Simultaneous Estimation of All the Parameters of a Stepwise Mutation Model

Corresponding author: Yun-Xin Fu, Human Genetics Center, University of Texas at Houston, 6901 Bertner Ave., Houston, TX 77030., fu{at}hgc.sph.uth.tmc.edu (E-mail).

Communicating editor: G. B. GOLDING

Minisatellite and microsatellite are short tandemly repetitive sequences dispersed in eukaryotic genomes, many of which are highly polymorphic due to copy number variation of the repeats. Because mutation changes copy numbers of the repeat sequences in a generalized stepwise fashion, stepwise mutation models are widely used for studying the dynamics of these loci. We propose a minimum chi-square (MCS) method for simultaneous estimation of all the parameters in a stepwise mutation model and the ancestral allelic type of a sample. The MCS estimator requires knowing the mean number of alleles of a certain size in a sample, which can be estimated using Monte Carlo samples generated by a coalescent algorithm. The method is applied to samples of seven (CA)_n repeat loci from eight human populations and one chimpanzee population. The estimated values of parameters suggest that there is a general tendency for microsatellite alleles to expand in size, because (1) each mutation has a slight tendency to cause size increase and (2) the mean size increase is larger than the mean size decrease for a mutation. Our estimates also suggest that most of these CA-repeat loci evolve according to multistep mutation models rather than single-step mutation models. We also introduced several quantities for measuring the quality of the estimation of ancestral allelic type, and it appears that the majority of the estimated ancestral allelic types are reasonably accurate. Implications of our analysis and potential extensions of the method are discussed.

SINCE the discovery that a large number of loci with tandemly repeated sequences in human and many eukaryote species are highly polymorphic because of copy number variation of the repeats in different individuals (JEFFREYS 1985; LITT and LUTY 1989 ; WEBER and MAY 1989 ), allele size data from such loci are rapidly becoming the dominant source of genetic markers for genome mapping, forensic testing, and population studies. Loci with repeat sequences longer than 5 bp are generally referred to as minisatellite or variable number tandem repeat loci, and those with repeat sequences between 2 to 5 bp are referred to as microsatellite or short tandem repeat loci (TAUTZ 1993 ). Because mutations change the copy number of such loci in a stepwise fashion, rapid accumulation of population samples from minisatellite and microsatellite loci has resurrected the interest of the stepwise mutation model (SMM), which was popular in the 1970s.

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