Unifying Within- and Between-Generation Bet-Hedging Theories: An Ode to J. H. Gillespie

In the 1970s, John Gillespie introduced two principles in which evolution selects for genotypes with lower variation in offspring numbers. First, if the variation in offspring number primarily occurs within generations, the strength of this selective force is inversely proportional to population size. Second, if this variation primarily occurs between generations, the strength of this selective force is proportional to the variance and independent of population size. These principles lie at the core of bet-hedging theory. Using the common currency of fixation probabilities, I derive a general principle for which within-generation correlation of individual fitness acts as a dial between Gillespie's limiting cases. At low correlations, within-generation variation is the primary selective force. At high correlations, between-generation variation is the dominant selective force. As corollary of this general principle, selection for diversified bet-hedging strategies is shown to require higher within-generation environmental correlations in smaller populations.