Estimating dispersal kernels using genetic parentage data

Dispersal kernels are the standard method in biology for describing and predicting the relationship between dispersal and distance. Statistically fitted dispersal kernels allow observations of a limited number of dispersal events to be extrapolated across a wider landscape, and form the basis of a wide range of theories and methods in ecology, evolution and conservation. Genetic parentage data are an increasingly common source of dispersal information, particularly for species where dispersal is difficult to observe directly. In particular, parentage analysis is now routinely applied to coral reef fish, whose larvae can potentially disperse over many kilometres, and are too small to track in situ. It is not straightforward to estimate dispersal kernels from parentage data, and existing methods all have substantial limitations. These include the omission of important population processes such as density-dependent mortality, and data on unassigned juveniles. Here we develop and proof a new likelihood estimator for fitting dispersal kernels to parentage data, applying it to simulated parentage datasets for coral reef fish on the Great Barrier Reef (GBR). The method incorporates a series of factors not previously considered in other methods: the partial sampling of adults and juveniles on sampled sites; the existence of unassigned dispersers from unsampled habitat patches; and post-settlement processes (e.g. density-dependent mortality) that follow dispersal but precede parentage sampling. Including these additional factors requires an estimate of adult populations on unsampled habitat patches, but the result is a superior estimate of dispersal kernels and mean dispersal distances. Our power analyses suggest that the parentage datasets currently available for reef fishes are large enough to fit accurate dispersal kernels. Based on the analyses in one particular region of the GBR, parentage sampling should be distributed equally between adults and juveniles, and should sample more than 3% of the adult population. However, while the resulting dispersal kernels offer reasonable estimates of mean dispersal, they fail to capture important variation in realistic dispersal patterns