Fixation probability favors increased fecundity over reduced generation time

The cornerstone of population genetics is a probabilistic understanding of the ultimate fate--survival or extinction--of rare mutations. If a mutation is beneficial, it enables its carrier to reproduce faster than native wild-type individuals. In classic derivations and in the considerable body of research that has followed, "faster" has been defined mathematically to mean "able to produce more surviving offspring per generation." Many organisms, however, may increase their reproductive rate by producing the same number of offspring in a shorter generation time: a mutant bacterium, for example, may complete the cell cycle and produce two offspring more quickly than the wild type. We find that the ultimate fixation probability of a mutation conferring a shorter generation time differs from that of a mutation conferring more offspring by a factor of 2 ln(2)-nearly 40%. This predicts a reduction in the overall substitution rate for any mutation that decreases the generation time: fixation probability is biased toward increased offspring number.     

Relationship between DNA Polymorphism and Fixation Time

When there is no recombination among nucleotide sites in DNA sequences, DNA polymorphism and fixation of mutants at nucleotide sites are mutually related. Using the method of gene genealogy, the relationship between the DNA polymorphism and the fixation of mutant nucleotide was quantitatively investigated under the assumption that mutants are selectively neutral, that there is no recombination among nucleotide sites, and that the population is a random mating population with N diploid individuals. The results obtained indicate that the expected number of nucleotide differences between two DNA sequences randomly sampled from the population is 42% less when a mutant at a particular nucleotide site reaches fixation than at a random time, and that heterozygosity is also expected to be less when fixation takes place than at a random time, but the amount of reduction depends on the value of 4Nv in this case, where v is the mutation rate per DNA sequence per generation. The formula for obtaining the expected number of nucleotide differences between the two DNA sequences for a given fixation time is also derived, and indicates that, even when it takes a large number of generations for a mutant to reach fixation, this number is 33% less than at a random time. The computer simulation conducted suggests that the expected number of nucleotide differences between the two DNA sequences at the time when an advantageous mutant becomes fixed is essentially the same as that of neutral mutant if the fixation time is the same. The effect of recombination on the amount of DNA polymorphism was also investigated by using computer simulation.     

Heterosis in age‐specific selected populations of a seed beetle: Sex differences in longevity and reproductive behavior

We tested mutation accumulation hypothesis for the evolution of senescence using short‐lived and long‐lived populations of the seed‐feeding beetle, Acanthoscelides obtectus (Say), obtained by selection on early‐ and late‐life for many generations. The expected consequence of the mutation accumulation hypothesis is that in short‐lived populations, where the force of natural selection is the strongest early in life, the late‐life fitness traits should decline due to genetic drift which increases the frequency of mutations with deleterious effects in later adult stages. Since it is unlikely that identical deleterious mutations will increase in several independent populations, hybrid vigor for late‐life fitness is expected in offspring obtained in crosses among populations selected for early‐life fitness traits. We tested longevity of both sexes, female fecundity and male reproductive behavior for hybrid vigor by comparing hybrid and nonhybrid short‐lived populations. Hybrid vigor was confirmed for male virility, mating speed and copulation duration, and longevity of both sexes at late ages. In contrast to males, the results on female fecundity in short‐lived populations did not support mutation accumulation as a genetic mechanism for the evolution of this trait. Contrary to the prediction of this hypothesis, male mating ability indices and female fecundity in long‐lived populations exhibited hybrid vigor at all assayed age classes. We demonstrate that nonhybrid long‐lived populations diverged randomly regarding female and male reproductive fitness, indicating that sexually antagonistic selection, when accompanied with genetic drift for female fecundity and male virility, might be responsible for overriding natural selection in the independently evolving long‐lived populations.     

Factors affecting the genetic load in Drosophila: synergistic epistasis and correlations among fitness components

Two factors that can affect genetic load, synergistic epistasis and sexual selection, were investigated in Drosophila melanogaster. A set of five chromosomal regions containing visible recessive mutations were put together in all combinations to create a full set of 32 homozygous lines fixed for different numbers of known mutations. Two measures of fitness were made for each line: productivity (a combined measure of fecundity and egg-to-adult survivorship) and competitive male mating success. Productivity, but not male mating success, showed a pattern of strong average synergistic epistasis, such that the log fitness declined nonlinearly with increasing numbers of mutations. Synergistic epistasis is known to reduce the mutation load. Both fitness components show some positive and some negative interactions between specific sets of mutations. Furthermore, alleles with deleterious effects on productivity tend to also diminish male mating success. Given that male mating success can affect relative fitness without changing the mean productivity of a population, these additional effects would lead to lower frequencies and lower fixation rates of deleterious alleles without higher costs to the mean fitness of the population.     

Fixation probabilities when generation times are variable: the burst death model

Estimating the fixation probability of a beneficial mutation has a rich history in theoretical population genetics. Typically, to attain mathematical tractability, we assume that generation times are fixed, while the number of offspring per individual is stochastic. However, fixation probabilities are extremely sensitive to these assumptions regarding life history. In this article, we compute the fixation probability for a "burst-death" life-history model. The model assumes that generation times are exponentially distributed, but the number of offspring per individual is constant. We estimate the fixation probability for populations of constant size and for populations that grow exponentially between periodic population bottlenecks. We find that the fixation probability is, in general, substantially lower in the burst-death model than in classical models. We also note striking qualitative differences between the fates of beneficial mutations that increase burst size and mutations that increase the burst rate. In particular, once the burst size is sufficiently large relative to the wild type, the burst-death model predicts that fixation probability depends only on burst rate.     

Sources of stochasticity in models of sex allocation in spatially structured populations

There are many ways to include stochastic effects in models of sex allocation evolution. These include variability in the number of mating partners and fecundity in a rich literature that goes back 20 years. The effects of variance in the fecundity and number of mating partners have typically been considered separately from the stochastic effects of mortality. However, I show that these processes produce mathematically equivalent models with subtly different biological details. These scenarios differ in the way that information becomes available to individuals because the parents often have information on mating partners while they are making sex allocation decisions, but must make these decisions before brood mortality takes place. This makes it possible to test which mechanism, stochastic mortality or variation in mating partners, is responsible for observed sex ratios. Alternatively, asymmetric variance between sexual functions can cause skewed sex allocation, even in the absence of local mate competition. This allows the evolution of either female- or male-biased sex ratios depending on which sexual function is more variable.     

Sexual dimorphism in white campion: complex control of carpel number is revealed by y chromosome deletions

Sexual dimorphism in the dioecious plant white campion (Silene latifolia = Melandrium album) is under the control of two main regions on the Y chromosome. One such region, encoding the gynoecium-suppressing function (GSF), is responsible for the arrest of carpel initiation in male flowers. To generate chromosomal deletions, we used pollen irradiation in male plants to produce hermaphroditic mutants (bsx mutants) in which carpel development was restored. The mutants resulted from alterations in at least two GSF chromosomal regions, one autosomal and one located on the distal half of the (p)-arm of the Y chromosome. The two mutations affected carpel development independently, each mutation showing incomplete penetrance and variegation, albeit at significantly different levels. During successive meiotic generations, a progressive increase in penetrance and a reduction in variegation levels were observed and quantified at the level of the Y-linked GSF (GSF-Y). Possible mechanisms are proposed to explain the behavior of the bsx mutations: epigenetic regulation or/and second-site mutation of modifier genes. In addition, studies on the inheritance of the hermaphroditic trait showed that, unlike wild-type Y chromosomes, deleted Y chromosomes can be transmitted through both the male and the female lines. Altogether, these findings bring experimental support, on the one hand, to the existence on the Y chromosome of genic meiotic drive function(s) and, on the other hand, to models that consider that dioecy evolved through multiple mutation events. As such, the GSF is actually a system containing more than one locus and whose primary component is located on the Y chromosome.     

A model for evolution of male parental care and female multiple mating

In most animals, males gain a fitness benefit by mating with many females, whereas the number of progeny per female is unlikely to increase as a function of additional mates. Furthermore, males of internally fertilizing species run the risk of investing in offspring of other males if they provide parental care. Nevertheless, males of many avian species and a minority of mammalian species provide parental care, and females of various species mate with multiple males. I investigate a two-locus genetic model for evolution of male parental care and female multiple mating in which females gain a direct benefit by multiple mating from the paternal care they thereby elicit for their offspring. The model suggests that, first, male parental care can evolve when it strongly enhances offspring survival and the direct costs of female multiple mating (e.g., loss of energy, risk of injury, exposure to infectious diseases) are greater than its indirect benefit (e.g., acquisition of good genes, increased genetic diversity among offspring); second, female multiple mating can evolve when paternal care is important for offspring survival or the indirect benefit of multiple mating is larger than its direct cost; and, finally, male parental care and female multiple mating can co-occur.     

Superior sperm competitors sire higher-quality young

The evolution of polyandry remains controversial. This is because, unlike males, in many cases multiple mating by females does not increase fecundity and inevitably involves some costs. As a result, a large number of indirect benefit models have been proposed to explain polyandry. One of these, the good sperm hypothesis, posits that high-quality males are better sperm competitors and sire higher-quality offspring. Hence, by mating multiply, females produce offspring of superior quality. Despite being potentially widely applicable across species, this idea has received little attention. In a laboratory experiment with yellow dung flies ( Scathophaga stercoraria ) we found that males that were more successful in sperm competition also had offspring that developed faster. There was no relationship between paternal success in sperm competition and the ability of offspring to survive post-emergence starvation. Since faster development times are likely to be advantageous in this species, our data provide some support for polyandry evolving as a means of producing higher-quality offspring via sperm competition.     

INBREEDING AND THE COST OF MEIOSIS: THE EVOLUTION OF SELFING IN POPULATIONS PRACTICING BIPARENTAL INBREEDING

The effect of biparental inbreeding on the conditions governing the evolution of selfing is examined using recursions in mating-type frequencies. Sibmating in combination with random outcrossing influences two key determinants of the adaptive value of selfing: 1) the meiotic cost of biparental reproduction and 2) the level of inbreeding depression due to deleterious mutations. Biparental inbreeding serves to maintain biparental reproduction by increasing relatedness between parents and their biparentally derived offspring and introduces the possibility of an optimal mating system that incorporates both modes of reproduction. Biparental inbreeding serves to promote uniparental reproduction by reducing the relative inbreeding depression suffered by uniparental offspring. The net effect of these two antagonistic trends depends upon the extent to which mutational load accounts for differences in the numbers of the two types of offspring. A brief summary of the empirical literature suggests that: 1) biparental inbreeding may occur in populations exhibiting mixed mating systems; 2) while inbreeding depression represents an important factor, it does not account entirely for differences in offspring number between the two modes of reproduction.     

Effects of Partial Inbreeding on Fixation Rates and Variation of Mutant Genes

Diffusion methods were used to investigate the fixation probability, average time until fixation and extinction, and cumulative heterozygosity and genetic variance for single mutant genes in finite populations with partial inbreeding. The critical parameters in the approximation are the coefficient of inbreeding due to nonrandom mating (F) and the effective population size (Ne), which also depends on F and the variance of family size. For large Ns, the fixation probability (u) is u = 2(Ne/N)s (F + h - Fh), where N is the population census, s is the coefficient of selection of the mutant homozygote and h is the coefficient of dominance. For Poisson family size (independent Poisson distributions of selfed and nonselfed offspring with partial selfing, and independent Poisson distributions of male and female numbers with partial sib mating), Ne = N/(1 + F), and the time until fixation is approximately equal to Ne/N times the time to fixation with random mating, but this relation does not hold, however, for other distributions of family size. The cumulative nonadditive variance until fixation or loss for dominant genes is reduced with increasing F while for recessive genes it is increased with intermediate values of F. The average time until extinction of deleterious mutations is reduced by increasing F. This reduction, when expressed as a proportion, is approximately independent of the initial gene frequency as well as the selective disadvantage if this is large.     

Paternal genetic effects on offspring fitness are context dependent within the extrapair mating system of a socially monogamous passerine

Avian extrapair mating systems provide an interesting model to assess the role of genetic benefits in the evolution of female multiple mating behavior, as potentially confounding nongenetic benefits of extrapair mate choice are seen to be of minor importance. Genetic benefit models of extrapair mating behavior predict that females engage in extrapair copulations with males of higher genetic quality compared to their social mates, thereby improving offspring reproductive value. The most straightforward test of such good genes models of extrapair mating implies pairwise comparisons of maternal half-siblings raised in the same environment, which permits direct assessment of paternal genetic effects on offspring traits. But genetic benefits of mate choice may be difficult to detect. Furthermore, the extent of genetic benefits (in terms of increased offspring viability or fecundity) may depend on the environmental context such that the proposed differences between extrapair offspring (EPO) and within-pair offspring (WPO) only appear under comparatively poor environmental conditions. We tested the hypothesis that genetic benefits of female extrapair mate choice are context dependent by analyzing offspring fitness-related traits in the coal tit (Parus ater) in relation to seasonal variation in environmental conditions. Paternal genetic effects on offspring fitness were context dependent, as shown by a significant interaction effect of differential paternal genetic contribution and offspring hatching date. EPO showed a higher local recruitment probability than their maternal half-siblings if born comparatively late in the season (i.e., when overall performance had significantly declined), while WPO performed better early in the season. The same general pattern of context dependence was evident when using the number of grandchildren born to a cuckolding female via her female WPO or EPO progeny as the respective fitness measure. However, we were unable to demonstrate that cuckolding females obtained a general genetic fitness benefit from extrapair fertilizations in terms of offspring viability or fecundity. Thus, another type of benefit could be responsible for maintaining female extrapair mating preferences in the study population. Our results suggest that more than a single selective pressure may have shaped the evolution of female extrapair mating behavior in socially monogamous passerines.     

Polyandry promotes enhanced offspring survival in decorated crickets

Although female multiple mating is ubiquitous in insects, its adaptive significance remains poorly understood. Benefits to multiple mating can accrue via direct material benefits, indirect genetic benefits, or both. We investigated the effects of multiple mating in the decorated cricket, Gryllodes sigillatus, by simultaneously varying the number of times that females mated and the number of different males with which they mated, measuring aspects of female fecundity and elements of offspring performance and viability. Multiple matings resulted in enhanced female fitness relative to single matings when females mated with different partners, but not when females mated repeatedly with the same male. Specifically, polyandrous females produced significantly more offspring surviving to reproductive maturity than did monogamous females mating once or mating repeatedly with the same male. These results suggest that the benefit females gain from multiple mating is influenced primarily by genetic and not material benefits.     

Environmental Fluctuations and Level of Density-Compensation Strongly Affects the Probability of Fixation and Fixation Times

The probability of, and time to, fixation of a mutation in a population has traditionally been studied by the classic Wright–Fisher model where population size is constant. Recent theoretical expansions have covered fluctuating populations in various ways but have not incorporated models of how the environment fluctuates in combination with different levels of density-compensation affecting fecundity. We tested the hypothesis that the probability of, and time to, fixation of neutral, advantageous and deleterious mutations is dependent on how the environment fluctuates over time, and on the level of density-compensation. We found that fixation probabilities and times were dependent on the pattern of autocorrelation of carrying capacity over time and interacted with density-compensation. The pattern found was most pronounced at small population sizes. The patterns differed greatly depending on whether the mutation was neutral, advantageous, or disadvantageous. The results indicate that the degree of mismatch between carrying capacity and population size is a key factor, rather than population size per se, and that effective population sizes can be very low also when the census population size is far above the carrying capacity. This study highlights the need for explicit population dynamic models and models for environmental fluctuations for the understanding of the dynamics of genes in populations.     

Evolutionary Consequences of Mutation and Selection within an Individual

Whether in sexual or asexual organisms, selection among cell lineages during development is an effective way of eliminating deleterious mutations. Using a mathematical analysis, we find that relatively small differences in cell replication rates during development can translate into large differences in the proportion of mutant cells within the adult, especially when development involves a large number of cell divisions. Consequently, intraorganismal selection can substantially reduce the deleterious mutation rate observed among offspring as well as the mutation load within a population, because cells rather than individuals provide the selective ``deaths' necessary to stem the tide of deleterious mutations. The reduction in mutation rate among offspring is more pronounced in organisms with plastic development than in those with structured development. It is also more pronounced in asexual organisms that produce multicellular rather than unicellular offspring. By effecting the mutation rate, intraorganismal selection may have broad evolutionary implications; as an example, we consider its influence on the evolution of ploidy levels, finding that cell-lineage selection is more effective in haploids and tends to favor their evolution.     

Paternity costs from polyandry compensated by increased fecundity in the hide beetle

Polyandry-induced sperm competition is assumed to impose costson males through reduced per capita paternity success. In contrast,studies focusing on the consequences of polyandry for femalesreport increased oviposition rates and fertility. For thesespecies, there is potential for the increased female fecundityassociated with polyandry to offset the costs to males of sharedpaternity. We tested this hypothesis by comparing the proportionand number of offspring sired by males mated with monandrousand polyandrous females in the hide beetle, Dermestes maculates,both for males mating with different females and for males rematingwith the same female. In 4 mating treatments, monandrous femalesmated either once or twice with the same male and polyandrousfemales mated either twice with 2 different males or thricewith 2 males (where 1 male mated twice). Polyandrous and twice-matingmonandrous females displayed greater fecundity and fertilitythan singly mating monandrous females. Moreover, males rematedto the same female had greater paternity regardless of whetherthat female mated with another male. In both polyandrous treatments,male mating order did not affect paternity success. Finally,although the proportion of eggs sired decreased if a male matedwith a polyandrous female, multiply mating females or femalesthat remated with a previous mate laid significantly more eggsand thus the actual number of eggs sired was comparable. Thus,males do not necessarily accrue a net fitness loss when matingwith polyandrous females. This may explain the absence of anyobvious defensive paternity-protection traits in hide beetlesand other species.     

With selection for fecundity the mean fitness does not necessarily increase

A population with two alleles at one locus is considered. It is assumed that there is random mating of adults and that matings in which a particular pair of genotypes is involved may have a different mean number of offspring, or fecundity, than other types of matings. There is assumed to be no other selection. It is shown that the genotypic frequencies that maximize the mean fecundity of the population are not necessarily the same as the stable equilibrium frequencies. Thus, examples can be found for which the mean fecundity decreases from one generation to the next, and one such example is presented. An example in which there is no stable equilibrium, and the mean fecundity oscillates, is also given.     

X-linked meiotic drive can boost population size and persistence

X-linked meiotic drivers cause X-bearing sperm to be produced in excess by male carriers, leading to female-biased sex ratios. Here, we find general conditions for the spread and fixation of X-linked alleles. Our conditions show that the spread of X-linked alleles depends on sex-specific selection and transmission rather than the time spent in each sex. Applying this logic to meiotic drive, we show that polymorphism is heavily dependent on sperm competition induced both by female and male mating behavior and the degree of compensation to gamete loss in the ejaculate size of drive males. We extend these evolutionary models to investigate the demographic consequences of biased sex ratios. Our results suggest driving X-alleles that invade and reach polymorphism (or fix and do not bias segregation excessively) will boost population size and persistence time by increasing population productivity, demonstrating the potential for selfish genetic elements to move sex ratios closer to the population-level optimum. However, when the spread of drive causes strong sex-ratio bias, it can lead to populations with so few males that females remain unmated, cannot produce offspring, and go extinct. This outcome is exacerbated when the male mating rate is low. We suggest that researchers should consider the potential for ecologically beneficial side effects of selfish genetic elements, especially in light of proposals to use meiotic drive for biological control.     

How multiple mating by females affects sexual selection

Multiple mating by females is widely thought to encourage post-mating sexual selection and enhance female fitness. We show that whether polyandrous mating has these effects depends on two conditions. Condition 1 is the pattern of sperm utilization by females; specifically, whether, among females, male mating number, m (i.e. the number of times a male mates with one or more females) covaries with male offspring number, o. Polyandrous mating enhances sexual selection only when males who are successful at multiple mating also sire most or all of each of their mates'' offspring, i.e. only when Cov_♂(m,o), is positive. Condition 2 is the pattern of female reproductive life-history; specifically, whether female mating number, m, covaries with female offspring number, o. Only semelparity does not erode sexual selection, whereas iteroparity (i.e. when Cov_♀(m,o), is positive) always increases the variance in offspring numbers among females, which always decreases the intensity of sexual selection on males. To document the covariance between mating number and offspring number for each sex, it is necessary to assign progeny to all parents, as well as identify mating and non-mating individuals. To document significant fitness gains by females through iteroparity, it is necessary to determine the relative magnitudes of male as well as female contributions to the total variance in relative fitness. We show how such data can be collected, how often they are collected, and we explain the circumstances in which selection favouring multiple mating by females can be strong or weak.     

The Baker's Yeast Diploid Genome Is Remarkably Stable in Vegetative Growth and Meiosis

Accurate estimates of mutation rates provide critical information to analyze genome evolution and organism fitness. We used whole-genome DNA sequencing, pulse-field gel electrophoresis, and comparative genome hybridization to determine mutation rates in diploid vegetative and meiotic mutation accumulation lines of Saccharomyces cerevisiae. The vegetative lines underwent only mitotic divisions while the meiotic lines underwent a meiotic cycle every ∼20 vegetative divisions. Similar base substitution rates were estimated for both lines. Given our experimental design, these measures indicated that the meiotic mutation rate is within the range of being equal to zero to being 55-fold higher than the vegetative rate. Mutations detected in vegetative lines were all heterozygous while those in meiotic lines were homozygous. A quantitative analysis of intra-tetrad mating events in the meiotic lines showed that inter-spore mating is primarily responsible for rapidly fixing mutations to homozygosity as well as for removing mutations. We did not observe 1–2 nt insertion/deletion (in-del) mutations in any of the sequenced lines and only one structural variant in a non-telomeric location was found. However, a large number of structural variations in subtelomeric sequences were seen in both vegetative and meiotic lines that did not affect viability. Our results indicate that the diploid yeast nuclear genome is remarkably stable during the vegetative and meiotic cell cycles and support the hypothesis that peripheral regions of chromosomes are more dynamic than gene-rich central sections where structural rearrangements could be deleterious. This work also provides an improved estimate for the mutational load carried by diploid organisms.