Selection theory for selfed progenies

Summary The purpose of this article was to extend the model used to predict selection response with selfed progeny from 2 alleles per locus to a model which is general for number and frequency of alleles at loci. To accomplish this, 4 areas had to be dealt with: 1) simplification of the derivation and calculation of the condensed coefficients of identity; 2) presentation of the genetic variances expressed among and within selfed progenies as linear function of 5 population parameters; 3) presentation of selection response equations for selfed progenies as functions of these 5 population parameters; and 4) to identify a set of progeny to evaluate, such that one might be able to estimate these 5 population parameters.The five population parameters used in predicting gains were the additive genetic variance, the dominance variance, the covariance of additive and homozygous dominance deviations, the variance of the homozygous dominance deviations and a squared inbreeding depression term.Contribution from the Missouri Agricultural Experiment Station. Journal Series No. 9971     

Predicting response to selection on a quantitative trait: a comparison between models for mixed-mating populations

Two different theoretical frameworks have been developed to predict response to selection in a mixed mating population (in which reproduction occurs by a mixture of outcrossing and self-fertilization). The genotypic covariance model (GCM) and the structured linear model (SLM) rely on the same assumptions regarding quantitative trait inheritance, but use different genetic summary statistics. Here, we demonstrate the algebraic relationships between the various genetic metrics used in each theory. This is accomplished by reformulating the GCM in terms of the Wright-Kempthorne equation. We use stochastic simulations to investigate the relative accuracy of each theory for a range of selfing rates. The SLM is generally more accurate than the GCM, the most pronounced differences emerging in simulations with inbreeding depression for fitness. In fact, with strong inbreeding depression and high selfing rates, evolution can occur opposite the direction predicted by the GCM. The simulations also indicate that direct application of random mating models to partially selfing populations can produce very inaccurate predictions if quantitative trait loci exhibit dominance.     

The Genetic Variance for Viability and Its Components in a Local Population of DROSOPHILA MELANOGASTER

Two hundred and ninety second chromosomes extracted from a natural population of Drosophila melanogaster were analyzed to estimate the genetic variance of viability and its components by means of a partial diallel cross (Design II of Comstock and Robinson 1952). The additive and dominance variances are estimated to be 0.009 and 0.0012. Using the dominance variance and the inbreeding depression, the effective number of overdominant loci contributing to the variance in viability is estimated to be very small, a dozen or less. Either the actual number of loci is small, or the distribution of viabilities is strongly skewed with a large majority of very weakly selected loci. The additive variance in viability appears to be too large to be accounted for by recurrent harmful mutants or by overdominant loci at equilibrium with various genetic parameters estimated independently. The excess might be due to frequency-dependent selection, to negative correlations between viability and fertility, or possibly to the presence of a mutator. The selection for viability and fertility, or possibly to the presence of a mutator. The selection for viability at the average polymorphic locus must be very slight, of the order of 10(-3) or less.     

Prediction of additive and dominance effects in selected or unselected populations with inbreeding

Summary A genetic model with either 64 or 1,600 unlinked biallelic loci and complete dominance was used to study prediction of additive and dominance effects in selected or unselected populations with inbreeding. For each locus the initial frequency of the favourable allele was 0.2, 0.5, or 0.8 in different alternatives, while the initial narrow-sense heritability was fixed at 0.30. A population of size 40 (20 males and 20 females) was simulated 1,000 times for five generations. In each generation 5 males and 10 or 20 females were mated, with each mating producing four or two offspring, respectively. Breeding individuals were selected randomly, on own phenotypic performance or such yielding increased inbreeding levels in subsequent generations. A statistical model containing individual additive and dominance effects but ignoring changes in mean and genetic covariances associated with dominance due to inbreeding resulted in significantly biased predictions of both effects in generations with inbreeding. Bias, assessed as the average difference between predicted and simulated genetic effects in each generation, increased almost linearly with the inbreeding coefficient. In a second statistical model the average effect of inbreeding on the mean was accounted for by a regression of phenotypic value on the inbreeding coefficient. The total dominance effect of an individual in that case was the sum of the average effect of inbreeding and an individual effect of dominance. Despite a high mean inbreeding coefficient (up to 0.35), predictions of additive and dominance effects obtained with this model were empirically unbiased for each initial frequency in the absence of selection and 64 unlinked loci. With phenotypic selection of 5 males and only 10 females in each generation and 64 loci, however, predictions of additive and dominance effects were significantly biased. Observed biases disappeared with 1,600 loci for allelic frequencies at 0.2 and 0.5. Bias was due to a considerable change in allelic frequency with phenotypic selection. Ignoring both the covariance between additive and dominance effects with inbreeding and the change in dominance variance due to inbreeding did not significantly bias prediction of additive and dominance effects in selected or unselected populations with inbreeding.     

Modelling the effects of genetics and habitat on the demography of a grassland herb

There is growing evidence that genetic and ecological factors interact in determining population persistence. The demographic effects of inbreeding depression can largely depend on the ecological milieu. We used demographic data of the perennial herb Succisa pratensis from six populations in grazed and ungrazed sites with different soil moisture. We built an individual-based model assessing the demographic consequences of inbreeding depression in populations with different management and habitat. Today this plant has to cope with severe landscape fragmentation, deteriorating habitat conditions in terms of decreasing grazing intensity, and the effects of inbreeding depression. For each population we performed simulations testing two inbreeding depression hypotheses (partial dominance and overdominance) and three epistatic functions among loci. The results indicated stronger inbreeding depression effects for populations in unfavourable sites without grazing or in xeric habitats compared to populations in favourable mesic sites with grazing. Overall, we found stronger effects with overdominance, a result that emphasizes the importance of understanding the genetic mechanisms of inbreeding depression. Hence, management practices can interact with the genetic consequences of inbreeding depression in population dynamics, which may have important implications for plant population ecology and evolutionary dynamics of inbreeding depression.     

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.     

Genetic components of variation in Nemophila menziesii undergoing inbreeding: morphology and flowering time.

The standard approaches to estimation of quantitative genetic parameters and prediction of response to selection on quantitative traits are based on theory derived for populations undergoing random mating. Many studies demonstrate, however, that mating systems in natural populations often involve inbreeding in various degrees (i.e. , self matings and matings between relatives). Here we apply theory developed for estimating quantitative genetic parameters for partially inbreeding populations to a population of Nemophila menziesii recently obtained from nature and experimentally inbred. Two measures of overall plant size and two of floral size expressed highly significant inbreeding depression. Of three dominance components of phenotypic variance that are defined under partial inbreeding, one was found to contribute significantly to phenotypic variance in flower size and flowering time, while the remaining two components contributed only negligibly to variation in each of the five traits considered. Computer simulations investigating selection response under the more complete genetic model for populations undergoing mixed mating indicate that, for parameter values estimated in this study, selection response can be substantially slowed relative to predictions for a random mating population. Moreover, inbreeding depression alone does not generally account for the reduction in selection response.     

Theoretical Modifications of Reciprocal Recurrent Selection

Reciprocal recurrent selection (RRS), which assumes overdominant loci to be important, alters two genetically different populations to improve their crossbred mean. Individual plants from two populations (A and B) are selfed and also crossed with plants from the reciprocal female tester population (B and A, respectively). Selection is based on the mean of crossbred families, and the selected individuals are randomly mated within A and B to form new populations.—We propose two alternatives to RRS. The first (RRS-I) uses, as the tester of population A, a population (LB) that is derived from population B by family selection for low yield. The second (RRS-II) is similar to RRS-I, but also uses, as the tester of B, a population (LA) that is derived from population A by family selection for low yield.—The expected crossbred means of RRS, RRS-I, and RRS-II were compared, assuming equal σP, at several cycles of selection for incomplete and complete dominance, and for several cases of overdominance (depending on the gene frequencies in A and B, and on the equilibrium gene frequency).—The choice of selection method depends on the importance of the effects of overdominant loci compared to loci exhibiting incomplete or complete dominance. If overdominance is unimportant, RRS-II is the best selection method, followed by RRS-I and RRS. If overdominance is important, both RRS and RRS-I are superior to RRS-II; RRS is preferred to RRS-I if the effects of overdominant loci are sufficiently important. If the genetic model is a mixture of levels of dominance at different loci, a combination of selection systems is suggested.     

Environment-dependent inbreeding depression: its ecological and evolutionary significance

Inbreeding depression is a major evolutionary and ecological force that influences population dynamics and the evolution of inbreeding-avoidance traits such as mating systems and dispersal. There is now compelling evidence that inbreeding depression is environment-dependent. Here, we discuss ecological and evolutionary consequences of environment-dependent inbreeding depression. The environmental dependence of inbreeding depression may be caused by environment-dependent phenotypic expression, environment-dependent dominance, and environment-dependent natural selection. The existence of environment-dependent inbreeding depression challenges classical models of inbreeding as caused by unconditionally deleterious alleles, and suggests that balancing selection may shape inbreeding depression in natural populations; loci associated with inbreeding depression in some environments may even contribute to adaptation to others. Environment-dependent inbreeding depression also has important, often neglected, ecological and evolutionary consequences: it can influence the demography of marginal or colonizing populations and alter adaptive optima of mating systems, dispersal, and their associated traits. Incorporating the environmental dependence of inbreeding depression into theoretical models and empirical studies is necessary for understanding the genetic and ecological basis of inbreeding depression and its consequences in natural populations.     

The Effects of a Bottleneck on Inbreeding Depression and the Genetic Load

We study the effects of a population bottleneck on the inbreeding depression and genetic load caused by deleterious mutations in an outcrossing population. The calculations assume that loci have multiplicative fitness effects and that linkage disequilibrium is negligible. Inbreeding depression decreases immediately after a sudden reduction of population size, but the drop is at most only several percentage points, even for severe bottlenecks. Highly recessive mutations experience a purging process that causes inbreeding depression to decline for a number of additional generations. On the basis of available parameter estimates, the absolute fall in inbreeding depression may often be only a few percentage points for bottlenecks of 10 or more individuals. With a very high lethal mutation rate and a very slow population growth, however, the decline may be on the order of 25%. We examine when purging might favor a switch from outbreeding to selfing and find it occurs only under very limited conditions unless population growth is very slow. In contrast to inbreeding depression, a bottleneck causes an immediate increase in the genetic load. Purging causes the load to decline and then overshoot its equilibrium value. The changes are typically modest: the absolute increase in the total genetic load will be at most a few percentage points for bottlenecks of size 10 or more unless the lethal mutation rate is very high and the population growth rate very slow.     

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.     

Efficiency of selection, as measured by single nucleotide polymorphism variation, is dependent on inbreeding rate in Drosophila melanogaster

It is often hypothesized that slow inbreeding causes less inbreeding depression than fast inbreeding at the same absolute level of inbreeding. Possible explanations for this phenomenon include the more efficient purging of deleterious alleles and more efficient selection for heterozygote individuals during slow, when compared with fast, inbreeding. We studied the impact of inbreeding rate on the loss of heterozygosity and on morphological traits in Drosophila melanogaster. We analysed five noninbred control lines, 10 fast inbred lines and 10 slow inbred lines; the inbred lines all had an expected inbreeding coefficient of approximately 0.25. Forty single nucleotide polymorphisms in DNA coding regions were genotyped, and we measured the size and shape of wings and counted the number of sternopleural bristles on the genotyped individuals. We found a significantly higher level of genetic variation in the slow inbred lines than in the fast inbred lines. This higher genetic variation was resulting from a large contribution from a few loci and a smaller effect from several loci. We attributed the increased heterozygosity in the slow inbred lines to the favouring of heterozygous individuals over homozygous individuals by natural selection, either by associative over‐dominance or balancing selection, or a combination of both. Furthermore, we found a significant polynomial correlation between genetic variance and wing size and shape in the fast inbred lines. This was caused by a greater number of homozygous individuals among the fast inbred lines with small, narrow wings, which indicated inbreeding depression. Our results demonstrated that the same amount of inbreeding can have different effects on genetic variance depending on the inbreeding rate, with slow inbreeding leading to higher genetic variance than fast inbreeding. These results increase our understanding of the genetic basis of the common observation that slow inbred lines express less inbreeding depression than fast inbred lines. In addition, this has more general implications for the importance of selection in maintaining genetic variation.     

Evaluation of major genetic loci contributing to inbreeding depression for survival and early growth in a selfed family of Pinus taeda

The magnitude of fitness effects at genetic loci causing inbreeding depression at various life stages has been an important question in plant evolution. We used genetic mapping in a selfed family of loblolly pine (Pinus taeda L.) to gain insights on inbreeding depression for early growth and viability. Two quantitative trait loci (QTLs) were identified that explain much of the phenotypic variation in height growth through age 3 and may account for more than 13% inbreeding depression in this family. One of these QTLs maps to the location of cad-nl, a lignin biosynthesis mutation. Both QTLs show evidence of overdominance, although evidence for true versus pseudo-overdominance is inconclusive. Evidence of directional dominance for height growth was noted throughout the genome, suggesting that additional loci may contribute to inbreeding depression. A chlorophyll-deficiency mutation, spf did not appear to be associated with growth effects, but had significant effects on survival through age 3. Previously identified embryonic viability loci had little or no overall effect on germination, survival, or growth. Our results challenge, at least in part, the prevailing hypothesis that inbreeding depression for growth is due to alleles of small effect. However, our data support predictions that loci affecting inbreeding depression are largely stage specific.     

Overdominant epistatic loci are the primary genetic basis of inbreeding depression and heterosis in rice. I. Biomass and grain yield

To understand the genetic basis of inbreeding depression and heterosis in rice, main-effect and epistatic QTL associated with inbreeding depression and heterosis for grain yield and biomass in five related rice mapping populations were investigated using a complete RFLP linkage map of 182 markers, replicated phenotyping experiments, and the mixed model approach. The mapping populations included 254 F(10) recombinant inbred lines derived from a cross between Lemont (japonica) and Teqing (indica) and two BC and two testcross hybrid populations derived from crosses between the RILs and their parents plus two testers (Zhong 413 and IR64). For both BY and GY, there was significant inbreeding depression detected in the RI population and a high level of heterosis in each of the BC and testcross hybrid populations. The mean performance of the BC or testcross hybrids was largely determined by their heterosis measurements. The hybrid breakdown (part of inbreeding depression) values of individual RILs were negatively associated with the heterosis measurements of their BC or testcross hybrids, indicating the partial genetic overlap of genes causing hybrid breakdown and heterosis in rice. A large number of epistatic QTL pairs and a few main-effect QTL were identified, which were responsible for >65% of the phenotypic variation of BY and GY in each of the populations with the former explaining a much greater portion of the variation. Two conclusions concerning the loci associated with inbreeding depression and heterosis in rice were reached from our results. First, most QTL associated with inbreeding depression and heterosis in rice appeared to be involved in epistasis. Second, most ( approximately 90%) QTL contributing to heterosis appeared to be overdominant. These observations tend to implicate epistasis and overdominance, rather than dominance, as the major genetic basis of heterosis in rice. The implications of our results in rice evolution and improvement are discussed.     

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.     

Segregation and the evolution of sex under overdominant selection

The segregation of alleles disrupts genetic associations at overdominant loci, causing a sexual population to experience a lower mean fitness compared to an asexual population. To investigate whether circumstances promoting increased sex exist within a population with heterozygote advantage, a model is constructed that monitors the frequency of alleles at a modifier locus that changes the relative allocation to sexual and asexual reproduction. The frequency of these modifier alleles changes over time as a correlated response to the dynamics at a fitness locus under overdominant selection. Increased sex can be favored in partially sexual populations that inbreed to some extent. This surprising finding results from the fact that inbred populations have an excess of homozygous individuals, for whom sex is always favorable. The conditions promoting increased levels of sex depend on the selection pressure against the homozygotes, the extent of sex and inbreeding in the population, and the dominance of the invading modifier allele.     

Effects of Population Size and Selection Intensity on Correlated Responses to Selection for Postweaning Gain in Mice

Correlated responses to selection for postweaning gain in mice were studied to determine the influence of population size and selection intensity. Correlated traits measured were three-, six- and eight-week body weights, litter size, twelve-day litter weight, proportion infertile matings and two indexes of reproductive performance. In general, the results agreed with observations made on direct response: correlated responses in the body weight traits and litter size increased as (1) selection intensity increased and (2) effective population size increased. Correlated responses in the body weight traits and litter size were positive in the large population size lines (16 pairs), as expected from the positive genetic correlation between these traits and postweaning gain. However, several negative correlated responses were observed at small population sizes (one and two pairs). Within each level of selection intensity, traits generally associated with fitness tended to decline most in the very small populations (one and two pairs) and in the large populations (16 pairs) for apparently different reasons. The fitness decline at the small effective population sizes was attributable to inbreeding depression. In contrast, it was postulated that the fitness decline at the large effective population size was due to selection moving the population mean for body weight and a trait positively correlated genetically with body weight (i.e., percent body fat) away from an optimum.     

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.     

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.     

Selection,linkage, and dominance in small populations

Summary Linkage, dominance, and selection interact significantly to alter the mean coefficient of inbreeding. The effect of one is not predictable without the other two. Close linkage between adjacent loci in the presence of intense selection caused a different response with overdominant gene action from with partial dominance. When selection was random, effects of linkage and dominance on the coefficient of inbreeding were nonexistent; but when selection was by either phenotype or genotype, linkage and dominance became important. Joint effects between linkage, dominance, and selection are illustrated in specific simulated populations.