Density Dependent, Age Structured Population Models
We discuss our long-term program to understand the dynamics of general classes of density dependent, age structured (Leslie) population models. For some families we find a plethora of extremely complicated dynamical behaviors, several of which have not been previously observed in age structured population models, and which may give rise to new paradigms in population biology. We attempt to provide a rigorous foundation for the population biologist's notion of "ergodicity" by constructing SRB or natural measures for some of these models.
Using 20 years of population data from a local research stream, my Penn State fisheries colleague Robert Carline has discovered density (and seasonal stream flow) dependence of some survival probabilities for brown trout. I will discuss our preliminary progress in modeling this trout population using a density dependent, age structured model.