On the interpretation of the operation of natural selection in class-structured populations

Biological adaptation is the outcome of allele-frequency change by natural selection. At the same time, populations are usually class structured as individuals occupy different states such as sex, stage or age. This is known to result in the differential transmission of alleles called class transmission, and thus also affects allele-frequency change even in the absence of selection. How does one then isolate the allele-frequency change due to selection from that owing to class transmission? We show how reproductive values can be used to decompose multigenerational arithmetic allele-frequency change between any two generations of the evolutionary process in terms of effects of selection and class transmission. This provides a missing relationship between allele-frequency change and the operation of selection. It allows to define an appropriate measure of fitness summarizing the effect of selection in a multigenerational process, which connects asymptotically to invasion fitness and quantitative trait evolution under weak selection.