Beyond theory to application and evaluation: Diffusion approximations for population viability analysis

Census data on endangered species are often plagued by problems that make quantitative population viability analysis (PVA) a challenge. This paper addresses four such problems: sampling error, density dependence, nonstable age structure, and population supplementation that masks the true population status. Estimating trends and extinction risks using such corrupted data presents serious parameter estimation difficulties. Here I review diffusion approximation (DA) methods for estimating population status and risks from time series data. A variety of parameterization methods are available for DA models; some correct for data corruption and others do not. I illustrate how stochastic Leslie matrix models can be used to evaluate the performance of a proposed DA model and to select among different DA parameterization methods for a given application. Presenting the uncertainty in estimated risks is critical, especially when the data are highly corrupted and estimated parameters are more uncertain. Using a Bayesian approach, I demonstrate how the level of data support for different risk levels can be calculated using DA parameter likelihood functions.