Variation, natural selection, and information content--a simulation

In Neo-Darwinism, variation and natural selection are the two evolutionary mechanisms that propel biological evolution. Variation implies changes in the gene pool of a population, enlarging the genetic variability from which natural selection can choose. But in the absence of natural selection, variation causes dissipation and randomization. Natural selection, in contrast, constrains this variability by decreasing the survival and fertility of the less-adapted organisms. The objective of this study is to propose a highly simplified simulation of variation and natural selection, and to relate the observed evolutionary changes in a population to its information content. The model involves an imaginary population of individuals. A quantifiable character allows the individuals to be categorized into bins. The distribution of bins (a histogram) was assumed to be Gaussian. The content of each bin was calculated after one to twelve cycles, each cycle spanning N generations (N being undefined). In a first study, selection was simulated in the absence of variation. This was modeled by assuming a differential fertility factor F that increased linearly from the lower bins (F<1.00) to the higher bins (F>1.00). The fertility factor was applied as a multiplication factor during each cycle. Several ranges of fertility were investigated. The resulting histograms became skewed to the right. In a second study, variation was simulated in the absence of selection. This was modeled by assuming that during each cycle each bin lost a fixed percentage of its content (variation factor Y) to its two adjacent bins. The resulting histograms became broader and flatter, while retaining their bilateral symmetry. Different values of Y were monitored. In a third study, various values of F and Y were combined. Our model allows the straightforward application of Shannon's equation and the calculation of a Shannon-entropy (SE) values for each histogram. Natural selection was, thus, shown to result in a progressive decrease in SE as a function of F. In other words, natural selection, when acting alone, progressively increased the information content of the population. In contrast, variation resulted in a progressive increase in SE as a function of Y. In other words, variation acting alone progressively decreased the information content of a population. When both factors, F and Y, were applied simultaneously, their relative weight determined the progressive change in SE.