The decline in fitness with inbreeding: evidence for negative dominance‐by‐dominance epistasis in Drosophila melanogaster

Genetic interactions can play an important role in the evolution of reproductive strategies. In particular, negative dominance‐by‐dominance epistasis for fitness can theoretically favour sex and recombination. This form of epistasis can be detected statistically because it generates nonlinearity in the relationship between fitness and inbreeding coefficient. Measures of fitness in progressively inbred lines tend to show limited evidence for epistasis. However, tests of this kind can be biased against detecting an accelerating decline due to line losses at higher inbreeding levels. We tested for dominance‐by‐dominance epistasis in Drosophila melanogaster by examining viability at five inbreeding levels that were generated simultaneously, avoiding the bias against detecting nonlinearity that has affected previous studies. We find an accelerating rate of fitness decline with inbreeding, indicating that dominance‐by‐dominance epistasis is negative on average, which should favour sex and recombination.     

The effects of parasitism and inbreeding on the competitive ability in Daphnia magna: evidence for synergistic epistasis

Synergistic epistasis for fitness is often assumed in models of how selection acts on the frequency and distribution of deleterious mutations. Evidence for synergistic epistasis would exist if the logarithm of fitness declines more quickly with number of deleterious mutations, than predicted by a linear decline. This can be studied indirectly by quantifying the effect of different levels of inbreeding on fitness. Here, six sets (different genetic backgrounds) of three increasingly inbred Daphnia magna clones were used to assess their relative fitness according to changes in frequency in a competition experiment against a tester clone. A novelty of the mating procedure was that the inbreeding coefficients (F) of the three clones belonging to each set increased in steps of 0.25 independent of the (unknown) inbreeding coefficient of the common ancestor. The equal increase of the inbreeding coefficients is important, because deviations influence the quantification of inbreeding depression, its variance and the detection of epistasis. In a simple mathematical model we show that when working with a partially inbred population inbreeding depression is underestimated, the variance of fitness is increased, and the detection of epistasis more difficult. Further, to examine whether an interaction between inbreeding and parasitism exists, each inbred clone was tested with and without a microsporidium infection (Octosporea bayeri). We found a nonlinear decrease of the logarithm of fitness across the three levels of inbreeding, indicating synergistic epistasis. The interaction term between parasitism and inbreeding was not significant. Our results suggest that deleterious mutations may be purged effectively once the level of inbreeding is high, but that parasitism seems not to influence this effect.     

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.     

Multigenerational effects of inbreeding in Cucurbita pepo ssp. texana (Cucurbitaceae)

The shape of the fitness function relating the decline in fitness with coefficient of inbreeding (f) can provide evidence concerning the genetic basis of inbreeding depression, but few studies have examined inbreeding depression across a range of f using noncultivated species. Futhermore, studies have rarely examined the effects of inbreeding depression in the maternal parent on offspring fitness. To estimate the shape of the fitness function, we examined the relationship between f and fitness across a range off from 0.000 to 0.875 for components of both male and female fitness in Cucurbita pepo ssp. texana. Each measure of female fitness declined with f, including pistillate flower number, fruit number, seed number per fruit, seed mass per fruit, and percentage seed germination. Several aspects of male fitness also declined with f, including staminate flower number, pollen number per flower, and the number of days of flowering, although cumulative inbreeding depression was less severe for male (0.34) than for female function (0.39). Fitness tended to decline linearly with f between f = 0.00 and f = 0.75 for most traits and across cumulative lifetime fitness (mean = 0.66), suggesting that individual genes causing inbreeding depression are additive and the result of many alleles of small effect. However, most traits also showed a small reduction in inbreeding depression between f = 0.75 and f = 0.875, and evidence of purging or diminishing epistasis was found for in vitro pollen-tube growth rate. To examine inbreeding depression as a maternal effect, we performed outcross pollinations on f = 0.0 and f = 0.5 mothers and found that depression due to maternal inbreeding was 0.07, compared to 0.10 for offspring produced through one generation of selfing. In at least some families, maternal inbreeding reduced fruit number, seed number and mass, staminate flower number, pollen diameter, and pollen-tube growth rate. Collectively these results suggest that, while the fitness function appears to be largely linear for most traits, maternal effects may compound the effects of inbreeding depression in multigenerational studies, though this may be partially offset by purging or diminishing epistasis.     

Evidence for epistasis: reply to Trouve et al.

Salathé and Ebert (2003, J. Evol. Biol. 16: 976–985) have shown that the mean logarithmic fitness of Daphnia magna clones declined faster than linearly with increasing inbreeding coefficient F. They interpreted this result as evidence for synergistic epistasis. Trouve et al. (2004, J. Evol. Biol., doi: 10.1111/j.1420‐9101.2004.00755.x) suggested that hybrid vigour could be an alternative explanation for this finding. We use a population genetic model to support the original claim that the marked deviation from linearity cannot be explained without epistasis. We further argue that the relevant reference population is the metapopulation and not the subpopulation. Taken together, we believe that synergistic epistasis between recessive deleterious alleles segregating in the D. magna metapopulation is the most likely explanation for the finding of Salathé and Ebert.     

Epistasis in monkeyflowers

Epistasis contributes significantly to intrapopulation variation in floral morphology, development time, and male fitness components of Mimulus guttatus. This is demonstrated with a replicated line-cross experiment involving slightly over 7000 plants. The line-cross methodology is based on estimates for means. It thus has greater power than the variance partitioning approaches historically used to estimate epistasis within populations. The replication of the breeding design across many pairs of randomly extracted, inbred lines is necessary given the diversity of multilocus genotypes residing within an outbred deme. Male fitness is shown to exhibit synergistic epistasis, an accelerating decline in fitness with inbreeding. Synergism is a necessary, but not sufficient, condition for a mutational deterministic hypothesis for the evolutionary maintenance of sexual reproduction. Unlike male fitness measures, flower morphology and development time yield positive evidence of epistasis but not of synergism. The results for these traits suggest that epistatic effects are variable across genetic backgrounds or sets of interacting loci.     

EFFECTS OF DIFFERENT LEVELS OF INBREEDING ON FITNESS COMPONENTS IN MIMULUS GUTTATUS

Recent theoretical work has shown that there can be selection favoring the maintenance of sexual reproduction and the evolution of increased recombination when deleterious mutations at different loci interact synergistically, such that the logarithm of fitness declines at a greater than linear rate with the number of harmful mutations per genome. The purpose of this experimental study was to determine whether synergism exists for genes affecting fitness components in two partially selfing populations of the monkey flower Mimulus guttatus. For each wild population, a large randomly mated base population was constructed and many independent lines, inbred to differing degrees, were extracted from this base population. Lines with expected inbreeding coefficients of 0, 0.25, 0.5, and 0.75 were raised simultaneously in the greenhouse and were scored for germination, flowering, flower production, and pollen viability. All fitness traits except germination success declined with increased inbreeding, but in spite of the substantial inbreeding depression found in this study, relatively little evidence of synergistic epistasis was found. The only trait that showed evidence of synergism was pollen viability. These results indicate that synergism is not strong for the fitness components measured in this study. The evidence for synergism from other published studies is also reviewed.     

EFFECTS OF DIFFERENT LEVELS OF INBREEDING ON PROGENY FITNESS IN PLANTAGO CORONOPUS

Inbreeding depression (δ) is a major selective force favoring outcrossing in flowering plants. Many phenotypic and genetic models of the evolution of selfing conclude that complete outcrossing should evolve whenever inbreeding depression is greater than one-half, otherwise selfing should evolve. Recent theoretical work, however, has challenged this view and emphasized (1) the importance of variation in inbreeding depression among individuals within a population; and (2) the nature of gene action between deleterious mutations at different loci (epistasis) as important determinants for the evolution of plant mating systems. The focus of this study was to examine the maintenance of inbreeding depression and the relationship between inbreeding level and inbreeding depression at both the population and the individual level in one population of the partially self-fertilizing plant Plantago coronopus (L.). Maternal plants, randomly selected from an area of about 50 m² in a natural population, were used to establish lines with expected inbreeding coefficients (f) of 0, 0.25, 0.50, 0.75, and 0.875. Inbreeding depression was estimated both in the greenhouse and at the site of origin of the maternal plants by comparing growth, survival, flowering, and seed production of the progeny with different inbreeding coefficients. No significant inbreeding depression for these fitness traits was detected in the greenhouse after 16 weeks. This was in strong contrast to the field, where the traits all displayed significant inbreeding depression and declined with increased inbreeding. The results were consistent with the view that mutation to mildly deleterious alleles is the primary cause of inbreeding depression. At the family level, significantly different maternal line responses (maternal parent × inbreeding level interaction) provide a mechanism for the invasion of a selfing variant into the population through any maternal line exhibiting purging of its genetic load. At the population level, evidence for synergistic epistasis was detected for the probability of flowering, but not for total seed production. At the family level, however, a significant interaction between inbreeding level and maternal families for both traits was observed, indicating that epistasis could play a role in the expression of inbreeding depression among maternal lines.     

An Analysis of Heterosis VS. Inbreeding Effects with an Autotetraploid Cross-Fertilized Plant: MEDICAGO SATIVA L

Self-fertilization and crossing were combined to produce a large number of levels of inbreeding and of degrees of kinship. The inbreeding effect increases with the complexity of the character and with its supposed relationship with fitness. A certain amount of heterozygosity appears to be necessary for the expression of variability. With crossing of unrelated noninbred plants, genetic variance is mainly additive, but with inbreeding its major part is nonadditive. High additivity in crossing, therefore, coexists with strong inbreeding depression. However, even in inbreeding the genetic coefficient of covariation among relatives appears to be strongly and linearly related to the classical coefficient of kinship. This means that deviations from the additive model with inbreeding could be partly due to an effect of inbreeding on variances through an effect on means. An attempt to analyze genetic effects from a theoretical model, based upon the identity by descent relationship at the level of means and of covariances between relatives, tends to show that allelic interactions are more important and nonallelic interactions are less important for a character closely related to fitness. For a complex character, these results lead to the conception of a genome organized in polygenic complementary blocks integrating epistasis and dominance. Some consequences for plant breeding are also discussed.     

WILL POPULATION BOTTLENECKS AND MULTILOCUS EPISTASIS INCREASE ADDITIVE GENETIC VARIANCE?

We apply new analytical methods to understand the consequences of population bottlenecks for expected additive genetic variance. We analyze essentially all models for multilocus epistasis that have been numerically simulated to demonstrate increased additive variance. We conclude that for biologically plausible models, large increases in expected additive variance--attributable to epistasis rather than dominance--are unlikely. Naciri-Graven and Goudet (2003) found that as the number of epistatically interacting loci increases, additive variance tends to be inflated more after a bottleneck. We argue that this result reflects biologically unrealistic aspects of their models. Specifically, as the number of loci increases, higher-order epistatic interactions become increasingly important in these models, with an increasing fraction of the genetic variance becoming nonadditive, contrary to empirical observations. As shown by Barton and Turelli (2004), without dominance, conversion of nonadditive to additive variance depends only on the variance components and not on the number of loci per se. Numerical results indicating that more inbreeding is needed to produce maximal release of additive variance with more loci follow directly from our analytical results, which show that high levels of inbreeding (F > 0.5) are needed for significant conversion of higher-order components. We discuss alternative approaches to modeling multilocus epistasis and understanding its consequences.     

Inter-locus interactions: A review of experimental evidence

In quantitative genetics, experiments designed to elucidate the nature of gene action and hence the importance of epistasis, have included analysis of genetic differences among individuals in random mating populations (partitioning of genetic variation, analysis of selection responses), of differences among inbred lines or selected populations (variance components in crosses among lines, chromosome analysis using genetic markers and crossover suppression), of the effects of inbreeding, and of population structure. Evidence in population genetic studies has come from studies of linkage disequilibrium and co-adaptation in natural populations, and of multilocus fitness estimation and linkage disequilibrium and associative overdominance in experimental populations. While it is clear that epistasis does contribute to the genetic variation in some quantitative characters, and in particular reproductive fitness, much of the evidence is equivocal and unsatisfying.     

Reciprocal sign epistasis is a necessary condition for multi-peaked fitness landscapes

Having multiple peaks within fitness landscapes critically affects the course of evolution, but whether their presence imposes specific requirements at the level of genetic interactions remains unestablished. Here we show that to exhibit multiple fitness peaks, a biological system must contain reciprocal sign epistatic interactions, which are defined as genetic changes that are separately unfavorable but jointly advantageous. Using Morse theory, we argue that it is impossible to formulate a sufficient condition for multiple peaks in terms of local genetic interactions. These findings indicate that systems incapable of reciprocal sign epistasis will always possess a single fitness peak. However, reciprocal sign epistasis should be pervasive in nature as it is a logical consequence of specificity in molecular interactions. The results thus predict that specific molecular interactions may yield multiple fitness peaks, which can be tested experimentally.     

Variation in the intensity of inbreeding depression among successive life-cycle stages and generations in gynodioecious Silene vulgaris (Caryophyllaceae)

Inbreeding depression is one of the hypotheses explaining the maintenance of females within gynodioecious plant populations. However, the measurement of fitness components in selfed and outcrossed progeny depends on life-cycle stage and the history of inbreeding. Comparative data indicate that strong inbreeding depression is more likely to occur at later life-cycle stages. We used hermaphrodite individuals of Silene vulgaris originating from three populations located in different valleys in the Swiss Alps to investigate the effect of two generations of self- and cross-fertilization on fitness components among successive stages of the life cycle in a glasshouse experiment. We detected significant inbreeding depression for most life-cycle stages including: the number of viable and aborted seeds per fruit, probability of germination, above ground biomass, probability of flowering, number of flowers per plant, flower size and pollen viability. Overall, the intensity of inbreeding depression increased among successive stages of the life cycle and cumulative inbreeding depression was significantly stronger in the first generation (delta approximately 0.5) compared with the second generation (delta approximately 0.35). We found no evidence for synergistic epistasis in our experiment. Our finding of more intense inbreeding depression during later stages of the life cycle may help to explain the maintenance of females in gynodioecious populations of S. vulgaris because purging of genetic load is less likely to occur.     

Marker-Based Inferences about Epistasis for Genes Influencing Inbreeding Depression

We describe a multilocus, marker-based regression method for inferring interactions between genes controlling inbreeding depression in self-fertile organisms. It is based upon selfing a parent heterozygous for several unlinked codominant markers, then analyzing the fitness of progeny marker genotypes. If loci causing inbreeding depression are linked to marker loci, then viability selection is manifested by distorted segregation of markers, and fecundity selection by dependence of the fecundity character upon the marker genotype. To characterize this selection, fitness is regressed on the proportion of loci homozygous for markers linked to deleterious alleles, and epistasis is detected by nonlinearity of the regression. Alternatively, fitness can be regressed on the proportion of heterozygous loci. Other modes of selection can be incorporated with a bivariate regression involving both homozygote and heterozygote marker genotypes. The advantage of this marker-based approach is that ``purging' is minimized and specific chromosomal segments are identified; its disadvantage lies in low statistical power when linkage is not strong and/or the linkage phase between marker and selected loci is uncertain. Using this method, in the wildflower Mimulus guttatus, we found predominant multiplicative gene interaction determining fecundity and some negative synergistic (nonmultiplicative) interaction for viability.     

EFFECTS OF SERIAL INBREEDING ON FITNESS COMPONENTS IN IMPATIENS CAPENSIS

Studies of inbreeding depression in wild plants customarily compare the fitness of outcrossed progeny to progeny derived from one generation of self-pollination. We compare levels of inbreeding depression in a greenhouse in two populations of jewelweed using progeny derived from random outcrosses, one generation of self-pollination, and three generations of selling. The progeny have expected inbreeding coefficients of, respectively, 0, 0.5, and 0.875. Seedling survivorship declined linearly with the level of inbreeding in both populations. Inbreeding also increased the variability of emergence date. Maternal family membership affected early seedling performance and often interacted significantly with the level of inbreeding. In contrast, path analyses reveal that inbreeding had both negative linear and positive quadratic direct effects on seed and final plant weight, causing the highly inbred progeny to outperform progeny derived from one generation of selfing. These results suggest either the rapid purging of deleterious alleles or diminishing epistasis among the loci affecting these characters. It is not clear why the loci affecting survival responded differently.     

Heterosis and inbreeding depression in bottlenecked populations: a test in the hermaphroditic freshwater snail Lymnaea stagnalis

Small population size is expected to induce heterosis, due to the random fixation and accumulation of mildly deleterious mutations, whereas within‐population inbreeding depression should decrease due to increased homozygosity. Population bottlenecks, although less effective, may have similar consequences. We tested this hypothesis in the self‐fertile freshwater snail Lymnaea stagnalis, by subjecting experimental populations to a single bottleneck of varied magnitude. Although patterns were not strong, heterosis was significant in the most severely bottlenecked populations, under stressful conditions. This was mainly due to hatching rate, suggesting that early acting and highly deleterious alleles were involved. Although L. stagnalis is a preferential outcrosser, inbreeding depression was very low and showed no clear relationship with bottleneck size. In the less reduced populations, inbreeding depression for hatching success increased under high inbreeding. This may be consistent with the occurence of synergistic epistasis between fitness loci, which may contribute to favour outcrossing in L. stagnalis.     

The effects of age and environment on the expression of inbreeding depression in Eucalyptus globulus

Inbreeding adversely affects fitness traits in many plant and animal species, and the magnitude, stability and genetic basis of inbreeding depression (ID) will have short- and long-term evolutionary consequences. The effects of four degrees of inbreeding (selfing, f=50%; full- and half-sib matings, f=25 and 12.5%; and unrelated outcrosses, f=0%) on survival and growth of an island population of Eucalyptus globulus were studied at two sites for over 14 years. For selfs, ID in survival increased over time, reaching a maximum of 49% by age 14 years. However, their inbreeding depression for stem diameter remained relatively stable with age, and ranged from 28 to 36% across years and sites. ID for survival was markedly greater on the more productive site, possibly due to greater and earlier onset of inter-tree competition, but was similar on both sites for the diameter of survivors. The deleterious trait response to increasing inbreeding coefficients was linear for survival and diameter. Non-significant quadratic effects suggested that epistasis did not contribute considerably to the observed ID at the population level. Among- and within-family coefficients of variation for diameter increased with inbreeding degree, and the variance among the outcrossed families was significant only on the more productive site. The performance of self-families for diameter was highly stable between sites. This suggests that, for species with mixed mating systems, environmentally stable inbreeding effects in open-pollinated progenies may tend to mask the additive genotype-by-environment interaction for fitness traits and the adaptive response to the environment.     

Perspective: Sign epistasis and genetic constraint on evolutionary trajectories

Epistasis for fitness means that the selective effect of a mutation is conditional on the genetic background in which it appears. Although epistasis is widely observed in nature, our understanding of its consequences for evolution by natural selection remains incomplete. In particular, much attention focuses only on its influence on the instantaneous rate of changes in frequency of selected alleles via epistatic contribution to the additive genetic variance for fitness. Thus, in this framework epistasis only has evolutionary importance if the interacting loci are simultaneously segregating in the population. However, the selective accessibility of mutational trajectories to high fitness genotypes may depend on the genetic background in which novel mutations appear, and this effect is independent of population polymorphism at other loci. Here we explore this second influence of epistasis on evolution by natural selection. We show that it is the consequence of a particular form of epistasis, which we designate sign epistasis. Sign epistasis means that the sign of the fitness effect of a mutation is under epistatic control; thus, such a mutation is beneficial on some genetic backgrounds and deleterious on others. Recent experimental innovations in microbial systems now permit assessment of the fitness effects of individual mutations on multiple genetic backgrounds. We review this literature and identify many examples of sign epistasis, and we suggest that the implications of these results may generalize to other organisms. These theoretical and empirical considerations imply that strong genetic constraint on the selective accessibility of trajectories to high fitness genotypes may exist and suggest specific areas of investigation for future research.     

An essay on the necessity and feasibility of conservation genomics

The basic premise of conservation genetics is that small populations may be genetically threatened. The two steps leading to this premise are: (1) due to prominent influence of random genetic drift and inbreeding allelic and genotypic diversity in small populations is expected to be low, and (2) low allelic diversity and high homozygosity are expected to lead to immediate fitness decreases (inbreeding depression) and a compromised potential for evolutionary adaptation. Conservation genetic research has been strongly stimulated by the application of neutral molecular markers like microsatellites and AFLPs. In general these marker studies have provided evidence for step 1. It is less evident how these markers may provide evidence for step 2. In this essay we argue that, in order to get detailed insight in step 2, adopting a conservation genomic approach, in which conservation genetics will use approaches from ecological and evolutionary functional genomics (ecogenomics), is both necessary and feasible. Conservation genomics is necessary for studying functional genomic variation as function of drift and inbreeding, for studying the mechanisms that relate low genetic variation to low fitness, for integrating environmental and genetic approaches to conservation biology, and for developing modern, fast monitoring tools. The rapid technical and financial developments in genomics currently make conservation genomics feasible, and will improve feasibility in the very near future even further. We therefore argue that conservation genomics personifies part of the near future of conservation genetics.     

Epistasis from functional dependence of fitness on underlying traits

Epistasis between mutations in two genes is thought to reflect an interdependence of their functions. While sometimes epistasis is predictable using mechanistic models, its roots seem, in general, hidden in the complex architecture of biological networks. Here, we ask how epistasis can be quantified based on the mathematical dependence of a system-level trait (e.g. fitness) on lower-level traits (e.g. molecular or cellular properties). We first focus on a model in which fitness is the difference between a benefit and a cost trait, both pleiotropically affected by mutations. We show that despite its simplicity, this model can be used to analytically predict certain properties of the ensuing distribution of epistasis, such as a global negative bias, resulting in antagonism between beneficial mutations, and synergism between deleterious ones. We next extend these ideas to derive a general expression for epistasis given an arbitrary functional dependence of fitness on other traits. This expression demonstrates how epistasis relative to fitness can emerge despite the absence of epistasis relative to lower level traits, leading to a formalization of the concept of independence between biological processes. Our results suggest that epistasis may be largely shaped by the pervasiveness of pleiotropic effects and modular organization in biological networks.