Compensatory evolution in diploid populations

Compensatory mutations are individually deleterious but harmless in appropriate combinations either at more than two sites within a gene or on separate genes. Considering that dominance effects of selection and heterodimer formation of gene products may affect the rate of compensatory evolution, we investigate compensatory neutral mutation models for diploid populations. Our theoretical analysis on the average time until fixation of compensatory mutations shows that these factors play an important role in reducing the fixation time of compensatory mutations if mutation rates are not low. Compensatory evolution of heterodimers is shown to occur more easily if the deleterious effects of single mutants are recessive.     

Compensatory mutations are repeatable and clustered within proteins

Compensatory mutations improve fitness in genotypes that contain deleterious mutations but have no beneficial effects otherwise. As such, compensatory mutations represent a very specific form of epistasis. We show that intragenic compensatory mutations occur non-randomly over gene sequence. Compensatory mutations are more likely to appear at some sites than others. Moreover, the sites of compensatory mutations are more likely than expected by chance to be near the site of the original deleterious mutation. Furthermore, compensatory mutations tend to occur more commonly in certain regions of the protein even when controlling for clustering around the site of the deleterious mutation. These results suggest that compensatory evolution at the protein level is partially predictable and may be convergent.     

Simulation Study of a Multigene Family, with Special Reference to the Evolution of Compensatory Advantageous Mutations

We investigate the evolution of a multigene family incorporating the forces of drift, mutation, gene conversion, unequal crossing over and selection. The use of simulation studies is required due to the complexity of the model. Selection is modeled in two modes: positive selection as a function of the number of different beneficial alleles and negative selection against deleterious alleles. We assume that gene conversion is unbiased, and that all mutations are initially deleterious. Compensation between mutants creates beneficial and neutral alleles, and allowances are made for compensatory mutations either within or between the members of a multigene family. We find that gene conversion can enhance the rate of acquisition of compensatory advantageous mutations when genes are redundant.     

Time for Spreading of Compensatory Mutations under Gene Duplication

Evolution by compensatory mutations is accelerated by gene duplication because selective constraint is relaxed by gene redundancy. A mutation is called compensatory if it corrects the effect of an earlier deleterious mutation. Without duplication, Kimura has shown that the time for spreading of compensatory mutations is much reduced by tight linkage between the two chromosomal sites of mutations. In this report, the time for spreading with gene duplication was studied by using the diffusion equation method of Kimura, together with computer simulations. It was shown that, when 2Nv- is much less than unity, the time for spreading is greatly shortened by gene duplication as compared with the case of complete linkage between the two sites of mutations, where 2N is the effective population size (haploid) and v- is the rate of compensatory mutations. However, if 2Nv- greater than 1, gene duplication is not effective for accelerating the evolution by such mutations.     

FURTHER SIMULATION STUDIES ON EVOLUTION BY GENE DUPLICATION

In order to understand the origin of multigene families, Monte Carlo simulations were performed to see how a genetic system evolves under unequal crossing-over, mutation, random genetic drift and natural selection, starting from a single gene copy. Both haploid and diploid models were examined. Beneficial, neutral, and detrimental mutations were incorporated, and “positive” selection favors those chromosomes (haploid) or individuals (diploid) with more beneficial mutations than others. The same model for haploids was previously investigated with special reference to the evolution of gene organization, and the ratio of the numbers of beneficial genes to pseudogenes was found to be a rough indicator of the relative strengths of positive and negative (against deleterious alleles) natural selection (Ohta, 1987b). In the present paper, the evolution of gene organization and of sequence divergence among genes in the multigene family is examined. It is shown that positive selection accelerates the accumulation of arrays containing different beneficial mutations, but that total divergence including both neutral and beneficial mutations is not very sensitive to positive selection, under this model. The proportion of beneficial mutations in the total mutations accumulated is a better indicator of positive selection than is the total divergence. It is pointed out that various observed examples in which amino-acid substitutions are accelerated, as compared with synonymous substitutions in duplicated genes (Li, 1985), may reflect the effect of selection similar to the present scheme. The diploid model is shown to be more efficient for accumulating beneficial mutations in duplicated genes than the haploid one, and the relevance of this finding to the advantage of sexual reproduction is discussed.     

Role of gene duplication in evolution

It is now known that many multigene and supergene families exist in eukaryote genomes: multigene families with uniform copy members like genes for ribosomal RNA, those with variable members like immunoglobulin genes, and supergene families such as those for various growth factor and hormone receptors. Many such examples indicate that gene duplication and subsequent differentiation are extremely important for organismal evolution. In particular, gene duplication could well have been the primary mechanism for the evolution of complexity in higher organisms. Population genetic models for the origin of gene families with diverse functions are presented, in which natural selection favors those genomes with more useful mutants in duplicated genes. Since any gene has a certain probability of degenerating by mutation, success versus failure in acquiring a new gene by duplication may be expressed as the ratio of probabilities of spreading of useful versus detrimental mutations in redundant gene copies. Also examined are the effects of gene duplication on evolution by compensatory advantageous mutations. Results of the analyses show that both natural selection and random drift are important for the origin of gene families. In addition, interaction between molecular mechanisms such as unequal crossing-over and gene conversion, and selection or drift is found to have a large effect on evolution by gene duplication.     

History can matter: non-Markovian behavior of ancestral lineages

Although most of the important evolutionary events in the history of biology can only be studied via interspecific comparisons, it is challenging to apply the rich body of population genetic theory to the study of interspecific genetic variation. Probabilistic modeling of the substitution process would ideally be derived from first principles of population genetics, allowing a quantitative connection to be made between the parameters describing mutation, selection, drift, and the patterns of interspecific variation. There has been progress in reconciling population genetics and interspecific evolution for the case where mutation rates are sufficiently low, but when mutation rates are higher, reconciliation has been hampered due to complications from how the loss or fixation of new mutations can be influenced by linked nonneutral polymorphisms (i.e., the Hill-Robertson effect). To investigate the generation of interspecific genetic variation when concurrent fitness-affecting polymorphisms are common and the Hill-Robertson effect is thereby potentially strong, we used the Wright-Fisher model of population genetics to simulate very many generations of mutation, natural selection, and genetic drift. This was done so that the chronological history of advantageous, deleterious, and neutral substitutions could be traced over time along the ancestral lineage. Our simulations show that the process by which a nonrecombining sequence changes over time can markedly deviate from the Markov assumption that is ubiquitous in molecular phylogenetics. In particular, we find tendencies for advantageous substitutions to be followed by deleterious ones and for deleterious substitutions to be followed by advantageous ones. Such non-Markovian patterns reflect the fact that the fate of the ancestral lineage depends not only on its current allelic state but also on gene copies not belonging to the ancestral lineage. Although our simulations describe nonrecombining sequences, we conclude by discussing how non-Markovian behavior of the ancestral lineage is plausible even when recombination rates are not low. As a result, we believe that increased attention needs to be devoted to the robustness of evolutionary inference procedures that rely upon the Markov assumption.     

Selectionism and neutralism in molecular evolution

Charles Darwin proposed that evolution occurs primarily by natural selection, but this view has been controversial from the beginning. Two of the major opposing views have been mutationism and neutralism. Early molecular studies suggested that most amino acid substitutions in proteins are neutral or nearly neutral and the functional change of proteins occurs by a few key amino acid substitutions. This suggestion generated an intense controversy over selectionism and neutralism. This controversy is partially caused by Kimura's definition of neutrality, which was too strict (|2Ns|< or =1). If we define neutral mutations as the mutations that do not change the function of gene products appreciably, many controversies disappear because slightly deleterious and slightly advantageous mutations are engulfed by neutral mutations. The ratio of the rate of nonsynonymous nucleotide substitution to that of synonymous substitution is a useful quantity to study positive Darwinian selection operating at highly variable genetic loci, but it does not necessarily detect adaptively important codons. Previously, multigene families were thought to evolve following the model of concerted evolution, but new evidence indicates that most of them evolve by a birth-and-death process of duplicate genes. It is now clear that most phenotypic characters or genetic systems such as the adaptive immune system in vertebrates are controlled by the interaction of a number of multigene families, which are often evolutionarily related and are subject to birth-and-death evolution. Therefore, it is important to study the mechanisms of gene family interaction for understanding phenotypic evolution. Because gene duplication occurs more or less at random, phenotypic evolution contains some fortuitous elements, though the environmental factors also play an important role. The randomness of phenotypic evolution is qualitatively different from allele frequency changes by random genetic drift. However, there is some similarity between phenotypic and molecular evolution with respect to functional or environmental constraints and evolutionary rate. It appears that mutation (including gene duplication and other DNA changes) is the driving force of evolution at both the genic and the phenotypic levels.     

The Structural Determinants of Intra-Protein Compensatory Substitutions

Compensatory substitutions happen when one mutation is advantageously selected because it restores the loss of fitness induced by a previous deleterious mutation. How frequent such mutations occur in evolution and what is the structural and functional context permitting their emergence remain open questions. We built an atlas of intra-protein compensatory substitutions using a phylogenetic approach and a dataset of 1,630 bacterial protein families for which high-quality sequence alignments and experimentally derived protein structures were available. We identified more than 51,000 positions coevolving by the mean of predicted compensatory mutations. Using the evolutionary and structural properties of the analyzed positions, we demonstrate that compensatory mutations are scarce (typically only a few in the protein history) but widespread (the majority of proteins experienced at least one). Typical coevolving residues are evolving slowly, are located in the protein core outside secondary structure motifs, and are more often in contact than expected by chance, even after accounting for their evolutionary rate and solvent exposure. An exception to this general scheme is residues coevolving for charge compensation, which are evolving faster than noncoevolving sites, in contradiction with predictions from simple coevolutionary models, but similar to stem pairs in RNA. While sites with a significant pattern of coevolution by compensatory mutations are rare, the comparative analysis of hundreds of structures ultimately permits a better understanding of the link between the three-dimensional structure of a protein and its fitness landscape.     

Fixation probability of rare nonmutator and evolution of mutation rates

Although mutations drive the evolutionary process, the rates at which the mutations occur are themselves subject to evolutionary forces. Our purpose here is to understand the role of selection and random genetic drift in the evolution of mutation rates, and we address this question in asexual populations at mutation‐selection equilibrium neglecting selective sweeps. Using a multitype branching process, we calculate the fixation probability of a rare nonmutator in a large asexual population of mutators and find that a nonmutator is more likely to fix when the deleterious mutation rate of the mutator population is high. Compensatory mutations in the mutator population are found to decrease the fixation probability of a nonmutator when the selection coefficient is large. But, surprisingly, the fixation probability changes nonmonotonically with increasing compensatory mutation rate when the selection is mild. Using these results for the fixation probability and a drift‐barrier argument, we find a novel relationship between the mutation rates and the population size. We also discuss the time to fix the nonmutator in an adapted population of asexual mutators, and compare our results with experiments.     

The Rate of Compensatory Evolution

A two-locus model is presented to analyze the evolution of compensatory mutations occurring in stems of RNA secondary structures. Single mutations are assumed to be deleterious but harmless (neutral) in appropriate combinations. In proceeding under mutation pressure, natural selection and genetic drift from one fitness peak to another one, a population must therefore pass through a valley of intermediate deleterious states of individual fitness. The expected time for this transition is calculated using diffusion theory. The rate of compensatory evolution, k(c), is then defined as the inverse of the expected transition time. When selection against deleterious single mutations is strong, k(c) depends on the recombination fraction r between the two loci. Recombination generally reduces the rate of compensatory evolution because it breaks up favorable combinations of double mutants. For complete linkage, k(c) is given by the rate at which favorable combinations of double mutants are produced by compensatory mutation. For r>0, k(c) decreases exponentially with r. In contrast, k(c) becomes independent of r for weak selection. We discuss the dynamics of evolutionary substitutions of compensatory mutants in relation to WRIGHT's shifting balance theory of evolution and use our results to analyze the substitution process in helices of mRNA secondary structures.     

Compensatory adaptation to the deleterious effect of antibiotic resistance in Salmonella typhimurium

Most chromosomal mutations that cause antibiotic resistance impose fitness costs on the bacteria. This biological cost can often be reduced by compensatory mutations. In Salmonella typhimurium, the nucleotide substitution AAA42 --> AAC in the rpsL gene confers resistance to streptomycin. The resulting amino acid substitution (K42N) in ribosomal protein S12 causes an increased rate of ribosomal proofreading and, as a result, the rate of protein synthesis, bacterial growth and virulence are decreased. Eighty-one independent lineages of the low-fitness, K42N mutant were evolved in the absence of antibiotic to ameliorate the costs. From the rate of fixation of compensated mutants and their fitness, the rate of compensatory mutations was estimated to be > or = 10-7 per cell per generation. The size of the population bottleneck during evolution affected fitness of the adapted mutants: a larger bottleneck resulted in higher average fitness. Only four of the evolved lineages contained streptomycin-sensitive revertants. The remaining 77 lineages contained mutants that were still fully streptomycin resistant, had retained the original resistance mutation and also acquired compensatory mutations. Most of the compensatory mutations, resulting in at least 35 different amino acid substitutions, were novel single-nucleotide substitutions in the rpsD, rpsE, rpsL or rplS genes encoding the ribosomal proteins S4, S5, S12 and L19 respectively. Our results show that the deleterious effects of a resistance mutation can be compensated by an unexpected variety of mutations.     

The coupon collector and the suppressor mutation: estimating the number of compensatory mutations by maximum likelihood

Compensatory mutation occurs when a loss of fitness caused by a deleterious mutation is restored by its epistatic interaction with a second mutation at a different site in the genome. How many different compensatory mutations can act on a given deleterious mutation? Although this quantity is fundamentally important to understanding the evolutionary consequence of mutation and the genetic complexity of adaptation, it remains poorly understood. To determine the shape of the statistical distribution for the number of compensatory mutations per deleterious mutation, we have performed a maximum-likelihood analysis of experimental data collected from the suppressor mutation literature. Suppressor mutations are used widely to assess protein interactions and are under certain conditions equivalent to compensatory mutations. By comparing the maximum likelihood of a variety of candidate distribution functions, we established that an L-shaped gamma distribution (alpha=0.564, theta=21.01) is the most successful at explaining the collected data. This distribution predicts an average of 11.8 compensatory mutations per deleterious mutation. Furthermore, the success of the L-shaped gamma distribution is robust to variation in mutation rates among sites. We have detected significant differences among viral, prokaryotic, and eukaryotic data subsets in the number of compensatory mutations and also in the proportion of compensatory mutations that are intragenic. This is the first attempt to characterize the overall diversity of compensatory mutations, identifying a consistent and accurate prior distribution of compensatory mutation diversity for theoretical evolutionary models.     

Mitochondrial-nuclear interactions and accelerated compensatory evolution: evidence from the primate cytochrome C oxidase complex

Accelerated rates of mitochondrial protein evolution have been proposed to reflect Darwinian coadaptation for efficient energy production for mammalian flight and brain activity. However, several features of mammalian mtDNA (absence of recombination, small effective population size, and high mutation rate) promote genome degradation through the accumulation of weakly deleterious mutations. Here, we present evidence for "compensatory" adaptive substitutions in nuclear DNA- (nDNA) encoded mitochondrial proteins to prevent fitness decline in primate mitochondrial protein complexes. We show that high mutation rate and small effective population size, key features of primate mitochondrial genomes, can accelerate compensatory adaptive evolution in nDNA-encoded genes. We combine phylogenetic information and the 3D structure of the cytochrome c oxidase (COX) complex to test for accelerated compensatory changes among interacting sites. Physical interactions among mtDNA- and nDNA-encoded components are critical in COX evolution; amino acids in close physical proximity in the 3D structure show a strong tendency for correlated evolution among lineages. Only nuclear-encoded components of COX show evidence for positive selection and adaptive nDNA-encoded changes tend to follow mtDNA-encoded amino acid changes at nearby sites in the 3D structure. This bias in the temporal order of substitutions supports compensatory weak selection as a major factor in accelerated primate COX evolution.     

QUANTITATIVE VARIATION IN FINITE PARTHENOGENETIC POPULATIONS: WHAT STOPS MULLER'S RATCHET IN THE ABSENCE OF RECOMBINATION?

Finite parthenogenetic populations with high genomic mutation rates accumulate deleterious mutations if back mutations are rare. This mechanism, known as Muller's ratchet, can explain the rarity of parthenogenetic species among so called higher organisms. However, estimates of genomic mutation rates for deleterious alleles and their average effect in the diploid condition in Drosophila suggest that Muller's ratchet should eliminate parthenogenetic insect populations within several hundred generations, provided all mutations are unconditionally deleterious. This fact is inconsistent with the existence of obligatory parthenogenetic insect species. In this paper an analysis of the extent to which compensatory mutations can counter Muller's ratchet is presented. Compensatory mutations are defined as all mutations that compensate for the phenotypic effects of a deleterious mutation. In the case of quantitative traits under stabilizing selection, the rate of compensatory mutations is easily predicted. It is shown that there is a strong analogy between the Muller's ratchet model of Felsenstein (1974) and the quantitative genetic model considered here, except for the frequency of compensatory mutations. If the intensity of stabilizing selection is too small or the mutation rate too high, the optimal genotype becomes extinct and the population mean drifts from the optimum but still reaches a stationary distribution. This distance is essentially the same as predicted for sexually reproducing populations under the same circumstances. Hence, at least in the short run, compensatory mutations for quantitative characters are as effective as recombination in halting the decline of mean fitness otherwise caused by Muller's ratchet. However, it is questionable whether compensatory mutations can prevent Muller's ratchet in the long run because there might be a limit to the capacity of the genome to provide compensatory mutations without eliminating deleterious mutations at least during occasional episodes of sex.     

Sexual recombination under the joint effects of mutation,selection, and random sampling drift

The advantage or disadvantage of sexual reproduction or recombination for the accumulation of mutant genes in a population is studied under the joint effects of recurrent mutations, selection, and random sampling drift. To obtain the rate at which mutant genes are incorporated three different methods are used; numerical integration of Kolmogorov backward equations, simulation of stochastic difference equations, and Monte Carlo experiments. The first two methods are used in a two-locus system to obtain the fixation probability of double mutants and other related quantities under five different selection models. The third one is conducted for a multiple-locus system and the rate of accumulation of mutant genes per locus is studied. Comparison of the results between sexual and asexual populations shows that the effect of recombination depends on initial linkage disequilibrium, mutation rate v, selection intensity s, and population size N_e. The mode of selection is also an important factor and the large effect of recombination is observed when mutant genes are individually deleterious but collectively favorable. Under a given model of selection, the great advantage or disadvantage of recombination is achieved when a large extent of genetic polymorphism is produced not by mutation but by recombination. Extreme values of N_es and N_ev make the effect insignificant. The results of Monte Carlo experiments also reveal the presence of interaction between selection and sampling drift even when the loci segregate independently and selection is multiplicative. Although this interaction is usually small, there are cases in which one locus theory cannot be used freely. In those cases, the effect of recombination is prominent and one locus theory gives an overestimate of the rate.     

Evolution by small steps and rugged landscapes in the RNA virus phi6

Fisher's geometric model of adaptive evolution argues that adaptive evolution should generally result from the substitution of many mutations of small effect because advantageous mutations of small effect should be more common than those of large effect. However, evidence for both evolution by small steps and for Fisher's model has been mixed. Here we report supporting results from a new experimental test of the model. We subjected the bacteriophage phi6 to intensified genetic drift in small populations and caused viral fitness to decline through the accumulation of a deleterious mutation. We then propagated the mutated virus at a range of larger population sizes and allowed fitness to recover by natural selection. Although fitness declined in one large step, it was usually recovered in smaller steps. More importantly, step size during recovery was smaller with decreasing size of the recovery population. These results confirm Fisher's main prediction that advantageous mutations of small effect should be more common. We also show that the advantageous mutations of small effect are compensatory mutations whose advantage is conditional (epistatic) on the presence of the deleterious mutation, in which case the adaptive landscape of phi6 is likely to be very rugged.     

Genetic constraints on protein evolution

Evolution requires the generation and optimization of new traits ("adaptation") and involves the selection of mutations that improve cellular function. These mutations were assumed to arise by selection of neutral mutations present at all times in the population. Here we review recent evidence that indicates that deleterious mutations are more frequent in the population than previously recognized and that these mutations play a significant role in protein evolution through continuous positive selection. Positively selected mutations include adaptive mutations, i.e. mutations that directly affect enzymatic function, and compensatory mutations, which suppress the pleiotropic effects of adaptive mutations. Compensatory mutations are by far the most frequent of the two and would allow potentially adaptive but deleterious mutations to persist long enough in the population to be positively selected during episodes of adaptation. Compensatory mutations are, by definition, context-dependent and thus constrain the paths available for evolution. This provides a mechanistic basis for the examples of highly constrained evolutionary landscapes and parallel evolution reported in natural and experimental populations. The present review article describes these recent advances in the field of protein evolution and discusses their implications for understanding the genetic basis of disease and for protein engineering in vitro.     

Stochastic traits of molecular evolution--acceptance of point mutations in native actin genes

A stochastic matrix of nucleotide mutation probabilities is derived by counting differences and identities in alignments of native actin genes, with the aim of obtaining a more reliable data base for regular modes of molecular evolution. The evolution of DNA sequences is thereby considered as a Markov process consisting of events (point mutations) characterized by a stochastic matrix for codon-codon interchanges. The genetic distance is set to 1 PAM (percentage of accepted point mutations). The results can be reproduced by Monte Carlo simulations which are subjected to selective constraints. The latter are observed as nonrandom codon usage and ratios of silent to recognizable point mutations. Specific patterns within the matrix of mutation probabilities attest to preferences of natural selection in the evolution of a specific protein.     

Selection intensity against deleterious mutations in RNA secondary structures and rate of compensatory nucleotide substitutions

A two-locus model of reversible mutations with compensatory fitness interactions is presented; single mutations are assumed to be deleterious but neutral in appropriate combinations. The expectation of the time of compensatory nucleotide substitutions is calculated analytically for the case of tight linkage between sites. It is shown that selection increases the substitution time dramatically when selection intensity Ns > 1, where N is the diploid population size and s the selection coefficient. Computer simulations demonstrate that recombination increases the substitution time, but the effect of recombination is small when selection is weak. The amount of linkage disequilibrium generated in the process of compensatory substitution is also investigated. It is shown that significant linkage disequilibrium is expected to be rare in natural populations. The model is applied to the mRNA secondary structure of the bicoid 3' untranslated region of Drosophila. It is concluded that average selection intensity Ns against single deleterious mutations is not likely to be much larger than 1.