The estimation of genetic divergence

Summary We have independently repeated the computer simulations on which Nei and Tateno (1978) base their criticism of REH theory and have extended the analysis to include mRNAs as well as proteins. The simulation data confirm the correctness of the REH method. The high average value of the fixation intensity ₂ found by Nei and Tateno is due to two factors: 1) they reported only the five replications in which ₂ was high, excluding the forty-five replications containing the more representative data;and 2) the lack of information, inherent to protein sequence data, about fixed mutations at the third nucleotide position within codons, as the values are lower when the estimate is made from the mRNAs that code for the proteins. REH values calculated from protein or nucleic acid data on the basis of the equiprobability of genetic events underestimate, not overestimate, the total fixed mutations. In REH theory the experimental data determine the estimate T₂ of the time average number of codons that have been free to fix mutations during a given period of divergence. In the method of Nei and Tateno it is assumed, despite evidence to the contrary, that every amino acid position may fix a mutation. Under the latter assumption, the measure X₂ of genetic divergence suggested by Nei and Tateno is not tenable: values of X₂ for the hemoglobin divergences are less than the minimum number of fixed substitutions known to have occurred.Within the context of REH theory, a paradox, first posed by Zuckerkandl, with respect to the high rate of covarion turnover and the nature of general function sites in proteins is resolved.     

Estimating the total number of nucleotide substitutions since the common ancestor of a pair of homologous genes: Comparison of several methods and three beta hemoglobin messenger RNA's

Summary The mRNA sequences of beta hemoglobin for human, mouse and rabbit were examined. Observations included the following: (1) there is a significant bias against the use of codons only one nucleotide different from terminating codons; (2) less than 4% of the codons end in adenine; (3), guanine is the most common third position nucleotide but it never follows a second position cytosine; (4) nearest neighbor (doublet) nucleotides are non-random with the greatest contributor to non-randomness being the third position suggesting that codon choice for a given amino acid rather than a choice among amino acids is the more important contributor; (5) the CG dinucleotide is even rarer in positions other than the first and second of the codon than it is in those two, suggesting that the need for arginine has in fact elevated the CG frequency in those positions; (6) 77 per cent of the nucleotides are unsubstituted among these three taxa, which could be a sampling effect, but there is strong evidence that about one-third of them are in fact unsubstitutable because of selective constrainsts; (7) the two longest stretches of unsubstituted nucleotides (32 and 35 consecutive nucleotides) surround the points of the two non-coding insertion sequences; (8) over half the substitutions occur in the third nucleotide position of the codons; (9) silent (non-amino acid changing) substitutions occur at about four times the rate of non-silent substitutions on the basis of their relative opportunity to occur; (10) silent substitutions occur slightly but significantly more often in codons that also have non-silent substitutions than independence of the two events would predict; (11) substitutions occur in adjacent nucleotides significantly more often than chance would predict; (12) among four-fold degenerate codons, third position transitions (principally cytosine-uracil interchanges) outnumber transversions by two to one although the reverse ratio would be expected.The analysis of these messengers provided an opportunity to evaluate the random evolutionary hit (REH) theory. I observed that: (1) the REH theory is premised upon five assumptions, all false; (2) the theory leads to contradictory estimates of the number of varions; (3) the REH values are underestimates; (4) the REH values frequently violate the triangle inequality; (5) the REH values, contrary to claim, are not concordant either with accepted point mutations (PAMs) or augmented distances; (6) the REH values are more likely than values uncorrected for multiple substitutions to give incorrect phylogenies; and (7) the REH values have statistical problems probably associated with a large variance in its fundamental parameter, r_e. From this I conclude that REH theory is not suitable for its intended purpose of estimating from protein sequences of nucleotide substitutions since the common ancestor of two gene products.     

The old REH theory remains unsatisfactory and the new REH theory is problematical - a reply to holmquist and jukes

Summary In response to criticism of REH theory (Fitch 1980), Holmquist and Jukes (1981) have mostly avoided the criticism or misunderstood it. Since they themselves state in their response that Amino acid sequence data alone cannot be used to estimate total nucleotide substitutions, they agree with the criticism. Most of their paper treats the newer theory (here designated as the REHN theory) which attempts to use the nucleotide sequences encoding proteins to better estimate total nucleotide substitutions (Holmquist and Pearl 1980). Since I made no criticism of REHN theory, their comments are frequently beside the point of my original criticism of REH theory. Nevertheless, it is shown here that REHN theory is also unsatisfactory in that: One, the varions are now more clearly defined but in such a way as to preclude the same codon from suffering a nucleotide substitution in more than one evolutionary interval. Two, the set of codons that accepts silent substitutions is identical to the set that accepts amino acid changing nucleotide substitutions. Three, the uncertainty in the REH estimate is considerable in that alternative excellent fits to the same observatuonal data may give alternative REH values that differ significantly even before stochastic variation and selective bias are considered. Four, the fit of their model to data is an irrelevancy where there are zero degrees of freedom.     

The reh theory of protein and nucleic acid divergence: A retrospective update

Summary Over half a decade has passed since the quantitative REH theory of evolutionary divergence in nucleic acids and proteins was published. The principle tenant of this theory is that natural selection and stochastic processes interact, the main effect of the former being to restrict those codon sites which may fix mutations. At the time it was published the theory predicted a magnitude for the total number of fixed nucleotide replacements that was appreciably larger than estimates then current. 'In the last two years these predictions have been confirmed in those protein families for which the experimental data base is large: cytochromec, -hemoglobin,-hemoglobin, and myoglobin.It has come to our attention, chiefly through private correspondance, but also in one published review, that certain aspects of the REH theory have caused confusion among some users. This paper discusses these particular aspects in some detail, restates the theory in a manner which emphasizes its essential simplicity, analyzes the magnitude of possible sources of errors, and considers some important statistical matters not dealt with elsewhere. The calculational methodology is simplified by replacing tables and graphs by polynomial expressions, and deriving a more simple expression for calculating the number of codons which have been free to fix mutations during some part of the period of divergence of two species. A statistical bias in the estimation of the fixation intensity is corrected.It is hoped these changes will make the method more accessible to those without extensive computing facilities.     

Evolutionary analysis ofα andβ hemoglobin genes by reh theory under the assumption of the equiprobability of genetic events

Summary It is shown how REH theory in conjunction with mRNA or gene sequence data can be used to obtain estimates of the fixation intensity, the number of varions, and the total mutations fixed between homologous pairs of nucleic acids. These estimates are more accurate than those that can be derived from amino acid sequence data. The method is illustrated for and hemoglobin genes and these improved estimates are compared with those made from the amino acid sequences for which those genes code. Significant differences are found between the estimates made by these two methods. For the hemoglobin gene sequences examined here, the fixation intensity is some-what less than the protein data had suggested, and the number of rations is considerably greater. Depending on the gene sequences examined, between 62 and 83% of the codons appear able to fix mutations during the divergences considered. This reflects the constraints of natural selection on acceptable mutations. The total number of base replacements separating the genes for human, mouse, and rabbit hemoglobin varies from 61 to 105 depending on the pair examined. Rabbit and hemoglobin are separated by at least 290 fixed mutations. For such distantly related sequences estimates made from protein and mRNA data differ less, reflecting the higher quality of information from the many observed changes in primary structure. The effects of nonrandom gene structure on these evolutionary estimates and the fact that various genetic events are not equiprobable are discussed.     

The population genetics of adaptation: the adaptation of DNA sequences

I describe several patterns characterizing the genetics of adaptation at the DNA level. Following Gillespie (1983, 1984, 1991), I consider a population presently fixed for the ith best allele at a locus and study the sequential substitution of favorable mutations that results in fixation of the fittest DNA sequence locally available. Given a wild type sequence that is less than optimal, I derive the fitness rank of the next allele typically fixed by natural selection as well as the mean and variance of the jump in fitness that results when natural selection drives a substitution. Looking over the whole series of substitutions required to reach the best allele, I show that the mean fitness jumps occurring throughout an adaptive walk are constrained to a twofold window of values, assuming only that adaptation begins from a reasonably fit allele. I also show that the first substitution and the substitution of largest effect account for a large share of the total fitness increase during adaptation. I further show that the distribution of selection coefficients fixed throughout such an adaptive walk is exponential (ignoring mutations of small effect), a finding reminiscent of that seen in Fisher's geometric model of adaptation. Last, I show that adaptation by natural selection behaves in several respects as the average of two idealized forms of adaptation, perfect and random.     

Theoretical foundations for quantitative paleogenetics

Summary REH theory is extended by deriving the theoretical equations that permit one to analyze the nonrandom molecular divergence of homologous genes and proteins. The nonrandomicities considered are amino acid and base composition, the frequencies with which each of the four nucleotides is replaced by one of the other three, unequal usage of degenerate codons, distribution of fixed base replacements at the three nucleotide positions within codons, and distributions of fixed base replacements among codons. The latter two distributions turn out to dominate the accuracy of genetic distance estimates. The negative binomial density is used to allow for the unequal mutability of different codon sites, and the implications of its two limiting forms, the Poisson and geometric distributions, are considered. It is shown that the fixation intensity — the average number of base replacements per variable codon - is expressible as the simple product of two factors, the first describing the asymmetry of the distribution of base replacements over the gene and the second defining the ratio of the average probability that a codon will fix a mutation to the probability that it will not. Tables are given relating these features to experimentally observable quantities in hemoglobin, hemoglobin, myoglobin, cytochromec, and the parvalbumin group of proteins and to the structure of their corre-sponding genes or mRNAs. The principal results are (1) more accurate methods of estimating parameters of evolutionary interest from experimental gene and protein sequence data, and (2) the fact that change in gene and protein structure has been a much less efficient process than previously believed in the sense of requiring many more base replacements to effect a given structural change than earlier estimation procedures had indicated. This inefficiency is directly traceable to Darwinian selection for the nonrandom gene or protein structures necessary for biological function. The application of these methods is illustrated by detailed consideration of the rabbit -and hemoglobin mRNAs and the proteins for which they code. It is found that these two genes are separated by about 425 fixed base replacements, which is a factor of two greater than earlier estimates. The replacements are distributed over approximately 114 codon sites that were free to accept base mutations during the divergence of these two genes.     

Defined order of evolutionary adaptations: experimental evidence

Organisms often adapt to new conditions by means of beneficial mutations that become fixed in the population. Often, full adaptation requires several different mutations in the same cell, each of which may affect a different aspect of the behavior. Can one predict order in which these mutations become fixed? To address this, we experimentally studied evolution of Escherichia coli in a growth medium in which the effects of different adaptations can be easily classified as affecting growth rate or the lag‐phase duration. We find that adaptations are fixed in a defined and reproducible order: first reduction of lag phase, and then an increase of the exponential growth rate. A population genetics theory explains this order, and suggests growth conditions in which the order of adaptations is reversed. We experimentally find this order reversal under the predicted conditions. This study supports a view in which the evolutionary path to adaptation in a new environment can be captured by theory and experiment.     

Fitness Is Strongly Influenced by Rare Mutations of Large Effect in a Microbial Mutation Accumulation Experiment

Our understanding of the evolutionary consequences of mutation relies heavily on estimates of the rate and fitness effect of spontaneous mutations generated by mutation accumulation (MA) experiments. We performed a classic MA experiment in which frequent sampling of MA lines was combined with whole genome resequencing to develop a high-resolution picture of the effect of spontaneous mutations in a hypermutator (ΔmutS) strain of the bacterium Pseudomonas aeruginosa. After ∼644 generations of mutation accumulation, MA lines had accumulated an average of 118 mutations, and we found that average fitness across all lines decayed linearly over time. Detailed analyses of the dynamics of fitness change in individual lines revealed that a large fraction of the total decay in fitness (42.3%) was attributable to the fixation of rare, highly deleterious mutations (comprising only 0.5% of fixed mutations). Furthermore, we found that at least 0.64% of mutations were beneficial and probably fixed due to positive selection. The majority of mutations that fixed (82.4%) were base substitutions and we failed to find any signatures of selection on nonsynonymous or intergenic mutations. Short indels made up a much smaller fraction of the mutations that were fixed (17.4%), but we found evidence of strong selection against indels that caused frameshift mutations in coding regions. These results help to quantify the amount of natural selection present in microbial MA experiments and demonstrate that changes in fitness are strongly influenced by rare mutations of large effect.     

Rates of evolution: Is there a conflict between neo-darwinian evolutionary theory and the fossil record?

Neo-darwinian and population genetics theory assumes that the necessary and sufficient set of conditions for all genetic, therefore evolutionary, change has been identified. Punctuationalists have assumed the opposite and cite the fossil record as evidence for change too rapid to be explained in neo-darwinian theory. Data is given here to provide estimates of the rate of evolution in hominid fossils, in living populations, and of that rate which would qualify as punctuational in the hominid fossil record. Evolution in living populations is orders of magnitude greater than that found in the fossil record and far greater than necessary to create apparently instantaneous saltations in the fossil record. It is suggested that such saltations may not represent more rapid rates of evolution but, rather, the persistence of evolutionary change in a given direction for a longer than normal period.     

Clonal interference is alleviated by high mutation rates in large populations

When a beneficial mutation is fixed in a population that lacks recombination, the genetic background linked to that mutation is fixed. As a result, beneficial mutations on different backgrounds experience competition, or "clonal interference," that can cause asexual populations to evolve more slowly than their sexual counterparts. Factors such as a large population size (N) and high mutation rates (mu) increase the number of competing beneficial mutations, and hence are expected to increase the intensity of clonal interference. However, recent theory suggests that, with very large values of Nmu, the severity of clonal interference may instead decline. The reason is that, with large Nmu, genomes including both beneficial mutations are rapidly created by recurrent mutation, obviating the need for recombination. Here, we analyze data from experimentally evolved asexual populations of a bacteriophage and find that, in these nonrecombining populations with very large Nmu, recurrent mutation does appear to ameliorate this cost of asexuality.     

Mutation-selection balance for environmental variance

The role of mutation-selection balance in maintaining environmental variance (V(E)) of quantitative traits is investigated under the assumption that genotypes differ in the magnitude of phenotypic variance, given genotypic value. Thus, V(E) can be regarded as a quantitative trait. As stabilizing selection on phenotype favors genotypes contributing low V(E), mutations that decrease V(E) are more likely to become fixed than those that increase it, and therefore V(E) should decline. If, however, essentially all mutants increase V(E) and overall selection is sufficiently strong that no mutants become fixed, then V(E) can be maintained. The heritability of the trait is determined by the relative sizes of mutational effects on phenotypic mean and residual variance and is independent of mutation rate and pleiotropic effects. This conclusion is not robust for small populations because some mutants may become fixed, which indicates that other selective forces must be involved, such as an intrinsic cost of homogeneity.     

The fitness effect of mutations across environments: a survey in light of fitness landscape models

The fitness effects of mutations on a given genotype are rarely constant across environments to which this genotype is more or less adapted, that is, between more or less stressful conditions. This can have important implications, especially on the evolution of ecological specialization. Stress is thought to increase the variance of mutations' fitness effects, their average, or the number of expressed mutations. Although empirical evidence is available for these three mechanisms, their relative magnitude is poorly understood. In this paper, we propose a simple approach to discriminate between these mechanisms, using a survey of empirical measures of mutation effects in contrasted environments. This survey, across various species and environments, shows that stress mainly increases the variance of mutations' effects on fitness, with a much more limited impact on their average effect or on the number of expressed mutations. This pattern is consistent with a simple model in which fitness is a Gaussian function of phenotypes around an environmentally determined optimum. These results suggest that a simple, mathematically tractable landscape model may not be quantitatively as unrealistic as previously suggested. They also suggest that mutation parameter estimates may be strongly biased when measured in stressful environments.     

Effects of spontaneous mutation accumulation on sex ratio traits in a parasitoid wasp

Sex allocation theory has proved extremely successful at predicting when individuals should adjust the sex of their offspring in response to environmental conditions. However, we know rather little about the underlying genetics of sex ratio or how genetic architecture might constrain adaptive sex-ratio behavior. We examined how mutation influenced genetic variation in the sex ratios produced by the parasitoid wasp Nasonia vitripennis. In a mutation accumulation experiment, we determined the mutability of sex ratio, and compared this with the amount of genetic variation observed in natural populations. We found that the mutability (h(2)(m)) ranges from 0.001 to 0.002, similar to estimates for life-history traits in other organisms. These estimates suggest one mutation every 5-60 generations, which shift the sex ratio by approximately 0.01 (proportion males). In this and other studies, the genetic variation in N. vitripennis sex ratio ranged from 0.02 to 0.17 (broad-sense heritability, H(2)). If sex ratio is maintained by mutation-selection balance, a higher genetic variance would be expected given our mutational parameters. Instead, the observed genetic variance perhaps suggests additional selection against sex-ratio mutations with deleterious effects on other fitness traits as well as sex ratio (i.e., pleiotropy), as has been argued to be the case more generally.     

Simulation of protein evolution by random fixation of allowed codons

Summary Computer simulation of protein evolution is based on a simple model consisting of random fixation of allowed codons (RFAC). Random replacement of single nucleotides occurs in a DNA sequence. If this results in any of the synonomous codons for allowed amino acids the mutation is fixed, if not, there is no change in the DNA and the cycle is repeated. Multiple fixations at the same nucleotide site, back mutations, degenerate fixations and coincidental identity of amino acids all occur. RFAC simulation begins with a single DNA sequence and follows a phylogeny based on the fossil record. The rate of fixation at the level of DNA is constant. The model upon which RFAC simulation is based is the same as the neutral theory of molecular evolution. The simulation is therefore a test of this theory. The results of simulated and real evolution are compared for fibrinopeptides A in mammals and cytochromes C and hemoglobin and chains in vertebrates. In each case the allowed variation at each site has been set equal to that observed, twice that observed and all protein amino acids. Rates of fixation vary from 2.4 × 10^–10 to 10^–5 accepted nucleotide fixations per codon per year. There is some, although never excellent, agreement between real and simulated evolution, the better fits are obtained in the cases of fibrinopeptides A and cytochromes C. The major source of discrepancy between real evolution and simulation is irregularities in the rates of real evolution. RFAC simulation is compared with the random evolutionary hit (REH) model, augmented maximum parsimony and the accepted point mutations (PAM) approach.     

Environment dependence of mutational parameters for viability in Drosophila melanogaster

The genomic rate of mildly deleterious mutations (U) figures prominently in much evolutionary and ecological theory. In Drosophila melanogaster, estimates of U have varied widely, from <0.1 to nearly 1 per zygote. The source of this variation is unknown, but could include differences in the conditions used for assaying fitness traits. We examined how assay conditions affect estimates of the rates and effects of viability-depressing mutations in two sets of lines with accumulated spontaneous mutations on the second chromosome. In each set, the among-line variance in egg-to-adult viability was significantly greater when viability was assayed using a high parental density than when it was assayed using a low density. In contrast, the proportional decline in viability due to new mutations did not differ between densities. Two other manipulations, lowering the temperature and adding ethanol to the medium, had no significant effects on either the mean decline or among-line variance. Cross-environment genetic correlations in viability were generally close to one, implying that most mutations reduced viability in all environments. Using data from the low-density, lower-bound estimates of U approached the classic, high values of Mukai and Ohnishi; at the high density, U estimates were similar to recently reported low values. The difference in estimated mutation rates, taken at face value, would imply that many mutations affected fitness at low density but not at high density, but this is shown to be incompatible with the observed high cross-environment correlations. Possible reasons for this discrepancy are discussed. Regardless of the interpretation, the results show that assay conditions can have a large effect on estimates of mutational parameters for fitness traits.     

Difference between evolutionarily effective and germ line mutation rate due to stochastically varying haplogroup size

Within a Y-chromosome haplogroup defined by unique event mutations, variation in microsatellites can accumulate due to their rapid mutation. Estimates based on pedigrees for the Y-chromosome microsatellite mutation rate are 3 or more times greater than the same estimates from evolutionary considerations. We show by simulation that the haplogroups that survive the stochastic processes of drift and extinction accumulate microsatellite variation at a lower rate than predicted from corresponding pedigree estimates; in particular, under constant total population size, the accumulated variance is on average 3-4 times smaller.     

Comparative genomics and the study of evolution by natural selection

Genomics profoundly affects most areas of biology, including ecology and evolutionary biology. By examining genome sequences from multiple species, comparative genomics offers new insight into genome evolution and the way natural selection moulds DNA sequence evolution. Functional divergence, as manifested in the accumulation of nonsynonymous substitutions in protein-coding genes, differs among lineages in a manner seemingly related to population size. For example, the ratio of nonsynonymous to synonymous substitution (d_N/d_S) is higher in apes than in rodents, compatible with Ohta's nearly neutral theory of molecular evolution, which suggests that the fixation of slightly deleterious mutations contributes to protein evolution at an extent negatively correlated with effective population size. While this supports the idea that functional evolution is not necessarily adaptive, comparative genomics is uncovering a role for positive Darwinian selection in 10–40% of all genes in different lineages, estimates that are likely to increase when the addition of more genomes gives increased power. Again, population size seems to matter also in this context, with a higher proportion of fixed amino acid changes representing advantageous mutations in large populations. Genes that are particularly prone to be driven by positive selection include those involved with reproduction, immune response, sensory perception and apoptosis. Genetic innovations are also frequently obtained by the gain or loss of complete gene sequences. Moreover, it is increasingly realized, from comparative genomics, that purifying selection conserves much more than just the protein-coding part of the genome, and this points at an important role for regulatory elements in trait evolution. Finally, genome sequencing using outbred or multiple individuals has provided a wealth of polymorphism data that gives information on population history, demography and marker evolution.     

A Bayesian approach to the inference of diploid genotypes using haploid genotypes

Morris and Spieth (1978) described a method of calculating unbiased estimates of diploid genotype frequencies given information on the genotypes of haploid cells derived from diploid individuals. They concluded that three haploids per diploid would minimize sampling variance of genotype frequencies, given a fixed total number of haploids examined. If the identity of individual diploid genotypes is needed, Morris and Spieth (1978) stated that more haploids should be collected per diploid. We extend this work by showing from a Bayesian perspective that the probability of misclassification of individuals depends not only on the number of haploids sampled, but also on the genetic structure of the population since misclassification error will increase as the frequency of heterozygotes increases. Since information on the genetic structure (allele frequencies, inbreeding coefficient) of a population is rarely known prior to the initiation of an empirical study, the usefulness of our Bayesian approach is in experimental design, by revealing the magnitude of possible misclassification errors given a particular choice of number of haploids.