Substitution Rates In Genes Research Articles

Cytochrome c: Gene structure, homology and ancestral relationships

In this paper, the author notes the recommended definition of the word "homology" (i.e., indicating an ancestral relationship) and the recommended stipulation that "evidence for homology should be explicitly laid out". The postulated homology for somatic and testes-specific isozymes of cytochrome c is then examined, using recent data obtained from the study of cytochrome c genes. Consideration is also given to some newer findings of molecular biology and possibilities are considered for various types of change in the genome of an organism. Possible roles of introns, pseudogenes and multigene families are considered. The relationship of testes-specific cytochrome c to somatic cytochrome c is carefully considered from data obtained in experimental studies of genes of these two isozymes. If one assumes that these isozymes arose as a consequence of a gene duplication, data from rat and mouse genes indicate that the testes-specific isozyme has incorporated more amino acid changes than the somatic isozyme since the time of their divergence. However, when the 15 amino acid differences (testes-specific vs. somatic isozyme) are considered, there is virtually no similarity in these 15 positions of the testes-specific isozyme with any of the hypothetical ancestral sequences of the somatic isozyme. Nucleotide differences in cytochrome c genes have been evaluated by comparing genes for the two rodent cytochrome c isozymes to cytochrome c genes of fruit flies, chickens and humans. Comparisons of nucleotide substitution rates in genes for the two cytochrome c isozymes in rodents confirm the conclusions from amino acid sequence comparisons; namely, that more rapid nucleotide changes have occurred in the testes-specific cytochrome c gene, than in the somatic cytochrome c gene. Possible explanations for these findings are considered.

A Unifying Model for the Substitutional Genetic Load

In this paper, a general deterministic model for gene substitution at all segregating loci is derived. The results of a rigorous mathematical analysis of the equations are stated and found to be consistent with results derived by making typical simplifying assumptions. All previous deterministic calculations of possible rates of gene substitution and the 'substitutional genetic load' are shown to be special cases of the model. New expressions for the substitutional genetic load and rate of substitution in hard selection with cth-order epistasis are given. In addition, the concept of 'threshold selection' is generalized to less extreme 'rank selection', and formulae for the relationship between the substitution rate and the selection coefficient are given. The 'load argument' for the neutral theory is reviewed in light of the new findings and strongly rejected. Several other areas of disagreement, such as the effect of population dynamics and competition on the substitutional genetic load, are sorted out using the model. Some remarks regarding experimental input are made.

Genetic diversity and population structure of Piceaglauca on an altitudinal gradient in interior Alaska

Allozyme variation at 13 loci for 11 enzyme systems was studied in four white spruce (Piceaglauca (Moench) Voss) populations extending from a floodplain at 120 m above sea level to the altitudinal tree limit at 750 m above sea level in interior Alaska. Although 97% of the total genetic diversity was among trees within stands and 1% was among stands within populations, frequencies of several allozymes and allozyme genotypes were significantly different (P < 0.05) among populations. Ninety-two percent of the loci were polymorphic. Total heterozygosity was 0.276. Heterozygosity and allozyme frequencies were not related to altitude. The population at the tree limit was as genetically diverse as populations at low elevations [Formula: see text] and contained four of seven rare alleles observed in all populations. These observations suggested that white spruce is genetically diverse in interior Alaska and the tree-limit population will continue to colonize new habitats. Genetic distance was not related to altitude and geographic distance and was less between the tree-limit and upper slope populations than among other populations A detectable gene substitution rate was estimated at 10−6 per year. Populations on the upper slope and at the tree limit may have diverged about 2500 years ago and reached tree-limit altitudes only recently. Populations at low altitudes may have diverged during early Holocene white spruce expansion. We concluded that white spruce is genetically diverse in a small geographic area in interior Alaska. Results suggested that local white spruce populations should be regenerated from indigenous seed and that provenance research is needed to support afforestation programs.

The Relative Rates of Evolution of Sex Chromosomes and Autosomes

We develop models of the rates of evolution at sex-linked and autosomal loci and of the rates of fixation of chromosomal rearrangements involving sex chromosomes and autosomes. We show that the substitution of selectively favorable mutations often proceeds more rapidly for X- or Y-linked loci than for the autosomes, provided that mutations are recessive or partially recessive on the average. Selection acting on a quantitative character is expected to result in similar long-term rates of gene substitution for X-linked and autosomal loci, unless there is strong directional dominance. Short-term responses to such selection often preferentially fix alleles at autosomal loci. The fixation of slightly deleterious alleles by random drift and the stochastic turnover of alleles at loci controlling quantitative characters under stabilizing selection usually proceed somewhat more slowly at sex-linked loci. In contrast, the fixation of underdominant chromosomal rearrangements by random genetic drift is faster with sex linkage. Sex-specific selection may also differentially favor the fixation of sex-linked rearrangements. These results are discussed in relation to genetic and cytological data on species differences. We show that the frequently disproportionate effects of the sex chromosomes on interspecific inviability or sterility are consistent with the hypothesis that the gene differences concerned involve recessive or partially recessive alleles fixed by selection. Haldane's rule is readily interpreted in this light. There is little evidence for strong effects of the sex chromosomes on quantitative characters in interspecific crosses, in accordance with our theoretical results. Thus, the evolution of reproductive isolation may not be the byproduct of selective change in additively inherited, polygenic traits. Rather, it may be due mainly to the fixation of favorable mutations whose effects on fitness reflect locus-specific effects on the phenotype. These mutations behave as major genes in the sense of contributing the bulk of the genetic variance in the characters that they control during the course of the mutations' substitution. The data on the genetics of short-term responses to selection in Drosophila are hard to interpret, but, in accordance with theory, these responses do not usually seem to involve the X chromosome disproportionately. In some groups, there is evidence for a disproportionate role of the sex chromosomes in chromosomal changes, but others show no clear pattern. Factors that may distort the expectations of the simple models of chromosomal evolution are discussed.

Misuse and Modification of Nei's Genetic Distance

The use and misuse of various measures of genetic in electrophoretic studies of systematics have recently been subject of considerable attention (Mickevich and Johnson, 1976; Throckmorton, 1978; Baverstock et al., 1979; Avise et al., 1980; Farris, 1981; Mickevich and Mitter, 1981; Patton et al., 1981; Sites et al., 1981; Thorpe, 1982). Despite problems associated with use of genetic distances in construction of phylogenetic trees, convenience and general utility of such measures have resulted in their continued and widespread application. The most commonly-used such distance is Nei's D (Hedrick, 1983). This measure purportedly assesses accumulated number of gene substitutions per if the rate of gene substitution per locus is same for all (Nei, 1972:283). However, assumption of equal rates of gene substitution at all loci is rarely, if ever, considered by investigators before employing Nei's D. Because this assumption is probably never met in an interspecific electrophoretic survey that involves more than one locus (Sarich, 1977; Thorpe, 1982), it is important to examine effects of not meeting this assumption. Nei (1972) defined normalized identity between two randomly mating diploid populations as

Evolution of a finite population under gene conversion.

Evolution at a multiallelic locus under the joint action of gene conversion, mutation, selection, and random genetic drift is studied. Generations are discrete and nonoverlapping; the diploid, monoecious population mates at random. Under the assumption that all four evolutionary forces are weak, a diffusion approximation is established for the dynamics of the gene frequencies. For two alleles, the inclusion of gene conversion merely alters one of the two selection parameters of the thoroughly investigated diffusion process without conversion. Therefore, all results for this classical process, some of which are reviewed and extended here, are immediately applicable to the biologically more general problem. Small conversional disparities can dramatically affect the fixation probability (and hence the rate of gene substitution) and can greatly reduce the mean conditional fixation time of a new mutant. The mean absorption and fixation times are often sufficiently short to imply that biased gene conversion can be an important mechanism for the loss of genetic variability in and the genetic divergence of isolated populations.

GENETIC VARIABILITY AND RATE OF GENE SUBSTITUTION IN A FINITE POPULATION UNDER MUTATION AND FLUCTUATING SELECTION

By using a numerical method of solving stochastic difference equations, the level of genetic variability maintained in a finite population and the rate of gene substitution under several models of fluctuating selection intensities were studied. It is shown that mutation and random genetic drift both play an important role in determining genetic variability and the rate of gene substitution. Compared with the case of neutral mutations, the fluctuation of selection intensity caused by temporal and spatial heterogeneity of environments generally increases the rate of gene substitution, but the level of genetic variability may be increased or decreased, depending upon the model and the parameters used. Although such a type of selection per se can not be ruled out, when mutation is taken into account, it is difficult to explain both the observed amount of genetic variability and the rough constancy of evolutionary rate within a framework of fluctuating selection models.

The theory of genetic distance and evolution of human races.

1. Theoretical works on Nei's genetic distance and its extensions are discussed. New formulae for the sampling variances of genetic distance estimates are presented. Formulae for the genetic identity of genes at the electrophoretic level when the mutation rate varies from locus to locus are also presented. 2. Empirical data suggests that the rate of gene substitution or mutation rate per locus varies considerably among protein loci, and if this factor is taken into account, the rate of decline of genetic identity (I) is no longer constant but decreases with evolutionary time. Using both the infiniteallele model and the stepwise mutation model, the numerical relationship betweenI and evolutionary time is presented. This relationship may be used for estimating the time after divergence between populations. The value of genetic distance or genetic identity is also affected considerably by the bottleneck effect. The bottleneck effect generally accelerates the increase of genetic distance with time, and the effect remains for a long time after the population size returns to the original level. A method for correcting for this effect is presented. 3. Application of the theory of genetic distance to data on protein polymorphism in man indicates that the genetic variation between the three major races, Caucasoid, Negroid, and Mongoloid, is much smaller than the variation within them, despite the fact that there is a conspicuous difference in some morphological characters such as pigmentation, facial structure, and hair texture. It is proposed that the differentiation of these morphological characters was brought about by relatively strong natural selection through a small number of gene substitutions, whereas general protein loci are subject to little or very weak selection. Analysis of blood group gene frequency data gives essentially the same result as those from protein loci, though they are likely to have been affected by nonrandom sampling of the loci. It is also shown that at the protein level the racial differences in man correspond to those between local races in other organisms. 4. Rough estimates of the number of codon differences between an individual of man and his various relatives are presented. It seems that the mean number of codon differences between man and chimpanzee is about 10 times larger than that between second degree relatives in Caucasians or Japanese, but about 1/19 of that between man and horse. 5. Genetic distance estimates suggest that among the three major races of man the first divergence occurred about 120,000 years ago between Negroid and a group of Caucasoid and Mongoloid and then the latter group split into Caucasoid and Mongoloid around 60,000 years ago. It is also shown that the genetic identity between man and chimpanzee corresponds to a divergence time of 4–6 million years if the assumption of constant rate of amino acid substitution is correct. 6. Methods of constructing a phylogenetic tree from genetic distance estimates are discussed. For constructing the topology of a tree, Fitch and Margoliash's method is quite efficient. For estimating branch lengths, however, Nei's method of averaging distances seems to be better. 7. A phylogenetic tree for twelve races of man is constructed by using gene frequency data for 11 protein and 11 blood group loci. This tree roughly agrees with what we expect intuitively from the morphological characters and the historical record of these races.

Eukaryotic evolution based on information in chromosomes on allele frequencies

A model for eukaryotic evolution is proposed, postulating a pressure for a frequency increase of rare recessive alleles by gene conversion, the amount of pressure being inversely related to the frequency. Such a mechanism would lead to high rates of gene substitution at low genetic loads and it would explain the widespread occurrence of polymorphic states. It requires, however, information in the chromosomes on the frequencies of different alleles. It is proposed that each gene is associated with a series of copies of homologous alleles from previous generations and that this constitutes the required information. Such a mechanism requires sexual reproduction and a pairing during meiosis chromomere by chromomere. The gene copies are assumed to exert their action during meiosis by transcription and base pairing of the resulting RNA with the genes. The proposed mechanism should not only increase the frequency of rare established recessives, it should also lead to the formation for each common gene of several synonymous template lines. The mechanism can explain the extensive transcription occurring during meiosis, the occurrence of DNA in families of related but not identical sequences and the fact that most DNA has the dinucleotide composition characteristic for certain genes. It also explains the large size of eukaryotic genetic units and the finding that the larger part of such a unit can be deleted without measurable phenotypic effects. Further support of the model is found in the chromosome cycle of the gall midges.

Evolutionary Rates and Host Defenses Against Avian Brood Parasitism

Experiments investigating host defenses against the brood parasitism of the brown-headed cowbird revealed that, within most species, nearly all individuals either accept or reject cowbird eggs. Therefore, species are easily designated as "accepters" or "rejecters". The results of these experiments differ somewhat from data on natural cowbird parasitism, where some species seem to be variable in their response. However, much of what appears in natural cowbird parasitism to be variable expressions of host defenses are probably not responses specific to cowbird parasitism but are manifestations of standard avian behavior patterns. I hypothesize that few intermediate species exist, because host defenses are selected so strongly that the time span over which any species shows an intermediate rejection rate is of short duration. Hence, the number of species in transition from accepter to rejecter is always low. Most accepters did show low rates (less than 20%) of apparent rejection to experimental cowbird parasitism, but it is not likely that all these species are currently beginning the transition to rejecter species. Like most observed rejections of natural cowbird parasitism, these rejections by the accepters were probably not expressions of evolved host defenses but of behaviors related to other facets of breeding. The hypothesis that species rapidly become fixed for rejection is tested by a model that derives the selection coefficient for the two alternative character states of acceptance and rejection. Parameters in the model are the probability of being parasitized, P, and values for the reproductive outputs of parasitized anal unparasitized accepter and rejecter individuals. The model is difficult to apply to present-day rejecters. However, the selective value that rejection will have when and if it evolves in current accepter species can be calculated by assuming that, once a bird removes a cowbird egg, its eggs have the same probability of success as if a cowbird egg had never been present. Selection coefficients for hypothetical rejection behavior in the four best-studied accepter species range from .14 to .34. Making certain assumptions about the genetic determinants of rejection behavior and using these selection coefficients to calculate rates of gene substitution results in a range of 20-100 years as the time necessary for these species to change from accepters to rejecters. Features of the present-day rejecter species indicate that the selection coefficients in these species could have been high enough to have resulted in similarly rapid rates of gene substitution. The high selection coefficients calculated and the rapid rates of gene substitution estimated support the hypothesis explaining the scarcity of species with intermediate rates of rejection of cowbird eggs.

Enzyme polymorphisms: gene frequency distributions with mutation and selection for optimal activity.

Gene frequency distributions observed in large-scale surveys of species of Drosophila are shown to be incompatible with a genetic model involving neutral mutations and genetic drift alone. The data are, however, qualitatively similar to predictions based on an alternative model of natural selection for an optimal level of enzyme activity in addition to drift and mutation. The intensity of selection detected reduces the mean rate ofgene substitution to less than one-quarter that expected on the neutral-allele hypothesis.

Population size and rate of evolution

It is suggested that in evolution there is much substitution of nearly neutral mutations, for which the selection intensity varies from time to time or from region to region. Since the variance among the selection coefficients of new mutants decreases when the environment becomes uniform, the probability of a mutant being advantageous to the species as a whole increases in more uniform environment (Fig. 1).Therefore the rate of gene substitution increases in smaller populations, as smaller populations are likely to be distributed over less varied environments.The adequacy of the model was discussed in relation with the following facts or plausible postulates. 1. A large number of amino acid substitutions during a period corresponding to the formation of new species. 2. Rapid evolution at the phenotypic level of populations having a small size. 3. Many extinctions and expansions of the species in the past.

Patterns of Genetic Differentiation in the Slender Wild Oat Species Avena barbata

Allozyme frequencies at five enzyme loci were determined for 14 California populations of Avena barbata, a species introduced to California from the Mediterranean Basin during the colonization of North America. Allelic frequencies at these loci were also determined in Mediterranean collections of this species. The pattern of divergence of the California populations from the ancestral gene pool was not random and was strongly correlated with environment; thus, the pattern is not in accord with the hypothesis that most electrophoretically detectable variants are adaptively neutral. Rates of gene substitution in California were also not in accord with the neutrality hypothesis. The observations are, however, compatible with predictions of Neo-Darwinian evolutionary theory. We interpret these observations to indicate that natural selection plays a major role in determining the unique patterns of distribution of genetic variability in the slender wild oat in California.

Genetic Distance between Populations

A measure of genetic distance (D) based on the identity of genes between populations is formulated. It is defined as D = -logeI, where I is the normalized identity of genes between two populations. This genetic distance measures the accumulated allele differences per locus. If the rate of gene substitution per year is constant, it is linearly related to the divergence time between populations under sexual isolation. It is also linearly related to geographical distance or area in some migration models. Since D is a measure of the accumulated number of codon differences per locus, it can also be estimated from data on amino acid sequences in proteins even for a distantly related species. Thus, if enough data are available, genetic distance between any pair of organisms can be measured in terms of D. This measure is applicable to any kind of organism without regard to ploidy or mating scheme.

CORRIGENDUM

IOCHEMICAL studies of certain proteins have recently shown that the rate of evolution or gene substitution is much higher than that previously thought (KIMURA 1968; DAYHOFF 1969). This high rate of gene substitution has aroused a great deal of controversy about HALDANE’S (1957; 1960) theory of the cost of natural selection. HALDANE postulated that the genetic deaths needed to secure gene substitution by natural selection lower the average fitness of a population, so that there is an upper limit to the number of gene substitutions per unit length of time, depending on the fertility of the species in question. In this case the fitness of a genotype was assumed to be constant. HALDANE’S theory was accepted by KIMURA (1960; 1967) and CROW (1968) but questioned by a number of authors. Among others, SVED (1968) and MAYNARD SMITH (1968) have argued that if the population size is regulated in a density-dependent manner and gene substitution occurs by competitive selection, the mean fitness of the population would not necessarily be reduced. They produced a model of threshold selection in which gene substitutions may occur at a much higher rate than HALDANE’S computation allows. Recently, MATHER (1969) developed an interesting model of competitive selection and showed that many classical formulae for the change in gene frequency hold true under competitive selection. He, however, argued that the cost of natural selection should be re-examined, taking into account competitive selection and the effect of selection on population size. He thought that the cost of selection would be much less than HALDANE’S computation suggests. Another type of model for competitive selection was developed by SCHUTZ and UZANIS (1969). In this model, however, neither the cause and process of competition nor the mechanism of population regulation was studied in detail. The purpose of the present paper is first to develop mathematical models for natural selection in regulated populations and then examine the adequacy of the theory of the cost of natural selection. The cost of natural selection will be looked at from a slightly different angle, and the fertility excess or genetic variance of fitness necessary for a given rate of gene substitution will be studied. It will be shown that competition itself does not lead to threshold selection and HALDANE’S conclusion is essentially correct.

Remarks on the substitutional load

The concept of substitutional load is claimed by some authors to be totally misguided, and by other to have considerable merit. Without expressing any view on this question, this paper considers some consequences of the concept once it is accepted. It suggests that it is important to view the concept by considering the various substitutions in progress during any generation, rather than by following through the substitution process at one locus over many generations. It then appears that the maximum substitution rate is rather higher than suggested by Haldane and subsequently Kimura. In particular, the observed rates of gene substitution in mammals to not appear incompatible with values of selective differences of order 0.001–0.1. A consequence is that it does not appear necessary to conclude, with Kimura (1968), that most substitutions refer to neutral or nearly neutral alleles.

Possible Rates of Gene Substitution in Evolution

Maximum rates of gene substitution are calculated, showing that Haldane's estimate (1957) of one completed gene substitution per 300 generations may be much too low. The approach differs conceptually from Haldane's in postulating that the mean fitness of the population is not affected by its genotype. The rate of death is assumed to be set by density-dependent factors, and rates of substitution and selective intensities consistent with this death rate are calculated. This formulation leads to no obvious upper limit for the rate of substitution. Rates of one completed substitution per generation or more are by no means excluded. The selective value consistent with a given death rate or set of fitness differentals is not independent of the rate of substitution but is approximately inversely proportional to it. The result is little affected by the degree of dominance or by the initial gene frequency.