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.     

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.     

Inbreeding depression in small populations of self-incompatible plants.

Self-incompatibility (SI) is a widespread mechanism that prevents inbreeding in flowering plants. In many species, SI is controlled by a single locus (the S locus) where numerous alleles are maintained by negative frequency-dependent selection. Inbreeding depression, the decline in fitness of selfed individuals compared to outcrossed ones, is an essential factor in the evolution of SI systems. Conversely, breeding systems influence levels of inbreeding depression. Little is known about the joint effect of SI and drift on inbreeding depression. Here we studied, using a two-locus model, the effect of SI (frequency-dependent selection) on a locus subject to recurrent deleterious mutations causing inbreeding depression. Simulations were performed to assess the effect of population size and linkage between the two loci on the level of inbreeding depression and genetic load. We show that the sheltering of deleterious alleles linked to the S locus strengthens inbreeding depression in small populations. We discuss the implications of our results for the evolution of SI systems.     

Inbreeding rate modifies the dynamics of genetic load in small populations

The negative fitness consequences of close inbreeding are widely recognized, but predicting the long-term effects of inbreeding and genetic drift due to limited population size is not straightforward. As the frequency and homozygosity of recessive deleterious alleles increase, selection can remove (purge) them from a population, reducing the genetic load. At the same time, small population size relaxes selection against mildly harmful mutations, which may lead to accumulation of genetic load. The efficiency of purging and the accumulation of mutations both depend on the rate of inbreeding (i.e., population size) and on the nature of mutations. We studied how increasing levels of inbreeding affect offspring production and extinction in experimental Drosophila littoralis populations replicated in two sizes, N = 10 and N = 40. Offspring production and extinction were measured over 25 generations concurrently with a large control population. In the N = 10 populations, offspring production decreased strongly at low levels of inbreeding, then recovered only to show a consistent subsequent decline, suggesting early expression and purging of recessive highly deleterious alleles and subsequent accumulation of mildly harmful mutations. In the N = 40 populations, offspring production declined only after inbreeding reached higher levels, suggesting that inbreeding and genetic drift pose a smaller threat to population fitness when inbreeding is slow. Our results suggest that highly deleterious alleles can be purged in small populations already at low levels of inbreeding, but that purging does not protect the small populations from eventual genetic deterioration and extinction.     

Selection, load and inbreeding depression in a large metapopulation

The subdivision of a species into local populations causes its response to selection to change, even if selection is uniform across space. Population structure increases the frequency of homozygotes and therefore makes selection on homozygous effects more effective. However, population subdivision can increase the probability of competition among relatives, which may reduce the efficacy of selection. As a result, the response to selection can be either increased or decreased in a subdivided population relative to an undivided one, depending on the dominance coefficient F(ST) and whether selection is hard or soft. Realistic levels of population structure tend to reduce the mean frequency of deleterious alleles. The mutation load tends to be decreased in a subdivided population for recessive alleles, as does the expected inbreeding depression. The magnitude of the effects of population subdivision tends to be greatest in species with hard selection rather than soft selection. Population structure can play an important role in determining the mean fitness of populations at equilibrium between mutation and selection.     

Joint effects of self-fertilization and population structure on mutation load, inbreeding depression and heterosis

Both the spatial distribution of organisms and their mode of reproduction have important effects on the change in allele frequencies within populations. In this article, we study the combined effect of population structure and the rate of partial selfing of organisms on the efficiency of selection against recurrent deleterious mutations. Assuming an island model of population structure and weak selection, we express the mutation load, the within- and between-deme inbreeding depression, and heterosis as functions of the frequency of deleterious mutants in the metapopulation; we then use a diffusion model to calculate an expression for the equilibrium probability distribution of this frequency of deleterious mutants. This allows us to derive approximations for the average mutant frequency, mutation load, inbreeding depression, and heterosis, the simplest ones being Equations 35-39 in the text. We find that population structure can help to purge recessive deleterious mutations and reduce the load for some parameter values (in particular when the dominance coefficient of these mutations is <0.2-0.3), but that this effect is reversed when the selfing rate is above a given value. Conversely, within-deme inbreeding depression always decreases, while heterosis always increases, with the degree of population subdivision, for all selfing rates.     

Effects of Interference Between Selected Loci on the Mutation Load,Inbreeding Depression,and Heterosis

A classical prediction from single-locus models is that inbreeding increases the efficiency of selection against partially recessive deleterious alleles (purging), thereby decreasing the mutation load and level of inbreeding depression. However, previous multilocus simulation studies found that increasing the rate of self-fertilization of individuals may not lead to purging and argued that selective interference among loci causes this effect. In this article, I derive simple analytical approximations for the mutation load and inbreeding depression, taking into account the effects of interference between pairs of loci. I consider two classical scenarios of nonrandomly mating populations: a single population undergoing partial selfing and a subdivided population with limited dispersal. In the first case, correlations in homozygosity between loci tend to reduce mean fitness and increase inbreeding depression. These effects are stronger when deleterious alleles are more recessive, but only weakly depend on the strength of selection against deleterious alleles and on recombination rates. In subdivided populations, interference increases inbreeding depression within demes, but decreases heterosis between demes. Comparisons with multilocus, individual-based simulations show that these analytical approximations are accurate as long as the effects of interference stay moderate, but fail for high deleterious mutation rates and low dominance coefficients of deleterious alleles.     

Effects of population size and isolation on heterosis, mean fitness, and inbreeding depression in a perennial plant

? In small isolated populations, genetic drift is expected to increase chance fixation of partly recessive, mildly deleterious mutations, reducing mean fitness and inbreeding depression within populations and increasing heterosis in outcrosses between populations. ? We estimated relative effective sizes and migration among populations and compared mean fitness, heterosis, and inbreeding depression for eight large and eight small populations of a perennial plant on the basis of fitness of progeny produced by hand pollinations within and between populations. ? Migration was limited, and, consistent with expectations for drift, mean fitness was 68% lower in small populations; heterosis was significantly greater for small (mean?=?70%, SE?=?14) than for large populations (mean?=?7%, SE?=?27); and inbreeding depression was lower, although not significantly so, in small (mean?=?-0.29%, SE?=?28) than in large (mean?=?0.28%, SE?=?23) populations. ? Genetic drift promotes fixation of deleterious mutations in small populations, which could threaten their persistence. Limited migration will exacerbate drift, but data on migration and effective population sizes in natural populations are scarce. Theory incorporating realistic variation in population size and patterns of migration could better predict genetic threats to small population persistence.     

A threefold genetic allee effect: population size affects cross-compatibility, inbreeding depression and drift load in the self-incompatible Ranunculus reptans

A decline in population size can lead to the loss of allelic variation, increased inbreeding, and the accumulation of genetic load through drift. We estimated the fitness consequences of these processes in offspring of controlled within-population crosses from 13 populations of the self-incompatible, clonal plant Ranunculus reptans. We used allozyme allelic richness as a proxy for long-term population size, which was positively correlated with current population size. Crosses between plants of smaller populations were less likely to be compatible. Inbreeding load, assessed as the slope of the relationship between offspring performance and parental kinship coefficients, was not related to population size, suggesting that deleterious mutations had not been purged from small populations. Offspring from smaller populations were on average more inbred, so inbreeding depression in clonal fitness was higher in small populations. We estimated variation in drift load from the mean fitness of outbred offspring and found enhanced drift load affecting female fertility within small populations. We conclude that self-incompatibility systems do not necessarily prevent small populations from suffering from inbreeding depression and drift load and may exacerbate the challenge of finding suitable mates.     

SEXUAL SELECTION COUNTERACTS EXTINCTION OF SMALL POPULATIONS OF THE BULB MITES

Genetic drift in small populations can increase frequency of deleterious recessives and consequently lead to inbreeding depression and population extinction. On the other hand, as homozygosity at deleterious recessives increases, they should be purged from populations more effectively by selection. Sexual selection has been postulated to strengthen selection against deleterious mutations, and should thus decrease extinction rate and intensify purging of inbreeding depression. We tested these predictions in the bulb mite Rhizoglyphus robini. We created 100 replicate lines of small populations (five males and five females) and in half of them experimentally removed sexual selection by enforcing monogamy. The lines were propagated for eight generations and then assayed for purging of inbreeding depression. We found that proportion of lines which went extinct was lower with sexual selection than without. We also found evidence for purging of inbreeding depression in the lines with sexual selection, but not in lines without sexual selection. Our results suggest that purging of inbreeding depression was more effective against mutations with relatively large deleterious effects. Thus, although our data clearly indicate a positive impact of sexual selection on short‐term survival of bottlenecked populations, long‐term consequences are less clear as they may be negatively impacted by accumulation of deleterious mutations of small effect.     

Drift load in populations of small size and low density

According to theory, drift load in randomly mating populations is determined by past population size, because enhanced genetic drift in small populations causes accumulation and fixation of recessive deleterious mutations of small effect. In contrast, segregating load due to mutations of low frequency should decline in smaller populations, at least when mutations are highly recessive and strongly deleterious. Strong local selection generally reduces both types of load. We tested these predictions in 13 isolated, outcrossing populations of Arabidopsis lyrata that varied in population size and plant density. Long-term size was estimated by expected heterozygosity at 20 microsatellite loci. Segregating load was assessed by comparing performance of offspring from selfings versus within-population crosses. Drift load was the heterosis effect created by interpopulation outbreeding. Results showed that segregating load was unrelated to long-term size. However, drift load was significantly higher in populations of small effective size and low density. Drift load was mostly expressed late in development, but started as early as germination and accumulated thereafter. The study largely confirms predictions of theory and illustrates that mutation accumulation can be a threat to natural populations.     

Inbreeding depression and low between-population heterosis in recently diverged experimental populations of a selfing species

In fragmented populations, genetic drift and selection reduce genetic diversity, which in turn results in a loss of fitness or in a loss of evolvability. Genetic rescue, that is, controlled input of diversity from distant populations, may restore evolutionary potential, whereas outbreeding depression might counteract the positive effect of this strategy. We carried out self-pollination and crosses within and between populations in an experimental subdivided population of a selfing species, Triticum aestivum L., to estimate the magnitude of these two phenomena. Surprisingly, for a self-fertilizing species, we found significant inbreeding depression within each population for four of the six traits studied, indicating that mildly deleterious mutations were still segregating in these populations. The progeny of within- and between-population crosses was very similar, indicating low between-population heterosis and little outbreeding depression. We conclude that relatively large population effective sizes prevented fixation of a high genetic load and that local adaptation was limited in these recently diverged populations. The kinship coefficient estimated between the parents using 20 neutral markers was a poor predictor of the progeny phenotypic values, indicating that there was a weak link between neutral diversity and genes controlling fitness-related traits. These results show that when assessing the viability of natural populations and the need for genetic rescue, the use of neutral markers should be complemented with information about the presence of local adaptation in the subdivided population.     

Genetic load in sexual and asexual diploids: segregation, dominance and genetic drift

In diploid organisms, sexual reproduction rearranges allelic combinations between loci (recombination) as well as within loci (segregation). Several studies have analyzed the effect of segregation on the genetic load due to recurrent deleterious mutations, but considered infinite populations, thus neglecting the effects of genetic drift. Here, we use single-locus models to explore the combined effects of segregation, selection, and drift. We find that, for partly recessive deleterious alleles, segregation affects both the deterministic component of the change in allele frequencies and the stochastic component due to drift. As a result, we find that the mutation load may be far greater in asexuals than in sexuals in finite and/or subdivided populations. In finite populations, this effect arises primarily because, in the absence of segregation, heterozygotes may reach high frequencies due to drift, while homozygotes are still efficiently selected against; this is not possible with segregation, as matings between heterozygotes constantly produce new homozygotes. If deleterious alleles are partly, but not fully recessive, this causes an excess load in asexuals at intermediate population sizes. In subdivided populations without extinction, drift mostly occurs locally, which reduces the efficiency of selection in both sexuals and asexuals, but does not lead to global fixation. Yet, local drift is stronger in asexuals than in sexuals, leading to a higher mutation load in asexuals. In metapopulations with turnover, global drift becomes again important, leading to similar results as in finite, unstructured populations. Overall, the mutation load that arises through the absence of segregation in asexuals may greatly exceed previous predictions that ignored genetic drift.     

HOW ARE DELETERIOUS MUTATIONS PURGED? DRIFT VERSUS NONRANDOM MATING

Accumulation of deleterious mutations has important consequences for the evolution of mating systems and the persistence of small populations. It is well established that consanguineous mating can purge a part of the mutation load and that lethal mutations can also be purged in small populations. However, the efficiency of purging in natural populations, due to either consanguineous mating or to reduced population size, has been questioned. Consequences of consanguineous mating systems and small population size are often equated under "inbreeding" because both increase homozygosity, and selection is though to be more efficient against homozygous deleterious alleles. I show that two processes of purging that I call "purging by drift" and "purging by nonrandom mating" have to be distinguished. Conditions under which the two ways of purging are effective are derived. Nonrandom mating can purge deleterious mutations regardless of their dominance level, whereas only highly recessive mutations can be purged by drift. Both types of purging are limited by population size, and sharp thresholds separate domains where purging is either effective or not. The limitations derived here on the efficiency of purging are compatible with some experimental studies. Implications of these results for conservation and evolution of mating systems are discussed.     

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.     

Genetic load in subdivided populations: interactions between the migration rate, the size and the number of subpopulations

We assess the relative importance of migration rate, size and number of subpopulations on the genetic load of subdivided populations. Using diffusion approximations, we show that in most cases subdivision has detrimental effects on fitness. Moreover, our results suggest that fitness increases with subpopulation size, so that for the same total population size, genetic load is relatively lower when there are a small number of large subpopulations. Using elasticity analysis, we show that the size of the subpopulations appears to be the parameter that most strongly determines genetic load. interconnecting subpopulations via migration would also be of importance for population fitness when subpopulations are small and gene flow is low. Interestingly, the number of subpopulations has minor influence on genetic load except for the case of both very slightly deleterious mutations and small subpopulations. Elasticities decrease as the magnitude of deleterious effects increases. In other words, population structure does not matter for very deleterious alleles, but strongly affects fitness for slightly deleterious alleles.     

Heterosis in an isolated, effectively small, and self-fertilizing population of the flowering plant Leavenworthia alabamica

Mildly deleterious mutations are thought to play a major role in the extinction of natural populations, especially those that are small, isolated, or inbred. Self-fertilization should reduce the effective size of populations and simultaneously reduce migration between populations. A history of self-fertilization should therefore cause a population to harbor a substantial "local drift load" caused by the fixation of mildly deleterious mutations. This hypothesis was tested in Leavenworthia alabamica, which contains large, self-incompatible populations and smaller self-compatible populations with adaptations for self-fertilization. The fitness of offspring from within- and between-population crosses was compared to quantify heterosis caused by the masking of deleterious alleles in the heterozygous state. Little heterosis was observed in crosses between five large, self-incompatible populations and two of the three small, self-fertilizing populations of L. alabamica. However, the most geographically isolated and genetically divergent self-fertilizing population (Tuscumbia) exhibited a 110.2% increase in germination and a 73.6% increase in fitness, which is consistent with a sizeable local drift load. The finding of substantial heterosis for fitness supports the idea that small effective size, reproductive isolation, and self-fertilization can make populations particularly vulnerable to mutation accumulation.     

Reviewing the consequences of genetic purging on the success of rescue programs

Genetic rescue is increasingly considered a promising and underused conservation strategy to reduce inbreeding depression and restore genetic diversity in endangered populations, but the empirical evidence supporting its application is limited to a few generations. Here we discuss on the light of theory the role of inbreeding depression arising from partially recessive deleterious mutations and of genetic purging as main determinants of the medium to long-term success of rescue programs. This role depends on two main predictions: (1) The inbreeding load hidden in populations with a long stable demography increases with the effective population size; and (2) After a population shrinks, purging tends to remove its (partially) recessive deleterious alleles, a process that is slower but more efficient for large populations than for small ones. We also carry out computer simulations to investigate the impact of genetic purging on the medium to long term success of genetic rescue programs. For some scenarios, it is found that hybrid vigor followed by purging will lead to sustained successful rescue. However, there may be specific situations where the recipient population is so small that it cannot purge the inbreeding load introduced by migrants, which would lead to increased fitness inbreeding depression and extinction risk in the medium to long term. In such cases, the risk is expected to be higher if migrants came from a large non-purged population with high inbreeding load, particularly after the accumulation of the stochastic effects ascribed to repeated occasional migration events. Therefore, under the specific deleterious recessive mutation model considered, we conclude that additional caution should be taken in rescue programs. Unless the endangered population harbors some distinctive genetic singularity whose conservation is a main concern, restoration by continuous stable gene flow should be considered, whenever feasible, as it reduces the extinction risk compared to repeated occasional migration and can also allow recolonization events.

     

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.