Spatiotemporal predictions of bycatch (i.e., catch of nontargeted species) have shown promise as dynamic ocean management tools for reducing bycatch. However, which spatiotemporal model framework to use for generating these predictions is unclear. We evaluated a relatively new method, Gaussian Markov random fields (GMRFs), with two other frameworks, generalized additive models (GAMs) and random forests. We fit geostatistical delta-models to fisheries observer bycatch data for six species with a broad range of movement patterns (e.g., highly migratory sea turtles versus sedentary rockfish) and bycatch rates (percentage of observations with nonzero catch, 0.3%–96.2%). Random forests had better interpolation performance than the GMRF and GAM models for all six species, but random forests performance was more sensitive when predicting data at the edge of the fishery (i.e., spatial extrapolation). Using random forests to identify and remove the 5% highest bycatch risk fishing events reduced the bycatch-to-target species catch ratio by 34% on average. All models considerably reduced the bycatch-to-target ratio, demonstrating the clear potential of species distribution models to support spatial fishery management.