Application of diffusion approximation for risk assessments of sea turtle populations.

Population viability analysis (PVA) to forecast extinction risk is a commonly used tool in decision- and policy-making processes of governments and conservation organizations. A drawback to PVA is the high degree of uncertainty in these forecasts due to both population stochasticity and parameter estimation uncertainty. With sparse or noisy data, extinction probabilities frequently have 95% confidence intervals ranging from 0 to 1. To make stochastic simulation results more interpretable, we present a new metric, susceptibility to quasi-extinction (SQE), to assess whether or not a population is at risk of declining to a prespecified level (quasi-extinction). Following standard methods for diffusion approximation of extinction risk, we use a parametric bootstrap to determine the 95% CI for the probability of quasi-extinction. SQE is the proportion of this parametric bootstrap that indicates a high (defined as > or = 0.90) probability of quasi-extinction, resulting in a point estimate that integrates both parameter uncertainty and stochasticity in extinction forecasting. We demonstrate the application of the metric with sea turtle nest census data, which have a high degree of year-to-year variance and represent only a small fraction of the total population. Using population simulations, we found that for these types of data a critical SQE value of 0.40 corresponds to populations that have a true risk of quasi-extinction. The metric has an accuracy of > 80%, which can be increased further by lowering the 0.40 threshold and trading off Type I error (considering a population to be "not at risk" when it actually is) and Type II error (considering a population to be "at risk" when it actually is not), giving managers a flexible and quantitative tool for assessments of population status.