Spatial delay-difference models for estimating spatiotemporal variation in juvenile production and population abundance

Abstract

Many important ecological questions require accounting for spatial variation in demographic rates (e.g., survival) and population variables (e.g., abundance per unit area). However, ecologists have few spatial modelling approaches that (i) fit directly to spatially referenced data, (ii) represent population dynamics explicitly and mechanistically, and (iii) estimate parameters using rigorous statistical methods. We therefore demonstrate a new and computationally efficient approach to spatial modelling that uses random fields in place of the random variables typically used in spatially aggregated models. We adapt this approach to delay-difference dynamics to estimate the impact of fishing and natural mortality, recruitment, and individual growth on spatial population dynamics for a fish population. In particular, we develop this approach to estimate spatial variation in average production of juvenile fishes (termed recruitment), as well as annual variation in the spatial distribution of recruitment. We first use a simulation experiment to demonstrate that the spatial delay-difference model can, in some cases, explain over 50% of spatial variance in recruitment. We also apply the spatial delay-difference model to data for rex sole (Glyptocephalus zachirus) in the Gulf of Alaska and show that average recruitment (across all years) is greatest near Kodiak Island but that some years show greatest recruitment in Southeast Alaska or the western Gulf of Alaska. Using model developments and software advances presented here, we argue that future research can develop models to approximate adult movement, incorporate spatial covariates to explain annual variation in recruitment, and evaluate management procedures that use spatially explicit estimates of population abundance.