Predicting Yellow Perch Population Responses Using a Density-Dependent Age-Structured Matrix Projection Model: How Many Annual Data Points Are Needed?

Abstract

Density-dependent matrix projection models are commonly used to simulate fish population dynamics. Much of the data needed to specify the density-dependent relationships are annual; thus, determining how many years of data are needed to accurately specify these relationships is critical. We used 200 years of simulated output from an individual-based model (IBM) as “data,” and we estimated density-dependent age-0 survival, yearling survival, and adult growth (affected maturity and fecundity) for an age-structured matrix projection model. We divided the 200-year baseline simulation into 34 data sequences: three 60-year sequences, four 40-year sequences, nine 20-year sequences, and eighteen 10-year sequences. We refitted the density-dependent survival and growth functions to each reduced data sequence and compared their shapes; we then substituted the refitted functions into a matrix model specific to each data sequence. We compared key output variables for the baseline simulations and the responses to decreased egg survival among the IBM, the matrix model based on 200 years, and the 34 matrix models based on the different data sequences. The variation in shape and the number of sequences that resulted in density-independent survival and depensatory growth increased greatly for the 20- and 10-year sequences. Predicted population dynamics under baseline and predicted responses to reduced egg survival were reasonably similar to those under the IBM and matrix model based on 200 years for the 60- and 40-year sequences but showed increasing divergence for the 20- and 10-year sequences. We suggest that 40 or more years of annual data will allow for reasonable estimation of density-dependent relationships in age-structured matrix projection models. Many applications of similar models used in management are based on fewer than 40 years of data, and yet their use is intended to generate predictions with sufficient precision and accuracy to resolve differences between relatively small changes in survival rates.