Directionality theory and mortality patterns across the primate lineage.

Empirical studies of aging in primates show that local selective forces rather than phylogenetic history determine the exceptional nature of human longevity (Bronikowski et al., Science 331:1325-1328, 2011). This article proposes an evolutionary rationale for this pattern of primate mortality by invoking the parameter, Life-Table Entropy, a measure of the uncertainty in the life span of a randomly chosen newborn. Life-table entropy is positively correlated with maximal life span, that is, the mean life span of a species living under favourable conditions.The logic which underlies the exceptional nature of human longevity derives from the terrestrial life-history of humans - a singularity within the primate lineage; and the concomitant ecological constraints-the hunter-gatherer, agricultural, and industrial modes of subsistence, that have defined human evolutionary history. The effect of these ecological constraints on the evolution of life span is encoded in the Entropic Principle of Longevity: life-table entropy increases in equilibrium species, populations evolving in environments with stable, renewable resources; and decreases in opportunistic species, populations subject to fluctuating resource endowments.The Entropic Principle of Longevity is a derivative of Directionality Theory, an analytic study of the evolutionary process of variation and selection based on Evolutionary Entropy, a statistical measure of the uncertainty in the age of the mother of a randomly chosen newborn. Evolutionary entropy is the organizing concept of The Entropic Principle of Evolution: Evolutionary Entropy increases in equilibrium species and decreases in opportunistic species.

Darwinian fitness and the intensity of natural selection: studies in sensitivity analysis.

Darwinian fitness, the capacity of a variant type to establish itself in competition with the resident population, is determined by evolutionary entropy, a measure of the uncertainty in age of the mother of a randomly chosen newborn. This article shows that the intensity of natural selection, as measured by the sensitivity of entropy with respect to changes in the age-specific fecundity and mortality variables, is a convex function of age, decreasing at early and increasing at later ages. We exploit this result to provide quantitative evolutionary explanations of the large variation in survivorship curves observed in natural populations. Previous studies to explain variation in survivorship curves have been based on the proposition that Darwinian fitness is determined by the Malthusian parameter. Hence the intensity of natural selection will be determined by the sensitivity of the Malthusian parameter with respect to changes in the age-specific fecundity and mortality variables. This measure of the selection gradient is known to be a decreasing function of age, with implications which are inconsistent with empirical observations of survivorship curves in human and animal populations. The analysis described in this paper point to the mitigated import of sensitivity studies based on the Malthusian parameter. Our analysis provides theoretical and empirical support for the ecological and evolutionary significance of sensitivity analysis based on entropy, which is the appropriate measure of Darwinian fitness.

Darwinian fitness.

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.

Directionality theory: an empirical study of an entropic principle in life-history evolution.

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.