A comparison of individual-based and matrix projection models to applied to fish population and community dynamics

Abstract

Matrix projection models and individual-based models (IBM) are commonly used for the analysis and management of fish populations. Matrix models break down the population into age or stage classes, while IBMs track individuals. I perform a series of quantitative comparisons between the predictions of the two modeling approaches using the IBM as the standard of comparison to demonstrate when individual variation, species interactions, and spatial heterogeneity adversely affect matrix model performance. I first evaluate the matrix approach for predicting yellow perch population responses when perch are involved in size-specific predator-prey interactions with walleye. I created density-dependent and stochastic age-structured and stage-within-age matrix models from an Oneida Lake walleye-yellow perch IBM, and then changed perch survival rates within the matrix models and IBM and compared their predicted responses. The matrix models simulated yellow perch responses reasonably well when density-dependent YOY survival was correctly defined. At least 20 years of data (IBM output) were needed to correctly estimate the density-dependent relationships in the matrix models. Second, I developed a 2-species matrix model by linking the elements between perch and walleye matrix models. The 2-species model simulated yellow perch prey responses reasonably well, but was unable to correctly predict walleye predator responses. Third, I developed a new IBM that simulated a 6-species tidal marsh community on a fine-scale spatial grid of habitat cells. The IBM was used to scale individual-level effects of lowered dissolved oxygen and habitat degradation to population-level responses, and used to estimate relatively simple stage-based matrix models for grass shrimp and gulf killifish populations. Equilibrium analysis of the simple matrix models was insufficient for predicting population responses. This study showed that stochastic, density-dependent matrix projection models were able to mimic density- dependent survival processes and species interactions relatively well, while equilibrium analysis of simple matrix models was inadequate. The matrix approach consistently had trouble estimating density-dependent and inter-specific growth relationships that were important for accurate model predictions. I recommend the use of IBMs and relatively complicated matrix models (stage-within-age, stochastic, density-dependent, multispecies) for simulation of fish population and community dynamics.