Problems in Extinction Model Selection and Parameter Estimation

Abstract

It is a vexing problem to achieve a consensus about the proper scientific way to assess population viability for habitat conservation plans. Rather than a hypothesis-testing approach, here it is proposed to select population models, estimate extinction parameters, and assess prediction uncertainty using a pragmatic, empirical Bayesian approach. The simplest usable models include the effects of population growth, r; carrying capacity, K; Allee threshold, N(A); and environmental stochasticity, v(r). Analytic predictions of expected extinction times are available for such models. Models that are more complex can be elaborated from this basis. Selection from a hierarchy of nesting population models can often be done through the evaluation of parameters. The estimation of the most important extinction parameters can be undertaken in a variety of ways. Time series can be analyzed to estimate r(d), v(r), rho, and K. Habitat models and individualistic population models may help estimate N(A) and K and demographic stochasticity. Fine-scale biogeography and climatological data may be useful in the estimation of a variety of parameters. Because it takes many years to estimate extinction parameters accurately for a given population of interest, the most efficient estimation procedures are desirable. I propose the use of prior information from an (as yet nonexistent) population biology database. The accumulation of local information through monitoring will improve our estimates allowing adaptive management. Uncertainty in the estimates will always remain, but it may be quantified by the posterior distributions. A crude example is discussed using treefrog population data. Although the motivations, beliefs, and biases of competing stakeholders will differ, a habitat conservation plan could accommodate this variation in the prior distributions. Field experience from monitoring will increasingly clear up any discrepancies between the opposing beliefs and the real ecosystem. As the world is an uncertain place and because there is no universal scientific method, there will always be controversy and surprises. The best we can do is (1) agree about our prior information, (2) agree about the strategy of model selection and parameter estimation, and (3) agree about our strategy for adaptive management. Perhaps the greatest impediment to such prior agreements for HCPs is the likely paranoia inspired by the use of unfamiliar statistical methodology. We need to train students of ecology in a more flexible and deeper understanding of statistics and philosophy of science.