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.     

Reduced inbreeding depression due to historical inbreeding in Drosophila melanogaster: evidence for purging

An important issue in conservation biology and the study of evolution is the extent to which inbreeding depression can be reduced or reversed by natural selection. If the deleterious recessive alleles causing inbreeding depression can be 'purged' by natural selection, outbred populations that have a history of inbreeding are expected to be less susceptible to inbreeding depression. This expectation, however, has not been realized in previous laboratory experiments. In the present study, we used Drosophila melanogaster as a model system to test for an association between inbreeding history and inbreeding depression. We created six 'purged' populations from experimental lineages that had been maintained at a population size of 10 male-female pairs for 19 generations. We then measured the inbreeding depression that resulted from one generation of full-sib mating in the purged populations and in the original base population. The magnitude of inbreeding depression in the purged populations was approximately one-third of that observed in the original base population. In contrast to previous laboratory experiments, therefore, we found that inbreeding depression was reduced in populations that have a history of inbreeding. The large purging effects observed in this study may be attributable to the rate of historical inbreeding examined, which was slower than that considered in previous experiments.     

Sexual selection is ineffectual or inhibits the purging of deleterious mutations in Drosophila melanogaster

The effects of sexual selection on population mean fitness are unclear and a subject of debate. Recent models propose that, because reproductive success may be condition dependent, much of the genome may be a target of sexual selection. Under this scenario, mutations that reduce health, and thus nonsexual fitness, may also be deleterious with respect to reproductive success, meaning that sexual selection may contribute to the purging of deleterious alleles. We tested this hypothesis directly by subjecting replicate Drosophila melanogaster populations to two treatments that altered the opportunity for sexual selection and then tracked changes in the frequency of six separate deleterious alleles with recessive and visible phenotypic effects. While natural selection acted to decrease the frequency of all six mutations, the addition of sexual selection did not aid in the purging of any of them, and for three of them appears to have hampered it. Courtship and mating have harmful effects in this species and mate choice assays showed that males directed more courtship and mating behavior toward wild-type over mutant females, providing a likely explanation for sexual selection's cost. Whether this cost extends to other mutations (e.g., those lacking visible phenotypic effects) is an important topic for future research.     

Reduction in the cumulative effect of stress-induced inbreeding depression due to intragenerational purging in Drosophila melanogaster

Environmental stress generally exacerbates the harmful effects of inbreeding and it has been proposed that this could be exploited in purging deleterious alleles from threatened inbred populations. However, understanding what factors contribute to variability in the strength of inbreeding depression (ID) observed across adverse environmental conditions remains a challenge. Here, we examined how the nature and timing of stress affects ID and the potential for purging using inbred and outbred Drosophila melanogaster larvae exposed to biotic (larval competition, bacteria infection) and abiotic (ethanol, heat) stressors compared with unstressed controls. ID was measured during (larval survival) and after (male mating success) stress exposure. The level of stress imposed by each stressor was approximately equal, averaging a 42% reduction in outbred larval survival relative to controls. All stressors induced on average the same ID, causing a threefold increase in lethal equivalents for larval survival relative to controls. However, stress-induced ID in larval success was followed by a 30% reduction in ID in mating success of surviving males. We propose that this fitness recovery is due to ‘intragenerational purging'' whereby fitness correlations facilitate stress-induced purging that increases the average fitness of survivors in later life history stages. For biotic stressors, post-stress reductions in ID are consistent with intragenerational purging, whereas for abiotic stressors, there appeared to be an interaction between purging and stress-induced physiological damage. For all stressors, there was no net effect of stress on lifetime ID compared with unstressed controls, undermining the prediction that stress enhances the effectiveness of population-level purging across generations.     

The effect of linkage and population size on inbreeding depression due to mutational load.

Using a stochastic model of a finite population in which there is mutation to partially recessive detrimental alleles at many loci, we study the effects of population size and linkage between the loci on the population mean fitness and inbreeding depression values. Although linkage between the selected loci decreases the amount of inbreeding depression, neither population size nor recombination rate have strong effects on these quantities, unless extremely small values are assumed. We also investigate how partial linkage between the loci that determine fitness affects the invasion of populations by alleles at a modifier locus that controls the selfing rate. In most of the cases studied, the direction of selection on modifiers was consistent with that found in our previous deterministic calculations. However, there was some evidence that linkage between the modifier locus and the selected loci makes outcrossing less likely to evolve; more losses of alleles promoting outcrossing occurred in runs with linkage than in runs with free recombination. We also studied the fate of neutral alleles introduced into populations carrying detrimental mutations. The times to loss of neutral alleles introduced at low frequency were shorter than those predicted for alleles in the absence of selected loci, taking into account the reduction of the effective population size due to inbreeding. Previous studies have been confined to outbreeding populations, and to alleles at frequencies close to one-half, and have found an effect in the opposite direction. It therefore appears that associations between neutral and selected loci may produce effects that differ according to the initial frequencies of the neutral alleles.     

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.     

Inbreeding depression due to mildly deleterious mutations in finite populations: size does matter

We studied the effects of population size on the inbreeding depression and genetic load caused by deleterious mutations at a single locus. Analysis shows how the inbreeding depression decreases as population size becomes smaller and/or the rate of inbreeding increases. This pattern contrasts with that for the load, which increases as population size becomes smaller but decreases as inbreeding rate goes up. The depression and load both approach asymptotic limits when the population size becomes very large or very small. Numerical results show that the transition between the small and the large population regimes is quite rapid, and occurs largely over a range of population sizes that vary by a factor of 10. The effects of drift on inbreeding depression may bias some estimates of the genomic rate of deleterious mutation. These effects could also be important in the evolution of breeding systems in hermaphroditic organisms and in the conservation of endangered populations.     

An investigation of inbreeding depression and purging in captive pedigreed populations

We use regression models to investigate the effects of inbreeding in 119 zoo populations, encompassing 88 species of mammals, birds, reptiles and amphibians. Meta-analyses show that inbreeding depression for neonatal survival was significant across the 119 populations although the severity of inbreeding depression appears to vary among taxa. However, few predictors of a population's response to inbreeding are found reliable. The models are most likely to detect inbreeding depression in large populations, that is, in populations in which their statistical power is maximised. Purging was found to be significant in 14 populations and a significant trend of purging was found across populations. The change in inbreeding depression due to purging averaged across the 119 populations is <1%, however, suggesting that the fitness benefits of purging are rarely appreciable. The study re-emphasises the necessity to avoid inbreeding in captive breeding programmes and shows that purging cannot be relied upon to remove deleterious alleles from zoo populations.     

Effect of selection against deleterious mutations on the decline in heterozygosity at neutral loci in closely inbreeding populations.

Transition matrices for selfing and full-sib mating were derived to investigate the effect of selection against deleterious mutations on the process of inbreeding at a linked neutral locus. Selection was allowed to act within lines only (selection type I) or equally within and between lines (type II). For selfing lines under selection type I, inbreeding is always retarded, the retardation being determined by the recombination fraction between the neutral and selected loci and the inbreeding depression from the selected locus, irrespective of the selection coefficient (s) and dominance coefficient (h) of the mutant allele. For selfing under selection type II or full-sib mating under both selection types, inbreeding is delayed by weak selection (small s and sh), due to the associative overdominance created at the neutral locus, and accelerated by strong selection, due to the elevated differential contributions between alternative alleles at the neutral locus within individuals and between lines (for selection type II). For multiple fitness loci under selection, stochastic simulations were run for populations with selfing, full-sib mating, and random mating, using empirical estimates of mutation parameters and inbreeding load in Drosophila. The simulations results are in general compatible with empirical observations.     

A simulation study on detecting purging of inbreeding depression in captive populations

Inbreeding depression threatens the survival of small populations of both captive and wild outbreeding species. In order to fully understand this threat, it is necessary to investigate what role purging plays in reducing inbreeding depression. Ballou (1997) undertook such an investigation on 25 mammalian populations, using an ancestral inbreeding regression model to detect purging. He concluded that there was a small but highly significant trend of purging on neonatal survival across the populations. We tested the performance of the regression model that Ballou used to detect purging on independently simulated data. We found that the model has low statistical power when inbreeding depression is caused by the build-up of mildly deleterious alleles. It is therefore possible that Ballou's study may have underestimated the effects of ancestral inbreeding on the purging of inbreeding depression in captive populations if their inbreeding depression was caused mainly by mildly deleterious mutations. We also developed an alternative regression model to Ballou's, which showed an improvement in the detection of purging of mildly deleterious alleles but performed less well if deleterious alleles were of a large effect.     

Role of inbreeding depression and purging in captive breeding and restoration programmes

Inbreeding depression is a major force affecting the evolution and viability of small populations in captive breeding and restoration programmes. Populations that experience small sizes may be less susceptible to future inbreeding depression because they have been purged of deleterious recessive alleles. We review issues related to purging, as they apply to the management of small populations, and discuss an experiment we conducted examining purging in populations of mosquitofish (Gambusia affinis). Purging is an important process in many small populations, but the literature contains a diversity of responses to purging both within and among studies. With the exception that slow inbreeding results in more purging and less threat to population viability, there seem to be few consistent trends that aid in prediction of how a purging event will affect a population. In our examination of purging on population viability in mosquitofish, single or multiple bottlenecks do not appear to have resulted in any purging of the influence of genetic load on population growth. Rather, serial bottlenecks resulted in a marked decline in population growth and an increase in extinction. Our results, taken together with those of reviewed studies, suggest that in small populations there is great uncertainty regarding the success of any single purging event in eliminating inbreeding depression, together with the high likelihood that purging will depress population viability through the fixation of deleterious alleles. In management of captive breeding and restoration programmes, the common practice of avoiding inbreeding and small population sizes should be followed whenever possible.     

Selection on a modifier of recombination rate due to linked deleterious mutations

Several models have been suggested to explain the origin and maintenance of recombination. Here I present the results from computer simulations of multilocus haploid and diploid genotypes in small populations. Each chromosome consisted of 1001 loci where deleterious mutations occurred. At "equilibrium" for mutation-selection-genetic drift balance a single recombination variant was introduced to the population in the middle of a chromosome. On average 75,000 replicates for each combination of parameters were followed to fixation or loss of the modifier allele. The results show that, in a small population, increased recombination can be selected, even in the absence of epistasis or beneficial mutations. The effect of the mutation rate for deleterious mutations depends on the ploidy level and the recessiveness of deleterious mutations. A higher deleterious mutation rate is required for an increase in recombination rate to be favored in haploid populations. Increased recombination could not evolve in the case of strong associative overdominance.     

Environmental complexity and the purging of deleterious alleles

Sexual interactions among adults can generate selection on both males and females with genome‐wide consequences. Sexual selection through males is one component of this selection that has been argued to play an important role in purging deleterious alleles. A common technique to assess the influence of sexual selection is by a comparison of experimental evolution under enforced monogamy versus polygamy. Mixed results from past studies may be due to the use of highly simplified laboratory conditions that alter the nature of sexual interactions. Here, we examine the rate of purging of 22 gene disruption mutations in experimental polygamous populations of Drosophila melanogaster in each of two mating environments: a simple, high‐density environment (i.e., typical fly vials), and a lower density, more spatially complex environment. Based on past work, we expect sexual interactions in the latter environment to result in stronger selection in both sexes. Consistent with this, we find that mutations tend to be purged more quickly in populations evolving in complex environments. We discuss possible mechanisms by which environmental complexity might modulate the rate at which deleterious alleles are purged and putatively ascribe a role for sexual interactions in explaining the treatment differences in our experiment.     

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.     

Purging of inbreeding depression within the Irish Holstein-Friesian population

The objective of this study was to investigate whether inbreeding depression in milk production or fertility performance has been partially purged due to selection within the Irish Holstein-Friesian population. Classical, ancestral (i.e., the inbreeding of an individual''s ancestors according to two different formulae) and new inbreeding coefficients (i.e., part of the classical inbreeding coefficient that is not accounted for by ancestral inbreeding) were computed for all animals. The effect of each coefficient on 305-day milk, fat and protein yield as well as calving interval, age at first calving and survival to second lactation was investigated. Ancestral inbreeding accounting for all common ancestors in the pedigree had a positive effect on 305-day milk and protein yield, increasing yields by 4.85 kg and 0.12 kg, respectively. However, ancestral inbreeding accounting only for those common ancestors, which contribute to the classical inbreeding coefficient had a negative effect on all milk production traits decreasing 305-day milk, fat and protein yields by -8.85 kg, -0.53 kg and -0.33 kg, respectively. Classical, ancestral and new inbreeding generally had a detrimental effect on fertility and survival traits. From this study, it appears that Irish Holstein-Friesians have purged some of their genetic load for milk production through many years of selection based on production alone, while fertility, which has been less intensely selected for in the population demonstrates no evidence of purging.     

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     

Estimation of the amount of inbreeding due to subdivision of a population

In a large population which is subdivided into isolated or partially isolated subpopulations polymorphic for a gene locus, there is an excess of homozygotes due to the subdivision. This excess increases with the variance of the gene frequency. The excess can be measured by the “coefficient of inbreeding.” The aim of this paper is to estimate this coefficient, which is a function of various population parameters. We suggest several different estimates, which are the same functional form of unbiased estimates of the population parameters. These estimates are shown to be consistent. They have been compared by numerical methods among themselves and with two other estimates suggested previously.     

Evidence for inbreeding depression and post-pollination selection against inbreeding in the dioecious plant Silene latifolia

In many species, inbred individuals have reduced fitness. In plants with limited pollen and seed dispersal, post-pollination selection may reduce biparental inbreeding, but knowledge on the prevalence and importance of pollen competition or post-pollination selection after non-self pollination is scarce. We tested whether post-pollination selection favours less related pollen donors and reduces inbreeding in the dioecious plant Silene latifolia. We crossed 20 plants with pollen from a sibling and an unrelated male, and with a mix of both. We found significant inbreeding depression on vegetative growth, age at first flowering and total fitness (22% in males and 14% in females). In mixed pollinations, the unrelated male sired on average 57% of the offspring. The greater the paternity share of the unrelated sire, the larger the difference in relatedness of the two males to the female. The effect of genetic similarity on paternity is consistent with predictions for post-pollination selection, although paternity, at least in some crosses, may be affected by additional factors. Our data show that in plant systems with inbreeding depression, such as S. latifolia, pollen or embryo selection after multiple-donor pollination may indeed reduce inbreeding.     

Genomic analysis reveals depression due to both individual and maternal inbreeding in a free‐living mammal population

There is ample evidence for inbreeding depression manifested as a reduction in fitness or fitness‐related traits in the focal individual. In many organisms, fitness is not only affected by genes carried by the individual, but also by genes carried by their parents, for example if receiving parental care. While maternal effects have been described in many systems, the extent to which inbreeding affects fitness directly through the focal individual, or indirectly through the inbreeding coefficients of its parents, has rarely been examined jointly. The Soay sheep study population is an excellent system in which to test for both effects, as lambs receive extended maternal care. Here, we tested for both maternal and individual inbreeding depression in three fitness‐related traits (birthweight and weight and hindleg length at 4 months of age) and three fitness components (first‐year survival, adult annual survival and annual breeding success), using either pedigree‐derived inbreeding or genomic estimators calculated using ~37 000 SNP markers. We found evidence for inbreeding depression in 4‐month hindleg and weight, first‐year survival in males, and annual survival and breeding success in adults. Maternal inbreeding was found to depress both birthweight and 4‐month weight. We detected more instances of significant inbreeding depression using genomic estimators than the pedigree, which is partly explained through the increased sample sizes available. In conclusion, our results highlight that cross‐generational inbreeding effects warrant further exploration in species with parental care and that modern genomic tools can be used successfully instead of, or alongside, pedigrees in natural populations.