Distribution of nucleotide differences between two randomly chosen cistrons in a population of variable size

The distribution of the number of nucleotide differences between two randomly chosen cistrons in a finite population is studied here when the population size changes from generation to generation. When genetic variability is measured by heterozygosity (i.e., the probability that two cistrons are different), by the probability that two cistrons differ at two or more nucleotide sites, or by mean number of site differences between cistrons, it is seen that in a population going through a small bottleneck all of these measures decline rapidly but, as soon as population size becomes large, they start to increase owing to new mutations. The amount of reduction in these measures depends not only on the size of bottleneck but also on the rate of population growth. The implications of this study explaining the observed variations in the rates of amino acid substitutions during the evolutionary process are also discussed.