Spatially explicit modeling of metapopulation dynamics of broadcast spawners and stabilizing/destabilizing effects of heterogeneity of quality across local habitats

Abstract

Many coastal invertebrate species are broadcast spawners. These species have a highly sedentary adult stage and disperse by oceanic transport of planktonic larvae. One commercially important group of broadcast spawners is abalones, which live in suitable habitat patches of rock reefs that are discretely distributed. Because of these life-history and habitat characteristics, abalones tend to exhibit a metapopulation structure. Despite fisheries management and the release of juveniles, wild populations of broadcast spawners have undergone dramatic reductions in density due to overexploitation, which has been partly attributed to a failure to account for spatial structure. To clarify the relationship between the persistence of a metapopulation and the bottleneck that occurs during reproduction and dispersal processes caused by spatial structure, we developed a spatially explicit metapopulation model accounting for the effects of both life history and fishery pressure. By analyzing the model, we derived a metric to evaluate metapopulation quality as the leading eigenvalue of a non-negative matrix (the landscape matrix). Using this measure, we clarified that the effect of spatial structure on metapopulation stability is explained well by the mean and variance of parameter values across patches under the condition in which the heterogeneity of the metapopulation network is weak. In particular, the presence of both a higher average and higher variance of quality in the landscape could indicate stable fishery stocks under certain conditions. For example, when the decline in the mean longevity of local patch due to the fishery pressures gradually diminishes, the rescue effects by good patches would work more effectively than the negative effect of bad patches and then the stabilizing effect of spatial heterogeneity could be observed in a metapopulation. Furthermore, optimal patch characteristics for the improvement of quality strongly depend on specific parameter values. For example, when adult fertility is improved, a patch with higher “source” ability is more suitable. In contrast, when the settlement success of planktonic larvae is improved or fishery pressure is reduced, a patch with higher “buffer” ability is more suitable for the improvement of fishery management.