No abstract

A measure of difference between populations for a trait should reflect not only the differences in the relative frequencies of the trait states but also the trait differences between the states. Common approaches to measuring differences between populations rely on distance, probability, or variance concepts. To overcome conceptual problems of these approaches, a new difference measure D is presented that is based on both frequency and trait differences. For two populations, D expresses the degree to which the frequency distribution of the trait states within one population must be transformed in order to make it match the distribution in the other population. This is done by shifting the relative frequency excesses of trait states to other trait states of deficient frequency, where shifts occur between as similar states as possible. D equals the minimum sum of the shifted frequencies weighted by the respective trait differences. Its bounds are functions of the difference measure d 0 , which considers only differences in relative frequency. The computer program DeltaS applies an algorithm from operations research to calculate D. The effect of including trait differences is demonstrated by the topological differences observed between D-and d 0 -dendrograms constructed from microsatellite allele frequencies in four riparian stands of black poplar (Populus nigra), where the trait difference between two alleles equals the difference in numbers of tandem repeats. D is applicable to all traits for which trait differences are measurable, and it is shown to have elementary linearity properties that considerably simplify its interpretation.

A single locus, diallelic selection model with female and male viability differences is studied. If the variables are ratios of allele frequencies in each sex, a 2-dimensional difference equation describes the model. Because of the strong monotonicity of the resulting map, every initial genotypic structure converges to an equilibrium structure assuming that no equilibrium has eigenvalues on the unit circle.

The term Darwinian fitness refers to the capacity of a variant type to invade and displace the resident population in competition for available resources. Classical models of this dynamical process claim that competitive outcome is a deterministic event which is regulated by the population growth rate, called the Malthusian parameter. Recent analytic studies of the dynamics of competition in terms of diffusion processes show that growth rate predicts invasion success only in populations of infinite size. In populations of finite size, competitive outcome is a stochastic process--contingent on resource constraints--which is determined by the rate at which a population returns to its steady state condition after a random perturbation in the individual birth and death rates. This return rate, a measure of robustness or population stability, is analytically characterized by the demographic parameter, evolutionary entropy, a measure of the uncertainty in the age of the mother of a randomly chosen newborn. This article appeals to computational and numerical methods to contrast the predictive power of the Malthusian and the entropic principles. The computational analysis rejects the Malthusian model and is consistent with of the entropic principle. These studies thus provide support for the general claim that entropy is the appropriate measure of Darwinian fitness and constitutes an evolutionary parameter with broad predictive and explanatory powers.

Understanding the relationship between ecological constraints and life-history properties constitutes a central problem in evolutionary ecology. Directionality theory, a model of the evolutionary process based on demographic entropy, a measure of the uncertainty in the age of the mother of a randomly chosen newborn, provides an analytical framework for addressing this problem. The theory predicts that in populations that spend the greater part of their evolutionary history in the stationary growth phase (equilibrium species), entropy will increase. Equilibrium species will be characterized by high iteroparity and strong demographic stability. In populations that spend the greater part of their evolutionary history in the exponential growth phase (opportunistic species), entropy will decrease when population size is large, and will undergo random variation when population size is small. Opportunistic species will be characterized by weak iteroparity and weak demographic stability when population size is large, and random variations in these attributes when population size is small. This paper assesses the validity of these predictions by employing a demographic dataset of 66 species of perennial plants. This empirical analysis is consistent with directionality theory and provides support for its significance as an explanatory and predictive model of life-history evolution.