Spatiotemporal modeling of mature‐at‐length data using a sliding window approach

Assessing maturity status of fish and invertebrate species is important for understanding population dynamics with results (e.g., estimates of reproductive potential) often used to inform fisheries management strategies (e.g., the setting of minimum legal size requirements for fishing). Maturity rates may vary substantially across a population's range, as well as between years. In addition, maturity data are typically obtained from fisheries‐independent surveys that may be incomplete (or missing) from year to year. Here we propose a spatial generalized linear mixed model (GLMM) framework for maturity data that includes spatially correlated random effects to address variations in space, and a sliding window approach to deal with unbalanced maturity data in both space and time. We demonstrate, with both real data and a simulation study, that this combined approach results in unbiased estimates of important growth parameters. Results of using our spatial GLMM framework with Greenland halibut (Rheinhardtius hippoglossoides) mature‐at‐length data from surveys of the eastern Canadian Arctic show that females mature at a much larger size than do males. The length at which 50% of the stock is mature (L50$$ {L}_{50} $$) is found to be higher in Baffin Bay compared to Davis Strait, and a declining trend in the L50$$ {L}_{50} $$ in recent years is revealed for both sexes. Our proposed methodology extends far beyond our current application in being useful for analyzing unbalanced spatiotemporal data from an array of diverse scientific fields.