Neutral Mutation Rate Research Articles

Statistical tests for detecting gene conversion.

Statistical tests for detecting gene conversion are described for a sample of homologous DNA sequences. The tests are based on imbalances in the distribution of segments on which some pair of sequences agrees. The methods automatically control for variable mutation rates along the genome and do not depend on a priori choices of potentially monophyletic subsets of the sample. The tests show strong evidence for multiple intragenic conversion events at two loci in Escherichia coli. The gnd locus in E. coli shows a highly significant excess of maximal segments of length 70-200 bp, which suggests conversion events of that size. The data also indicate that the rate of these short conversion events might be of the order of neutral mutation rate. There is also evidence for correlated mutation in adjacent codon positions. The same tests applied to a locus in an RNA virus were negative.

How often are polymorphic restriction sites due to a single mutation?

An approximate expression is obtained for the probability that a restriction site, which is polymorphic in a random sample, is a site at which two or more mutations have occurred in the descent to the sample from the most recent common ancestor of the sample. The analysis is based on the assumption that the population from which the sample is obtained is at equilibrium under a selectively neutral Wright-Fisher model. Monte Carlo simulations show that the approximation is quite accurate. For commonly observed levels of genetic variation in humans and in natural populations of Drosophila, it is found that multiple mutations would occur at 5 to 10 percent of polymorphic restriction sites assuming that six-cutter enzymes are used on samples of size 50 to 100. Simulations are also used to investigate the bias and mean square error of four estimators of 4 Nu, where N is the population size and u is the neutral mutation rate per nucleotide site. Two of the estimators are biased by approximately 20 percent when levels of variation are similar to those which have been observed in natural populations of Drosophila.

Molecular evolutionary clock and the neutral theory.

From the standpoint of the neutral theory of molecular evolution, it is expected that a universally valid and exact molecular evolutionary clock would exist if, for a given molecule, the mutation rate for neutral alleles per year were exactly equal among all organisms at all times. Any deviation from the equality of neutral mutation rate per year makes the molecular clock less exact. Such deviation may be due to two causes: one is the change of the mutation rate per year (such as due to change of generation span), and the other is the alteration of the selective constraint of each molecule (due to change of internal molecular environment). A statistical method was developed to investigate the equality of evolutionary rates among lineages. This was used to analyze protein data to demonstrate that these two causes are actually at work in molecular evolution. It was emphasized that departures from exact clockwise progression of molecular evolution by no means invalidates the neutral theory. It was pointed out that experimental studies should be done to settle the issue of whether the mutation rate for nucleotide change is more constant per year or per generation among organisms whose generation spans are very different.

Copper/Zinc superoxide dismutase: How likely is gene transfer from ponyfish toPhotobacterium leiognathi?

The proposed transfer of the gene for Cu/Zn superoxide dismutase from the ponyfish to its symbiotic bacteriumPhotobacterium leiognathi has been evaluated by an extensive analysis of all available Cu/Zn superoxide dismutase sequences. By the use of four different computer programs, phylogenetic trees were constructed from the sequences of the superoxide dismutases of human, ox, pig, horse, swordfish, fruit fly, yeast, andNeurospora crassa to find out whether superoxide dismutase sequences can reliably be used for the reconstruction of genealogical relationships. All programs arrived at the same most parsimonious tree (one requiring 232 amino acid replacements), the topology of which conformed to established opinions about the phylogenetic relations among these eukaryotes, except that it placed humans closer to the artiodactyls ox and pig than it placed horses. This could be corrected at the cost of two amino acid replacements. The sequence ofP. leiognathi superoxide dismutase was then connected at all possible positions to the corrected eukaryotic tree. It was slighly more parsimonious to link the bacterial sequence to the root of the tree than to the fish branch: The former required 316 (or 317) amino acid replacements, versus 319 for the latter. This relative lack of discrimination between such distinct alternative topologies may be a general complication in the comparison of prokaryotic and eukaryotic proteins: Bacterial cytochrome c sequences also were found to be connected as parsimoniously to the root of the eukaryotic tree as to any terminal or ancestral branch. It was calculated that the rate of evolution of the bacterial superoxide dismutase gene, if transfer occurred 30 million years (Myr) ago, must have amounted to 487 amino acid replacements per 100 residues per 100 Myr. This is more than 5 times the highest rate observed in any protein (that found for fibrinopeptides), and even much higher than the maximum rate of protein evolution that can be deduced from the neutral mutation rate of unconstrained DNA. Also, no significant evidence that shared derived amino acid replacements are present in swordfish andP. leiognathi superoxide dismutase, as might be expected had gene transfer occurred, was found. On the basis of the available data it seems more reasonable to ascribe the isolated occurrence of Cu/Zn superoxide dismutase inP. leiognathi (as well as inCaulobacter crescentus) to irregular patterns of gene expression and inactivation in the course of divergent evolution than to undocumented processes of gene transfer from eukaryotes to prokaryotes.

The sampling distribution of linkage disequilibrium under an infinite allele model without selection.

The sampling distributions of several statistics that measure the association of alleles on gametes (linkage disequilibrium) are estimated under a two-locus neutral infinite allele model using an efficient Monte Carlo method. An often used approximation for the mean squared linkage disequilibrium is shown to be inaccurate unless the proper statistical conditioning is used. The joint distribution of linkage disequilibrium and the allele frequencies in the sample is studied. This estimated joint distribution is sufficient for obtaining an approximate maximum likelihood estimate of C = 4Nc, where N is the population size and c is the recombination rate. It has been suggested that observations of high linkage disequilibrium might be a good basis for rejecting a neutral model in favor of a model in which natural selection maintains genetic variation. It is found that a single sample of chromosomes, examined at two loci cannot provide sufficient information for such a test if C less than 10, because with C this small, very high levels of linkage disequilibrium are not unexpected under the neutral model. In samples of size 50, it is found that, even when C is as large as 50, the distribution of linkage disequilibrium conditional on the allele frequencies is substantially different from the distribution when there is no linkage between the loci. When conditioned on the number of alleles at each locus in the sample, all of the sample statistics examined are nearly independent of theta = 4N mu, where mu is the neutral mutation rate.

Estimation of the neutral mutation rate in a finite population from DNA sequence data

The sampling theory for the infinite site model taking into account the phylogenetic relationship between the alleles is developed for those cases in which two or three alleles are observed in the sample. From this theory a maximum likelihood estimate of θ = 4 Nμ can be obtained. Unlike the maximum likelihood estimate of θ based on the infinite allele model or the number of segregating sites, this estimate of θ is a function of the frequencies of the alleles. This method is used to estimate θ for mitochondrial DNA in Drosophila melanogaster and D. virilis from data obtained by Shah and Langley (1979. Nature (London) 281, 696–699) using restriction endonucleases.

Properties of a neutral allele model with intragenic recombination

An infinite-site neutral allele model with crossing-over possible at any of an infinite number of sites is studied. A formula for the variance of the number of segregating sites in a sample of gametes is obtained. An approximate expression for the expected homozygosity is also derived. Simulation results are presented to indicate the accuracy of the approximations. The results concerning the number of segregating sites and the expected homozygosity indicate that a two-locus model and the infinite-site model behave similarly for 4 Nu ⩽ 2 and r ⩽ 5 u, where N is the population size, u is the neutral mutation rate, and r is the recombination rate. Simulations of a two-locus model and a four-locus model were also carried out to determine the effect of intragenic recombination on the homozygosity test of Watterson ( Genetics 85, 789–814; 88, 405–417) and on the number of unique alleles in a sample. The results indicate that for 4 Nu ⩽ 2 and r ⩽ 10 u, the effect of recombination is quite small.

TESTING THE CONSTANT-RATE NEUTRAL ALLELE MODEL WITH PROTEIN SEQUENCE DATA.

Langley and Fitch (1973, 1974) and Fitch and Langley (1976) statistically analyzed the pattern of nucleotide substitutions in seven proteins and 17 taxa and rejected the null hypothesis of a constantrate Poisson model of protein evolution. Their rejection of the constant-rate model was based on the extremely large observed value of a statistic (henceforth referred to as X2LF), which has a standard Chi-squared distribution under their null hypothesis. Gillespie and Langley (1979) showed that under a constant-rate neutral allele model, X2LF is not Chi-squared distributed. Though they did not obtain the exact distribution Of X2LF, they were able to show that the expectation Of X2LF is an increasing function of 0 = 4Nu, where N is the population size and u is the neutral mutation rate. Thus, the Langley and Fitch analysis does not constitute a test of the constant-rate neutral model. Evidently no test of the neutral model is possible using only the statistic X2LF, since no matter how large the observed value Of X2LF, a sufficiently large value of 0 could account for the observation. If one knew the distribution Of X2LF as a function of 0, one could use the observed value Of X2LF to estimate 0. I report here the results of Monte Carlo simulations that were used to characterize the distribution Of X2LF for several values of 0. The simulations were used to determine 0, the value of 0 for which the mean value Of X2LF over many simulation trials equals the observed value Of X2LF. The simulations were also used to determine Omil, the value of 6 for which approximately 5% of the simulation trials produced values Of X2LF greater than or equal to the observed val-

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.

Population size and protein variation in man.

SUMMARYThe ‘neutral mutation theory’ holds that most amino acid substitutions in evolution are selectively neutral. The known pattern of variation in human haemoglobins can only be made consistent with this theory if the human species has passed through a bottleneck of numbers in the recent past. If this theory is true, estimates of the necessary size and duration of this bottleneck can be made. A theory is developed which leads to an estimate ofYg, n, the number of alleles present in a population which arise betweengandngenerations ago, and hence to the estimatewhereuis the neutral mutation rate andNethe effective population size, for the probability that a population contains no such alleles. Using data on haemoglobins, this gives an approximate upper limit to the time elapsed since the bottleneck in human numbers. Either such a bottleneck occurred, or the neutral mutation theory is false; data on other proteins will enable a choice between these possibilities to be made.

Population Size, Polymorphism, and the Rate of Non-Darwinian Evolution

The possibility that a high rate of selectively neutral mutation can account for both genetic polymorphism and gene substitution in evolution is investigated theoretically. A species divided into partially isolated local populations is considered, and relations found between the local population size, the number of populations, the migration and mutation rates, and the degree of polymorphism within and between populations. It is shown that if selectively neutral mutation rates are high enough (perhaps 10-6 per generation per cistron) to account for observed rates of evolution, then either the total population size of a species, now or in the geologically recent past, must be small (⩽106), or hybrids between local populations will be heterozygous at almost all loci.