The reason to spend effort on arriving at a proper fitness definition is primarily pragmatical. Prediction of evolutionary outcomes by maximizing fitness is a huge industry. Literally interpreted, a fair part of the older evolutionary ecology literature makes no sense as it (1) recommends maximizing the Malthusian parameter without ever mentioning environments and (2) invokes Fisher's fundamental theorem as justification. Yet, in practice, it did a good job. The reason is that at evolutionary stops, invasion fitness cannot but be maximal for the environment generated by the corresponding population dynamics, for if it were not, there would be many possible mutants that by invading could set evolution moving again (an idea put forward by Hamilton, and made popular through the efforts of Maynard Smith). Hence, if one does not account for the dynamics of the environment but just measures it, it is possible to predict the properties of organisms through fitness maximization. Such predictions can work when environments stay unperturbed, but not if one wants to predict the consequences of, for example, climate change, as then any evolutionary change necessarily carries population dynamically generated environmental change in its wake.
The above characterization of evolutionary stops is usually referred to as the ESS criterion. ESS is an abbreviation of'evolutionarily stable strategy', which, however, is a misnomer as the so-defined strategies need not be evolutionarily stable in the standard meaning of the word stable. The latter requires that the ESS through the continued substitution of mutations be approached from nearby strategies. Evolutionary attractiveness can only be judged by seeing how the fitness landscape changes with a change in the resident strategy. Hence, the abbreviation will here be supposed to read 'evolutionarily steady strategy'. For evolutionary predictions only attracting ESSs, often called CSSs, matter.
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