Bio demographic aspects of population entropy in quantifying population heterogeneity and its consequences for population fitness and species adaptation

Entropy is a well-established measure of population variability and already used in contingency in life table analysis. Such an entropy, denoted H, is a measure of heterogeneity of the distribution of deaths in a cohort and consist of a touchstone to compare life strategies in different populations or species. Since environmental change affects directly life history traits of populations, entropy as crude demographic parameter may be used to quantitative such trends. Particularly for poikilotherms, entropy may serve as highly quantitative predictor of species net reproductive success under optimum and/or non favorable biotic conditions for growth and development. Nevertheless, entropy has been also used as a more general dynamic measure of species fitness and adaptation to variable ecological conditions. In principle, such demographic-population entropy is an analogue of the Gibbs–Boltzmann entropy in statistical mechanics, H=-Σpilnpi. Here, pi represents the probability density function of the age of reproducing individuals and therefore maximization of entropy is equivalent to maximization of the uncertainty of age reproduction. In such a context, population entropy consist of a dynamic measure and maximization of H under various constrains yield to different distributions of reproduction and survivorship. Moreover, considering that demographic dynamics are formally equivalent to the dynamics of a Markov chain, demographic entropy can be further used under an expression of the classical Leslie model by means of stationary Markov chains to estimate the convergence rate of population transitions to stable age distributions and demographic equilibriums. Populations may differ by terms of robustness captured by evolutionary entropy: the rate at which populations return to demographic equilibrium after a certain perturbation. Hence, under the hypothesis that resource abundance is unlimited and that the only factor affecting population dynamics are inherent properties of species, population entropy may be used to predict the selective advantage among different populations according to the entropic principle. From an applied population-ecological standpoint, considering that that entropy may differ among genera, species and populations, the capacity of each organism to adapt to new environments may be quantified. From an environmental management standpoint, demographic properties of a population do constrain to the rate of which species adapt to human disturbed environments. The adaptive value of a population can be interpreted as distance measure between the variability of the mortality distribution, where no environmental forces interfere and the conditional entropy, estimated given the known unperturbed reference mortality. Repeated use of pesticides for instance, can cause undesirable changes in the gene pool leading of a species due to artificial selection. Through this operation, populations with the favored demographic properties gradually develop resistance to the pesticide showing fitness advantages in the presence of the artificial selection factor. Thus, reproductive trends captured by demographic entropy may reflect macroevolutionary changes such as adaptation and extinction under variable conditions.