Incorporating model selection and decision analysis into population dynamics modeling

Abstract

Model selection tools are an integral part of biological inference. However, with the advent of recent software packages, researchers may be placing less thought into model selection uncertainty. After reviewing the existing literature on these methods, evidence for three specific biological processes are examined: intraspecific competition, population catastrophes, and Allee effects. Building on previous research, multiple models of west coast harbor seal population dynamics are compared using four model selection criteria (Akaike's Information Criterion, Schwarz Information Criterion, Deviance Information Criterion, Bayes factor). Bayesian model selection tools appear to favor intraspecific competition to a greater extent than frequentist tools. When random effects are included in the population growth rate, approximately equal weight is given to the model with competition and a model without competition. After developing state-space population models that include catastrophes, the catastrophe model is applied to four populations of harbor seals on the west coast. Because complete population time series do not exist, time series of pup production are used as an index of the total population. The catastrophe model allows the probability of a catastrophe occurring to vary by ecosystem (California, Alaska), but assumes that process error variances are shared among all populations. For the California populations, the catastrophes appear to reduce the pup production by and average of 75% percent per year. The Alaskan populations continue to decline, but do not appear to be strongly influenced by catastrophes. As a third question, the rarity of Allee dynamics is addressed using several thousand population time series in the Global Population Dynamics Database. Using a simple extension of the logistic model that allows for depensation, I illustrate that the Bayes factor estimates the frequency of Allee effects to be 5-6 times larger when compared to estimates from likelihood ratio tests. Because all models compared are nested, Bayesian model averaging is used to calculate parameter estimates across models.