Yoshio Tateno

Mean and variance of FST in a finite number of incompletely isolated populations

Abstract In the presence of migration F ST in a finite number of incompletely isolated populations first increases, but after reaching a certain maximum value, it starts to decline and eventually becomes 0. The mean and variance of F ST in this process are studied by using the recurrence formulas for the moments of gene frequencies in the island model of finite size as well as by using Monte Carlo simulation. The mean and variance in the early generations can be predicted by the approximate formulas developed. On the other hand, if we exclude the cases of an allele being fixed in all subpopulations, the mean of F ST eventually reaches a steady-state value. This value is given by 1 − 2 N T (1 − λ ) approximately, where N T is the total population size and λ is the rate of decay of heterozygosity at steady state. It is shown that the mean and variance of F ST depend on the initial gene frequency and when this is close to 0 or 1, Lewontin and Krakauers test of the neutrality of polymorphic genes is not valid.

Goodman et al.'s method for augmenting the number of nucleotide substitutions.

SummaryStatistical properties of Goodman et al.s (1974) method of compensating for undetected nucleotide substitutions in evolution are investigated by using computer simulation. It is found that the method tends to overcompensate when the stochastic error of the number of nucleotide substitutions is large. Furthermore, the estimate of the number of nucleotide substitutions obtained by this method has a large variance. However, in order to see whether this method gives overcompensation when applied together with the maximum parsimony method, a much larger scale of simulation seems to be necessary.

Nonrandom amino acid substitution and estimation of the number of nucleotide substitutions in evolution

SummaryA method of estimating the number of nucleotide substitutions from amino acid sequence data is developed by using Dayhoffs mutation probability matrix. This method takes into account the effect of nonrandom amino acid substitutions and gives an estimate which is similar to the value obtained by Fitchs counting method, but larger than the estimate obtained under the assumption of random substitutions (Jukes and Cantors formula). Computer simulations based on Dayhoffs mutation probability matrix have suggested that Jukes and Holmquists method of estimating the number of nucleotide substitutions gives an overestimate when amino acid substitution is not random and the variance of the estimate is generally very large. It is also shown that when the number of nucleotide substitutions is small, this method tends to give an overestimate even when amino acid substitution is purely at random.

Estimating evolutionary distance from restriction maps of mitochondrial DNA with arbitrary G+C content

SummaryWe develop a mathematical model for estimating evolutionary distance from restriction enzyme maps, which incorporates non-uniformity of the rate of base substitution into the theory and allows for an arbitrary G+C content at equilibrium. When the G+C content differs significantly from 1/2, the traditional model of base changes can introduce a systematic bias which depends upon the base composition of the restriction site. In addition, the accuracy of estimated evolutionary distance depends heavily upon the choice of restriction enzyme in that the expected number of sites is also affected. Monte Carlo experiments are conducted to check the validity of the present theoretical treatment and from which we draw several cautionary notes on estimation. An application is made to the available data on restriction enzyme maps of human mitochondrial DNA where the G+C content is approximately 1/3.

Statistical properties of molecular tree construction methods under the neutral mutation model

SummaryThe statistical properties of three molecular tree construction methods—the unweighted pair-group arithmetic average clustering (UPG), Farris, and modified Farris methods—are examined under the neutral mutation model of evolution. The methods are compared for accuracy in construction of the topology and estimation of the branch lengths, using statistics of these two aspects. The distribution of the statistic concerning topological construction is shown to be as important as its mean and variance for the comparison.Of the three methods, the UPG method constructs the tree topology with the least variation. The modified Farris method, however, gives the best performance when the two aspects are considered simultaneously. It is also shown that a topology based on two genes is much more accurate than that based on one gene.There is a tendency to accept published molecular trees, but uncritical acceptance may lead one to spurious conclusions. It should always be kept in mind that a tree is a statistical result that is affected strongly by the stochastic error of nucleotide substitution and the error intrinsic to the tree construction method itself.

Statistical properties of the Jukes-Holmquist method of estimating the number of nucleotide substitutions: reply to Holmquist and Conroy's criticism.

SummaryConducting computer simulations, Nei and Tateno (1978) have shown that Jukes and Holmquists (1972) method of estimating the number of nucleotide substitutions tends to give an overestimate and the estimate obtained has a large variance. Holmquist and Conroy (1980) repeated some parts of our simulation and claim that the overestimation of nucleotide substitutions in our paper occurred mainly because we used selected data. Examination of Holmquist and Conroys simulation indicates that their results are essentially the same as ours when the Jukes-Holmquist method is used, but since they used a different method of computation their estimates of nucleotide substitutions differed substantially from ours. Another problem in Holmquist and Conroys Letter is that they confused the expected number of nucleotide substitution with the number in a sample. This confusion has resulted in a number of unnecessary arguments. They also criticized ourX2 measure, but this criticism is apparently due to a misunderstanding of the assumptions of our method and a failure to use our method in the way we described. We believe that our earlier conclusions remain unchanged.