Restoration of eastern oyster populations with positive density dependence.

Positive density dependence (i.e., Allee effects) can create a threshold of population states below which extinction of the population occurs. The existence of this threshold, which can often be a complex, multi-dimensional surface, rather than a single point, is of particular importance in degraded populations for which there is a desire for successful restoration. Here, we incorporated positive density dependence into a closed, size- and age-structured integral projection model parameterized with empirical data from an eastern oyster, Crassostrea virginica, population in Pamlico Sound, North Carolina, USA. To understand the properties of the threshold surface, and implications for restoration, we introduced a general method based on a linearization of the threshold surface at its unique, unstable equilibrium. We estimated the number of oysters of a particular age (i.e., stock enhancement), or the surface area of dead shell substrate required (i.e., habitat enhancement) to move a population from an extinction trajectory to a persistence trajectory. The location of the threshold surface was strongly affected by changes in the amount of local larval retention. Traditional stock enhancement with oysters <1 yr old (i.e., spat) required three times as many oysters relative to stock enhancement with oysters between ages 3 and 7 yr old, while the success of habitat enhancement depended upon the initial size distribution of the population. The methodology described here demonstrates the importance of considering positive density dependence in oyster populations, and also provides insights into effective management and restoration strategies when dealing with a high dimensional threshold separating extinction and persistence.