Parental manipulation

Definition
The major competing explanations of the evolution of eusociality are parental manipulation and kin selection. Parental manipulation has been proposed by Alexander (1974) and Michener and Brothers (1974) and accounts for the evolution of altruism by selection on parents.

Parents which increase their total output of fertile offspring by first producing sterile helpers, that aid them in raising subsequent broods, will be fitter than parents which do not do this, and so will have selective advantage.

Formula
The conditions for the evolution of eusociality with diploid workers in haplodiploid populations were determined using computer simulations. Parental manipulation, in which alleles act on mothers to force their daughters to become workers, and kin selection, in which the alleles act directly on daughters to become altruists, were modeled. Workers (= altruists) were completely sterile, and raised siblings of both sexes. A dominant or recessive parental manipulation allele was selected for if K 0.5, where K is the benefit/cost ratio, expressed as the ratio of the number of siblings raised by a worker to the number of offspring she would have raised if selfish.

The rate of change of gene frequency increased with increasing family size and with an increasingly female-biased sex ratio. When K = 1, kin selection alleles were selected against if dominant, slightly against if co dominant, and for if recessive. This is because r', the ratio (relatedness to siblings)/(relatedness to offspring), changes from unity when genotype frequencies diverge from Hardy-Weinberg proportions, with r' 1 for a recessive allele and r' 1 for a codominant or dominant allele. The value of r' varies with gene frequency, p, and approaches one when p is near zero or one. Biasing the sex ratio towards females or increasing family size increases the rate of change of p irrespective of its direction. When K 1.06, even a dominant kin selection allele is selected for at all gene frequencies if the sex ratio is 1:1.