• isolation by distance;
  • kin selection;
  • population structure;
  • probability of fixation;
  • relatedness

The analysis of kin selection in subdivided populations has been hampered by the lack of well-defined measures of genealogical relatedness in the presence of localized dispersal. Furthermore, the usual arguments underlying the definition of game-theoretical measures of inclusive fitness are not exact under localized dispersal. We define such measures to give the first-order effects of selection on the probability of fixation of an allele. The derived measures of kin selection and relatedness are valid in finite populations and under localized dispersal. For the infinite island model, the resulting measure of kin selection is equivalent to a previously used measure. In other cases its definition is based on definitions of relatedness which are different from the usual ones. To illustrate the approach, we reanalyse a model with localized dispersal. We consider sex ratio evolution under sex-specific dispersal behaviour, and the results confirm the earlier conclusion that the sex ratio is biased towards the sex with the dispersal rate closer to the optimal dispersal rate in the absence of sex-specific dispersal behaviour.