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By: Q. Ilja, M.A.S., M.D.

Program Director, Johns Hopkins University School of Medicine The two data sets are two of ten replicate samples generated as described in the text treatment 20 best 1mg kytril. These P values are meaningful only as a measure of fit to a Poisson because the pairwise differences are of course not independent medications ending in pril 2mg kytril. Even for the distribution shown in Figure 5B 72210 treatment generic 1mg kytril, however medicine x xtreme pastillas trusted 2mg kytril, the observed distribution does not appear to be very different from a Poisson. Another way to interpret these results is to note that in Figure 5,none of the pairwise differences were zero, which means that there were no short branches in the gene tree. In the other replicates, less than one in one thousand pairwise comparisons had differzero ences. In contrast, there were always large fractions of the pairwise comparisons with zero differences for the model of constant population size, as shown in Figure 3. We conclude then that if the observed distribution of pairwise differences is close to a Poisson, that it is consistentwith the hypothesis thatthe population from which those genes were sampled has been growing exponentially in size. Estimating population growth rates: Our results for the model of exponential population growth suggest that it is possible to estimate the population growth rate, r, under some conditions. In particular, if the distribution of pairwisedifferences were similar to a Poisson distribution, that would indicate that the gene tree is nearly a star phylogeny which we have shown is consistent with a model of exponential > growth with a = Nor > 1. Then we use the approximate estimate of the mean pairwise coalescent time, t = (In(Nor)- ~) / rto, obtain the estimate of the mean pairwise difference, r = 2p[ln(Nor)- T]/T-. Assume that the population from which the sample was taken has an effective size ofthe female population of No = lo6. In making such an estimate of r, it is important to realize that an approximately Poisson distribution of pairwise differences does not imply that there has been exponential growth of the population at a constant rate. Consequently it is not possible to use the observation of an approximately Poisson distribution of pairwise differences to conclude that there was exponential growth during the history of the population sampled. If that assumption about population growth is accepted, the value of i can be used to estimate the time of the sudden increase in population size: t = i/(2p). Figure 6 illustrates different growth trajectories that wouldalllead to nearly a Poisson distribution of pairwise differences. Yet another possibility is natural selection in favor of one mitochondrial genotype over previously existing ones. Such selection would result in a rapid increase in the number of individuals carrying the favored mitochondrial type. We simulated this possibility as well and found that distributions of pairwisedifferences are very similar to those found for an exponentially growing population. They concluded that effective population sizes were in fact muchsmaller than current censussizes,suggesting that past bottlenecks in population size had occurred. The distribution of pairwise differences for redwings does have a unimodal distribution of a form similar to those in Figure 5. Distributions of pairwise differences that are similar to a Poisson distribution are also found for human (data. They plotted the distribution of pairwise differences of 6 populations (Sardinians, Middle Easterners, Japanese, American Indians,! Kung and 199 Pygmies samples are clearly not similar to a Poisson but the others are. As we have emphasized, this similarity does not ensure that therehas beenexponential growth of these populations in the recent past but it does indicate that demographic events in the past have forced coalescent events into a narrow time window. They found that the Sardinian sam69) were not consistentwith the ples(samplesize neutral hypothesis butthe MiddleEasternsamples (sample size 42) were consistent. It is difficult, however, to compare such a graph with a geometric distribution and reject the nullhypothesis that the genes sampled were from a randomly mating population of constant size. Our results for an exponentially growing population suggest that the distribution of pairwise differences can provide useful information if the distribution is nearly a Poisson distribution. That pattern would alsobe detected in the gene tree directly if branch lengths were known.   