Allele-Frequency Change in a Class-Structured Population

Suppose that in a population with a class structure, we wish to calculate the change in frequency of an allele under the action of selection. If the allele affects the behavior of individuals in different classes differently and if parents of different classes have different class distributions of offspring, then the allele frequencies in different classes may be different, and any overall calculation of allele-frequency change must decide how to weight the different class frequencies. I show that the correct weights to use are the class reproductive values, and, using these, I formulate a covariance equation for allele-frequency change. This equation also provides the classical inclusive-fitness formulation if benefits (increased numbers of offspring) are calculated by weighting each offspring by the individual reproductive value that pertains to his class.