Deleterious mutations as an evolutionary factor. 1. The advantage of recombination

Gene organization of the mating type regions in the ectomycorrhizal fungus Laccaria bicolor reveals distinct evolution between the two mating type loci

In natural conditions, basidiomycete ectomycorrhizal fungi such as Laccaria bicolor are typically in the dikaryotic state when forming symbioses with trees, meaning that two genetically different individuals have to fuse or 'mate'. Nevertheless, nothing is known about the molecular mechanisms of mating in these ecologically important fungi. Here, advantage was taken of the first sequenced genome of the ectomycorrhizal fungus, Laccaria bicolor, to determine the genes that govern the establishment of cell-type identity and orchestrate mating. The L. bicolor mating type loci were identified through genomic screening. The evolutionary history of the genomic regions that contained them was determined by genome-wide comparison of L. bicolor sequences with those of known tetrapolar and bipolar basidiomycete species, and by phylogenetic reconstruction of gene family history. It is shown that the genes of the two mating type loci, A and B, are conserved across the Agaricales, but they are contained in regions of the genome with different evolutionary histories. The A locus is in a region where the gene order is under strong selection across the Agaricales. By contrast, the B locus is in a region where the gene order is likely under a low selection pressure but where gene duplication, translocation and transposon insertion are frequent.

Coevolution of robustness, epistasis, and recombination favors asexual reproduction

The prevalence of sexual reproduction remains one of the most perplexing phenomena in evolutionary biology. The deterministic mutation hypothesis postulates that sexual reproduction will be advantageous under synergistic epistasis, a condition in which mutations cause a greater reduction in fitness when combined than would be expected from their individual effects. The inverse condition, antagonistic epistasis, correspondingly is predicted to favor asexual reproduction. To assess this hypothesis, we introduce a finite population evolutionary process that combines a recombination modifier formalism with a gene-regulatory network model. We demonstrate that when reproductive mode and epistasis are allowed to coevolve, asexual reproduction outcompetes sexual reproduction. In addition, no correlation is found between the level of synergistic epistasis and the fixation time of the asexual mode. However, a significant correlation is found between the level of antagonistic epistasis and asexual mode fixation time. This asymmetry can be explained by the greater reduction in fitness imposed by sexual reproduction as compared with asexual reproduction. Our findings present evidence and suggest plausible explanations that challenge both the deterministic mutation hypothesis and recent arguments asserting the importance of emergent synergistic epistasis in the maintenance of sexual reproduction.

VARIABLE EPISTATIC EFFECTS BETWEEN MUTATIONS AT HOST RECOGNITION SITES IN ?X174 BACTERIOPHAGE

Epistatic interactions between mutations are widespread. Theoretical investigations have shown that variability in epistatic effects influences fundamental evolutionary processes, yet few empirical studies have identified causes or the extent of this variation. We examined variation in epistatic effects of mutations at two host recognition sites in phiX174 bacteriophage. We calculated epistatic effects from the sum of fitness effects (log scale) of two single mutants and their corresponding double mutant for five combinations of mutations in six conditions. We found that epistatic effects differed in sign, degree, and variability across conditions. The data highlight that even between single mutations at the same two sites the sign and variability of epistatic effects are affected by environment. We discuss these findings in the context of studying the role of epistasis in evolution.

The evolution of sex: empirical insights into the roles of epistasis and drift

Despite many years of theoretical and experimental work, the explanation for why sex is so common as a reproductive strategy continues to resist understanding. Recent empirical work has addressed key questions in this field, especially regarding rates of mutation accumulation in sexual and asexual organisms, and the roles of negative epistasis and drift as sources of adaptive constraint in asexually reproducing organisms. At the same time, new ideas about the evolution of sexual recombination are being tested, including intriguing suggestions of an important interplay between sex and genetic architecture, which indicate that sex and recombination could have affected their own evolution.

Adaptation of HIV-1 depends on the host-cell environment

Many viruses have the ability to rapidly develop resistance against antiviral drugs and escape from the host immune system. To which extent the host environment affects this adaptive potential of viruses is largely unknown. Here we show that for HIV-1, the host-cell environment is key to the adaptive potential of the virus. We performed a large-scale selection experiment with two HIV-1 strains in two different T-cell lines (MT4 and C8166). Over 110 days of culture, both virus strains adapted rapidly to the MT4 T-cell line. In contrast, when cultured on the C8166 T-cell line, the same strains did not show any increase in fitness. By sequence analyses and infections with viruses expressing either yellow or cyan fluorescent protein, we were able to show that the absence of adaptation was linked to a lower recombination rate in the C8166 T-cell line. Our findings suggest that if we can manipulate the host-cellular factors that mediate viral evolution, we may be able to significantly retard viral adaptability.

Evolution of sex: why do organisms shuffle their genotypes?

Sexual processes alter associations among alleles. To understand the evolution of sex, we need to know both the short-term and long-term consequences of changing these genetic associations. Ultimately, we need to identify which evolutionary forces--for example, selection, genetic drift, migration--are responsible for building the associations affected by sex.

Interference among deleterious mutations favours sex and recombination in finite populations

Sex and recombination are widespread, but explaining these phenomena has been one of the most difficult problems in evolutionary biology. Recombination is advantageous when different individuals in a population carry different advantageous alleles. By bringing together advantageous alleles onto the same chromosome, recombination speeds up the process of adaptation and opposes the fixation of harmful mutations by means of Muller's ratchet. Nevertheless, adaptive substitutions favour sex and recombination only if the rate of adaptive mutation is high, and Muller's ratchet operates only in small or asexual populations. Here, by tracking the fate of modifier alleles that alter the frequency of sex and recombination, we show that background selection against deleterious mutant alleles provides a stochastic advantage to sex and recombination that increases with population size. The advantage arises because, with low levels of recombination, selection at other loci severely reduces the effective population size and genetic variance in fitness at a focal locus (the Hill-Robertson effect), making a population less able to respond to selection and to rid itself of deleterious mutations. Sex and recombination reveal the hidden genetic variance in fitness by combining chromosomes of intermediate fitness to create chromosomes that are relatively free of (or are loaded with) deleterious mutations. This increase in genetic variance within finite populations improves the response to selection and generates a substantial advantage to sex and recombination that is fairly insensitive to the form of epistatic interactions between deleterious alleles. The mechanism supported by our results offers a robust and broadly applicable explanation for the evolutionary advantage of recombination and can explain the spread of costly sex.

Why have sex? The population genetics of sex and recombination

One of the greatest puzzles in evolutionary biology is the high frequency of sexual reproduction and recombination. Given that individuals surviving to reproductive age have genomes that function in their current environment, why should they risk shuffling their genes with those of another individual? Mathematical models are especially important in developing predictions about when sex and recombination can evolve, because it is difficult to intuit the outcome of evolution with several interacting genes. Interestingly, theoretical analyses have shown that it is often quite difficult to identify conditions that favour the evolution of high rates of sex and recombination. For example, fitness interactions among genes (epistasis) can favour sex and recombination but only if such interactions are negative, relatively weak and not highly variable. One reason why an answer to the paradox of sex has been so elusive is that our models have focused unduly on populations that are infinite in size, unstructured and isolated from other species. Yet most verbal theories for sex and recombination consider a finite number of genotypes evolving in a biologically and/or physically complex world. Here, we review various hypotheses for why sex and recombination are so prevalent and discuss theoretical results indicating which of these hypotheses is most promising.

Pronounced differences of recombination activity at the sex determination locus of the honeybee, a locus under strong balancing selection

Recombination decreases the association of linked nucleotide sites and can influence levels of polymorphism in natural populations. When coupled with selection, recombination may relax potential conflict among linked genes, a concept that has played a central role in research on the evolution of recombination. The sex determination locus (SDL) of the honeybee is an informative example for exploring the combined forces of recombination, selection, and linkage on sequence evolution. Balancing selection at SDL is very strong and homozygous individuals at SDL are eliminated by worker bees. The recombination rate is increased up to four times that of the genomewide average in the region surrounding SDL. Analysis of nucleotide diversity (pi) reveals a sevenfold increase of polymorphism within the sex determination gene complementary sex determiner (csd) that rapidly declines within 45 kb to levels of genomewide estimates. Although no recombination was observed within SDL, which contains csd, analyses of heterogeneity, shared polymorphic sites, and linkage disequilibrium (LD) show that recombination has contributed to the evolution of the 5' part of some csd sequences. Gene conversion, however, has not obviously contributed to the evolution of csd sequences. The local control of recombination appears to be related to SDL function and mode of selection. The homogenizing force of recombination is reduced within SDL, which preserves allelic differences and specificity, while the increase of recombination activity around SDL relaxes conflict between SDL and linked genes.

The dynamics of the rec-system in variable environments: haploid selection in a cyclical two-state environment

The dynamics of a 3-locus infinite population with non-overlapping generations and panmixia was studied. Loci are di-allelic: two loci affect fitness under cyclical symmetric haploid selection while the third one is a modifier of recombination (rec-modifier). Selection favors alternatively haplotypes AB and ab or Ab and aB. It has been proven that under alternating selection (when period of selection consists of two generations) a dominant suppressor of recombination is displaced and the allele for non-zero recombination becomes fixed within the population. For populations with inversion heterozygosity within the selective system (i.e. with zero recombination in heterozygote for rec-modifier and non-zero for homozygotes) fixation of one of the alleles (depending on the initial point) at the rec-modifier locus is predicted. For other values of recombination parameters, the behavior of the system was studied numerically. A full bifurcation picture of parameters was obtained. Many of the results related to the case of a two-generation period hold also in the case of longer period lengths.

On the evolution of epistasis I: diploids under selection

One interpretation of recent literature on the evolution of phenotypic modularity is that evolution should act to decrease the degree of interaction between genes that contribute to different phenotypes. This issue is addressed directly here using a fitness scheme determined by two genetic loci and a third locus which modifies a measure of statistical interaction between the fitnesses due to the first two. The equilibrium structure of such an epistasis-modifying locus is studied. It is shown that under well-specified conditions a modifying allele that increases epistasis succeeds. In other words, genetic interactions tend to become stronger. It is speculated that this occurs because the mean fitness in such models is locally increasing as a function of the degree of epistasis.

Parasites and mutational load: an experimental test of a pluralistic theory for the evolution of sex

Ecological and mutational explanations for the evolution of sexual reproduction have usually been considered independently. Although many of these explanations have yielded promising theoretical results,experimental support for their ability to overcome a twofold cost of sex has been limited. For this reason, it has recently been argued that a pluralistic approach, combining effects from multiple models, may be necessary to explain the apparent advantage of sex. One such pluralistic model proposes that parasite load and synergistic epistasis between deleterious mutations might interact to create an advantage for recombination.Here, we test this proposal by comparing the fitness functions of parasitized and parasite-free genotypes of Escherichia coli bearing known numbers of transposon-insertion mutations. In both classes, we failed to detect any evidence for synergistic epistasis. However, the average effect of deleterious mutations was greater in parasitized than parasite-free genotypes. This effect might broaden the conditions under which another proposed model combining parasite-host coevolutionary dynamics and mutation accumulation can explain the maintenance of sex. These results suggest that, on average, deleterious mutations act multiplicatively with each other but in synergy with infection in determining fitness.

Evolution of recombination due to random drift

In finite populations subject to selection, genetic drift generates negative linkage disequilibrium, on average, even if selection acts independently (i.e., multiplicatively) upon all loci. Negative disequilibrium reduces the variance in fitness and hence, by Fisher's (1930) fundamental theorem, slows the rate of increase in mean fitness. Modifiers that increase recombination eliminate the negative disequilibria that impede selection and consequently increase in frequency by "hitchhiking." Thus, stochastic fluctuations in linkage disequilibrium in finite populations favor the evolution of increased rates of recombination, even in the absence of epistatic interactions among loci and even when disequilibrium is initially absent. The method developed within this article allows us to quantify the strength of selection acting on a modifier allele that increases recombination in a finite population. The analysis indicates that stochastically generated linkage disequilibria do select for increased recombination, a result that is confirmed by Monte Carlo simulations. Selection for a modifier that increases recombination is highest when linkage among loci is tight, when beneficial alleles rise from low to high frequency, and when the population size is small.

The opportunity for canalization and the evolution of genetic networks

There has been a recent revival of interest in how genetic interactions evolve, spurred on by an increase in our knowledge of genetic interactions at the molecular level. Empirical work on genetic networks has revealed a surprising amount of robustness to perturbations, suggesting that robustness is an evolved feature of genetic networks. Here, we derive a general model for the evolution of canalization that can incorporate any form of perturbation. We establish an upper bound to the strength of selection on canalization that is approximately equal to the fitness load in the system. This method makes it possible to compare different forms of perturbation, including genetic, developmental, and environmental effects. In general, load that arises from mutational processes is low because the mutation rate is itself low. Mutation load can create selection for canalization in a small network that can be achieved through dominance evolution or gene duplication, and in each case selection for canalization is weak at best. In larger genetic networks, selection on genetic canalization can be reasonably strong because larger networks have higher mutational load. Because load induced through migration, segregation, developmental noise, and environmental variance is not mutation limited, each can cause strong selection for canalization.

Modes of reproduction and the accumulation of deleterious mutations with multiplicative fitness effects

Mutational load depends not only on the number and nature of mutations but also on the reproductive mode. Traditionally, only a few specific reproductive modes are considered in the search of explanations for the maintenance of sex. There are, however, many alternatives. Including these may give radically different conclusions. The theory on deterministic deleterious mutations states that in large populations segregation and recombination may lead to a lower load of deleterious mutations, provided that there are synergistic interactions. Empirical research suggests that effects of deleterious mutations are often multiplicative. Such situations have largely been ignored in the literature, since recombination and segregation have no effect on mutation load in the absence of epistasis. However, this is true only when clonal reproduction and sexual reproduction with equal male and female ploidy are considered. We consider several alternative reproductive modes that are all known to occur in insects: arrhenotoky, paternal genome elimination, apomictic thelytoky, and automictic thelytoky with different cytological mechanisms to restore diploidy. We give a method that is based on probability-generating functions, which provides analytical and numerical results on the distributions of deleterious mutations. Using this, we show that segregation and recombination do make a difference. Furthermore, we prove that a modified form of Haldane's principle holds more generally for thelytokous reproduction. We discuss the implications of our results for evolutionary transitions between different reproductive modes in insects. Since the strength of Muller's ratchet is reduced considerably for several forms of automictic thelytoky, many of our results are expected to be also valid for initially small populations.

Dominance and Overdominance of Mildly Deleterious Induced Mutations for Fitness Traits inCaenorhabditis elegans

We estimated the average dominance coefficient of mildly deleterious mutations (h, the proportion by which mutations in the heterozygous state reduce fitness components relative to those in the homozygous state) in the nematode Caenorhabditis elegans. From 56 worm lines that carry mutations induced by the point mutagen ethyl methanesulfonate (EMS), we selected 19 lines that are relatively high in fitness and estimated the viabilities, productivities, and relative fitnesses of heterozygotes and homozygotes compared to the ancestral wild type. There was very little effect of homozygous or heterozygous mutations on egg-to-adult viability. For productivity and relative fitness, we found that the average dominance coefficient, h, was ∼0.1, suggesting that mildly deleterious mutations are on average partially recessive. These estimates were not significantly different from zero (complete recessivity) but were significantly different from 0.5 (additivity). In addition, there was a significant amount of variation in h among lines, and analysis of average dominance coefficients of individual lines suggested that several lines showed overdominance for fitness. Further investigation of two of these lines partially confirmed this finding.

Deleterious mutations and the genetic variance of male fitness components in Mimulus guttatus

Deleterious mutations are relevant to a broad range of questions in genetics and evolutionary biology. I present an application of the "biometric method" for estimating mutational parameters for male fitness characters of the yellow monkeyflower, Mimulus guttatus. The biometric method rests on two critical assumptions. The first is that experimental inbreeding changes genotype frequencies without changing allele frequencies; i.e., there is no genetic purging during the experiment. I satisfy this condition by employing a breeding design in which the parents are randomly extracted, fully homozygous inbred lines. The second is that all genetic variation is attributable to deleterious mutations maintained in mutation-selection balance. I explicitly test this hypothesis using likelihood ratios. Of the three deleterious mutation models tested, the first two are rejected for all characters. The failure of these models is due to an excess of additive genetic variation relative to the expectation under mutation-selection balance. The third model is not rejected for either of two log-transformed male fitness traits. However, this model imposes only "weak conditions" and is not sufficiently detailed to provide estimates for mutational parameters. The implication is that, if biometric methods are going to yield useful parameter estimates, they will need to consider mutational models more complicated than those typically employed in experimental studies.

Experimental tests of the adaptive significance of sexual recombination

Numerous theories have been proposed to explain the advantages of sexual recombination the exchange of hereditary material between different genomes or homologous chromosomes. Many of these candidate benefits have been evaluated in controlled laboratory experiments, which, collectively, strongly indicate that sexual recombination provides important long-term advantages.

Resolving the paradox of sex and recombination

Sexual reproduction and recombination are ubiquitous. However, a large body of theoretical work has shown that these processes should only evolve under a restricted set of conditions. New studies indicate that this discrepancy might result from the fact that previous models have ignored important complexities that face natural populations, such as genetic drift and the spatial structure of populations.

Sexual recombination and the power of natural selection

Theory predicts that recombination will increase the effectiveness of natural selection. A Drosophila melanogaster model system was developed that increased experimental power with the use of high experimental replication, explicit tracking of individual genes, and high but natural levels of background selection. Each of 34 independent experiments traced the fate of a newly arisen mutation located within genome-wide, synthetic chromosomes that were propagated with or without recombination. An intrinsic advantage to recombination was demonstrated by the finding that the realized strength of selection on new mutations was markedly increased when recombination was present.

Epistasis and the mutation load: a measurement-theoretical approach

An approximate solution for the mean fitness in mutation-selection balance with arbitrary order of epistatic interaction is derived. The solution is based on the assumptions of coupling equilibrium and that the interaction effects are multilinear. We find that the effect of m-order epistatic interactions (i.e., interactions among groups of m loci) on the load is dependent on the total genomic mutation rate, U, to the mth power. Thus, higher-order gene interactions are potentially important if U is large and the interaction density among loci is not too low. The solution suggests that synergistic epistasis will decrease the mutation load and that variation in epistatic effects will elevate the load. Both of these results, however, are strictly true only if they refer to epistatic interaction strengths measured in the optimal genotype. If gene interactions are measured at mutation-selection equilibrium, only synergistic interactions among even numbers of genes will reduce the load. Odd-ordered synergistic interactions will then elevate the load. There is no systematic relationship between variation in epistasis and load at equilibrium. We argue that empirical estimates of gene interaction must pay attention to the genetic background in which the effects are measured and that it may be advantageous to refer to average interaction intensities as measured in mutation-selection equilibrium. We derive a simple criterion for the strength of epistasis that is necessary to overcome the twofold disadvantage of sex.

DNA shuffling method for generating highly recombined genes and evolved enzymes

We introduce a method of in vitro recombination or "DNA shuffling" to generate libraries of evolved enzymes. The approach relies on the ordering, trimming, and joining of randomly cleaved parental DNA fragments annealed to a transient polynucleotide scaffold. We generated chimeric libraries averaging 14.0 crossovers per gene, a several-fold higher level of recombination than observed for other methods. We also observed an unprecedented four crossovers per gene in regions of 10 or fewer bases of sequence identity. These properties allow generation of chimeras unavailable by other methods. We detected no unshuffled parental clones or duplicated "sibling" chimeras, and relatively few inactive clones. We demonstrated the method by molecular breeding of a monooxygenase for increased rate and extent of biodesulfurization on complex substrates, as well as for 20-fold faster conversion of a nonnatural substrate. This method represents a conceptually distinct and improved alternative to sexual PCR for gene family shuffling.

A test for epistasis among induced mutations in Caenorhabditis elegans

Synergistic epistasis, in which deleterious mutations tend to magnify each other's effects, is a necessary component of the mutational deterministic hypothesis for the maintenance of sexual production. We tested for epistasis for life-history traits in the soil nematode Caenorhabditis elegans by inducing mutations in two genetic backgrounds: a wild-type strain and a set of genetically loaded lines that contain large numbers of independent mildly detrimental mutations. There was no significant difference between the effect of new mutations on the wild-type background and the genetically loaded background for four out of five fitness correlates. In these four cases, the maximum level of epistasis compatible with the data was very low. The fifth trait, late productivity, is not likely to be an important component of fitness. This suggests either that specific environmental conditions are required to cause epistasis or that synergistic epistasis is not a general phenomenon. We also suggest a new mechanism by which deleterious mutations may provide an advantage to sexual reproduction under low selection coefficients.

Perspective: sex, recombination, and the efficacy of selection--was Weismann right?

The idea that sex functions to provide variation for natural selection to act upon was first advocated by August Weismann and it has dominated much discussion on the evolution of sex and recombination since then. The goal of this paper is to further extend this hypothesis and to assess its place in a larger body of theory on the evolution of sex and recombination. A simple generic model is developed to show how fitness variation and covariation interact with selection for recombination and illustrate some important implications of the hypothesis: (1) the advantage of sex and recombination can accrue both to reproductively isolated populations and to modifiers segregating within populations, but the former will be much larger than the latter; (2) forces of degradation that are correlated across loci within an individual can reduce or reverse selection for increased recombination; and (3) crossing-over (which can occur at different places in different meioses) will create more variability than having multiple chromosomes and so will have more influence on the efficacy of selection. Several long-term selection experiments support Weismann's hypothesis, including those showing a greater response to selection in populations with higher rates of recombination and higher rates of recombination evolving as a correlated response to selection for some other character. Weismann's hypothesis is also consistent with the sporadic distribution of obligate asexuality, which indicates that clones have a higher rate of extinction than sexuals. Weismann's hypothesis is then discussed in light of other patterns in the distribution of sexuality versus asexuality. To account for variation in the frequency of obligate asexuality in different taxa, a simple model is developed in which this frequency is a function of three parameters: the rate of clonal origin, the initial fitness of clones when they arise, and the rate at which that fitness declines over time. Variation in all three parameters is likely to be important in explaining the distribution of obligate asexuality. Facultative asexuality also exists, and for this to be stable it seems there must be ecological differences between the sexual and asexual propagules as well as genetic differences. Finally, the timing of sex in cyclical parthenogens is most likely set to minimize the opportunity costs of sex. None of these patterns contradict Weismann's hypothesis, but they do show that many additional principles unrelated to the function of sex are required to fully explain its distribution. Weismann's hypothesis is also consistent with what we know about the mechanics and molecular genetics of recombination, in particular the tendency for chromatids to recombine with a homolog rather than a sister chromatid at meiosis, which is opposite to what they do during mitosis. However, molecular genetic studies have shown that cis-acting sites at which recombination is initiated are lost by gene conversion as a result, a factor that can be expected to affect many fine details in the evolution of recombination. In summary, although Weismann's hypothesis must be considered the leading candidate for the function of sex and recombination, nevertheless, many additional principles are needed to fully account for their evolution.

Mild environmental stress elicits mutations affecting fitness in Chlamydomonas

Cultures of Chlamydomonas were exposed to a range of relatively mild stresses for a period of 24 h. These stresses comprised high and low temperatures, osmotic stress, low pH, starvation and toxic stress. They were then allowed to recuperate for around ten vegetative generations under near-optimal conditions in unmodified minimal medium. Fitness was then assayed as the rate of division of isolated cells on agar. We found that there was a strong tendency for stressed cultures to have lower mean fitness and greater standardized variance in fitness than the negative controls which had been cultured throughout in unmodified minimal medium. The same tendency was shown, as expected, by positive controls which received mutagenic doses of ultraviolet irradiation. We concluded that the most reasonable interpretation of these observations is that mild stress increases the genomic rate of mutation. This appears to be the first time that this phenomenon has been noticed in eukaryotes. The response might be adaptive because lineages in which higher mutation rates are elicited by stress can be favourably selected through the production of a few mutants which are fortuitously well adapted to the stressful environment. Other interpretations are not excluded, however. Regardless of the mechanism involved, the elevation of mutation rates under stress will affect the rate of evolutionary response to environmental change and also the maintenance of sexuality.

Unusually high recombination rate detected in the sex locus region of the honey bee (Apis mellifera)

Sex determination in Hymenoptera is controlled by haplo-diploidy in which unfertilized eggs develop into fertile haploid males. A single sex determination locus with several complementary alleles was proposed for Hymenoptera [so-called complementary sex determination (CSD)]. Heterozygotes at the sex determination locus are normal, fertile females, whereas diploid zygotes that are homozygous develop into sterile males. This results in a strong heterozygote advantage, and the sex locus exhibits extreme polymorphism maintained by overdominant selection. We characterized the sex-determining region by genetic linkage and physical mapping analyses. Detailed linkage and physical mapping studies showed that the recombination rate is <44 kb/cM in the sex-determining region. Comparing genetic map distance along the linkage group III in three crosses revealed a large marker gap in the sex-determining region, suggesting that the recombination rate is high. We suggest that a "hotspot" for recombination has resulted here because of selection for combining favorable genotypes, and perhaps as a result of selection against deleterious mutations. The mapping data, based on long-range restriction mapping, suggest that the Q DNA-marker is within 20,000 bp of the sex locus, which should accelerate molecular analyses.

The dynamics of infinitesimally rare alleles, applied to the evolution of mutation rates and the expression of deleterious mutations

A new method is presented for analysing the dynamics of a classical model where infinitesimally rare alleles segregate at an infinite number of unlinked loci, and where the alleles at different loci have equivalent effects. The dynamics of the distribution of the number of rare alleles per individual (the "phenotypic distribution") can be followed without knowing the frequencies of individual genotypes. Meiosis and random union of gametes have a very simple effect on the factorial cumulants of the phenotypic distribution which are consequently the natural set of variables to follow. An exact solution is presented for the dynamics of rare alleles under mutation and multiplicative selection. This solution has a simple representation in terms of the factorial cumulants. Unlike the QLE (quasi-linkage equilibrium) solution, this solution applies even when the population is far from linkage equilibrium. This approach is extended to analyse the joint dynamics of infinitesimally rare alleles at an infinite number of unlinked loci, together with a locus (with arbitrary allele frequencies) with which they interact. This more general method is used to investigate (1) the joint dynamics of a modifier of the mutation rate, together with deleterious alleles under mutation and multiplicative selection, and (2) the fate of an allele that ameliorates or exacerbates the fitness effects of deleterious alleles. When a new modifier allele causes a large change in the mutation rate, strong linkage disequilibrium is generated during its progress. However, using this new approach based on factorial cumulants, it is found that a remarkably simple invasion condition applies to alleles at the modifier locus, even when strong linkage disequilibrium is generated.

The population genetics of synthetic lethals

Synthetic lethals are variants at different loci that have little or no effect on viability singly but cause lethality in combination. The importance of synthetic lethals and, more generally, of synthetic deleterious loci (SDL) has been controversial. Here, we derive the expected frequencies for SDL under a mutation-selection balance for the complete haploid model and selected cases of the diploid model. We have also obtained simple approximations that demonstrate good fit to exact solutions based on numerical iterations. In the haploid case, equilibrium frequencies of carrier haplotypes (individuals with only a single mutation) are comparable to analogous single-locus results, after allowing for the effects of linkage. Frequencies in the diploid case, however, are much higher and more comparable to the square root of the single-locus results. In particular, when selection operates only on the double-mutant homozygote and linkage is not too tight, the expected frequency of the carriers is approximately the quartic root of the ratio between the mutation rate and the selection coefficient of the synthetics. For a reasonably wide set of models, the frequencies of carriers can be on the order of a few percent. The equilibrium frequencies of these deleterious alleles can be relatively high because, with SDL, both dominance and epistasis act to shield carriers from exposure to selection. We also discuss the possible role of SDL in maintaining genetic variation and in hybrid breakdown.

Testing for epistasis between deleterious mutations

Determining the way in which deleterious mutations interact in their effects on fitness is crucial to numerous areas in population genetics and evolutionary biology. For example, if each additional mutation leads to a greater decrease in log fitness than the last (synergistic epistasis), then the evolution of sex and recombination may be favored to facilitate the elimination of deleterious mutations. However, there is a severe shortage of relevant data. Three relatively simple experimental methods to test for epistasis between deleterious mutations in haploid species have recently been proposed. These methods involve crossing individuals and examining the mean and/or skew in log fitness of the offspring and parents. The main aim of this paper is to formalize these methods, and determine the most effective way in which tests for epistasis could be carried out. We show that only one of these methods is likely to give useful results: crossing individuals that have very different numbers of deleterious mutations, and comparing the mean log fitness of the parents with that of their offspring. We also reconsider experimental data collected on Chlamydomonas moewussi using two of the three methods. Finally, we suggest how the test could be applied to diploid species.

Rates of spontaneous mutation

Rates of spontaneous mutation per genome as measured in the laboratory are remarkably similar within broad groups of organisms but differ strikingly among groups. Mutation rates in RNA viruses, whose genomes contain ca. 10(4) bases, are roughly 1 per genome per replication for lytic viruses and roughly 0.1 per genome per replication for retroviruses and a retrotransposon. Mutation rates in microbes with DNA-based chromosomes are close to 1/300 per genome per replication; in this group, therefore, rates per base pair vary inversely and hugely as genome sizes vary from 6 x 10(3) to 4 x 10(7) bases or base pairs. Mutation rates in higher eukaryotes are roughly 0.1-100 per genome per sexual generation but are currently indistinguishable from 1/300 per cell division per effective genome (which excludes the fraction of the genome in which most mutations are neutral). It is now possible to specify some of the evolutionary forces that shape these diverse mutation rates.

Deleterious mutation accumulation and the regeneration of genetic resources

The accumulation of mildly deleterious mutations accompanying recurrent regeneration of plant germ plasm was modeled under regeneration conditions characterized by different amounts of selection and genetic drift. Under some regeneration conditions (sample sizes >/=75 individuals and bulk harvesting of seed) mutation accumulation was negligible, but under others (sample sizes <75 individuals or equalization of seed production by individual plants) mutation numbers per genome increased significantly during 25-50 cycles of regeneration. When mutations also are assumed to occur (at elevated rates) during seed storage, significant mutation accumulation and fitness decline occurred in 10 or fewer cycles of regeneration regardless of the regeneration conditions. Calculations also were performed to determine the numbers of deleterious mutations introduced and remaining in the genome of an existing variety after hybridization with a genetic resource and subsequent backcrossing. The results suggest that mutation accumulation has the potential to reduce the viability of materials held in germ plasm collections and to offset gains expected by the introduction of particular genes of interest from genetic resources.

Environmental stress and evolution: a theoretical study

A haploid population subject to recurrent deleterious mutations and two environments that provide two different profiles of selection coefficients over loci are modeled. The population is supposed to inhabit one "home" environment where it evolves the corresponding genetic constitution. One generation of the population is then exposed to the second, "foreign" environment. The decline in the mean population fitness is considered as a measure of stress in the population caused by the foreign environment. I define the relative strength of stress as 1 minus the ratio of the mean fitnesses in the foreign and home environments, and give the corresponding analytical expression. The stress strength is composed of three different contributors: the environmental component of stress, which is determined by purely external, non-genetic factors of the foreign environment (its carrying capacity), and two genetic components. The latter consists of the environment x genetic component, caused by the direct influence of the foreign environment on selection coefficients, and of the evolutionary component that is due to the adaptation of the population to the home environment. Among others, it is shown that even if the home and foreign environments were equivalent, so that both the environmental and environmental x genetic components of stress were absent, stress would still occur in the foreign environment due to the evolutionary component. The model also predicts that stressful foreign environments cause an increase in the genotypic variance of fitness. Some other features of population variability in stressful environments are discussed. A general conclusion that can be drawn from this model is that a certain environment may be claimed as stressful only if considered with respect to both a given population and the environment in which the population has evolved.

Deleterious mutations, variable epistatic interactions, and the evolution of recombination

In this paper, we examine the conditions that allow increased recombination to evolve in the presence of recurrent deleterious mutation. We focus on a three-locus model first studied by Feldman et al. (1980), which follows the dynamics of a modifier locus that alters the recombination rate between two loci subject to deleterious mutation. Although Feldman et al. (1980) indicated that increased recombination might be favored if there is diminishing-returns epistasis, we show that alleles that increase the recombination rate can only invade if there is synergistic epistasis between the loci under selection. Even with synergistic epistasis, evolution at the modifier locus will lead to decreased recombination if the modifier locus is loosely linked and epistasis is strong. Using the multi-locus analysis of Barton (1995), we show that variability among loci in the sign and strength of epistasis further decreases the parameter space over which increased recombination may evolve. We conclude that, even with negative epistasis, increased recombination may only be favored when linkage is tight, especially if, as seems likely, epistatic interactions are highly variable among loci.

Viral pathogens and the advantage of sex in the perennial grass Anthoxanthum odoratum

The ubiquity of sexual reproduction among plants and animals remains one of the major unresolved paradoxes of modern evolutionary biology. In order for sex to be maintained in populations, sex must confer immediate and substantial fitness benefits. Theoreticians have proposed numerous mechanisms to explain how such advantages arise, but experimental data are few. In one well-studied population of the perennial grass Anthoxanthum odoratum in a mown North Carolina field, sexual offspring have been found to have significantly higher fitness than asexual offspring. More recent field experiments show that an aphid-transmitted virus, barley yellow dwarf (BYDV)-strain SGV, specifically transmitted by Schizaphus graminum , frequently infects Anthoxanthum progeny soon after transplantation into the field, BYDV infection is asymptomatic in Anthoxanthum , but BYDV-inoculated clones planted directly in the field had significantly lower fitness than healthy controls. Sexual females have been hypothesized to gain a fitness advantage for their offspring in the presence of pathogens either by providing ‘an escape in time’ from pathogens preadapted to the parental genotype or through the production of rare genotypes, which escape frequency-dependent infection. When parental clones and seed-derived sexual offspring were planted in identical but separate arrays in sites near where the parent was collected, parental clones were twice as frequently infected as sexual offspring. Factors other than genetic variation may have contributed to differences in levels of infection between sexual and asexual progeny: in this experiment, clonally derived asexual offspring tillers were slightly larger than seed-derived sexual tillers; in field experiments, larger plants were more frequently infected than smaller plants. When different families were planted into a common site, there was evidence that genotypes were less frequently infected when locally rare than when common. Taken together, the data suggest that BYDV infection generates advantages for rare or sexually produced genotypes in Anthoxanthum . The pattern of infection is likely to result from a complex interaction between vector, host, and viral genetics and population structure, vector behaviour, and host and vector dispersal patterns. Sexually produced genotypes appear to benefit because they are both novel and rare, but the observed minority advantage was weak. Other viral, bacterial, and fungal pathogens in this Anthoxanthum population may act as frequency-dependent selective forces in different places in the field, collectively generating the substantial and observed overall fitness advantage of rare genotypes. Further study is needed to elucidate their role. Nevertheless, the data do show that viral pathogens, which are often asymptomatic, play a significant evolutionary role in plant populations.

The architecture of the life cycle in small organisms

The life cycle of eukaryotes has a dual nature, composed of a vegetative cycle of growth and reproduction, and a sexual cycle of fusion and reduction, linked by the spore. Large size is often favoured through interactions with other organisms, or as a means of exploiting locally or temporarily abundant resources, despite the metabolic penalty of size increase. Beyond a certain point, large organisms must be multicellular (or multinucleate) because of the requirement for more deoxyribonucleic acid (DNA) to service larger quantities of cytoplasm. Multicellularity evolves in some lineages but not in others because its evolution is constrained by the pattern of spore development, being favoured, for example, by the occurrence of multiple fission as the consequence of possessing a rigid cell wall. The separation of soma from germ is also the outcome of a developmental constraint, in this case the inability of cells to divide while flagellated, and also the necessity of remaining in motion. Once achieved, a general physiological advantage is realized through the specialization of soma as source and germ as sink. Large, complex multicellular organisms are fragile constructs that can only persist through deploying sophisticated devices for maintenance. Thus two crucial, and related, properties of life cycles are repair and repeatability. The dual life cycle achieves exogenous repair through spore production in the vegetative cycle and through outcrossing and recombination in the sexual cycle. Repeatability is enhanced by developmental mechanisms such as maternal control and germ-line sequestration, which by restricting the occurrence or the heritability of somatic mutations promote their own replication.

Population genetic perspectives on the evolution of recombination

Optimality arguments and modifier theory are reviewed as paradigms for the study of the evolution of recombination. Optimality criteria (such as maximization of mean fitness) may agree with results from models developed in terms of the evolution of recombination at modifier loci. Modifier models demonstrate, however, that equilibrium mean fitness can decrease during the evolution of recombination rates and is not always maximized. Therefore, optimality arguments do not successfully predict the conditions under which increased or decreased recombination will evolve. The results from modifier models indicate that decreased recombination rates are usually favored when the population is initially near a polymorphic equilibrium with linkage disequilibrium. When the population is subject to directional selection or to deleterious mutations, increased recombination may be favored under certain conditions, provided that there is negative epistasis among alleles.

Recombination load associated with selection for increased recombination

Experiments on Drosophila suggest that genetic recombination may result in lowered fitness of progeny (a 'recombination load'). This has been interpreted as evidence either for a direct effect of recombination on fitness, or for the maintenance of linkage disequilibria by epistatic selection. Here we show that such a recombination load is to be expected even if selection favours increased genetic recombination. This is because of the fact that, although a modifier may suffer an immediate loss of fitness if it increases recombination, it eventually becomes associated with a higher additive genetic variance in fitness, which allows a faster response to direction selection. This argument applies to mutation-selection balance with synergistic epistasis, directional selection on quantitative traits, and ectopic exchange among transposable elements. Further experiments are needed to determine whether the selection against recombination due to the immediate load is outweighed by the increased additive variance in fitness produced by recombination.