Characterizing the strength of density dependence in at-risk species through Bayesian model averaging

Developing effective conservation plans for at-risk species requires an understanding of the relationship between numbers of breeding adults and their subsequent offspring. In particular, establishing the degree to which density-dependent effects limit population size can be difficult due to errors in the data themselves, uncertainty in model parameters, and possible misspecification of model structure. Here we develop a Bayesian model averaging framework to fit four simple models of adult-offspring production and estimate the probabilities that negative (i.e., decreasing survival with increasing density) and positive (i.e., Allee effects) density dependence exists. As an example, we analyzed 48 at-risk populations of anadromous Chinook salmon (Oncorhynchus tshawytscha) from the northwestern United States. We found strong evidence that more than two-thirds of the populations exhibit negative density-dependent effects of adults. This result was somewhat unexpected given the large reductions in adult numbers relative to historical benchmarks, indicating that carrying capacity of spawning habitat has been reduced considerably. Approximately two thirds of the populations also had non-zero probabilities of positive density-dependent effects of adults, which could suggest that cumulative losses of spawning adults over the past century has led to decreased nutrient and energy subsidies from semelparous carcasses, and diminished bio-physical disturbance from nest-digging activity. Importantly, our analysis highlights the utility of Bayesian model averaging in a conservation context wherein errors in choosing the best model may have more severe consequences than errors in estimating model parameters themselves.