Multiple hypothesis testing and the declining-population paradigm in Steller sea lions.

We describe a novel spatially and temporally detailed approach for determining the cause or causes of a population decline, using the western Alaskan population of Steller sea lions (Eumetopias jubatus) as an example. Existing methods are mostly based on regression, which limits their utility when there are multiple hypotheses to consider and the data are sparse and noisy. Our likelihood-based approach is unbiased with regard to sample size, and its posterior probability landscape allows for the separate consideration of magnitude and certainty for multiple factors simultaneously. As applied to Steller sea lions, the approach uses a stochastic population model in which the vital rates (fecundity, pup survival, non-pup survival) at a particular rookery in each year are functions of one or more local conditions (total prey availability, species composition of available prey, fisheries activity, predation risk indices). Three vital rates and four scaling functions produce twelve nonexclusive hypotheses, of which we considered 10; we assumed a priori that fecundity would not be affected by fishery activities or predation. The likelihood of all the rookery- and year-specific census data was calculated by averaging across sample paths, using backward iteration and a beta-binomial structure for observation error. We computed the joint maximum likelihood estimates (MLE) of parameters associated with each hypothesis and constructed marginal likelihood curves to examine the support for each effect. We found strong support for a positive effect of total prey availability on pup recruitment, negative effects of prey species composition (pollock fraction) on fecundity and pup survival, and a positive effect of harbor seal density (our inverse proxy for predation risk) on non-pup survival. These results suggest a natural framework for adaptive management; for example, the areas around some of the rookeries could be designated as experimental zones where fishery quotas are contingent upon the results of pre-fishing season survey trawls. We contrast our results with those of previous studies, demonstrating the importance of testing multiple hypotheses simultaneously and quantitatively when investigating the causes of a population decline.