Calculating effective growth rate from a random Leslie model: Application to incidental mortality analysis

Abstract

Demographic models are commonly used to study cetacean population dynamics and are characterized by a wide range of age classes. The primary building blocks are age-specific survival or mortality and birth rates, which can be combined using a Leslie matrix protocol to provide estimates of maximum possible rates of increase for population size. In this context, specific mortality data are valuable for modeling the viability of threatened species. Depletion of prey, pollution, and other anthropogenic disturbances are believed to have contributed to the decline of populations, but the evidence is less conclusive for these factors than for bycatch. In an attempt to estimate a population growth rate that incorporates uncertainties in vital parameters, we apply a random Leslie analysis to calculate effective growth rate for the time-dependent mean-value population. Here we provide the algorithm to implement it for a general 13×13 random survival model. An effective growth rate can be characterized by studying the time evolution of the mean-value population vector state (in an age-structured description). We show that the asymptotic behavior of the mean-value vector state, which characterizes the population growth rate when the model has random vital parameters, exhibits a value that is below previously expected potential estimations. We demonstrate the procedure using bibliographic revision data of the harbor porpoise (Phocoena phocoena) in Canadian waters, subjected to incidental mortality.<br />