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The optimal probability and distance of dispersal largely depend on the risk to end up in unsuitable habitat. This risk is highest close to the habitat’s edge and consequently, optimal dispersal probability and distance should decline towards the habitat’s border. This selection should lead to the emergence of spatial gradients in dispersal strategies. However, gene flow caused by dispersal itself is counteracting local adaptation. Using an individual based model we investigate the evolution of local adaptations of dispersal probability and distance within a single, circular, habitat patch. We compare evolved dispersal probabilities and distances for six different dispersal kernels (two negative exponential kernels, two skewed kernels, nearest neighbour dispersal and global dispersal) in patches of different size. For all kernels a positive correlation between patch size and dispersal probability emerges. However, a minimum patch size is necessary to allow for local adaptation of dispersal strategies within patches. Beyond this minimum patch area the difference in mean dispersal distance between center and edge increases linearly with patch radius, but the intensity of local adaptation depends on the dispersal kernel. Except for global and nearest neighbour dispersal, the evolved spatial pattern are qualitatively similar for both, mean dispersal probability and distance. We conclude, that inspite of the gene-flow originating from dispersal local adaptation of dispersal strategies is possible if a habitat is of sufficient size. This presumably holds for any realistic type of dispersal kernel.
This thesis extends the classical theoretical work of Macevicz and Oster (1976, expanded by Oster and Wilson, 1978) on adaptive life history strategies in social insects. It focuses on the evolution of dynamic behavioural patterns (reproduction and activity) as a consequence of optimal allocation of energy and time resources. Mathematical modelling is based on detailed empirical observations in the model species Lasioglossum malachurum (Halictidae; Hymenoptera). The main topics are field observations, optimisation models for eusocial life histories, temporal variation in life history decisions, and annual colony cycles of eusocial insects.