Adaptive dynamics in a 2-patch environment:
a toy model for allopatric and parapatric speciation

Geza Meszena, Istvan Czibula and Stefan Geritz

Summary

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
represents a
branching singularity: The initially monomorphic population
first evolves towards the generalist strategy, there it
undergoes branching, and finally two specialist strategies form
an evolutionary stable coalition. Further increasing the
between-patch difference or decreasing migration causes the
generalist
to loose its convergence stability as well, and an initially
monomorphic
population evolves towards one of the specialists optimally
adapted to one of the two patches only. Bifurcation pattern of
the singularities is presented as a function of patch difference
and migration rate.

The transition from the generalist ESS to the coexisting pair of
specialist strategies is regarded a clonal prototype of
parapatric (if the difference increases) or allopatric (if the
migration decreases) speciation.