The effects of dispersal patterns on marine reserves: does the tail wag the dog?

The concept of marine reserves as a method of improving management of fisheries is gaining momentum. While the list of benefits from reserves is frequently promoted, precise formulations of theory to support reserve design are not fully developed. To determine the size of reserves and the distances between reserves an understanding of the requirements for persistence of local populations is required. Unfortunately, conditions for persistence are poorly characterized, as are the larval dispersal patterns on which persistence depends. With the current paucity of information regarding meroplanktonic larval transport processes, understanding the robustness of theoretical results to larval dispersal is of key importance. From this formulation a broad range of dispersal patterns are analyzed. Larval dispersal is represented by a probability distribution that defines the fraction of successful settlers from an arbitrary location, the origin of the distribution, to any other location along the coast. While the effects of specific dispersal patterns have been investigated for invasion processes, critical habitat size and persistence issues have generally been addressed with only one or two dispersal types. To that end, we formulate models based on integrodifference equations that are spatially continuous and temporally discrete. We consider a range of dispersal distributions from leptokurtic to platykurtic. The effect of different dispersal patterns is considered for a single isolated reserve of varying size receiving no external larvae, as well as multiple reserves with varying degrees of connectivity. While different patterns result in quantitative differences in persistence, qualitatively similar effects across all patterns are seen in both single- and multiple reserve models. Persistence in an isolated reserve requires a size that is approximately twice the mean dispersal distance and regardless of the dispersal pattern the population in a patch is not persistent if the reserve size is reduced to just the mean dispersal distance. With an idealized coastline structure consisting of an infinite line of equally spaced reserves separated by regions of coastline in which reproduction is nil, the relative settlement as a function of the fraction of coastline and size of reserve is qualitatively very similar over a broad range of dispersal patterns. The upper limit for the minimum fraction of coastline held in reserve is about 40%. As the fraction of coastline is reduced, the minimum size of reserve becomes no more than 1.25 times the mean dispersal distance.