Defining patch contribution in source-sink metapopulations: the importance of including dispersal and its relevance to marine systems

In metapopulations, individual patch contribution (source or sink) is typically calculated as a patch growth rate (the "intrinsic" lambda, lambda(I)) dependent only upon local demographics. We demonstrate that when dispersal is explicitly included in the model, the growth rates for all patches calculated in an analogous manner (the "observed" lambda, lambda(O)) equilibrate to the overall metapopulation growth rate and thus no longer serve as a useful reflection of the demographic and dispersive characteristics of a given patch. In these situations we suggest an alternative method of estimating patch contribution (the "contribution" lambda, lambda(C)) in which a patch is decremented for losses that occur within it and credited for gains that occur anywhere in the metapopulation because of it. We compare values of lambda(I), lambda(O), and lambda(C) for individual patches in discrete-time density-independent metapopulation models of two organisms with very different life histories, mayflies with adult dispersal, and reef fish with larval dispersal. Results confirm that when dispersal is included only lambda(C) clearly indicates the contribution of a particular patch. lambda(I)-lambda(C) comparisons indicate that inclusion of dispersal in the mayfly model was only important if connectivity patterns were random or directional. In the reef fish model, however, results were very different when dispersal was included and there were many cases of patches being misidentified (e.g., as a source when it was really a sink) depending upon the metric used (lambda(I) or lambda(C)). Our results demonstrate the importance of including dispersal in metapopulation models when considering the contribution of individual patches.