How to make a kin selection model.
Kin selection arguments, based on Hamilton's (1964) concept of inclusive fitness, provide a powerful heuristic and can therefore give us valuable insights into the different pathways through which natural selection acts. But their formulation can be quite tricky, requiring as they do, a close accounting of all the fitness effects of a particular item of behaviour. Here we propose a "direct fitness" formulation of inclusive fitness which often has a more straightforward derivation. Our method finds ESS trait values by the standard optimization techniques of simple differentiation plus two additional steps. First, slopes of group phenotype on individual genotype arise naturally during differentiation, and these slopes are replaced by coefficients of relatedness. Second, when behaviours influence different classes such as age, sex of recipient, or other life history components of fitness, the fitness effects on each component are weighted by reproductive value. We illustrate this technique first in a homogeneous population, with examples of group competition and partial dispersal behaviour, and then in a class-structured population, with examples of sex allocation and altruism between age classes.
Taylor
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Department of Mathematics and Statistics, Queen's University, Kingston, OT.
Frank
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D000367:Age Factors; D000818:Animals; D005075:Biological Evolution; D005260:Female; D008297:Male; D008954:Models, Biological; D012744:Sex Ratio; D012919:Social Behavior