Modeling spatially-varying ecological relationships using geographically weighted generalized linear model: A simulation study based on longline seabird bycatch

Geographically weighted regression (GWR) is a relatively new technique to explore spatially-varying relationships between biological and environmental processes. It allows parameters to vary over space and assumes data to follow a normal distribution. We extend GWR to a geographically weighted generalized linear model (GW-GLM) by incorporating statistical distributions other than the normal distribution (i.e., the binomial distribution). We demonstrate the application of GW-GLM with an empirical example, U.S. Atlantic pelagic longline seabird bycatch. Due to the high percentage of zero observations in the seabird bycatch data, we analyzed the positive catch rates (number of seabirds caught per 1000 hooks) and the probability of catching a seabird separately. Parameter estimates exhibited considerable spatial variation, especially for target catch rate when analyzing the positive catch data, and for intercept, water depth and water temperature when estimating the probability of catching seabirds. We compared model performance of GW-GLM with a global generalized linear model, a mixed effect model with a random areal effect, and a spatial expansion model that is an early technique to model spatially-varying ecological relationships by modeling each of the parameters as a function of location. The GW-GLM performed best. Simulations with hypothetical datasets having different percentages of zeros showed that, regardless of the zero percentage in the data, GW-GLM performed best on average. Applying a range of bandwidth indicated that the GW-GLM was more robust to an overestimated bandwidth than an underestimated bandwidth.