Indirect estimates of mutation rates in tribal Amerindians

Model of effectively neutral mutations in which selective constraint is incorporated

Based on the idea that selective neutrality is the limit when the selective disadvantage becomes indefinitely small, a model of neutral (and nearly neutral) mutations is proposed that assumes that the selection coefficient (s') against the mutant at various sites within a cistron (gene) follows a Gamma distribution; f(s') = alpha(beta)e(-alphas')s'(beta-1)/Gamma(beta), in which alpha = beta/ s' and s' is the mean selection coefficient against the mutants ( s' > 0; 1 [unk] beta > 0). The mutation rate for alleles whose selection coefficients s' lie in the range between 0 and 1/(2N(e)), in which N(e) is the effective population size, is termed the effectively neutral mutation rate (denoted by v(e)). Using the model of "infinite sites" in population genetics, formulas are derived giving the average heterozygosity ( h(e)) and evolutionary rate per generation (k(g)) in terms of mutant substitutions. It is shown that, with parameter values such as beta = 0.5 and s' = 0.001, the average heterozygosity increases much more slowly as N(e) increases, compared with the case in which a constant fraction of mutations are neutral. Furthermore, the rate of evolution per year (k(1)) becomes constant among various organisms, if the generation span (g) in years is inversely proportional to radicalN(e) among them and if the mutation rate per generation is constant. Also, it is shown that we have roughly k(g) = v(e). The situation becomes quite different if slightly advantageous mutations occur at a constant rate independent of environmental conditions. In this case, the evolutionary rate can become enormously higher in a species with a very large population size than in a species with a small population size, contrary to the observed pattern of evolution at the molecular level.

The influence of premeiotic clusters of mutation on indirect estimations of mutation rate

Based on the hypothesis that rare alleles are in mutation and random loss equilibrium, mutation rate can be indirectly estimated by measuring the number of rare variants and the average existing time of a mutant allele. This method can be applied to estimate the mutation rate in humans. However, this estimation of mutation rate is affected by the presence of premeiotic clusters of mutation. Mutation clusters change both the number of initial mutants and the average existing time of a mutant allele. As a result, the formula indirectly estimating mutation rate should be modified. The influence of premeiotic clusters is more obvious when the population size is small or the average cluster size is big. For example, if the population size is 3,000 and average cluster size is two, instead of one, the mutation rate is increased by about 9.4%.

The Fundamental Theorem of Neutral Evolution: Rates of Substitution and Mutation Should Factor in Premeiotic Clusters

Mutations do not always arise as single events. Many new mutations actually occur in the cell lineage before germ cell formation or meiosis and are therefore replicated pre-meiotically. The increased likelihood of substitutions caused by these clusters of new mutant alleles can change the fundamental theorem of neutral evolution.

Estimating mutation rate: how to count mutations?

Mutation rate is an essential parameter in genetic research. Counting the number of mutant individuals provides information for a direct estimate of mutation rate. However, mutant individuals in the same family can share the same mutations due to premeiotic mutation events, so that the number of mutant individuals can be significantly larger than the number of mutation events observed. Since mutation rate is more closely related to the number of mutation events, whether one should count only independent mutation events or the number of mutants remains controversial. We show in this article that counting mutant individuals is a correct approach for estimating mutation rate, while counting only mutation events will result in underestimation. We also derived the variance of the mutation-rate estimate, which allows us to examine a number of important issues about the design of such experiments. The general strategy of such an experiment should be to sample as many families as possible and not to sample much more offspring per family than the reciprocal of the pairwise correlation coefficient within each family. To obtain a reasonably accurate estimate of mutation rate, the number of sampled families needs to be in the same or higher order of magnitude as the reciprocal of the mutation rate.

Clusters of identical new mutation in the evolutionary landscape

In contrast to the common assumption that each new mutant results from a unique, independent mutation event, clusters of identical premeiotic mutant alleles are common. Clusters can produce large numbers of related individuals carrying identical copies of the same new genetic change. By entering the gene pool in multiple copies at one time, clusters can influence fundamental processes of population genetics. Here we report evidence that clusters can increase the arrival and fixation probabilities and can lengthen the average time to extinction of new mutations. We also suggest it may be necessary to reconsider other fundamental elements of population genetic theory.

Description and validation of a method for simultaneous estimation of effective population size and mutation rate from human population data

A method is presented for utilizing population data on electrophoretic variants of proteins to estimate simultaneously the effective sizes (Ne values) of the populations in question and the rate of mutation resulting in electromorphs at the loci whose products were surveyed. The method is applied to data from 12 relatively unacculturated Amerindian tribes for whom census data and independent estimates of the number of different electrophoretic variants at 27 loci are available. Because of tribal demographic structure, Ne should be less than the current number of reproductive-aged adults. In fact, it is substantially greater for 7 tribes, most likely due to intertribal migration and a recent decrease in tribal size. Estimates of locus mutation rates for the 27 loci vary by more than a factor of 20, with an average of 1.1 x 10(-5) per locus per generation. This latter estimate is in satisfactory agreement with the results of other indirect approaches to the estimation of mutation rates in these tribes but about two times higher than the results of direct estimates based on these same loci in studies on civilized populations. This discrepancy could be due to the above-hypothesized migration and to decreases in tribal size.

Population amalgamation and genetic variation: observations on artificially agglomerated tribal populations of Central and South America

The interpretation of data on genetic variation with regard to the relative roles of different evolutionary factors that produce and maintain genetic variation depends critically on our assumptions concerning effective population size and the level of migration between neighboring populations. In humans, recent population growth and movements of specific ethnic groups across wide geographic areas mean that any theory based on assumptions of constant population size and absence of substructure is generally untenable. We examine the effects of population subdivision on the pattern of protein genetic variation in a total sample drawn from an artificial agglomerate of 12 tribal populations of Central and South America, analyzing the pooled sample as though it were a single population. Several striking findings emerge. (1) Mean heterozygosity is not sensitive to agglomeration, but the number of different alleles (allele count) is inflated, relative to neutral mutation/drift/equilibrium expectation. (2) The inflation is most serious for rare alleles, especially those which originally occurred as tribally restricted "private" polymorphisms. (3) The degree of inflation is an increasing function of both the number of populations encompassed by the sample and of the genetic divergence among them. (4) Treating an agglomerated population as though it were a panmictic unit of long standing can lead to serious biases in estimates of mutation rates, selection pressures, and effective population sizes. Current DNA studies indicate the presence of numerous genetic variants in human populations. The findings and conclusions of this paper are all fully applicable to the study of genetic variation at the DNA level as well.

A revised indirect estimate of mutation rates in Amerindians

We have previously raised the possibility that the mutation rate resulting in rare electrophoretic variants is higher in tribal/tropical-dwelling/nonindustrialized societies than in civilized/temperate-dwelling/industrialized societies. Here, we report the results of examining 11 additional proteins for the occurrence of rare electrophoretic variants in 10 Amerindian tribes, for a total of 8,968 determinations and a total of 17,648 locus tests. When these data are combined with the results of all our previous similar studies of Amerindians, a total of 272,298 polypeptides, the products of 43 different loci, have been examined for the occurrence of rare electrophoretic variants. On the assumption that these variants are maintained by mutation pressure and are essentially neutral in their phenotypic effects, we have calculated by three different approaches that it requires an average mutation rate of 1.3 X 10(-5)/locus per generation to maintain the observed variant frequency. Concurrently, we are reporting elsewhere that a direct estimate of the mutation rate resulting in electromorphs in various studies of civilized industrialized populations is 0.3 X 10(-5)/locus per generation. Although this difference appears to have statistical significance, the nonquantifiable uncertainties to both approaches are such that our enthusiasm for a true difference in mutation rates between the two types of populations has diminished. However, even the lower of these estimates, when corrected for all the types of genetic variation that electrophoresis does not detect, implies total locus and gametic mutation rates well above those which in the past have dominated genetic thinking.

On three methods for estimating mutation rates indirectly

Methods for estimating a mutation rate mu has been proposed by Kimura and Ohta; Nei; and Rothman and Adams. It is shown here that all three methods are best applied to rare alleles and that they are all based upon the assumption that all alleles ultimately become extinct. If there is a neutral allele in a growing population, there is conditioning on ultimate extinction, which implies that the underlying stochastic process can be approximated by a branching process for which the mean number of offspring is less than 1. The low numerical values of t0, the mean time to extinction of a line descended from a single mutant, found in two simulation studies, can be attributed to two features. First, the data on which these studies were based came from a fairly rapidly growing population. In such a population, we would expect that extinction, if it does occur, takes place quickly. A second factor is that the effective population size is somewhat lower than the actual number of adults. Population subdivision and migration does not seem to play a significant role. Conservative high and low estimates of mutation rates are computed, and an estimate is obtained for the standard deviation of the estimate of mu. These allow a rough estimate of a 95% confidence interval, which contains estimates of mu found by Neel and Rothman.

Population bottlenecks and nonequilibrium models in population genetics. II. Number of alleles in a small population that was formed by a recent bottleneck

A model is presented in which a large population in mutation/drift equilibrium undergoes a severe restriction in size and subsequently remains at the small size. The rate of loss of genetic variability has been studied. Allelic loss occurs more rapidly than loss of genic heterozygosity. Rare alleles are lost especially rapidly. The result is a transient deficiency in the total number of alleles observed in samples taken from the reduced population when compared with the number expected in a sample from a steady-state population having the same observed heterozygosity. Alternatively, the population can be considered to possess excess gene diversity if the number of alleles is used as the statistical estimator of mutation rate. The deficit in allele number arises principally from a lack of those alleles that are expected to appear only once or twice in the sample. The magnitude of the allelic deficiency is less, however, than the excess that an earlier study predicted to follow a rapid population expansion. This suggests that populations that have undergone a single bottleneck event, followed by rapid population growth, should have an apparent excess number of alleles, given the observed level of genic heterozygosity and provided that the bottleneck has not occurred very recently. Conversely, such populations will be deficient for observed heterozygosity if allele number is used as the sufficient statistic for the estimation of 4Nev. Populations that have undergone very recent restrictions in size should show the opposite tendencies.

Estimation of relative electrophoretic mutation rates from rare alleles in a sample

The theoretical justifications for using the number of rare alleles observed in a sample and the heterozygosity contributed by such alleles to estimate the relative electrophoretic mutation rate (REMR) are given in this note. It is shown that the estimator using the number of alleles has comparatively less bias. While the total heterozygosity contributed by all alleles at a locus has been previously used to estimate REMR with success, an analogous estimator with only rare alleles has large bias over a wide range of effective population size and sample size.

Deleterious mutations as an evolutionary factor. 1. The advantage of recombination

A population withudeleterious mutations per genome per generation is considered in which only those individuals that carry less than a critical number ofkmutations are viable. It has been shown previously that under such conditions sexual reproduction is advantageous. Here we consider selection at a locus that determines recombination frequency of the whole genome. The valuev=u/ √khas been found to play the decisive role. Whenv< 0·35 the direction of selection for recombination may be different for different cases, but the intensity of selection is always very small. The advantage of recombination becomes considerable whenv> 0·5, its growth under increasingvbeing approximately linear. Ifv> 2 no less than 95% of the progeny are bound to die because of the selection against deleterious mutations. Since this seems to be too great a mutation load, we may assume 0·5 < v < 2·0 for any sexual population if mutation really maintains crossing-over. Results on selection at a locus which controls mutability provide evidence thatvis located within the specified interval if the physiological cost of a twofold reduction of the mutation rate is within the range 10–80%. A number of consequences of this hypothesis about the mechanism of selection for sex and recombination are discussed.

A "disproportion" between the frequency of rare electropmorphs and enzyme deficiency variants in Amerindians

Our previous studies have revealed a higher frequency of nonpolymorphic electrophoretic variants in blood samples from Amerindians than in similar samples from Caucasians and Japanese. Our present study finds, by contrast, that the frequency of deficiency variants of 11 erythrocyte enzymes, sampled in nine Amerindian tribes of Central and South America, is essentially the same (1.5/1,000 determinations) as in Caucasians or Japanese. Possible explanations of the elevated frequency of mobility variants in the tropical-zone/ unacculturated populations include: higher mutation rates resulting in both electrophoretic and activity variants in Amerindians but increased selection against deficiency variants in the Amerindians, or comparable mutation rates in both populations coupled with a greater probability of a mobility variant attaining a relatively high frequency among the Amerindians.

De novo mutations producing unstable Hbs or Hbs M. II. Direct estimates of minimum nucleotide mutation rates in man

Cases of unstable hemoglobin and hemoglobin M disease that have appeared as de novo mutants over a span of approximately 50 years were used to deriving minimal, direct estimates of mutation rates per nucleotide per generation in man. The estimates are based upon analysis of data related to 40 cases of unstable Hbs and 15 of Hbs M that arose in 13 countries. The estimated rate calculated using all de novo beta-gene mutants is 7.4 X 10(-9) per nucleotide per generation; that derived using de novo alpha-gene mutants is 10.0 X 10(-9). Subsequent calculations of mutation rates per alpha- and beta-chain gene and extrapolation of these rates to a hypothetical gene of 1000 nucleotides yield an estimated mutation rate of 8.6 X 10(-6) per 1000 nucleotides per generation. Even though some instances of false paternity may have biased these estimates in an upward direction, under-reporting of Hb M cases, and particularly of unstable hemoglobins, makes it likely that the cited values are minimal estimates of mutation rates at the molecular level.

Is there a difference among human populations in the rate with which mutation produces electrophoretic variants?

Data are summarized that suggest that tropical-zone/tribal/nonindustrialized populations have higher frequencies of certain types of protein variants than temperate-zone/civilized/industrial populations, and it is demonstrated that these differences are not an artifact produced by the contagious type of sampling used with respect to tribal populations. Evidence is reviewed that suggests that a possible explanation of this difference is higher mutation rates in the tribal populations studied.

Estimation of mutation rates from the number of rare alleles in a sample

To estimate the mutation rate from rare electrophoretic variants, a revised estimating equation is derived that takes into account the sampling distribution of the observed number of rare alleles in a sample drawn from the population. A check of the approximations used here suggests that the derived estimating equation is superior to the currently available one that is based on the expected number of rare alleles in the population. The new method is illustrated with a collation of electrophoretic data from literature. It is shown that the assumptions made in the theoretical treatment do not affect the estimate, per se, when the observed number of rare alleles is chosen as a statistic for estimating the mutation rates.

Frequency of private electrophoretic variants and indirect estimates of mutation rate in Papua New Guinea

Data on rare and private electrophoretic variants have been used to estimate mutation rates for populations belonging to 55 language groups in Papua New Guinea. Three different methods yield values of 1.42 x 10(-6), 1.40 x 10(-6), and 5.58 x 10(-6)/locus per generation. The estimates for three islands populations off the north coast of New Guinea--Manus, Karkar, and Siassi--are much lower. The variability in mutation rates estimated from rare electrophoretic variants as a function of population size is discussed. The mean mutation rate in Papua New Guinea is less than half the estimates obtained for Australian Aborigines and Amerindians.

Rate of spontaneous mutation at human loci encoding protein structure

The techniques of electrophoresis were used in a search for evidence of mutation affecting protein structure, the indicators being hemoglobin and a set of serum proteins and erythrocyte enzymes. Among 94,796 locus tests on Amerindians from Central and South America, there was no evidence for mutation. Among 105,649 locus tests on newborn infants in Ann Arbor, Michigan, there was also no evidence for mutation. We have previously failed to encounter any mutations in a series of 208,196 locus tests involving Japanese children [Neel, J. V., Satoh, C., Hamilton, H. B., Otake, M., Goriki, K., Kageoka, T., Fugita, M., Neriishi, S & Asakawa,J. (1980) Proc. Natl. Acad. Sci. USA 77, 4221-4225], and H. Harris, D. A. Hopkinson, and E. B. Robson [(1974) Ann. Hum. Genet. 37, 237-253] found no mutations in 113,478 locus tests on inhabitants of the United Kingdom. This failure to demonstrate any mutations of this type in a total of 522,119 locus tests excludes, at the 95% level of probability, a mutation rate greater than 0.6 X 10(-5)/locus per generation in this combination of populations.

Genetic studies on the Ticuna, an enigmatic tribe of Central Amazonas

The Ticuna are an Amerindian tribe of Central Amazonas, a key location in theories of the peopling of eastern South America. The results of typing some 1760 members of the tribe with respect to 37 different genetic systems are reported, as are the results of HLA typings on a subsample of 129 persons. Salient findings include the following. (1) Except for a high frequency of LMs allele and an unusual combination of HLA allele frequencies, there are no notable findings with respect to the commonly studied polymorphic systems. A multivariate treatment of six of the most commonly studied genetic polymorphisms accords the Ticuna an 'average' position among Amerindian tribes. (2) There is much less intervillage heterogenicity than usually encountered in Amerindian tribes; this is attributed to recent high rates of intervillage migration due to religious developments. (3) A thus-far unique polymorphism of ACP1 was identified, the responsible allele having a frequency of 0.111. (4) In proportion to the size of the tribe, there was a relative paucity of 'private' genetic variants, the ACP1 allele being the only one. This discrepancy is attributed to a relatively recent numerical expansion of the tribe; effective population size over the past several thousand years is thought to have been well below what present numbers would suggest. (5) The thesis is again advanced that 'private variants' (alleles not occurring as polymorphisms of wide distribution) are more common in Amerindian than in Caucasian or Japanese populations.

Relationship between single- and multi-locus measures of gene diversity in a subdivided population

A mathematical relationship between the coefficient of gene diversity as derived from average single locus statistics and Smouse and Spielman's multi-locus measure is established under the assumption of linkage equilibrium in a substructured population. A formula for estimating the average time of split of subpopulations from such gene diversity is also derived for the multi-locus criterion. Unlike the estimate derived for single-locus criterion, this estimate does not explicitely depend on the number of subpopulations. The method is illustrated with data on allozyme studies from the South American Indian populations.

The frequency of private electrophoretic variants in Australian aborigines and indirect estimates of mutation rate

The number of "private" electrophoretic variants of enzymes controlled by 25 loci has been used to obtain estimates of mutation rate in Australian Aborigines. Three different methods yield values of 6.11 X 10(-6), 2.78 X 10(-6), and 12.86 X 10(-6)/locus per generation for the total sample of Aborigines. One tribal population of Waljbiri in central Australia gives values of 2.99 X 10(-6) and 2.04 X 10(-6) for two of the methods, the third being unapplicable. The mean mutation rate for the total Aboriginal sample of 7.25 X 10(-6) is very similar to the value obtained by Neel and his colleagues for Amerindians in South America.

Gene mutations (de novo) found in electrophoretic studies of blood protein of infants with anomalous development

Twelve proteins of enzymic and nonenzymic nature in blood samples of infants that deviate from the average population in physical development (50 premature and 177 full-term infants with rough and multiple developmental defects) were studied by electrophoresis in polyacrylamide and starch gels. The control group consisted of 500 normal newborns. In infants with developmental disorders, the frequency of rare electrophoretic protein variants was found to be about one order of magnitude higher than in the control. It has been shown for at least five cases that such variants are de novo mutations. According to these data the mutation rate is approximately 2 x 10(-3) per locus per generation for the group selected and approximately 6 x 10(-5) for the total population. Despite the fact that further specification of the estimations found is required, we consider the results obtained as evidence in favor of the efficiency of the earlier substantiated monitoring model of gene mutations in the human population [Dubinin, N.P. & Altukhov, Yu. P. (1977) in Genetic Consequences of Environmental Pollution, ed. Dubinin, N.P. (Mysl, Moscow), pp. 14-45]. This approach, which infers electrophoretic screening of blood proteins in a specially selected group of newborns, makes it possible to reduce the size of samples needed for statistically reliable estimations of the alteration of mutation rate.