Fitting state-space integral projection models to size-structured time series data to estimate unknown parameters

Integral projection models (IPMs) have a number of advantages over matrix-model approaches for analyzing size-structured population dynamics, because the latter require parameter estimates for each age or stage transition. However, IPMs still require appropriate data. Typically they are parameterized using individual-scale relationships between body size and demographic rates, but these are not always available. We present an alternative approach for estimating demographic parameters from time series of size-structured survey data using a Bayesian state-space IPM (SSIPM). By fitting an IPM in a state-space framework, we estimate unknown parameters and explicitly account for process and measurement error in a dataset to estimate the underlying process model dynamics. We tested our method by fitting SSIPMs to simulated data; the model fit the simulated size distributions well and estimated unknown demographic parameters accurately. We then illustrated our method using nine years of annual surveys of the density and size distribution of two fish species (blue rockfish, Sebastes mystinus, and gopher rockfish, S. carnatus) at seven kelp forest sites in California. The SSIPM produced reasonable fits to the data, and estimated fishing rates for both species that were higher than our Bayesian prior estimates based on coast-wide stock assessment estimates of harvest. That improvement reinforces the value of being able to estimate demographic parameters from local-scale monitoring data. We highlight a number of key decision points in SSIPM development (e.g., open vs. closed demography, number of particles in the state-space filter) so that users can apply the method to their own datasets.