Bayesian analysis of size-dependent overwinter mortality from size-frequency distributions

Understanding the relationship between body size and mortality is an important problem in ecology. We introduce a novel Bayesian method that can be used to quantify this relationship when the only data available are size-frequency distributions of unmarked individuals measured at two successive time periods. The inverse Gaussian distribution provides a parametric form for the statistical model development, and we use Markov chain Monte Carlo methods to evaluate posterior distributions. We illustrate the method using data on threespine stickleback (Gasterosteus aculeatus) collected before and after the winter season in an Alaskan lake. Our method allows us to compare the intensity of size-biased mortality in different years. We discuss generalizations that include more complicated relationships between size and survival as well as time-series modeling.