A comparison of individual-based and matrix projection models for simulating yellow perch population dynamics in Oneida Lake, New York, USA

Abstract

Both individual-based models (IBMs) and matrix projection models are commonly used to simulate fish population dynamics. We questioned whether matrix models could be used to predict population responses of the prey in a highly coupled predator–prey system. The matrix approach was evaluated for predicting yellow perch population responses to changes in survival, and comparing the responses to those from a detailed IBM. The IBM explicitly modeled effects of walleye predation and competition with yellow perch, whereas the matrix models used averaged values, and in some cases density-dependent relationships, for survival, growth, and reproduction of yellow perch that implicitly included walleye effects. We used the output from a 200-year simulation of the IBM as data for estimating the elements of three alternative versions of a matrix projection model. We constructed an age-structured matrix model and two stage-within-age matrix models for yellow perch. The stage-within-age versions both represented the young-of-the-year (YOY) stages, but differed in the timestep used for updating their density-dependent relationships (annual or daily). The predictions of the matrix models were first compared with the IBM under baseline conditions to confirm that parameter estimation of the matrix models was reasonable. We then simulated reduced and increased egg or adult survival in each model, and compared the relative responses among the four models. Predicted yellow perch spawner abundance under baseline conditions was similar among the IBM and two matrix models that used annual density-dependence, but underestimated by the stage-within-age matrix model that used daily density-dependence. Averaged annual abundances, YOY and yearling survival rates, and sizes at age were generally similar between the IBM and matrix models under baseline conditions. Density-dependent YOY survival was critical for accurately predicting yellow perch responses to changed egg and adult survival rates. Predicted responses to changed survival rates from the stage-within-age matrix model with daily density-dependence differed most from the IBM, and consistently predicted changes in juvenile stage survival opposite to those predicted by the other models. The matrix models that used annual density-dependence predicted similar abundance responses as the IBM to changed egg and adult survival rates. If sufficient data are available, we recommend a population and multispecies modeling approach. If data are available only for the species of interest, then we favor the stage-within-age matrix model with annual density-dependence because the stage structure for YOY allows for flexibility and because it performed better than other matrix models when compared to the IBM.