Abstract
Using J. Felsenstein's random selection diffusion in n- allele space, the hypothesis of L. Slobodkin and A. Rapaport that smaller evolutionary steps are more stable, is reexamined. The curvature scalar of the diffusion plays a role both as a measure of the twisting effects of natural selection on genetic drift and as an important parameter in the asymptotic sojourn-time formula of Y. Takahashi and S. Watanabe. Examples which are drawn upon to demonstrate these responses to selection include soft coral chemical ecology on the Great Barrier Reef, diseases of scleractinian corals, mass mortality of Diadema antillarum, and others. The major conclusion is that small steps are stabilizing and large ones are not, and that this is robust.
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Antonelli, P., Sammarco, P.W. Evolution Via Random Walk on Adaptive Landscapes. Open Systems & Information Dynamics 6, 47–68 (1999). https://doi.org/10.1023/A:1009624217358
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DOI: https://doi.org/10.1023/A:1009624217358