We introduce a model of fishing behavior that features costly targeting of a spatially and temporally heterogeneous, multiple-species fish stock. We characterize fishing behavior under species-specific regulations including time-area-depth closures, per-trip landings limits and tradable harvest permits. Our behavioral model yields a system of Kuhn-Tucker necessary conditions which form the basis of our empirical estimation. Data from the Gulf of Mexico commercial reef fish fishery are used to estimate the model. The estimated harvest technology exhibits local weak output disposability which are linked to spatially and temporally dependent stock conditions in the reef fish fishery. The model predicts harvests, discards and fishing profit across multiple species, and importantly across continuous space and time dimensions. Policy simulations further identify behavioral responses to closure regulations, individual tradeable quota management and recent sea turtle bycatch management rules which impose limits on fishing depth. Our model overcomes limitations of discrete choice spatial fishing behavioral models, and offers a powerful tool for improving regulation of spatially and temporally heterogeneous, multi-species fisheries.