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.     

Evolution by Gene Duplication and Compensatory Advantageous Mutations

Relaxation of selective constraint is thought to play an important role for evolution by gene duplication, in connection with compensatory advantageous mutant substitutions. Models were investigated by incorporating gene duplication by unequal crossing over, selection, mutation and random genetic drift into Monte Carlo simulations. Compensatory advantageous mutations were introduced, and simulations were carried out with and without relaxation, when genes are redundant on chromosomes. Relaxation was introduced by assuming that deleterious mutants have no effect on fitness, so long as one or more genes free of such mutations remain in the array. Compensatory mutations are characterized by the intermediate deleterious step of their substitutions, and therefore relaxation by gene redundancy is important. Through extensive Monte Carlo simulations, it was found that compensatory mutant substitutions require relaxation in addition to gene duplication, when mutant effects are large. However when mutant effects are small, such that the product of selection coefficient and population size is around unity, evolution by compensatory mutation is enhanced by gene duplication even without relaxation.     

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.     

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.     

The probability of duplicate gene preservation by subfunctionalization

It has often been argued that gene-duplication events are most commonly followed by a mutational event that silences one member of the pair, while on rare occasions both members of the pair are preserved as one acquires a mutation with a beneficial function and the other retains the original function. However, empirical evidence from genome duplication events suggests that gene duplicates are preserved in genomes far more commonly and for periods far in excess of the expectations under this model, and whereas some gene duplicates clearly evolve new functions, there is little evidence that this is the most common mechanism of duplicate-gene preservation. An alternative hypothesis is that gene duplicates are frequently preserved by subfunctionalization, whereby both members of a pair experience degenerative mutations that reduce their joint levels and patterns of activity to that of the single ancestral gene. We consider the ways in which the probability of duplicate-gene preservation by such complementary mutations is modified by aspects of gene structure, degree of linkage, mutation rates and effects, and population size. Even if most mutations cause complete loss-of-subfunction, the probability of duplicate-gene preservation can be appreciable if the long-term effective population size is on the order of 10(5) or smaller, especially if there are more than two independently mutable subfunctions per locus. Even a moderate incidence of partial loss-of-function mutations greatly elevates the probability of preservation. The model proposed herein leads to quantitative predictions that are consistent with observations on the frequency of long-term duplicate gene preservation and with observations that indicate that a common fate of the members of duplicate-gene pairs is the partitioning of tissue-specific patterns of expression of the ancestral gene.     

Purging deleterious mutations under self fertilization: paradoxical recovery in fitness with increasing mutation rate in Caenorhabditis elegans

Background

The accumulation of deleterious mutations can drastically reduce population mean fitness. Self-fertilization is thought to be an effective means of purging deleterious mutations. However, widespread linkage disequilibrium generated and maintained by self-fertilization is predicted to reduce the efficacy of purging when mutations are present at multiple loci.

Methodology/Principal Findings

We tested the ability of self-fertilizing populations to purge deleterious mutations at multiple loci by exposing obligately self-fertilizing populations of Caenorhabditis elegans to a range of elevated mutation rates and found that mutations accumulated, as evidenced by a reduction in mean fitness, in each population. Therefore, purging in obligate selfing populations is overwhelmed by an increase in mutation rate. Surprisingly, we also found that obligate and predominantly self-fertilizing populations exposed to very high mutation rates exhibited consistently greater fitness than those subject to lesser increases in mutation rate, which contradicts the assumption that increases in mutation rate are negatively correlated with fitness. The high levels of genetic linkage inherent in self-fertilization could drive this fitness increase.

Conclusions

Compensatory mutations can be more frequent under high mutation rates and may alleviate a portion of the fitness lost due to the accumulation of deleterious mutations through epistatic interactions with deleterious mutations. The prolonged maintenance of tightly linked compensatory and deleterious mutations facilitated by self-fertilization may be responsible for the fitness increase as linkage disequilibrium between the compensatory and deleterious mutations preserves their epistatic interaction.     

The role of population size, pleiotropy and fitness effects of mutations in the evolution of overlapping gene functions

Sheltered from deleterious mutations, genes with overlapping or partially redundant functions may be important sources of novel gene functions. While most partially redundant genes originated in gene duplications, it is much less clear why genes with overlapping functions have been retained, in some cases for hundreds of millions of years. A case in point is the many partially redundant genes in vertebrates, the result of ancient gene duplications in primitive chordates. Their persistence and ubiquity become surprising when it is considered that duplicate and original genes often diversify very rapidly, especially if the action of natural selection is involved. Are overlapping gene functions perhaps maintained because of their protective role against otherwise deleterious mutations? There are two principal objections against this hypothesis, which are the main subject of this article. First, because overlapping gene functions are maintained in populations by a slow process of "second order" selection, population sizes need to be very high for this process to be effective. It is shown that even in small populations, pleiotropic mutations that affect more than one of a gene''s functions simultaneously can slow the mutational decay of functional overlap after a gene duplication by orders of magnitude. Furthermore, brief and transient increases in population size may be sufficient to maintain functional overlap. The second objection regards the fact that most naturally occurring mutations may have much weaker fitness effects than the rather drastic "knock-out" mutations that lead to detection of partially redundant functions. Given weak fitness effects of most mutations, is selection for the buffering effect of functional overlap strong enough to compensate for the diversifying force exerted by mutations? It is shown that the extent of functional overlap maintained in a population is not only independent of the mutation rate, but also independent of the average fitness effects of mutation. These results are discussed with respect to experimental evidence on redundant genes in organismal development.     

Linkage Disequilibrium and Genetic Variances under Mutation-Selection Balance

I determine the contribution of linkage disequilibrium to genetic variances using results for two loci and for induced or marginal systems. The analysis allows epistasis and dominance, but assumes that mutation is weak relative to selection. The linkage disequilibrium component of genetic variance is shown to be unimportant for unlinked loci if the gametic mutation rate divided by the harmonic mean of the pairwise recombination rates is much less than one. For tightly linked loci, linkage disequilibrium is unimportant if the gametic mutation rate divided by the (induced) per locus selection is much less than one.     

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.     

Recessive Lethal Mutations and the Maintenance of Duplication-Bearing Strains of Dictyostelium discoideum

Recessive lethal mutations have been isolated and used to maintain n + 1 aneuploid strains of Dictyostelium discoideum carrying a duplication of part or all of linkage group VII. The recessive lethal mutations, relA351 and relB352, arose spontaneously in diploids; no mutagenic treatment was used in the isolation of these mutations. The probable gene order on linkage group VII is: centromere, relB couA, bsgB, cobA, relA. Maintenance of aneuploids disomic for linkage group VII was made possible by complementation of a rel mutation on each linkage group VII homologue by the corresponding wild-type allele on the other linkage group VII homologue. The duplication-bearing disomic strains were slow-growing and produced faster-growing sectors on the colony edge. Haploid sectors probably arise by a combination of mitotic recombination and subsequent loss of one homologue, diploid sectors may be formed by chromosome doubling to 2n + 2, followed by chromosome loss to return to 2n, and aneuploid sectors may arise by deletion or new mutation.     

Recurrent locus-specific mutation resulting from a cryptic ectopic insertion in Neurospora

New mutations are found among approximately 20% of progeny when one or both parents carry eas allele UCLA191 (eas(UCLA), easily wettable, hydrophobin-deficient, linkage group II). The mutations inactivate the wild-type allele of cya-8 (cytochrome aa3 deficient, linkage group VII), resulting in thin, "transparent" mycelial growth. Other eas alleles fail to produce cya-8 mutant progeny. The recurrent cya-8 mutations are attributed to repeat-induced point mutation (RIP) resulting from a duplicated copy of cya-8+ that was inserted ectopically at eas when the UCLA191 mutation occurred. As expected for RIP, eas(UCLA)-induced cya-8 mutations occur during nuclear proliferation prior to karyogamy. When only one parent is eas(UCLA), the new mutations arise exclusively in eas(UCLA) nuclei. Mutation of cya-8 is suppressed when a long unlinked duplication is present. Stable cya-8 mutations are effectively eliminated in crosses homozygous for rid, a recessive suppressor of RIP. The eas(UCLA) allele is associated with a long paracentric inversion. A discontinuity is present in eas(UCLA) DNA. The eas promoter is methylated in cya-8 progeny of eas(UCLA), presumably by the spreading of methylation beyond the adjoining RIP-inactivated duplication. These findings support a model in which an ectopic insertion that created a mutation at the target site acts as a locus-specific mutator via RIP.     

Testing the neutral fixation of hetero-oligomerism in the archaeal chaperonin CCT

The evolutionary transition from homo-oligomerism to hetero-oligomerism in multimeric proteins and its contribution to function innovation and organism complexity remain to be investigated. Here, we undertake the challenge of contributing to this theoretical ground by investigating the hetero-oligomerism in the molecular chaperonin cytosolic chaperonin containing tailless complex polypeptide 1 (CCT) from archaea. CCT is amenable to this study because, in contrast to eukaryotic CCTs where sub-functionalization after gene duplication has been taken to completion, archaeal CCTs present no evidence for subunit functional specialization. Our analyses yield additional information to previous reports on archaeal CCT paralogy by identifying new duplication events. Analyses of selective constraints show that amino acid sites from 1 subunit have fixed slightly deleterious mutations at inter-subunit interfaces after gene duplication. These mutations have been followed by compensatory mutations in nearby regions of the same subunit and in the interface contact regions of its paralogous subunit. The strong selective constraints in these regions after speciation support the evolutionary entrapment of CCTs as hetero-oligomers. In addition, our results unveil different evolutionary dynamics depending on the degree of CCT hetero-oligomerism. Archaeal CCT protein complexes comprising 3 distinct classes of subunits present 2 evolutionary processes. First, slightly deleterious and compensatory mutations were fixed neutrally at inter-subunit regions. Second, sub-functionalization may have occurred at substrate-binding and adenosine triphosphate-binding regions after the 2nd gene duplication event took place. CCTs with 2 distinct types of subunits did not present evidence of sub-functionalization. Our results provide the 1st in silico evidence for the neutral fixation of hetero-oligomerism in archaeal CCTs and provide information on the evolution of hetero-oligomerism toward sub-functionalization in archaeal CCTs.     

Germ-line mutational analysis of the TSC2 gene in 90 tuberous-sclerosis patients.

Ninety patients with tuberous-sclerosis complex (TSC) were tested for subtle mutations in the TSC2 gene, by means of single-strand conformational analysis (SSCA) of genomic DNA. Patients included 56 sporadic cases and 34 familial probands. For all patients, SSCA was performed for each of the 41 exons of the TSC2 gene. We identified 32 SSCA changes, 22 disease-causing mutations, and 10 polymorphic variants. Interestingly, we detected mutations at a much higher frequency in the sporadic cases (32%) than in the multiplex families (9%). Among the eight families for which linkage to the TSC2 region had been determined, only one mutation was found. Mutations were distributed equally across the gene; they included 5 deletions, 3 insertions, 10 missense mutations, 2 nonsense mutations, and 2 tandem duplications. We did not detect an increase in mutations either in the GTPase-activating protein (GAP)-related domains of TSC2 or in the activating domains that have been identified in rat tuberin. We did not detect any mutations in the exons (25 and 31) that are spliced out in the isoforms. There was no evidence for correspondence between variability of phenotype and type of mutation (missense versus early termination). Diagnostic testing will be difficult because of the genetic heterogeneity of TSC (which has at least two causative genes: TSC1 and TSC2), the large size of the TSC2 gene, and the variety of mutations. More than half of the mutations that we identified (missense, small in-frame deletion, and tandem duplication) are not amenable to the mutation-detection methods, such as protein-truncation testing, that are commonly employed for genes that encode proteins with tumor-suppressor function.     

Two-locus,fourth-order gene frequency moments: Implications for the variance of squared linkage disequilibrium and the variance of homozygosity

Identity coefficients are used to construct a sufficient set of equations to determine the fourth-order moments of gene frequencies for two linked loci. This allows the variance of the expected squared linkage disequilibrium to be found. It is shown that the coefficient of variation is generally greater than one and if the mutation rate is small, the standard deviation is more than four times the size of the mean. This demonstrates that squared linkage disequilibrium is a highly variable quantity. The variance of homozygosity for a gene which consists of two sites can also be obtained. Recombination between these sites increases the variance of homozygosity, suggesting that intragenic recombination significantly changes all the expected moments of gene frequencies if 4Nμ > 1.0 and r > μ (where N is the population size, μ is the mutation rate of the gene to neutral alleles, and r is the recombination rate between two sites within the gene).     

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.     

Duplications between direct repeats stabilized by DNA secondary structure occur preferentially in the leading strand during DNA replication

To ascertain a leading or lagging strand preference for duplication mutations, several short DNA sequences, i.e. mutation inserts, were designed that should demonstrate an asymmetric propensity for duplication mutations in the two complementary DNA strands during replication. The design of the mutation insert involved a 7-bp quasi inverted repeat that forms a remarkably stable hairpin in one DNA strand, but not the other. The inverted repeat is asymmetrically placed between flanking direct repeats. This sequence was cloned into a modified chloramphenicol acetyltransferase (CAT) gene containing a −1 frameshift mutation. Duplication of the mutation insert restores the reading frame of the CAT gene resulting in a chloramphenicol resistant phenotype. The mutation insert showed greater than a 200-fold preference for duplication mutations during leading strand, compared with lagging strand, replication. This result suggests that misalignment stabilized by DNA secondary structure, leading to duplication between direct repeats, occurred preferentially during leading strand synthesis.     

The Effect of Linkage on Establishment and Survival of Locally Beneficial Mutations

We study invasion and survival of weakly beneficial mutations arising in linkage to an established migration–selection polymorphism. Our focus is on a continent–island model of migration, with selection at two biallelic loci for adaptation to the island environment. Combining branching and diffusion processes, we provide the theoretical basis for understanding the evolution of islands of divergence, the genetic architecture of locally adaptive traits, and the importance of so-called “divergence hitchhiking” relative to other mechanisms, such as “genomic hitchhiking”, chromosomal inversions, or translocations. We derive approximations to the invasion probability and the extinction time of a de novo mutation. Interestingly, the invasion probability is maximized at a nonzero recombination rate if the focal mutation is sufficiently beneficial. If a proportion of migrants carries a beneficial background allele, the mutation is less likely to become established. Linked selection may increase the survival time by several orders of magnitude. By altering the timescale of stochastic loss, it can therefore affect the dynamics at the focal site to an extent that is of evolutionary importance, especially in small populations. We derive an effective migration rate experienced by the weakly beneficial mutation, which accounts for the reduction in gene flow imposed by linked selection. Using the concept of the effective migration rate, we also quantify the long-term effects on neutral variation embedded in a genome with arbitrarily many sites under selection. Patterns of neutral diversity change qualitatively and quantitatively as the position of the neutral locus is moved along the chromosome. This will be useful for population-genomic inference. Our results strengthen the emerging view that physically linked selection is biologically relevant if linkage is tight or if selection at the background locus is strong.     

Variances and covariances of squared linkage disequilibria in finite populations

Analysis of linkage disequilibrium D among restriction sites or bases in DNA sequences, arising from mutations in finite populations, depends on a knowledge of the variance-covariance structure of measures such as D2 between different pairs of sites. This requires evaluation of the eighth moments of gene frequencies among two, three, and four loci, and the necessary methodology is derived here and results are computed. While primary emphasis is placed on disequilibrium arising from mutation or gene conversion, the methodology also allows for the joint effects of only drift and recombination. Numerical results confirm that squared linkage disequilibria can have high variances and covariances.     

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.     

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.