Estimation of parameters of deleterious mutations in partial selfing or partial outcrossing populations and in nonequilibrium populations

The Deng-Lynch method was developed to estimate the rate and effects of deleterious genomic mutations (DGM) in natural populations under the assumption that populations are either completely outcrossing or completely selfing and that populations are at mutation-selection (M-S) balance. However, in many plant and animal populations, selfing or outcrossing is often incomplete in that a proportion of populations undergo inbreeding while the rest are outcrossing. In addition, the degrees of deviation of populations from M-S balance are often not known. Through computer simulations, we investigated the robustness and the applicability of the Deng-Lynch method under different degrees of partial selfing or partial outcrossing and for nonequilibrium populations approaching M-S balance at different stages. The investigation was implemented under constant, variable, and epistatic mutation effects. We found that, generally, the estimation by the Deng-Lynch method is fairly robust if the selfing rate (S) is <0.10 in outcrossing populations and if S > 0.8 in selfing populations. The estimation may be unbiased under partial selfing with variable and epistatic mutation effects in predominantly outcrossing populations. The estimation is fairly robust in nonequilibrium populations at different stages approaching M-S balance. The dynamics of populations approaching M-S balance under various parameters are also studied. Under mutation and selection, populations approach balance at a rapid pace. Generally, it takes 400-2000 generations to reach M-S balance even when starting from homogeneous individuals free of DGM. Our investigation here provides a basis for characterizing DGM in partial selfing or outcrossing populations and for nonequilibrium populations.     

Estimation of the rate and effects of deleterious genomic mutations in finite populations with linkage disequilibrium

Under several assumptions such as infinite population size with unlinked loci at linkage equilibrium (LD) under mutation-selection (M-S) balance, the rate (U), and the average effects (dominance and selection coefficients h and s) of deleterious genomic mutations (DGM) can be estimated by the Deng-Lynch method in some natural populations. However, all natural populations are finite in size and many of them are not large enough to be considered as approximately infinite. In the absence of an analytical estimation approach to characterize DGM in finite populations, we test the robustness and applicability of the Deng-Lynch method in finite populations with computer simulations. The results indicate that the estimation obtained by the Deng-Lynch method in finite populations with LD is generally robust when population size is greater than 400. With constant mutation effects, in outcrossing populations, the estimates U and ? are unbiased or only slightly upwardly biased, and ? is unbiased for most cases. In highly selfing populations, U and ? are upwardly biased, U is no more than 1.5U and ? is less than 1.1 h, and ? is either unbiased or slightly downwardly biased. With variable mutation effects, U ranges from 0.56 to 0.72U, and s ranges from 1.4 to 1.8s. Generally speaking, with the same finite population size, the estimation in outcrossing populations is better than in highly selfing populations. Given that even the order of the magnitude of the parameters of DMG (U in particular) is controversial, our investigation here may provide a basis for using the Deng-Lynch method to characterize DGM in finite populations of size greater than 400 in the presence of LD.     

Inbreeding Depression and Inferred Deleterious-Mutation Parameters in Daphnia

DENG and LYNCH recently proposed a method for estimating deleterious genomic mutation parameters from changes in the mean and genetic variance of fitness traits upon inbreeding in outcrossing populations. Such observations are readily acquired in cyclical parthenogens. Selfing and life-table experiments were performed for two such Daphnia populations. We observed a significant inbreeding depression and an increase of genetic variance for all traits analyzed. DENG and LYNCH's original procedures were extended to estimate genomic mutation rate (U), mean dominance coefficient (h), mean selection coefficient (s), and scaled genomic mutational variance (V(m)/V(e)). On average, U, h, s and V(m)/V(e) (^ indicates an estimate) are 0.74, 0.30, 0.14 and 4.6E-4, respectively. For the true values, the U and h are lower bounds, and s and V(m)/V(e) upper bounds. The present U, h and V(m)/V(e) are in general concordance with earlier results. The discrepancy between the present s and that from mutation-accumulation experiments in Drosophila (~0.04) is discussed. It is shown that different reproductive modes do not affect gene frequency at mutation-selection equilibrium if mutational effects on fitness are multiplicative and not completely recessive.     

Characterization of deleterious mutations in outcrossing populations.

Deng and Lynch recently proposed estimating the rate and effects of deleterious genomic mutations from changes in the mean and genetic variance of fitness upon selfing/outcrossing in outcrossing/highly selfing populations. The utility of our original estimation approach is limited in outcrossing populations, since selfing may not always be feasible. Here we extend the approach to any form of inbreeding in outcrossing populations. By simulations, the statistical properties of the estimation under a common form of inbreeding (sib mating) are investigated under a range of biologically plausible situations. The efficiencies of different degrees of inbreeding and two different experimental designs of estimation are also investigated. We found that estimation using the total genetic variation in the inbred generation is generally more efficient than employing the genetic variation among the mean of inbred families, and that higher degree of inbreeding employed in experiments yields higher power for estimation. The simulation results of the magnitude and direction of estimation bias under variable or epistatic mutation effects may provide a basis for accurate inferences of deleterious mutations. Simulations accounting for environmental variance of fitness suggest that, under full-sib mating, our extension can achieve reasonably well an estimation with sample sizes of only approximately 2000-3000.     

Inferring deleterious-mutation parameters in natural daphnia populations

Deng and Lynch (1, 2) proposed to characterize deleterious genomic mutations from changes in the mean and genetic variance of fitness traits upon selfing in outcrossing populations. Such observations can be readily acquired in cyclical parthenogens. Selfing and life-table experiments were performed for two such Daphnia populations. A significant inbreeding depression and an increase of genetic variance for all traits analyzed were observed. Deng and Lynch’s (2) procedures were employed to estimate the genomic mutation rate (U), mean dominance coefficient $\left( {\bar h} \right)$ , mean selection coefficient $\left( {\bar s} \right)$ , and scaled genomic mutational variance (V m/Ve). On average, Û, $\left( {\hat \bar h} \right)$ , $\left( {\hat \bar s} \right)$ and $\frac{{\hat V_m }}{{V_e }}$ (^ indicates an estimate) are 0.84, 0.30, 0.14 and 4.6E-4 respectively. For the true values, the Û and $\hat \bar h$ are lower bounds, and $\hat \bar s$ and $\frac{{\hat V_m }}{{V_e }}$ upper bounds.     

Mutation accumulation in a selfing population: consequences of different mutation rates between selfers and outcrossers

Currently existing theories predict that because deleterious mutations accumulate at a higher rate, selfing populations suffer from more intense genetic degradation relative to outcrossing populations. This prediction may not always be true when we consider a potential difference in deleterious mutation rate between selfers and outcrossers. By analyzing the evolutionary stability of selfing and outcrossing in an infinite population, we found that the genome-wide deleterious mutation rate would be lower in selfing than in outcrossing organisms. When this difference in mutation rate was included in simulations, we found that in a small population, mutations accumulated more slowly under selfing rather than outcrossing. This result suggests that under frequent and intense bottlenecks, a selfing population may have a lower risk of genetic extinction than an outcrossing population.     

Slow Recovery from Inbreeding Depression Generated by the Complex Genetic Architecture of Segregating Deleterious Mutations

The deleterious effects of inbreeding have been of extreme importance to evolutionary biology, but it has been difficult to characterize the complex interactions between genetic constraints and selection that lead to fitness loss and recovery after inbreeding. Haploid organisms and selfing organisms like the nematode Caenorhabditis elegans are capable of rapid recovery from the fixation of novel deleterious mutation; however, the potential for recovery and genomic consequences of inbreeding in diploid, outcrossing organisms are not well understood. We sought to answer two questions: 1) Can a diploid, outcrossing population recover from inbreeding via standing genetic variation and new mutation? and 2) How does allelic diversity change during recovery? We inbred C. remanei, an outcrossing relative of C. elegans, through brother-sister mating for 30 generations followed by recovery at large population size. Inbreeding reduced fitness but, surprisingly, recovery from inbreeding at large populations sizes generated only very moderate fitness recovery after 300 generations. We found that 65% of ancestral single nucleotide polymorphisms (SNPs) were fixed in the inbred population, far fewer than the theoretical expectation of ∼99%. Under recovery, 36 SNPs across 30 genes involved in alimentary, muscular, nervous, and reproductive systems changed reproducibly across replicates, indicating that strong selection for fitness recovery does exist. Our results indicate that recovery from inbreeding depression via standing genetic variation and mutation is likely to be constrained by the large number of segregating deleterious variants present in natural populations, limiting the capacity for recovery of small populations.     

Inbreeding load, average dominance and the mutation rate for mildly deleterious alleles in Mimulus guttatus

The goal of this study is to provide information on the genetics of inbreeding depression in a primarily outcrossing population of Mimulus guttatus. Previous studies of this population indicate that there is tremendous inbreeding depression for nearly every fitness component and that almost all of this inbreeding depression is due to mildly deleterious alleles rather than recessive lethals or steriles. In this article I assayed the homozygous and heterozygous fitnesses of 184 highly inbred lines extracted from a natural population. Natural selection during the five generations of selfing involved in line formation essentially eliminated major deleterious alleles but was ineffective in purging alleles with minor fitness effects and did not appreciably diminish overall levels of inbreeding depression. Estimates of the average degree of dominance of these mildly deleterious alleles, obtained from the regression of heterozygous fitness on the sum of parental homozygous fitness, indicate that the detrimental alleles are partially recessive for most fitness traits, with h approximately 0.15 for cumulative measures of fitness. The inbreeding load, B, for total fitness is approximately 1.0 in this experiment. These results are consistent with the hypothesis that spontaneous mildly deleterious mutations occur at a rate >0.1 mutation per genome per generation.     

Patterns of self compatibility, inbreeding depression, outcrossing, and sex allocation in a marine bryozoan suggest the predominating influence of sperm competition

Sex allocation by simultaneous hermaphrodites is theoretically influenced by selfing rate, which is in turn influenced by the benefits of enhanced genomic transmission and reproductive assurance relative to the cost of inbreeding depression. The experimental investigation of these influences in seed plants has a rich pedigree, yet although such an approach is equally relevant to colonial invertebrates, which globally dominate subtidal communities on firm substrata, such studies have been scarce. We reared self‐compatible genets of the marine bryozoan Celleporella hyalina s.l. in the presence and absence of allosperm, and used molecular genetic markers for paternity analysis of progeny to test theoretical predictions that: (1) genets from focal populations with high selfing rates show less inbreeding depression than from focal populations with low selfing rates; (2) genets whose selfed progeny show inbreeding depression prefer outcross sperm (allosperm); and (3) genets bias sex allocation toward female function when reared in reproductive isolation. Offspring survivorship and paternity analysis were used to estimate levels of inbreeding depression and preference for outcrossing or selfing. Sex allocation was assessed by counting male and female zooids. As predicted, inbreeding depression was severe in selfed progeny of genets derived from the populations with low self‐compatibility rates, but, with one exception, was not detected in selfed progeny of genets derived from the populations with higher self‐compatibility rates. Also, as predicted, genets whose selfed progeny showed inbreeding depression preferred outcrossing, and a genet whose selfed progeny did not show inbreeding depression preferred selfing. Contrary to prediction, sex allocation in the majority of genets was not influenced by reproductive isolation. Lack of economy of male function may reflect the over‐riding influence of allosperm‐competition in typically dense breeding populations offering good opportunity for outcrossing. We suggest that hermaphroditism may be a plesiomorphic character of the crown group Bryozoa, prevented by phylogenetic constraint from being replaced by gonochorism and therefore not necessarily adaptive in all extant clades. © 2009 The Linnean Society of London, Biological Journal of the Linnean Society, 2009, 98 , 519–531.     

An explicit model for the inbreeding load in the evolutionary analysis of selfing

I present analytical predictions for the equilibrium inbreeding load expected in a population under mutation, selection, and a regular mating system for any population size and for any magnitude and recessivity of the deleterious effects. Using this prediction, I deduce the relative fitness of mutant alleles with small effect on selfing to explore the situations where selfing or outcrossing are expected to evolve. The results obtained are in agreement with previous literature, showing that natural selection is expected to lead to stable equilibria where populations show either complete outcrossing or complete selfing, and that selfing is promoted by large deleterious mutation rates. I find that the evolution of selfing is favored by a large recessivity of deleterious effects, while the magnitude of homozygous deleterious effects only becomes relevant in relatively small populations. This result contradicts the standard assumption that purging in large populations will only promote selfing when homozygous deleterious effects are large, and implies that previously published results obtained assuming lethal mutations in large populations can be extrapolated to nonlethal alleles of similar recessivity. This conclusion and the general approach used in this analysis can be useful in the study of the evolution of mating systems.     

Analysis of inbreeding depression in mixed-mating plants provides evidence for selective interference and stable mixed mating

Hermaphroditic individuals can produce both selfed and outcrossed progeny, termed mixed mating. General theory predicts that mixed-mating populations should evolve quickly toward high rates of selfing, driven by rapid purging of genetic load and loss of inbreeding depression (ID), but the substantial number of mixed-mating species observed in nature calls this prediction into question. Lower average ID reported for selfing than for outcrossing populations is consistent with purging and suggests that mixed-mating taxa in evolutionary transition will have intermediate ID. We compared the magnitude of ID from published estimates for highly selfing (r > 0.8), mixed-mating (0.2 ≤ r ≥ 0.8), and highly outcrossing (r < 0.2) plant populations across 58 species. We found that mixed-mating and outcrossing taxa have equally high average lifetime ID (δ= 0.58 and 0.54, respectively) and similar ID at each of four life-cycle stages. These results are not consistent with evolution toward selfing in most mixed-mating taxa. We suggest that prevention of purging by selective interference could explain stable mixed mating in many natural populations. We identify critical gaps in the empirical data on ID and outline key approaches to filling them.     

Rates of deleterious mutation and the evolution of sex in Caenorhabditis

A variety of models propose that the accumulation of deleterious mutations plays an important role in the evolution of breeding systems. These models make predictions regarding the relative rates of protein evolution and deleterious mutation in taxa with contrasting modes of reproduction. Here we compare available coding sequences from one obligately outcrossing and two primarily selfing species of Caenorhabditis to explore the potential for mutational models to explain the evolution of breeding system in this clade. If deleterious mutations interact synergistically, the mutational deterministic hypothesis predicts that a high genomic deleterious mutation rate (U) will offset the reproductive disadvantage of outcrossing relative to asexual or selfing reproduction. Therefore, C. elegans and C. briggsae (both largely selfing) should both exhibit lower rates of deleterious mutation than the obligately outcrossing relative C. remanei. Using a comparative approach, we estimate U to be equivalent (and < 1) among all three related species. Stochastic mutational models, Muller's ratchet and Hill-Robertson interference, are expected to cause reductions in the effective population size in species that rarely outcross, thereby allowing deleterious mutations to accumulate at an elevated rate. We find only limited support for more rapid molecular evolution in selfing lineages. Overall, our analyses indicate that the evolution of breeding system in this group is unlikely to be explained solely by available mutational models.     

The cost of selfing inEncyclia cochleata (Orchidaceae)

To determine whether inbreeding depression accounts for the maintenance of outcrossing in populations of the self-compatible orchidEncyclia cochleata, the estimated selective advantage of selfing was compared to a measure of inbreeding depression. Individuals from three populations ofE. cochleata and some of their progeny were phenotyped using isozyme analysis. The electrophoretic data were used to estimate the outcrossing rate and the theoretical cost of outcrossing. Inbreeding depression was estimated by comparing the fitness of the progeny resulting from both types of pollinations. The seeds from outcrossed and selfed hand-pollinations and naturally pollinated seeds from a population of the triandrous form ofE. cochleata were grown aseptically on culture media, and their development over the next three years recorded. Inbreeding was common, particularly in one population (outcrossing rate 40%). However, the level of inbreeding depression was only 1–2%, considerably less inbreeding depression than expected.     

THE EVOLUTION OF SELF-FERTILIZATION AND INBREEDING DEPRESSION IN PLANTS. I. GENETIC MODELS

The amounts of inbreeding depression upon selfing and of heterosis upon outcrossing determine the strength of selection on the selfing rate in a population when this evolves polygenically by small steps. Genetic models are constructed which allow inbreeding depression to change with the mean selfing rate in a population by incorporating both mutation to recessive and partially dominant lethal and sublethal alleles at many loci and mutation in quantitative characters under stabilizing selection. The models help to explain observations of high inbreeding depression (> 50%) upon selfing in primarily outcrossing populations, as well as considerable heterosis upon outcrossing in primarily selfing populations. Predominant selfing and predominant outcrossing are found to be alternative stable states of the mating system in most plant populations. Which of these stable states a species approaches depends on the history of its population structure and the magnitude of effect of genes influencing the selfing rate.     

Inbreeding depression and mixed mating in Leptosiphon jepsonii: a comparison of three populations

BACKGROUND AND AIMS: Inbreeding depression is thought to play a central role in the evolution and maintenance of cross-fertilization. Theory indicates that inbreeding depression can be purged with self-fertilization, resulting in positive feedback for the selection of selfing. Variation among populations of Leptosiphon jepsonii in the timing and rate of self-fertilization provides an opportunity to study the evolution of inbreeding depression and mating systems. In addition, the hypothesis that differences in inbreeding depression for male and female fitness can stabilize mixed mating in L. jepsonii is tested. METHODS: In a growth room experiment, inbreeding depression was measured in three populations with mean outcrossing rates ranging from 0.06 to 0.69. The performance of selfed and outcrossed progeny is compared at five life history stages. To distinguish between self-incompatibility and early inbreeding depression, aborted seeds and unfertilized ovules were counted in selfed and outcrossed fruits. In one population, pollen and ovule production was quantified to estimate inbreeding depression for male and female fitness. KEY RESULTS: Both prezygotic barriers and inbreeding depression limited self seed set in the most outcrossing population. Cumulative inbreeding depression ranged from 0.297 to 0.501, with the lowest value found in the most selfing population. Significant inbreeding depression for early life stages was found only in the more outcrossing populations. Inbreeding depression was not significant for pollen or ovule production. CONCLUSIONS: The results provide modest support for the hypothesized relationship between inbreeding depression and mating systems. The absence of early inbreeding depression in the more selfing populations is consistent with theory on purging. Differences in male and female expression of inbreeding depression do not appear to stabilize mixed mating in L. jepsonii. The current estimates of inbreeding depression for L. jepsonii differ from those of previous studies, underscoring the effects of environmental variation on its expression.     

How rapidly do self‐compatible populations evolve selfing? Mating system estimation within recently evolved self‐compatible populations of Azorean Tolpis succulenta (Asteraceae)

Genome‐wide genotyping and Bayesian inference method (BORICE) were employed to estimate outcrossing rates and paternity in two small plant populations of Tolpis succulenta (Asteraceae) on Graciosa island in the Azores. These two known extant populations of T. succulenta on Graciosa have recently evolved self‐compatibility. Despite the expectation that selfing would occur at an appreciable rate (self‐incompatible populations of the same species show low but nonzero selfing), high outcrossing was found in progeny arrays from maternal plants in both populations. This is inconsistent with an immediate transition to high selfing following the breakdown of a genetic incompatibility system. This finding is surprising given the small population sizes and the recent colonization of an island from self‐incompatible colonists of T. succulenta from another island in the Azores, and a potential paucity of pollinators, all factors selecting for selfing through reproductive assurance. The self‐compatible lineage(s) likely have high inbreeding depression (ID) that effectively halts the evolution of increased selfing, but this remains to be determined. Like their progeny, all maternal plants in both populations are fully outbred, which is consistent with but not proof of high ID. High multiple paternity was found in both populations, which may be due in part to the abundant pollinators observed during the flowering season.     

FLORAL CORRELATES AND FITNESS CONSEQUENCES OF MATING-SYSTEM VARIATION IN TURNERA ULMIFOLIA

Outcrossing rates varied from 0% to 69% among Jamaican populations of Turnera ulmifolia. A correlation between increasing herkogamy and outcrossing rate occurred among populations. Predictions from sex-allocation theory were tested by estimating allocation to reproductive functions. Significant differences in allocation patterns occurred among populations, but they were not correlated with outcrossing rates. The fitness consequences of inbreeding were assessed in high- and low-density greenhouse experiments for nine populations with variable outcrossing rates. No evidence for inbreeding depression occurred in early portions of the life history, but multiplicative fitness functions provide evidence for inbreeding depression. We tested the prediction that selfing populations have lower levels of inbreeding depression than outcrossing populations but found no significant correlation.     

Mutation-selection balance in mixed mating populations

An approximation to the average number of deleterious mutations per gamete, Q, is derived from a model allowing selection on both zygotes and male gametes. Progeny are produced by either outcrossing or self-fertilization with fixed probabilities. The genetic model is a standard in evolutionary biology: mutations occur at unlinked loci, have equivalent effects, and combine multiplicatively to determine fitness. The approximation developed here treats individual mutation counts with a generalized Poisson model conditioned on the distribution of selfing histories in the population. The approximation is accurate across the range of parameter sets considered and provides both analytical insights and greatly increased computational speed. Model predictions are discussed in relation to several outstanding problems, including the estimation of the genomic deleterious mutation rates (U), the generality of "selective interference" among loci, and the consequences of gametic selection for the joint distribution of inbreeding depression and mating system across species. Finally, conflicting results from previous analytical treatments of mutation-selection balance are resolved to assumptions about the life-cycle and the initial fate of mutations.     

Relatively weak inbreeding depression in selfing but also in outcrossing populations of North American Arabidopsis lyrata

Hermaphroditic plants can potentially self‐fertilize, but most possess adaptations that promote outcrossing. However, evolutionary transitions to higher selfing rates are frequent. Selfing comes with a transmission advantage over outcrossing, but self‐progeny may suffer from inbreeding depression, which forms the main barrier to the evolution of higher selfing rates. Here, we assessed inbreeding depression in the North American herb Arabidopsis lyrata, which is normally self‐incompatible, with a low frequency of self‐compatible plants. However, a few populations have become fixed for self‐compatibility and have high selfing rates. Under greenhouse conditions, we estimated mean inbreeding depression per seed (based on cumulative vegetative performance calculated as the product of germination, survival and aboveground biomass) to be 0.34 for six outcrossing populations, and 0.26 for five selfing populations. Exposing plants to drought and inducing defences with jasmonic acid did not magnify these estimates. For outcrossing populations, however, inbreeding depression per seed may underestimate true levels of inbreeding depression, because self‐incompatible plants showed strong reductions in seed set after (enforced) selfing. Inbreeding‐depression estimates incorporating seed set averaged 0.63 for outcrossing populations (compared to 0.30 for selfing populations). However, this is likely an overestimate because exposing plants to 5% CO₂ to circumvent self‐incompatibility to produce selfed seed might leave residual effects of self‐incompatibility that contribute to reduced seed set. Nevertheless, our estimates of inbreeding depression were clearly lower than previous estimates based on the same performance traits in outcrossing European populations of A. lyrata, which may help explain why selfing could evolve in North American A. lyrata.     

Inferring recent outcrossing rates using multilocus individual heterozygosity: application to evolving wheat populations

Using multilocus individual heterozygosity, a method is developed to estimate the outcrossing rates of a population over a few previous generations. Considering that individuals originate either from outcrossing or from n successive selfing generations from an outbred ancestor, a maximum-likelihood (ML) estimator is described that gives estimates of past outcrossing rates in terms of proportions of individuals with different n values. Heterozygosities at several unlinked codominant loci are used to assign n values to each individual. This method also allows a test of whether populations are in inbreeding equilibrium. The estimator's reliability was checked using simulations for different mating histories. We show that this ML estimator can provide estimates of outcrossing rates for the final generation outcrossing rate (t(0)) and a mean of the preceding rates (t(p)) and can detect major temporal variation in the mating system. The method is most efficient for low to intermediate outcrossing levels. Applied to nine populations of wheat, this method gave estimates of t(0) and t(p). These estimates confirmed the absence of outcrossing t(0) = 0 in the two populations subjected to manual selfing. For free-mating wheat populations, it detected lower final generation outcrossing rates t(0) = 0-0.06 than those expected from global heterozygosity t = 0.02-0.09. This estimator appears to be a new and efficient way to describe the multilocus heterozygosity of a population, complementary to Fis and progeny analysis approaches.