STATISTICAL PROPERTIES OF A DNA SAMPLE UNDER THE FINITE-SITES MODEL

Statistical properties of a DNA sample from a random-mating population of constant size are studied under the finite-sites model. It is assu med that there is no migration and no recombination occurs within the locus. A Markov process model is used for nucleotide substitution, all owing for multiple substitutions at a single site. The evolutionary ra tes among sites are treated as either constant or variable. The genera l likelihood calculation using numerical integration involves intensiv e computation and is feasible for three or four sequences only; it may be used for validating approximate algorithms. Methods are developed to approximate the probability distribution of the number of segregati ng sites in a random sample of n sequences, with either constant or va riable substitution rates across sites. Calculations using parameter e stimates obtained for human D-loop mitochondrial DNAs show that among- site rate variation has a major effect on the distribution of the numb er of segregating sites; the distribution under the finite-sites model with variable rates among sites is quite different from that under th e infinite-sites model.