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 due to overdominance in partially self-fertilizing plant populations

The effect of the rate of partial self-fertilization and viability selection on the magnitude of inbreeding depression was investigated for the overdominance genetic model. The influence of these factors was determined for populations with equilibrium genotypic frequencies. Inbreeding depression was measured as the normalized disadvantage in mean viability of selfed progeny as compared to outcrossed progeny. When caused by symmetric homozygous disadvantage at a single locus it is shown always to be less than one-third. Moreover, for fixed rates of self-fertilization, its maximum value is found at intermediate levels of homozygous disadvantage. As the rate of self-fertilization increases, inbreeding depression increases and the homozygote viability that results in maximum depression tends toward one-half the heterozygote viability. Symmetric selection against homozygotes at multiple loci can lead to substantially higher values than selection at a single-locus. As the number of independent loci involved increases, inbreeding depression can reach high levels even though the selfing rate is low. Viability distributions for progenies produced from both random mating and self-fertilization were derived for the case of symmetric selection at independently assorting multiple loci. Distributions of viabilities in progenies resulting from mixtures of selfing and outcrossing were shown to be bimodal when inbreeding depression is high.     

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.     

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.     

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.     

Effects of population structures and selection strategies on the purging of inbreeding depression due to deleterious mutations

Stochastic simulations were run to compare the effects of nine breeding schemes, using full-sib mating, on the rate of purging of inbreeding depression due to mutations with equal deleterious effect on viability at unlinked loci in an outbred population. A number of full-sib mating lines were initiated from a large outbred population and maintained for 20 generations (if not extinct). Selection against deleterious mutations was allowed to occur within lines only, between lines or equal within and between lines, and surviving lines were either not crossed or crossed following every one or three generations of full-sib mating. The effectiveness of purging was indicated by the decreased number of lethal equivalents and the increased fitness of the purged population formed from crossing surviving lines after 20 generations under a given breeding scheme. The results show that the effectiveness of purging, the survival of the inbred lines and the inbreeding level attained are generally highest with between-line selection and lowest with within-line selection. Compared with no crossing, line crossing could lower the risk of extinction and the inbreeding coefficient of the purged population substantially with little loss of the effectiveness of purging. Compromising between the effectiveness of purging, and the risk of extinction and inbreeding coefficient, the breeding scheme with equal within- and between-line selection and crossing alternatively with full-sib mating is generally the most desirable scheme for purging deleterious mutations. Unless most deleterious mutations have relatively large effects on fitness in species with reproductive ability high enough to cope with the depressed fitness and thus increased risk of extinction with inbreeding, it is not justified to apply a breeding programme aimed at purging inbreeding depression by inbreeding and selection to a population of conservation concern.     

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.     

Quasi-species evolution in subdivided populations favours maximally deleterious mutations

Most models of quasi-species evolution predict that populations will evolve to occupy areas of sequence space with the greatest concentration of neutral sequences, thus minimizing the deleterious mutation rate and creating mutationally 'robust' genomes. In contrast, empirical studies of the principal model of quasi-species evolution, RNA viruses, suggest that the effects of deleterious mutations are more severe than in similar DNA-based microbes. We demonstrate that populations divided into discrete patches connected by dispersal may favour genotypes where the deleterious effect of non-neutral mutations is maximized. This effect is especially strong in the absence of back mutation and when the amount of time spent in hosts prior to dispersal is intermediate. Our results indicate that RNA viruses that produce acute infections initiated by a small number of virions are expected to evolve fragile genetic architectures when compared with other RNA viruses.     

Gamma-tubulin complexes: size does matter.

gamma-Tubulin is a conserved component of all microtubule-organizing centres and is required for these organelles to nucleate microtubule polymerization. However, the mechanism of nucleation is not known. In addition to its localization to organizing centres, a large pool of gamma-tubulin exists in the cytoplasm in a complex with other proteins. The size of the gamma-tubulin complex and number of associated proteins vary among organisms, and the functional significance of these differences is unknown. Recently, the nature of these gamma-tubulin complexes has been explored in different organisms, and this has led us closer to a molecular understanding of microtubule nucleation.     

Dominance and overdominance of mildly deleterious induced mutations for fitness traits in Caenorhabditis elegans

We estimated the average dominance coefficient of mildly deleterious mutations (h, the proportion by which mutations in the heterozygous state reduce fitness components relative to those in the homozygous state) in the nematode Caenorhabditis elegans. From 56 worm lines that carry mutations induced by the point mutagen ethyl methanesulfonate (EMS), we selected 19 lines that are relatively high in fitness and estimated the viabilities, productivities, and relative fitnesses of heterozygotes and homozygotes compared to the ancestral wild type. There was very little effect of homozygous or heterozygous mutations on egg-to-adult viability. For productivity and relative fitness, we found that the average dominance coefficient, h, was approximately 0.1, suggesting that mildly deleterious mutations are on average partially recessive. These estimates were not significantly different from zero (complete recessivity) but were significantly different from 0.5 (additivity). In addition, there was a significant amount of variation in h among lines, and analysis of average dominance coefficients of individual lines suggested that several lines showed overdominance for fitness. Further investigation of two of these lines partially confirmed this finding.     

Accumulation of deleterious mutations in small abiotic populations of RNA

The accumulation of slightly deleterious mutations in populations leads to the buildup of a genetic load and can cause the extinction of populations of small size. Mutation-accumulation experiments have been used to study this process in a wide variety of organisms, yet the exact mutational underpinnings of genetic loads and their fitness consequences remain poorly characterized. Here, we use an abiotic system of RNA populations evolving continuously in vitro to examine the molecular events that can instigate a genetic load. By tracking the fitness decline of ligase ribozyme populations with bottleneck sizes between 100 and 3000 molecules, we detected the appearance and subsequent fixation of both slightly deleterious mutations and advantageous mutations. Smaller populations went extinct in significantly fewer generations than did larger ones, supporting the notion of a mutational meltdown. These data suggest that mutation accumulation was an important evolutionary force in the prebiotic RNA world and that mechanisms such as recombination to ameliorate genetic loads may have been in place early in the history of life.     

The influence of deleterious mutations on adaptation in asexual populations

We study the dynamics of adaptation in asexual populations that undergo both beneficial and deleterious mutations. In particular, how the deleterious mutations affect the fixation of beneficial mutations was investigated. Using extensive Monte Carlo simulations, we find that in the "strong-selection weak mutation (SSWM)" regime or in the "clonal interference (CI)" regime, deleterious mutations rarely influence the distribution of "selection coefficients of the fixed mutations (SCFM)"; while in the "multiple mutations" regime, the accumulation of deleterious mutations would lead to a decrease in fitness significantly. We conclude that the effects of deleterious mutations on adaptation depend largely on the supply of beneficial mutations. And interestingly, the lowest adaptation rate occurs for a moderate value of selection coefficient of deleterious mutations.     

Inbreeding depression in insular and central populations of Peromyscus mice

We tested the hypothesis that small, isolated populations would show less depression in fitness when inbred than would large, central populations. Laboratory stocks of Peromyscus leucopus and P. polionotus were established from insular, peninsular, and central populations. The isolated populations had one-third to one-half the genic diversity of central populations. Responses to inbreeding were highly varied: some populations had smaller litters, others experienced higher mortality, some showed slower growth rates, and one displayed no measurable effects when inbred. These results suggest that inbreeding depression is controlled by a small number of genes and that the size of the genetic load depends on which alleles are present in the founders of a population. The severity of fitness depression in inbred litters did not correlate with initial genic diversity of the stocks nor, therefore, with the size of the wild populations. Fitness measures appeared linearly related to the inbreeding coefficient of the liters, with no diminution of deleterious effects through subsequent generations of inbreeding. Thus overdominance of fitness traits probably contributed as much to the genetic load as did deleterious recessive alleles. The inbreeding level of the dam negatively affected the size, growth, and survival of litters only in genetically diverse populations, indicating that the load of recessive alleles negatively impacting maternal care may have been reduced by selection in the more peripheral populations during past bottlenecks.     

Inbreeding depression in self-incompatible and self-compatible populations of Leavenworthia alabamica

Inbreeding depression is one of the leading factors preventing the evolution of self-fertilization in plants. In populations where self-fertilization evolves, theory suggests that natural selection against partially recessive deleterious alleles will reduce inbreeding depression. The purpose of this study was to evaluate this hypothesis by comparing the magnitude of inbreeding depression in self-incompatible and self-compatible populations of Leavenworthia alabamica. Within-population crosses were conducted to compare the quantity and quality of offspring produced by outcrossing and self-fertilization. These progeny were grown in a common greenhouse and inbreeding depression was measured in germination, survival, biomass, transition rate to flowering, flower number, petal length, pollen grains/anther, pollen viability, and ovule number. In comparison to outcrossing, self-fertilization led to the production of fewer and smaller seeds within self-incompatible populations. Moreover, inbreeding depression was observed in eight of 11 offspring traits within self-incompatible populations of L. alabamica. In contrast, there was significant inbreeding depression only in flower number within self-compatible populations. The results of this study are consistent with the idea that self-fertilization selectively removes partially recessive deleterious alleles causing inbreeding depression in natural plant populations. However, in plant species such as L. alabamica where self-compatibility may evolve in small populations following long-distance dispersal, declines in inbreeding depression may also be facilitated by genetic drift.     

Inbreeding depression influences genet size distribution in a marine angiosperm

Although inbreeding depression is a major genetic phenomena influencing individual fitness, it is difficult to measure in wild populations. An alternative approach is to correlate heterozygosity, measured using highly polymorphic markers, with a fitness-correlated trait. In clonal plants, genet size is predicted to be fitness correlated. Here we test the prediction that the genet size distribution of the marine clonal plant Zostera marina (eelgrass) is influenced by inbreeding depression. We used nine polymorphic microsatellite markers to access the fine scale clonal structure and to measure individual heterozygosity within 4 plots (each corresponds to 256 m2, sampled at 1-m intervals) in two populations along the German Baltic Coast. The same plots were also sampled for flowering and vegetative shoots to obtain estimates for sexual reproductive output at the level of the genetic individual. We found substantial differences in the genet size distribution between the two populations that may be explained by different disturbance frequency. In both populations, clone size was significantly positively correlated with the total number of flowering shoots, indicating that larger clones have a higher reproductive output. Individual heterozygosity was significantly positively associated with clone size. The effect was much stronger in Falkenstein (low disturbance) than in Maasholm (high disturbance). The results indicate that in a low disturbance population the relatively outbred clones occupy a higher proportion of the available space, possibly because they outcompete relatively inbred neighbours.     

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.     

Inbreeding depression and drift load in small populations at demographic disequilibrium

Inbreeding depression is a major driver of mating system evolution and has critical implications for population viability. Theoretical and empirical attention has been paid to predicting how inbreeding depression varies with population size. Lower inbreeding depression is predicted in small populations at equilibrium, primarily due to higher inbreeding rates facilitating purging and/or fixation of deleterious alleles (drift load), but predictions at demographic and genetic disequilibrium are less clear. In this study, we experimentally evaluate how lifetime inbreeding depression and drift load, estimated by heterosis, vary with census (N_c) and effective (estimated as genetic diversity, H_e) population size across six populations of the biennial Sabatia angularis as well as present novel models of inbreeding depression and heterosis under varying demographic scenarios at disequilibrium (fragmentation, bottlenecks, disturbances). Our experimental study reveals high average inbreeding depression and heterosis across populations. Across our small sample, heterosis declined with H_e, as predicted, whereas inbreeding depression did not vary with H_e and actually decreased with N_c. Our theoretical results demonstrate that inbreeding depression and heterosis levels can vary widely across populations at disequilibrium despite similar H_e and highlight that joint demographic and genetic dynamics are key to predicting patterns of genetic load in nonequilibrium systems.     

Invasion success: does size really matter?

The recent paper by Roy et al . (2001) presents a compelling relationship between range limit shifts, climatic fluctuations, and body size for marine bivalves in the fossil record. However, their extension of body size as a correlate for contemporary marine bivalve introductions is problematic and requires further scrutiny. Unlike their analysis of the fossil assemblage, the approach used for contemporary invasions does not adequately control for dispersal mechanism (vector) or source region. First, their analysis included mariculture species, intentionally introduced because of their large size, creating a vector-specific bias. Second, successful invaders from multiple source regions (Northern Hemisphere) were compared with potential invaders from a single source region (north-eastern Pacific), leaving both source and vector as uncontrolled variables. We present an analysis of body size for bivalve introductions from a single vector and source region, indicating no correlation between body size and invasion success when eliminating intentional introduction, source region and transport vector as confounding factors.     

Changes in protein expression due to deleterious mutations in the FA/BRCA pathway

Inherited deleterious mutations in one of the Fanconi anemia genes lead to a disease, characterized by bone marrow failure, myeloid leukemia, and hypersensitivity to DNA damage. We identified proteins likely associated to the molecular signaling pathways involved in DNA repair of interstrand cross-link lesions and in mechanisms of genomic stability mediated by FA/BRCA pathways. We compared protein maps resolved by bidimensional electrophoresis and analyzed differentially expressed proteins, by mass spectrometry, between FA complementation group C (FANCC)-deficient cells, and their ectopically corrected counterpart in physiological conditions or after treatment with MMC. We found six differentially expressed proteins; among them, the checkpoint mediator protein MDC1 whose expression was disrupted in FANCC^−/− cells. The potential role of differentially expressed proteins in FA phenotype is discussed.