Dispersal per recruit: An efficient method for assessing sustainability in marine reserve networks

Marine reserves are an increasingly important tool for the management of marine ecosystems around the world. However, the effects of proposed marine reserve configurations on sustainability and yield of populations are typically not estimated because of the computational intensity of direct simulation and uncertainty in larval dispersal and density-dependent recruitment. Here we develop a method for efficiently assessing a marine reserve configuration for persistence and yield of a population with sedentary adults and dispersing larvae. The method extends the familiar sustainability criteria of individual replacement for single populations based on eggs-per-recruit (EPR) to spatially distributed populations with sedentary adults, a dispersing larval phase, and limited carrying capacity in the settlement-recruit relationship. We refer to this approach as dispersal-per-recruit (DPR). In some cases, a single DPR calculation, based on the assumption that post-settlement habitat is saturated (i.e., at maximum recruitment), is sufficient to determine population persistence, while in other cases further iterative calculations are required. These additional calculations reach an equilibrium more rapidly than a full simulation of age- or size-structured populations. From the DPR result, fishery yield can be computed from yield-per-recruit (YPR) at each point. We assess the utility of DPR calculations by applying them to single reserves, uniformly distributed systems of reserves, and randomly sized and spaced systems of reserves on a linear coast line. We find that for low levels of EPR in fished areas (e.g., 10% or less of the natural, unfished EPR when post-settlement habitats are saturated by 35% of natural settlement), a single DPR calculation is sufficient to determine persistence of the population. We also show that, in uniform systems of reserves with finite reserve size, maximal fisheries yield occurs when the density of reserves is such that all post-settlement habitat is nearly saturated with settlers. Finally, we demonstrate the application of this approach to a realistic proposed marine reserve configuration