An elementary treatment of the genetical theory of kin-selection

Hamilton's (coefficient of relation) rule for the spread of a gene influencing altruistic behavior is derived under a simple model (discrete generations, single locus, infinite population, panmictic mating) using elementary probability theory. The rule holds quite well with slow selection and it makes no difference whether the gene is dominant or recessive. The rule is altered, however, if the pool of relatives (in interaction) is finite, and I derive a correction factor for interaction between sibs in a sexual haploid. In general the ratio of benefit to cost (necessary for the altruist gene to be favored) increases as the family size decreases.