Summary
A stability analysis for geographic displacement clines between competing allospecies is presented. The competition model incorporates the effects of annual dispersal and of selective recruitment determined by geographically varying conditions at the breeding sites. It is assumed that a species gains a local competitive advantage wherever it attains sufficient numerical predominance. This assumption is valid when the species crosspair but the hybrids produced are not recruited into the adult population, because the minority species loses proportionately more of its reproductive potential.
It is shown that no stable equilibria occur when the competitive balance is independent of location, but that even a slight geographic variation in the competitive balance allows stable equilibria. The greater the length of the combined breeding ranges of the two species, the smaller the geographic shift in competitive balance needed to produce stability.
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Anderson, R.F.V. Stability of displacement clines arising in allospecies competition. J. Math. Biology 6, 131–144 (1978). https://doi.org/10.1007/BF02450784
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DOI: https://doi.org/10.1007/BF02450784