A population genetic study of the evolution of SINEs. II. Sequence evolution under the master copy model

A transient population genetic model of SINE (short interspersed repetitive element) evolution assuming the master copy model is theoretically investigated. Means and variances of consensus frequency of nucleotides, nucleotide homozygosity, and the number of shared differences that are considered to have caused by mutations occurring in the master copy lineages are computed. All quantities investigated are shown to be monotone functions of the duration of the expansion period. Thus, they can be used to estimate the expansion period although their sampling variances are generally large. Using the theoretical results, the Sb subfamily of human Alu sequences is analyzed. First, the expansion period is estimated from the observed mean and variance of homozygosity. The expansion period is shown to be short compared to the time since the end of the expansion of the subfamily. However, the observed number of the shared differences is more than twice that expected under the master copy model with the estimated expansion period. Alternative models including that with multiple master copy loci to explain this observation are discussed.