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.     

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.     

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

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

INBREEDING DEPRESSION,GENETIC LOAD,AND THE EVOLUTION OF OUTCROSSING RATES IN A MULTILOCUS SYSTEM WITH NO LINKAGE

We studied deterministic models of multilocus systems subject to mutation–selection balance with all loci unlinked, and with multiplicative interactions of the loci affecting fitness, in partially self-fertilizing populations. The aim was to examine the fitnesses of the zygotes produced by outcrossing and by selling, and the magnitude of inbreeding depression, in populations with different levels of inbreeding. The fates of modifiers of the outcrossing rate were also examined. With biologically plausible parameter values, inbreeding depression can be very large in moderately selfing populations, particularly when the mutant alleles are fairly recessive and selection is weak. A modifier allele reducing the selfing rate can be favored under these circumstances. In more inbred populations, inbreeding depression is lower, and selection favors alleles that increase the selfing rate. When inbreeding depression is caused by mutant alleles with strong selective disadvantage, modifiers causing large increases in selfing can often be favored even when the inbreeding depression exceeds one-half, though in these circumstances modifiers increasing selfing by smaller amounts are usually eliminated. Weaker selection appears to be more favorable to the maintenance of outcrossing.     

Epistasis,inbreeding depression,and the evolution of self-fertilization

Inbreeding depression resulting from partially recessive deleterious alleles is thought to be the main genetic factor preventing self-fertilizing mutants from spreading in outcrossing hermaphroditic populations. However, deleterious alleles may also generate an advantage to selfers in terms of more efficient purging, while the effects of epistasis among those alleles on inbreeding depression and mating system evolution remain little explored. In this article, we use a general model of selection to disentangle the effects of different forms of epistasis (additive-by-additive, additive-by-dominance, and dominance-by-dominance) on inbreeding depression and on the strength of selection for selfing. Models with fixed epistasis across loci, and models of stabilizing selection acting on quantitative traits (generating distributions of epistasis) are considered as special cases. Besides its effects on inbreeding depression, epistasis may increase the purging advantage associated with selfing (when it is negative on average), while the variance in epistasis favors selfing through the generation of linkage disequilibria that increase mean fitness. Approximations for the strengths of these effects are derived, and compared with individual-based simulation results.     

INBREEDING DEPRESSION WITH HETEROZYGOTE ADVANTAGE AND ITS EFFECT ON SELECTION FOR MODIFIERS CHANGING THE OUTCROSSING RATE

The equilibrium level of inbreeding depression in populations with different selfing rates is studied for models with symmetrical or asymmetrical heterozygous advantage at several loci with partial linkage. As for the case of a single locus, the inbreeding depression caused by loci with heterozygous advantage can be higher for partially selfing populations than for complete outcrossing. The spread of modifier alleles at another locus that affects the selfing rate is studied. The stability of outcrossing populations to invasion by alleles that give increased selfing is found to depend on levels of inbreeding depression being greater than one-half, in accordance with earlier models that assumed a fixed level of inbreeding depression. However, in partially selfing populations the spread of such alleles can be checked by smaller levels of inbreeding depression than one-half, so that they do not always spread to fixation. This is interpreted as being due to associations between the genotypes at the modifier locus and the selected loci, together with increasing inbreeding depression as selfing increases, and does not occur if the inbreeding depression is due to mutation-selection balance.     

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.     

The effect of self-fertilization, inbreeding depression, and population size on autopolyploid establishment

The minority cytotype exclusion principle describes how random mating between diploid and autotetraploid cytotypes hinders establishment of the rare cytotype. We present deterministic and stochastic models to ascertain how selfing, inbreeding depression, unreduced gamete production, and finite population size affect minority cytotype exclusion and the establishment of autotetraploids. Results demonstrate that higher selfing rates and lower inbreeding depression in autotetraploids facilitate establishment of autotetraploid populations. Stochastic effects due to finite population size increase the probability of polyploid establishment and decrease the mean time to tetraploid fixation. Our results extend the minority cytotype exclusion principle to include important features of plant reproduction and demonstrate that variation in mating system parameters significantly influences the conditions necessary for polyploid establishment.     

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.     

The genetic basis and experimental evolution of inbreeding depression in Caenorhabditis elegans

Determining the genetic basis of inbreeding depression is important for understanding the role of selection in the evolution of mixed breeding systems. Here, we investigate how androdioecy (a breeding system characterized by partial selfing and outcrossing) and dioecy (characterized by obligatory outcrossing) influence the experimental evolution of inbreeding depression in Caenorhabditis elegans. We derived inbred lines from ancestral and evolved populations and found that the dioecious lineages underwent more extinction than androdioecious lineages. For both breeding systems, however, there was selection during inbreeding because the diversity patterns of 337 single-nucleotide polymorphisms (SNPs) among surviving inbred lines deviated from neutral expectations. In parallel, we also followed the evolution of embryo to adult viability, which revealed similar starting levels of inbreeding depression in both breeding systems, but also outbreeding depression. Under androdioecy, diversity at a neutral subset of 134 SNPs correlated well with the viability trajectories, showing that the population genetic structure imposed by partial selfing affected the opportunity for different forms of selection. Our findings suggest that the interplay between the disruptions of coevolved sets of loci by outcrossing, the efficient purging of deleterious recessive alleles with selfing and overdominant selection with outcrossing can help explain mixed breeding systems.     

Maintenance of Inbreeding Depression in a Highly Self-Fertilizing Tree, Magnolia obovata Thunb

Inbreeding depression is a major selective force that maintains outcrossing in flowering plants. If the long life and large mature size of trees cause high inbreeding depression via mitotic mutations and half-sib competition, these characteristics may increase inbreeding depression sufficiently to maintain traits that facilitate outcrossing even with high primary selfing rates (proportion of selfed ovules). Here, I report the maintenance of inbreeding depression in a population of a tree (Magnolia obovata Thunb.) with primary selfing rates greater than 0.8 resulting from geitonogamy. The progenies exhibited inbreeding depression for germination, seedling survival, and seedling mass (δ = 0.29–0.38), but no significant difference between crossing type in seedling height. Cumulative inbreeding depression for early survival (from zygote to 2-year-old stage) estimated from these results and from prior data on embryonic survival was high (δ_e = 0.91). The fixation index at maturity based on six allozyme loci was low (F_is = 0.08), indicating that significant inbreeding depression for late survival results in a low level of inbreeding with respect to gene transmission to the next generation. From these results, I estimated that inbreeding depression for late and lifetime survival equaled 0.69 and 0.97, respectively. These results suggest that M. obovata trees maintain high inbreeding depression at both early and late life stages, resulting in a low level of inbreeding despite a high primary selfing rate. The high inbreeding depression can be explained by previous theories and is consistent with the predicted maintenance of inbreeding depression in highly self-fertilizing tree populations. The inbreeding load due to the high primary selfing rate represents a cost of this tree’s pollination system for outcrossing, which is based on automimicry and mass flowering. Co-ordinating editor: S.-M. Chang     

Inbreeding depression is high in a self‐incompatible perennial herb population but absent in a self‐compatible population showing mixed mating

High inbreeding depression is thought to be one of the major factors preventing evolutionary transitions in hermaphroditic plants from self‐incompatibility (SI) and outcrossing toward self‐compatibility (SC) and selfing. However, when selfing does evolve, inbreeding depression can be quickly purged, allowing the evolution of complete self‐fertilization. In contrast, populations that show intermediate selfing rates (a mixed‐mating system) typically show levels of inbreeding depression similar to those in outcrossing species, suggesting that selection against inbreeding might be responsible for preventing the transition toward complete self‐fertilization. By implication, crosses among populations should reveal patterns of heterosis for mixed‐mating populations that are similar to those expected for outcrossing populations. Using hand‐pollination crosses, we compared levels of inbreeding depression and heterosis between populations of Linaria cavanillesii (Plantaginaceae), a perennial herb showing contrasting mating systems. The SI population showed high inbreeding depression, whereas the SC population displaying mixed mating showed no inbreeding depression. In contrast, we found that heterosis based on between‐population crosses was similar for SI and SC populations. Our results are consistent with the rapid purging of inbreeding depression in the derived SC population, despite the persistence of mixed mating. However, the maintenance of outcrossing after a transition to SC is inconsistent with the prediction that populations that have purged their inbreeding depression should evolve toward complete selfing, suggesting that the transition to SC in L. cavanillesii has been recent. SC in L. cavanillesii thus exemplifies a situation in which the mating system is likely not at an equilibrium with inbreeding depression.     

Cryptic inbreeding depression in a growing population of a long‐lived species

Genetic effects are often overlooked in endangered species monitoring, and populations showing positive growth are often assumed to be secure. However, the continued reproductive success of a few individuals may mask issues such as inbreeding depression, especially in long‐lived species. Here, we test for inbreeding depression in little spotted kiwi (Apteryx owenii) by comparing a population founded with two birds to one founded with 40 birds, both from the same source population and both showing positive population growth. We used a combination of microsatellite genotypes, nest observations and modelling to examine the consequences of assessing population viability exclusively via population growth. We demonstrate (i) significantly lower hatching success despite significantly higher reproductive effort in the population with two founders; (ii) positive growth in the population with two founders is mainly driven by ongoing chick production of the founding pair; and (iii) a substantial genetic load in the population founded with two birds (10–15 diploid lethal equivalents). Our results illustrate that substantial, cryptic inbreeding depression may still be present when a population is growing, especially in long‐lived species with overlapping generations.     

Population genomics of the inbred Scandinavian wolf

The Scandinavian wolf population represents one of the genetically most well-characterized examples of a severely bottlenecked natural population (with only two founders), and of how the addition of new genetic material (one immigrant) can at least temporarily provide a 'genetic rescue'. However, inbreeding depression has been observed in this population and in the absence of additional immigrants, its long-term viability is questioned. To study the effects of inbreeding and selection on genomic diversity, we performed a genomic scan with approximately 250 microsatellite markers distributed across all autosomes and the X chromosome. We found linkage disequilibrium (LD) that extended up to distances of 50 Mb, exceeding that of most outbreeding species studied thus far. LD was particularly pronounced on the X chromosome. Overall levels of observed genomic heterozygosity did not deviate significantly from simulations based on known population history, giving no support for a general selection for heterozygotes. However, we found evidence supporting balancing selection at a number of loci and also evidence suggesting directional selection at other loci. For markers on chromosome 23, the signal of selection was particularly strong, indicating that purifying selection against deleterious alleles may have occurred even in this very small population. These data suggest that population genomics allows the exploration of the effects of neutral and non-neutral evolution on a finer scale than what has previously been possible.     

Pollination ecology and inbreeding depression control individual flowering phenologies and mixed mating

We analyze evolution of individual flowering phenologies by combining an ecological model of pollinator behavior with a genetic model of inbreeding depression for plant viability. The flowering phenology of a plant genotype determines its expected daily floral display which, together with pollinator behavior, governs the population rate of geitonogamous selfing (fertilization among flowers on the same plant). Pollinators select plant phenologies in two ways: they are more likely to visit plants displaying more flowers per day, and they influence geitonogamous selfing and consequent inbreeding depression via their abundance, foraging behavior, and pollen carry‐over among flowers on a plant. Our model predicts two types of equilibria at stable intermediate selfing rates for a wide range of pollinator behaviors and pollen transfer parameters. Edge equilibria occur at maximal or minimal selfing rates and are constrained by pollinators. Internal equilibria occur between edge equilibria and are determined by a trade‐off between pollinator attraction to large floral displays and avoidance of inbreeding depression due to selfing. We conclude that unavoidable geitonogamous selfing generated by pollinator behavior can contribute to the common occurrence of stable mixed mating in plants.     

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.     

THE EVOLUTION OF SELF-FERTILIZATION AND INBREEDING DEPRESSION IN PLANTS. II. EMPIRICAL OBSERVATIONS

A bimodal distribution of outcrossing rates was observed for natural plant populations, with more primarily selfing and primarily outcrossing species, and fewer species with intermediate outcrossing rate than expected by chance. We suggest that this distribution results from selection for the maintenance of outcrossing in historically large, outcrossing populations with substantial inbreeding depression, and from selection for selfing when increased inbreeding, due to pollinator failure or population bottlenecks, reduces the level of inbreeding depression. Few species or populations are fixed at complete selfing or complete outcrossing. A low level of selfing in primarily outcrossing species is unlikely to be selectively advantageous, but will not reduce inbreeding depression to the level where selfing is selectively favored, particularly if accompanied by reproductive compensation. Similarly, occasional outcrossing in primarily selfing species is unlikely to regularly provide sufficient heterosis to maintain selection for outcrossing through individual selection. Genetic, morphological and ecological constraints may limit the potential for outcrossing rates in selfers to be reduced below some minimum level.     

Some aspects of autotetraploid population dynamics

Summary Self-compatible autotetraploids are likely to set much of their seed by selfing. Formulae are presented for the frequencies in any generation of states of loci, from homozygous to quadri-allelic, considering the frequencies of selfing and of double reduction but not allowing for the effects of inbreeding depression on population structure. The changing structure of populations over generations is also explored by computer simulation, incorporating selection against inbreds but ignoring double reduction. The findings are discussed in relation to mass-selection programmes.     

The genetic basis of inbreeding depression

Data on the effects of inbreeding on fitness components are reviewed in the light of population genetic models of the possible genetic causes of inbreeding depression. Deleterious mutations probably play a major role in causing inbreeding depression. Putting together the different kinds of quantitative genetic data, it is difficult to account for the very large effects of inbreeding on fitness in Drosophila and outcrossing plants without a significant contribution from variability maintained by selection. Overdominant effects of alleles on fitness components seem not to be important in most cases. Recessive or partially recessive deleterious effects of alleles, some maintained by mutation pressure and some by balancing selection, thus seem to be the most important source of inbreeding depression. Possible experimental approaches to resolving outstanding questions are discussed.     

Evaluation of the extent of among-family variation in inbreeding depression in the perennial herb Scabiosa columbaria (Dipsacaceae)

Significantly different maternal line responses to inbreeding provide a mechanism for the invasion of a selfing variant into a population. The goal of this study was to examine the extent of family-level variation in inbreeding depression in the mixed-mating, perennial herb Scabiosa columbaria. Plants from one population were raised, and hand-pollinated to produce selfed and outcrossed progeny, and the effects of inbreeding depression on life-cycle traits were analyzed. Inbreeding depression significantly affected early life cycle traits. The pollination treatment by family interaction was significant for almost all traits, indicating a high family-level variation in inbreeding depression. The correlations between inbreeding depression values (e.g., percentage germination and flowering date, and flowering date and aboveground biomass) exhibited alternate signs, illustrating the type of association between inbreeding depression loci for different traits across the life cycle. Overall, it is concluded that the extent of among-family variation in inbreeding depression might allow a selfing variant of S. columbaria to invade an outcrossing population, though the pattern of correlations between inbreeding depression values might prevent effective purging of the deleterious genetic load.