When does spillover indicate benefits to fish abundance and catch?

Abstract Spillover is a term commonly applied to the movement of fish from inside a closed area to areas open to fishing outside of the closure and is usually identified by gradients in abundance or catch rates near the boundaries. It is commonly assumed that such gradients indicate that the closed area has benefitted the fishery and the total abundance of fish. We explore this assumption for spatially explicit models of closed areas with different intensities of fishing and fish movement and find that such gradients will be expected any time there is higher abundance inside the closed area. However, under most conditions it does not indicate a benefit to the fishery either in terms of total catch of catch rate, and unless fishing is intense total abundance is not expected to rise significantly. We examine one specific case of estimates spillover from the Papahānaumokuākea marine monument, one the largest no-take areas in the world, and see no evidence of spillover for yellowfin tuna and very slight evidence for bigeye tuna. These results are consistent with the theoretical models, the biology of the species and the intensity of fishing.