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RESEARCH PRODUCT

Reply from m. Heino, j.a.j. Metz and v. Kaitala.

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Eva Kisdi clarifies the relationships between frequency dependence, optimization and ESSs. We basically agree with all her comments. However, some further clarification may be useful.In the first paragraph of Kisdi's letter, ESSs and optimal strategies are seemingly opposed by saying that `finding an optimal strategy is a considerably stronger result than finding an ESS'. Although this statement is factually correct, it might engender a suggestion that is slightly wrong. Conceptually, ESSs are always primary: only ESSs matter from the viewpoint of long-term evolution. Optimization is secondary only, and must be justified by an ESS argument that explicitly accounts for the ecology in which the evolutionary problem is embedded. When we approach the problem from this angle it is found that there exist special ecological circumstances for which the ESSs satisfy an optimization principle (that is, the rather exceptional one-dimensional environments).Kisdi characterizes one-dimensional environments by assuming that `fitness is an increasing function of a single environmental factor'. Since precision matters here, mainly for technical reasons[1xSee all References[1], we suggest rephrasing this statement as `fitnesses depend uniformly monotonically on a single environmental factor'. Dependence on the environment is `uniformly monotonic' only if it is monotonic in the same direction for every possible value of the evolutionary trait. This condition is both necessary and sufficient for the ESS to be characterizable by an optimization principle.To conclude, we agree that the analysis of certain simple models can be done by optimization arguments in place of an ESS analysis. Since optimization tools are usually easier to use, such methods are preferable whenever they are appropriate. But considerable care is needed, as the conditions under which optimization methods apply are ecologically a lot more restrictive than is commonly realized.