes were not explicitly modelled. The inclusion of sampling variation in the estimate of ε_i will overestimate variation in population growth and inflate extinction risk. However, in the absence of explicit incorporation in the model of genetic processes (e.g., inbreeding depression), extinction risk may be underestimated. As I am unable to determine the magnitude of each effect, estimates of extinction risk are best interpreted when compared among different scenarios.

To evaluate the effects of different strategies for removing individuals to initiate a captive breeding program on the wild population, I used the models that best described DHP population dynamics for spring and fall from 1996 to 2013, and harvested (removed) different numbers of individuals (0–14) at the start of each simulated year. Harvest was done for each of three years to mimic building a new population for captive propagation. Median time to extinction and probability of extinction were evaluated from 10,000 iterations.

I used the same model to examine how risk of extinction changes with DHP population size to evaluate when to remove all pupfish individuals from Devils Hole based solely on changes in wild population risk without considering genetic goals for the captive population. The stochastic count-based PVA model was run for 10,000 iterations parameterized with the 1996–2013 measures of population growth, incrementally changing the initial population size.

Deterministic matrix demographic model to evaluate age classes to remove

A deterministic demographic model was developed to evaluate the effects of removing individuals of different life stages on DHP population dynamics by calculating for each life stage its reproductive value (i.e., expected future number of offspring produced) and elasticity (sensitivity of population growth to changes in demographic parameters associated with each stage). I sought opinions for constructing and parameterizing the model from 15 DHP and fisheries experts that attended the DHP Risk Analysis Workshop (8 Nov. 2013). Demographic data available for the DHP are so limited, and the uncertainties so large, that I could not justify the choice of particular rates or scenarios. Instead, I generated 5,000 matrices composed of random combinations of potential average demographic rates for the pupfish chosen from uniform distributions that sampled means between their possible minimum and maximum values (Fig. 2). This approach allowed exploration of the potential parameter space, resulting distribution of reproductive value and elasticity for stage classes, and relationships among them.

A post-breeding projection was chosen to enable inclusion of eggs as a life stage because they are potential targets for management. It was based on a life cycle diagram and projection matrix with 3 stages (Fig. 2): eggs, early life stage or ELS (from hatching at 4 mm to 11 mm in length) and adults (>12 mm). A 7-day time step was used based on the time required for an egg to hatch and become an ELS. I converted DHP demographic rates expressed in the literature on a monthly basis to a daily rate (divided by 30) and then to a weekly rate (multiplied by 7).

The model required estimates for the proportion of individuals that: (a) survive over a time step and remain Adults (P₃); (b) grow from Eggs and survive to become ELS (G₁); and (c) grow from ELS to become Adults (G₂), or survive and remain as ELS (P₂). It also required estimates for realized fecundity, which is the product of (d) the proportion of individuals that survive and remain (P₃ for Adults) or that grow to a reproductive stage over the time step (G₂ for ELS), and (e) their fecundity (m₃). Because male fecundity was not known, rates were based on females and sex ratio of eggs was assumed to be 50:50.

As the overall probability of survival (S) for a stage class is S = P + G, I estimated the proportion of individuals surviving and transitioning using the equation: (4)${\displaystyle G=\frac{S^t}{1+S+S^2+S^3\cdots S^{t-1}}}$ where t = number of time steps in a stage including the transition to the next stage. Estimating G₂ in this manner reduced the number of demographic estimates the model required to four (P₃, S₂, G₁, and m₃), but required an estimate of the number of time steps a newly arrived ELS (4 mm) needed to grow to be an adult (>11 mm). James (1969, p. 46) estimated growth rates of caged individuals of 4.7 mm per month for offspring in Devils Hole, which would require 1.6–2 months (7–8 weeks) for growth from ELS to Adult. Hybrid DHP, which may grow faster than nonhybrids, require 30–45 days to grow from hatching to adult (O Feuerbacher, pers. comm., 2013). I let the number of weeks (time steps) that ELS require to reach adult size range from 4 to 7.

Monthly survival rates in the literature are based on best professional judgment, as a DHP capture–recapture study has not been conducted in Devils Hole. Adult survival (P₃) in Dzul et al.’s (2013) model was assigned values of 0.70, 0.80, and 0.86, while Chernoff (1985) used 0.91. I explored values ranging from 0.7 to 0.9. Monthly survival (S₂) assigned by Dzul et al. (2013) to juveniles (ELS in my model) was 0.047, 0.072 and 0.097, based primarily on simulation runs of their model that resulted in the stable population growth observed during their one-year study. I allowed ELS monthly survival to range between 0.05 and 0.15.

Fecundity (m₃) has not been measured for DHP in the wild. Females are thought to lay a single egg with each spawn, which can occur at any time of year but peaks from mid-February to mid-May with a secondary peak from July–Sept (Hausner et al., 2013; Lyons, 2005). Fecundity is unrelated to size in the DHP (Minckley & Deacon, 1973; Mire & Millett, 1994; Shrode & Gerking, 1977). Minckley & Deacon (1973) stated that “an average female may have about 4–5 ova or 10–20% of her total complement in a mature condition during a peak reproductive season”. This suggests that a female might be capable of laying 20–50 eggs during her lifetime (minimum 4 × 5 = 20; maximum: 5 × 10 = 50) and that the eggs would be distributed differentially during the year. Chernoff (1985), using data in James (1969) and Minckley & Deacon (1973), estimated the average number of eggs spawned per female to be 24 and the average per female per month during the breeding season from 1–5. In summary, females may lay 0–4 eggs per week. Assuming a 50:50 sex ratio, I set reproductive rates to range from as low as 0.05 female eggs per week to as many as 2 female eggs per week. In the absence of hatching success measures, I assumed all eggs survived for one week and hatched, which may overemphasize their importance to population dynamics.

Estimation of population growth measures

Fits of density dependent and independent models of population growth (Table 1) reflect the shift in pupfish dynamics over time (Fig. 1). From 1972 to 1995, density dependent models provided the best fit for both spring and fall counts (cumulative AIC weight of 0.99–1.0), with the logistic model fitting best for both seasons (Table 1). Growth was positive before 1996 (r = 0.82; 95% CI [0.40–1.24]), with a carrying capacity of 216 (95% CI [194–237]) for spring and 444 (95% CI [390–498]) for fall. From 1996–2013, density independent models best fit the DHP counts, with a declining population growth (r) of −0.049 (95% CI [−0.24–0.15]) and −0.088 (95% CI [−0.27–0.09]) for spring and fall counts, respectively. Associated values for annual environmental variation were ε = 0.117 for spring and ε = 0.096 for fall.

Count-based risk analysis for the DHP in Devils Hole

Time to extinction for the DHP estimated separately from spring and fall counts followed the expected logarithmic distribution, resulting in most simulated populations becoming extinct within 50 years and a smaller number remaining extant for extended periods (Fig. 3A). Median and mean time to extinction were 26 and 27 years, and 17 and 22 years, respectively, for spring and fall counts (Fig. 3A). The chance of extinction within a decade was less than 5%, but rose rapidly to 26–33% by 20 years, ∼45% by 25 years, and 81–90% by 50 years (Fig. 3B).

Effect of harvest for captive propagation on extinction risk in Devils Hole

Risk to the wild population of removing pupfish from Devils Hole to initiate captive breeding depended on the level and timing of harvest (Fig. 4). Removing individuals in the fall had less impact on risk to the wild population than the same level of harvest in spring, due to the larger initial size of the pupfish population in fall. For both spring and fall harvest, risk increased linearly with the number of individuals removed at rates of up to 6 pupfish per year for 3 years. Above this level of harvest, extinction risk accelerated; the median time to extinction fell rapidly (Fig. 4A) and the probability of extinction increased at a greater rate (Figs. 4C and 4D), especially for spring harvest.

Surprisingly, extinction risk was relatively unaffected by the apportionment of the total harvest among years (Fig. 4B). Whether the total number of individuals was removed over one, two or three years had little effect on the probability of extinction at 20 years.

Impact of removing different age classes on DHP population dynamics

Analysis of reproductive value (RV) and elasticity both indicated that Adults were the stage class with the greatest influence on population dynamics (Table 2). RV for ELS (Stage 2) was nearly identical to RV of Eggs (Stage 1) and never exceeded 1.2 in the 5,000 iterations of matrices evaluated. RV for Adults, however, averaged 24.2 ± 0.3 and ranged from a minimum of 4.32 to a maximum of 123 with a median value of 17.7 (Fig. 5A). This pattern occurred partly because so few ELS survived to become adults. Adult RV was strongly negatively related to ELS growth and positively related to the stage duration (Fig. 5B). Elasticity results also indicated that changes in adult survival (P₃) had by far the greatest influence on population growth rates (Table 2).

Extinction risk vs. DHP population size in Devils Hole

As expected, the median time to extinction increased and probability of extinction in 10 years decreased when simulations were begun with larger initial population sizes (Fig. 6). Both metrics of extinction risk changed linearly with initial population sizes between 30 and 50 individuals, but accelerated when initial populations were less than 30 individuals.

Risks to the wild population when building the captive population

Removing individuals from the wild to initiate captive breeding will reduce the time to extinction of pupfish in Devils Hole (Fig. 4). Risks can be mitigated by harvesting wild pupfish in the fall, when the population tends to be larger, rather than in the spring, when less recruitment has occurred. However, risk to the wild population accelerated when more than six adults were harvested annually, although this effect is smaller in the fall. In any case, it may be unwise to harvest adults for captive propagation if eggs or early life-stage individuals are available and can be raised in captivity. Removing eggs has the least impact on the population dynamics of DHP in Devils Hole (Fig. 5, Table 2). The egg stage had the lowest reproductive value and the lowest elasticity, although population dynamics was nearly as insensitive to incremental, instantaneous changes in the rates of early life stage individuals.

Results from the two population models can be connected by translating reproductive value of the egg stage from the demographic matrix model to a number of adults that can be removed in the count-based models. The mean RV of an adult pupfish is roughly 25 times greater than that of a pupfish egg in Devils Hole (Table 2). From this perspective, removing 25 eggs for captive breeding is equivalent to removing a single adult in terms of its influence on population dynamics (Caswell, 2001).

The success of removing pupfish eggs or adults to build the captive population and support the wild population depends upon subsequent husbandry and (re)introduction. This requires success in each of a series of steps (Armstrong & Seddon, 2008; Snyder et al., 1996): (1) survival, growth and reproduction in captivity; (2) maintenance in captivity of genetic diversity and a viable gene pool; and (3) successful preconditioning and release to the wild, either to establish a new refuge in a secure location or to bolster the pupfish in Devils Hole, ideally after conditions that caused the population to decline have been identified and ameliorated. While the first step in the process has been successfully accomplished, as eggs taken from Devils Hole have been hatched in captivity, serious obstacles remain before releases of pupfish can occur. Unfortunately, the longer that pupfish remain in captivity before being returned to the wild, the greater the likelihood of selection for domestication and loss of behaviors needed to survive in the wild (Ford et al., 2008; Frankham, 2008; Kelley, Magurran & Macías García, 2006; Snyder et al., 1996). Avoidance of domestication will be a key priority in managing the captive population (LH Simons, pers. comm., 2014).

When to designate the “condor moment” and remove all pupfish from Devils Hole

Designating the “California Condor moment” for the DHP–when removing the remaining pupfish from Devils Hole would be the best course of action–is a management option conservation biologists have rarely considered. Similar situations have been faced in a few other extreme cases, such as the Hawaiian Crow (Corvus hawaiiensis) which was rescued from extinction but cannot be reintroduced to the wild due to the persistence of the toxoplasmosis responsible for its decline (Work et al., 2000), and the black-footed ferret (Mustela nigripes) which was captured for captive breeding after a few individuals were rediscovered in the 1980’s (Clark, 1990; Jachowski et al., 2011). I evaluated when to designate the condor moment by searching for nonlinearity in the relationship between risk of extinction and population size (Fig. 6). Extinction risk accelerated when population size fell below 30 individuals. However, the risk analysis presented here only partly addresses the issue of when to intervene by removing all individuals from the wild to save the DHP. The degree that genetic diversity of the wild population is represented in the captive population is a major concern that the model does not address.

There are many similarities between the situation currently facing the DHP and the decline of the California Condor in the mid-1980s (Meretsky et al., 2000; Snyder & Snyder, 2000; Snyder & Snyder, 1989). Both species experienced a rapid population decline occurring over decades as a result of poorly understood causes that were difficult to reverse. Neither species had a history of successful captive breeding, although experiences with the target or a surrogate species indicated the potential for success. Neither species was sufficiently represented in captivity to conserve genetic diversity. Concerns were voiced for condors that capturing the remaining individuals for captive breeding would reduce the need to conserve of habitats needed for their reintroduction, and similar issues relating to water rights affect the pupfish. Finally, a long history of management controversies and struggles to conserve each species has made them conservation icons.

Some key differences, however, between pupfish and condor life history and management could make it easier to recover the DHP. First, the “faster” life history of the DHP (early maturation, reproduction and short life span) promotes rapid population growth and recovery compared to the “slower” life history” of the condor (delayed age of first breeding, low level of reproduction and long life span). Yet, it also dictates that immediate reproductive success in captivity must occur, given the one year lifespan of the pupfish. Second, reintroduction of captive-reared DHP to the wild should be much easier than it has been for the condor. Reintroduction of condors has been on-going for two decades without achieving a self-supporting population due to poisoning from ingestion of lead fragments in their food, excessive tameness of released birds, parents feeding microtrash to nestlings, and other causes of mortality (Meretsky et al., 2000; Walters et al., 2010). DHP habitat is protected and threats to the species should be easier to control, at least in theory.

As a result of the potential for fast population growth in captivity, it is not too late to rescue the Devils Hole pupfish from extinction. Needed now to ensure success is a diagnosis of the causes of decline in Devils Hole in order to recover the wild population, an evaluation of the extent that the DHP harbors a significant genetic load and whether this requires a genetic restoration strategy (Martin et al., 2012), an analysis of the risks (e.g., introduction of diseases or parasites) and benefits (e.g., genetic and demographic rescue) of connectivity between the captive population and Devils Hole, and an evaluation of locations for new refugia to introduce the pupfish and better analysis of why refugia failed in the past. Of key importance will be maintaining the wild pupfish population in Devils Hole, while launching the new captive breeding facility.