The Devils Hole pupfish (Cyprinodon diabolis) is restricted to one wild population in a single aquifer-fed thermal pool in the Desert National Wildlife Refuge Complex in Nye County, Nevada. It lives primarily in the upper 10 m of Devils Hole, a pool and limestone cavern with a surface area of 50 m2 that is located 17 m below the land surface. Pupfish spawning takes place predominately on a shallow (∼0.35 m), submerged ∼2 × 4 m shelf. It is the only fish in Devils Hole, where it has resided since climate warming caused regional drying beginning ∼20,000 years ago.

Since 1995, the pupfish has been in a nearly steady decline, where it was perched on the brink of extinction at 35–68 fish in 2013. A major strategy for conserving the pupfish has been the establishment of additional captive or “refuge” populations, but all ended in failure. In 2013 a new captive propagation facility designed specifically to breed pupfish was opened.

A major question around establishing this captive population was how to best extract wild pupfish for breeding purposes without unduly accelerating the extinction risk for the population in Devil’s Hole. Dr. Steven Beissinger, Professor of Conservation Biology at the University of California, Berkeley, constructed a population variability analysis (PVA) using @RISK to better inform this dilemma.

## @RISK Models Pupfish Path to Extinction in the Wild

To create his models, Dr. Steven Beissinger gathered data from seasonal pupfish population counts, and used 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.

He then calculated the rate of population growth (r = ln(Nt+1/Nt)) from pairs of counts of population size (N) from consecutive years (t).

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 (εi) 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.

The counts used by Dr. Beissinger in his model included variation in population fluctuations due to: (1) demographic, environmental, and genetic stochasticity; (2) catastrophes; and (3) sampling error. The model showed that most simulated populations of the pupfish became extinct within 50 years. 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.

Next, to evaluate the effects of different strategies for removing individuals to initiate a captive breeding program on the wild population, Dr. Beissinger used the models that best described the pupfish 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.

*"@RISK makes Monte Carlo processes easy for professionals and students to understand. The nice thing about it, from my perspective, is that it functions within Excel, which makes visualizing the information a lot easier and more intuitive for people. It makes what would otherwise be a lot of tedious steps a lot easier to do."*

*Dr. Steven Beissinger
*

**Conservation Biology, University of California Berkeley**

### How Best To Harvest?

Dr. Beissinger also wanted to answer the question of which life-stage should pupfish be harvested. “We wanted to know what life stage—eggs, juvenile or adults, is the population growth least affected by removing,” he says.

To do this, he developed a deterministic demographic model created 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).

He sought opinions for constructing and parameterizing the model from 15 Devil’s Hole pupfish (DHP) and fisheries experts that attended the DHP Risk Analysis Workshop (8 Nov. 2013). He 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. This approach allowed exploration of the potential parameter space, resulting distribution of reproductive value and elasticity for stage classes, and relationships among them.

The model showed that removing pupfish eggs had the least effect on the wild population. Indeed, Dr. Beissinger calculated that removing 25 eggs for captive breeding is equivalent to removing a single adult in terms of its influence on population dynamics.

The modeling work done by Dr. Beissinger has helped to inform decisions made by the U.S. Fish and Wildlife Service to conserve the DHP, which has now begun to remove pupfish eggs from Devil’s Hole to start a captive population in its state-of-the-art breeding facility. “The modeling helped everyone to see what some of the trade-offs would be and made the various outcomes more explicit,” says Dr. Beissinger. Since these efforts, the pupfish population has rebounded, and stabilized at just below 100 individuals. The removal of eggs proved to be a safe and effective way to start a captive population without damaging the wild cohort.

### Decades of Endangered Species Analysis with @RISK

Since the early 1990’s when he first discovered the software tool, Dr. Beissinger has used @RISK in his in ecological conservation. “The principles of thinking about risk and reward in business are the same principals in managing wildlife,” he says. “We’re basically taking rates of past performance—whether it’s survival, reproduction, or revenue--and projecting them into the future.”

In addition to Dr. Beissinger’s work on the DHP, he’s used @RISK to help manage other Endangered Species, including analyses of the Puerto Rican parrot (with only about 240 living individuals) and the snail kite, (restricted to only 400-500 breeding pairs). He values the tool for its ease of use and transparency, and for any problem that needs Monte Carlo simulation. In addition to its usefulness as a data-crunching tool for his research, “@RISK makes Monte Carlo processes easy for professionals and students to understand,” says Dr. Beissinger. “The nice thing about it, from my perspective, is that it functions within Excel, which makes visualizing the information a lot easier and more intuitive for people. It makes what would otherwise be a lot of tedious steps a lot easier to do.”