Variance and Uncertainty Measures of Population Diversity Dynamics

Evolving systems have a two-tier structure: a micro level consisting of individuals whose behavior is in uenced by their genomes and whose interaction with their environment is governed by some explicit dynamics; and a macro level consisting of the population as a whole whose higher-level dynamics emerges statistically from the underlying micro processes. Following traditional population genetics, our approach to studying evolutionary dynamics is to de ne and observe macro-scale measures that re ect important aspects of a system's evolution (Packard 1989; Bedau and Packard 1992; Bedau, Ronneburg and Zwick 1992; Bedau and Bahm 1994; Bedau, Giger and Zwick 1995). We prefer measures that can be observed in a wide variety of arti cial and natural settings, for this facilitates the search for universal features of evolutionary dynamics. We think that the important stable features of an evolving population are dynamical; evolution is a dynamic equilibrium. By studying these measures in numerical simulations of simple evolving systems, we can respect the context-dependence of tness and other macro-level measures of evolution, we can explicitly treat many loci and many alleles per loci at the micro-level, and we can observe the dynamical properties of the measures. Various kinds of diversity are interesting macro-scale measures (Bedau, Ronneburg and Zwick 1992); one is the diversity of the genetic information in the population. Population diversity is interesting partly because it re ects exactly that aspect of the system that evolution directly changes|the genetic structure of the population. Thus, the dynamics of population diversity is a central aspect of the intrinsic dynamics of evolution. While diversity itself is de nable directly in terms of micro properties, its dynamics are in general unpredictable from the underlying micro dynamics and thus re ect an emergent property of the system. In addition, population diversity is both cause and e ect of a population's evolving interaction with its environment. For example, it is reasonable to suppose that a pop-