Abstract

We propose a measure of total population diversity D of an evolving population of genetically specied individuals. Total diversity D is the sum of two components, within-gene diversity Wg and betweengene diversity Bg. We observe the dynamics of diversity in the context of a particular model, a twodimensional world with organisms competing for resources and evolving by natural selection acting implicitly on genetic changes in their movement strategies. We examine how diversity dynamics and population performance|measured as the e ciency with which the population extracts energetic resources from its environment|depend on mutation rate and the presence or absence of selection. Systematic exploration of mutation rates reveals a bifurcation into qualitatively di erent classes of diversity dynamics, whether or not selection is present. Class I: At lowmutation rates, diversity dynamics exhibit \punctuated equilibria"|periods of static diversity values broken by rapid changes. Class II: At intermediate mutation rates, diversity undergoes large random uctuations without always approaching any evident equilibrium value. Class III: At high mutation rates, diversity is stable, with small uctuations around an equilibrium value. Optimal population performance occurs within a range of mutation rates that straddles the border between class I and class II. The relationships among diversity D and its components Wg and Bg re ects the typical features of these di erent classes of diversity dynamics as well as corresponding di erences in the gene pool, which ranges from genetically similar individuals in class I to genetically dissimilar individuals in class III. The fact that class I dynamics occur whether or not selection is present suggests that stochastically branching trait transmission processes have anintrinsic tendency to exhibit punctuated equilibria in population diversity over a critical range of branching (mutation) rates.

Citations