  Evolutionary graph theory has grown to be an area of intense study. Despite
the amount of interest in the field, it seems to have grown separate from other
subfields of population genetics and evolution. In the current work I introduce
the concept of Fisher's (1930) reproductive value into the study of evolution
on graphs. Reproductive value is a measure of the expected genetic contribution
of an individual to a distant future generation. In a heterogeneous
graph-structured population, differences in the number of connections among
individuals translates into differences in the expected number of offspring,
even if all individuals have the same fecundity. These differences are
accounted for by reproductive value. The introduction of reproductive value
permits the calculation of the fixation probability of a mutant in a neutral
evolutionary process in any graph-structured population for either the moran
birth-death or death-birth process.
