Adaptive Dynamics in a 2-patch Environment: a Simple Model for Allopatric and Parapatric Speciation

Adaptation to an environment consisting of two patches (each with different optimal strategy) is investigated. The patches have independent density regulation ('soft selection'). If the patches are similar enough and migration between them is strong, then evolution ends up with a generalist ESS. If either the difference between the patches increases or migration weakens, then the generalist strategy represent a branching singularity: The initially monomorphic population first evolves towards the generalist strategy, there it undergoes branching, and finally two specialist strategies form an evolutionarily stable coalition. Further increasing the between-patch difference or decreasing migration causes the generalist to lose its convergence stability as well, and an initially monomorphic population evolves towards one of the specialists optimally adapted to one of the two patches. Bifurcation pattern of the singularities is presented as a function of patch difference and migration rate.
Connection to speciation theory is discussed. The transition from the generalist ESS to the coexisting pair of specialist strategies is regarded as a clonal prototype of parapatric (if the between-patch difference increases) or allopatric (if the migration decreases) speciation. We conclude that the geographic and the competitive speciation modes are not distinct classes.

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