Dynamics of inbreeding depression due to deleterious mutations in small populations: mutation parameters and inbreeding rate

A multilocus stochastic model is developed to simulate the dynamics of mutational load in small populations of various sizes. Old mutations sampled from a large ancestral population at mutation-selection balance and new mutations arising each generation are considered jointly, using biologically plausible lethal and deleterious mutation parameters. The results show that inbreeding depression and the number of lethal equivalents due to partially recessive mutations can be partly purged from the population by inbreeding, and that this purging mainly involves lethals or detrimentals of large effect. However, fitness decreases continuously with inbreeding, due to increased fixation and homozygosity of mildly deleterious mutants, resulting in extinctions of very small populations with low reproductive rates. No optimum inbreeding rate or population size exists for purging with respect to fitness (viability) changes, but there is an optimum inbreeding rate at a given final level of inbreeding for reducing inbreeding depression or the number of lethal equivalents. The interaction between selection against partially recessive mutations and genetic drift in small populations also influences the rate of decay of neutral variation. Weak selection against mutants relative to genetic drift results in apparent overdominance and thus an increase in effective size (Ne) at neutral loci, and strong selection relative to drift leads to a decrease in Ne due to the increased variance in family size. The simulation results and their implications are discussed in the context of biological conservation and tests for purging.     

Consequences of life history for inbreeding depression and mating system evolution in plants

Many plants are perennial, but most studies of inbreeding depression and mating system evolution focus on annuals. This paper extends a population genetic model of inbreeding depression due to recessive deleterious mutations to perennials. The model incorporates life history and mating system variation, and multiplicative selection across many genetic loci. In the absence of substantial mitotic mutation, perennials have higher mean fitness and lower, or even negative, inbreeding depression than annuals with the same mating system. As in annuals, self fertilization exposes deleterious recessive mutations to selection, increasing mean fitness and decreasing inbreeding depression. Including mitotic mutation decreases mean fitness while increasing inbreeding depression. Perenniality introduces a kind of selective sieve, such that strongly recessive mutations contribute disproportionately to mean fitness and inbreeding depression. In the presence of high mitotic mutation, this selective sieve may provide a mechanistic basis for high inbreeding depression observed in some long lived perennials. Without substantial mitotic mutation, it is difficult to reconcile genetically based models of inbreeding depression with the empirical generalization that perennials outcross while related annuals self fertilize.     

Extinction of populations due to inbreeding depression with demographic disturbances

The process of population extinction due to inbreeding depression with constant demographic disturbances every generation is analysed using a population genetic and demographic model. The demographic disturbances introduced into the model represent loss of population size that is induced by any kind of human activities, e.g. through hunting and destruction of habitats. The genetic heterozygosity among recessive deleterious genes and the population size are assumed to be in equilibrium before the demographic disturbances start. The effects of deleterious mutations are represented by decreases in the growth rate and carrying capacity of a population. Numerical simulations indicate rapid extinction due to synergistic interaction between inbreeding depression and declining population size for realistic ranges of per-locus mutation rate, equilibrium population size, intrinsic rate of population growth, and strength of demographic disturbances. Large populations at equilibrium are more liable to extinction when disturbed due to inbreeding depression than small populations. This is a consequence of the fact that large populations maintain more recessive deleterious mutations than small populations. The rapid extinction predicted in the present study indicates the importance of the demographic history of a population in relation to extinction due to inbreeding depression.     

EFFECTIVENESS OF SELECTION IN REDUCING THE GENETIC LOAD IN POPULATIONS OF PEROMYSCUS POLIONOTUS DURING GENERATIONS OF INBREEDING

It has been hypothesized that natural selection reduces the “genetic load” of deleterious alleles from populations that inbreed during bottlenecks, thereby ameliorating impacts of future inbreeding. We tested the efficiency with which natural selection purges deleterious alleles from three subspecies of Peromyscus polionotus during 10 generations of laboratory inbreeding by monitoring pairing success, litter size, viability, and growth in 3604 litters produced from 3058 pairs. In P. p. subgriseus, there was no reduction across generations in inbreeding depression in any of the fitness components. Strongly deleterious recessive alleles may have been removed previously during episodes of local inbreeding in the wild, and the residual genetic load in this population was not further reduced by selection in the lab. In P. p. rhoadsi, four of seven fitness components did show a reduction of the genetic load with continued inbreeding. The average reduction in the genetic load was as expected if inbreeding depression in this population is caused by highly deleterious recessive alleles that are efficiently removed by selection. For P. p. leucocephalus a population that experiences periodic bottlenecks in the wild, the effect of further inbreeding in the laboratory was to exacerbate rather than reduce the genetic load. Recessive deleterious alleles may have been removed from this population during repeated bottlenecks in the wild; the population may be close to a threshold level of heterozygosity below which fitness declines rapidly. Thus, the effects of selection on inbreeding depression varied substantially among populations, perhaps due to different histories of inbreeding and selection.     

EVALUATING A SIMPLE APPROXIMATION TO MODELING THE JOINT EVOLUTION OF SELF‐FERTILIZATION AND INBREEDING DEPRESSION

A comprehensive understanding of plant mating system evolution requires detailed genetic models for both the mating system and inbreeding depression, which are often intractable. A simple approximation assuming that the mating system evolves by small infrequent mutational steps has been proposed. We examine its accuracy by comparing the evolutionarily stable selfing rates it predicts to those obtained from an explicit genetic model of the selfing rate, when inbreeding depression is caused by partly recessive deleterious mutations at many loci. Both models also include pollen limitation and pollen discounting. The approximation produces reasonably accurate predictions with a low or moderate genomic mutation rate to deleterious alleles, on the order of U = 0.02–0.2. However, for high mutation rates, the predictions of the full genetic model differ substantially from those of the approximation, especially with nearly recessive lethal alleles. This occurs because when a modifier allele affecting the selfing rate is rare, homozygous modifiers are produced mainly by selfing, which enhances the opportunity for purging nearly recessive lethals and increases the marginal fitness of the allele modifying the selfing rate. Our results confirm that explicit genetic models of selfing rate and inbreeding depression are required to understand mating system evolution.     

Environmental dependence of inbreeding depression and purging in Drosophila melanogaster

Elimination or reduction of inbreeding depression by natural selection at the contributing loci (purging) has been hypothesized to effectively mitigate the negative effects of inbreeding in small isolated populations. This may, however, only be valid when the environmental conditions are relatively constant. We tested this assumption using Drosophila melanogaster as a model organism. By means of chromosome balancers, chromosomes were sampled from a wild population and their viability was estimated in both homozygous and heterozygous conditions in a favourable environment. Around 50% of the chromosomes were found to carry a lethal or sublethal mutation, which upon inbreeding would cause a considerable amount of inbreeding depression. These detrimentals were artificially purged by selecting only chromosomes that in homozygous condition had a viability comparable to that of the heterozygotes (quasi-normals), thereby removing most deleterious recessive alleles. Next, these quasi-normals were tested both for egg-to-adult viability and for total fitness under different environmental stress conditions: high-temperature stress, DDT stress, ethanol stress, and crowding. Under these altered stressful conditions, particularly for high temperature and DDT, novel recessive deleterious effects were expressed that were not apparent under control conditions. Some of these chromosomes were even found to carry lethal or near-lethal mutations under stress. Compared with heterozygotes, homozygotes showed on average 25% additional reduction in total fitness. Our results show that, except for mutations that affect fitness under all environmental conditions, inbreeding depression may be due to different loci in different environments. Hence purging of deleterious recessive alleles can be effective only for the particular environment in which the purging occurred, because additional load will become expressed under changing environmental conditions. These results not only indicate that inbreeding depression is environment dependent, but also that inbreeding depression may become more severe under changing stressful conditions. These observations have significant consequences for conservation biology.     

Genetic load,inbreeding depression and heterosis in an age‐structured metapopulation

In a metapopulation, the process of recurrent local extinction and recolonization gives rise to an age structure among demes. Recently established demes will tend to differ from older demes in terms of the levels of genetic diversity found within them and the way this diversity is distributed among demes in the same and different ages. The effects of population turnover on average levels of genetic diversity among demes in a metapopulation have been the focus of much attention, both for neutral and nonneutral loci, but much less is known about the distribution of nonneutral genetic diversity among demes of different ages. In this paper, we used computer simulations to study the distribution of genetic load, inbreeding depression and heterosis in an age‐structured metapopulation. We found that, for mildly deleterious mutations, within‐deme inbreeding depression increased, whereas heterosis and genetic load decreased with deme age following severe colonization bottlenecks. In contrast, recessive lethal alleles tended to be purged during colonization, with older populations showing higher genetic load and higher within‐deme inbreeding depression. Heterosis caused by recessive lethal alleles and resulting from gene flow among different demes tended to be greatest for young demes, because the mutations responsible tended to be purged in the first few generations after colonization, but its effects increased again as populations grow older as a result of immigration. Our results point to a need for estimates of genetic diversity, genetic load, within‐deme inbreeding depression and heterosis in demes of different age classes separately.     

Detecting purging of inbreeding depression by a slow rate of inbreeding for various traits: the impact of environmental and experimental conditions

Inbreeding depression (ID) has since long been recognized as a significant factor in evolutionary biology. It is mainly the consequence of (partially) recessive deleterious mutations maintained by mutation-selection balance in large random mating populations. When population size is reduced, recessive alleles are increasingly found in homozygous condition due to drift and inbreeding and become more prone to selection. Particularly at slow rates of drift and inbreeding, selection will be more effective in purging such alleles, thereby reducing the amount of ID. Here we test assumptions of the efficiency of purging in relation to the inbreeding rate and the experimental conditions for four traits in D. melanogaster. We investigated the magnitude of ID for lines that were inbred to a similar level, F ≈ 0.50, reached either by three generations of full-sib mating (fast inbreeding), or by 12 consecutive generations with a small population size (slow inbreeding). This was done on two different food media. We observed significant ID for egg-to-adult viability and heat shock mortality, but only for egg-to-adult viability a significant part of the expressed inbreeding depression was effectively purged under slow inbreeding. For other traits like developmental time and starvation resistance, however, adaptation to the experimental and environmental conditions during inbreeding might affect the likelihood of purging to occur or being detected. We discuss factors that can affect the efficiency of purging and why empirical evidence for purging may be ambiguous.Subject terms: Evolutionary genetics, Inbreeding     

Inbreeding reveals stronger net selection on Drosophila melanogaster males: implications for mutation load and the fitness of sexual females

Stronger selection on males has the potential to lower the deleterious mutation load of females, reducing the cost of sex. However, few studies have directly quantified the strength of selection for both sexes. As the magnitude of inbreeding depression (ID) is related to the strength of selection, we measured the cost of inbreeding for both males and females in a laboratory population of Drosophila melanogaster. Using a novel technique for inbreeding, we found significant ID for both juvenile viability and adult fitness in both sexes. The genetic variation responsible for this depression in fitness appeared to be recessive for adult fitness (h=0.11) and partially additive for juvenile viability (h=0.29). ID was identical across the sexes in terms of juvenile viability but was significantly more deleterious for males than females as adults, even though female X-chromosome homogamety should predispose them to a higher inbreeding load. We estimated the strength of selection on adult males to be 1.24 greater than on adult females, and this appears to be a consequence of selection arising from competition for mates. Combined with the generally positive intersexual genetic correlation for inbred lines, our results suggest that the mutation load of sexual females could be meaningfully reduced by stronger selection acting on males.     

Joint evolution of dispersal and inbreeding load

Inbreeding avoidance is often invoked to explain observed patterns of dispersal, and theoretical models indeed point to a possibly important role. However, while inbreeding load is usually assumed constant in these models, it is actually bound to vary dynamically under the combined influences of mutation, drift, and selection and thus to evolve jointly with dispersal. Here we report the results of individual-based stochastic simulations allowing such a joint evolution. We show that strongly deleterious mutations should play no significant role, owing to the low genomic mutation rate for such mutations. Mildly deleterious mutations, by contrast, may create enough heterosis to affect the evolution of dispersal as an inbreeding-avoidance mechanism, but only provided that they are also strongly recessive. If slightly recessive, they will spread among demes and accumulate at the metapopulation level, thus contributing to mutational load, but not to heterosis. The resulting loss of viability may then combine with demographic stochasticity to promote population fluctuations, which foster indirect incentives for dispersal. Our simulations suggest that, under biologically realistic parameter values, deleterious mutations have a limited impact on the evolution of dispersal, which on average exceeds by only one-third the values expected from kin-competition avoidance.     

Variability of individual genetic load: consequences for the detection of inbreeding depression

Inbreeding depression is a key factor affecting the persistence of natural populations, particularly when they are fragmented. In species with mixed mating systems, inbreeding depression can be estimated at the population level by regressing the average progeny fitness by the selfing rate of their mothers. We applied this method using simulated populations to investigate how population genetic parameters can affect the detection power of inbreeding depression. We simulated individual selfing rates and genetic loads from which we computed fitness values. The regression method yielded high statistical power, inbreeding depression being detected as significant (5?% level) in 92?% of the simulations. High individual variation in selfing rate and high mean genetic load led to better detection of inbreeding depression while high among-individual variation in genetic load made it more difficult to detect inbreeding depression. For a constant sampling effort, increasing the number of progenies while decreasing the number of individuals per progeny enhanced the detection power of inbreeding depression. We discuss the implication of among-mother variability of genetic load and selfing rate on inbreeding depression studies.     

Individual Variation in Inbreeding Depression: The Roles of Inbreeding History and Mutation

We use mutation-selection recursion models to evaluate the relative contributions of mutation and inbreeding history to variation among individuals in inbreeding depression and the ability of experiments to detect associations between individual inbreeding depression and mating system genotypes within populations. Poisson mutation to deleterious additive or recessive alleles generally produces far more variation among individuals in inbreeding depression than variation in history of inbreeding, regardless of selfing rate. Moreover, variation in inbreeding depression can be higher in a completely outcrossing or selfing population than in a mixed-mating population. In an initially random mating population, the spread of a dominant selfing modifier with no pleiotropic effects on male outcross success causes a measurable increase in inbreeding depression variation if its selfing rate is large and inbreeding depression is caused by recessive lethals. This increase is observable during a short period as the modifier spreads rapidly to fixation. If the modifier alters selfing rate only slightly, it fails to spread or causes no measurable increase in inbreeding depression variance. These results suggest that genetic associations between mating loci and inbreeding depression loci could be difficult to demonstrate within populations and observable only transiently during rapid evolution to a substantially new selfing rate.     

Lack of nonadditive genetic effects on early fecundity in Drosophila melanogaster

Fecundity is usually considered as a trait closely connected to fitness and is expected to exhibit substantial nonadditive genetic variation and inbreeding depression. However, two independent experiments, using populations of different geographical origin, indicate that early fecundity in Drosophila melanogaster behaves as a typical additive trait of low heritability. The first experiment involved artificial selection in inbred and non-inbred lines, all of them started from a common base population previously maintained in the laboratory for about 35 generations. The realized heritability estimate was 0.151 +/- 0.075 and the inbreeding depression was very small and nonsignificant (0.09 +/- 0.09% of the non-inbred mean per 1% increase in inbreeding coefficient). With inbreeding, the observed decrease in the within-line additive genetic variance and the corresponding increase of the between-line variance were very close to their expected values for pure additive gene action. This result is at odds with previous studies showing inbreeding depression and, therefore, directional dominance for the same trait and species. All experiments, however, used laboratory populations, and it is possible that the original genetic architecture of the trait in nature was subsequently altered by the joint action of random drift and adaptation to captivity. Thus, we carried out a second experiment, involving inbreeding without artificial selection in a population recently collected from the wild. In this case we obtained, again, a maximum-likelihood heritability estimate of 0.210 +/- 0.027 and very little nonsignificant inbreeding depression (0.06 +/- 0.12%). The results suggest that, for fitness-component traits, low levels of additive genetic variance are not necessarily associated with large inbreeding depression or high levels of nonadditive genetic variance.     

The interdependence of mating structure and inbreeding depression

The level of inbreeding depression depends on the genetic structure and composition of a population, and is not a meaningful concept in its own right. Models are presented for the dynamics of alleles governing mating strategy when viability is determined by generalized heterosis or lethal recessive alleles. It is shown that a protected polymorphism for mating strategy may ensue from generalized heterosis, while lethal recessive alleles may favor the common mating strategy. Further, neither model provides the conditions allowing spread of an allele when rare (protection) which are obtained by assuming as constant the level of inbreeding depression associated with the equilibrium genetic structure dictated by the common mating strategy.     

INBREEDING DEPRESSION UNDER JOINT SELFING,OUTCROSSING, AND ASEXUALITY

Partial asexual reproduction was introduced into a model of inbreeding depression due to nearly recessive lethal mutations in a partially selfing population. The frequencies of asexuality, selfing, and outcrossing were either constant or occurred in cycles of a single sexual generation followed by one or more asexual generations. We found that increasing the degree of asexuality generally increases the inbreeding depression maintained in an equilibrium population with a given selfing rate. This is due to the increase in the number of mutations relative to sexual generations during which selfing-induced purging of mutations may take place. For very high genomic mutation rates, sufficient to produce a threshold rate of self-fertilization for purging recessive lethal mutations, asexuality can have the opposite effect, decreasing equilibrium inbreeding depression, because of an increase in the efficiency of selection against mutations in heterozygotes with asexuality.     

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.     

Evidence for overdominant selection maintaining X-linked fitness variation in Drosophila melanogaster

The role of balancing selection in maintaining genetic variation for fitness is largely unresolved. This reflects the inherent difficulty in distinguishing between models of recurrent mutation versus selection, which produce similar patterns of inbreeding depression, as well as the limitations of testing such hypotheses when fitness variation is averaged across the genome. Signatures of X-linked overdominant selection are less likely to be obscured by mutational variation because X-linked mutations are rapidly eliminated by purifying selection in males. Although models maintaining genetic variation for fitness are not necessarily mutually exclusive, a series of predictions for identifying X-linked overdominant selection can be used to separate its contribution from other underlying processes. We consider the role of overdominant selection in maintaining fitness variation in a sample of 12 X chromosomes from a population of Drosophila melanogaster. Substantial variation was observed for male reproductive success and female fecundity, with heterozygous-X genotypes exhibiting the greatest degree of variance, a finding that agrees well with predictions of the overdominance model. The importance of X-linked overdominant selection is discussed along with models of recurrent mutation and sexually antagonistic selection.     

Analysis of Autosomal Polygenic Variation for the Expression of Haldane''s Rule in Flour Beetles

Haldane's rule states that, in interspecific crosses, when hybrid viability or fertility is diminished more in one sex of the hybrids than in the other, the heterogametic sex is more adversely affected. We used quantitative genetic methods to investigate the genetic basis of variation for the expression of the viability aspect of Haldane's rule when Tribolium castaneum males are crossed to Tribolium freemani females. Using a half-sib design, we found significant genetic variance for the expression of Haldane's rule, i.e, variation among T. castaneum sires in the hybrid sex ratios produced by their sons. We also derived 23 independent lineages from the same base population by 8 generations of brother-sister mating. From the same experiments, we also found heritable variation among surviving hybrid males in the incidence of antennal deformities. Upon inbreeding, the variance of both traits (hybrid sex ratio and proportion deformities) increased substantially but the means changed little. Because fitness within T. castaneum lineages declined substantially with inbreeding, we infer that hybrid male viability may have a different genetic basis than viability fitness within species. Deleterious recessive alleles held within species by mutation/selection balance appear not to be a major contributor to hybrid incompatibility.     

The genetic consequences of fluctuating inbreeding depression and the evolution of plant selfing rates

The magnitude of inbreeding depression, a central parameter in the evolution of plant mating systems, can vary depending on environmental conditions. However, the underlying genetic mechanisms causing environmental fluctuations in inbreeding depression, and the consequences of this variation for the evolution of self‐fertilization, have been little studied. Here, we consider temporal fluctuations of the selection coefficient in an explicit genetic model of inbreeding depression. We show that substantial variance in inbreeding depression can be generated at equilibrium by fluctuating selection, although the simulated variance tends to be lower than has been measured in experimental studies. Our simulations also reveal that purging of deleterious mutations does not depend on the variance in their selection coefficient. Finally, an evolutionary analysis shows that, in contrast to previous theoretical approaches, intermediate selfing rates are never evolutionarily stable when the variation in inbreeding depression is due to fluctuations in the selection coefficient on deleterious mutations.     

Trait specific consequences of fast and slow inbreeding: lessons from captive populations of <Emphasis Type="Italic">Drosophila melanogaster</Emphasis>

The increased homozygosity due to inbreeding leads to expression of deleterious recessive alleles, which may cause inbreeding depression in small populations. The severity of inbreeding depression has been suggested to depend on the rate of inbreeding, with slower inbreeding being more effective in purging deleterious alleles of smaller effect. The effectiveness of purging is however dependent on various factors such as the effect of the deleterious, recessive alleles, the genetic background of inbreeding depression and the environment in which purging occurs. Investigations have shown inconclusive results as to whether purging efficiently diminish inbreeding depression. Here we used an ecologically relevant inbreeding coefficient (f ≈ 0.25) and generated ten slow and ten fast inbred lines of Drosophila melanogaster by keeping the effective population size constant at respectively 32 and 2 for 19 or 2 generations. These inbred lines were contrasted to non-inbred control lines. We investigated the effect of inbreeding and inbreeding rate in traits associated with fitness including heat, cold and desiccation stress resistance, egg-to-adult viability, development time, productivity, metabolic rate and wet weight under laboratory conditions. The results showed highly trait specific consequences of inbreeding and generally no support for the hypothesis that slow inbreeding is less deleterious than fast inbreeding. Egg-to-adult viability and development time were investigated under both benign and heat stress conditions. Reduced viability and increased developmental time were observed at stressful temperatures and inbreeding depression was on average more severe at stressful compared to benign temperatures.