Epistasis and the conversion of non-additive to additive genetic variance at population bottlenecks

The effect of population bottlenecks on the mean and the additive variance generated by two neutral independent epistatic loci has been studied theoretically. Six epistatic models, used in the analysis of binary disease traits, were considered. Ancestral values in an infinitely large panmictic population were compared with their expectations at equilibrium, after t consecutive bottlenecks of equal size N (derived values). An increase in the additive variance after bottlenecks (inversely related to N and t) will occur only if the frequencies of the negative allele at each locus are: (1) low, invariably associated to strong inbreeding depression; (2) high, always accompanied by an enhancement of the mean with inbreeding. The latter is an undesirable property, making the pertinent models unsuitable for the genetic analysis of disease. For the epistatic models considered, it is unlikely that the rate of evolution may be accelerated after population bottlenecks, in spite of occasional increments of the derived additive variance over its ancestral value.     

The effect of genetic drift on the variance/covariance components generated by multilocus additive x additive epistatic systems

The effect of population bottlenecks on the components of the genetic variance/covariance generated by n neutral independent additive x additive loci has been studied theoretically. In its simplest version, this situation can be modelled by specifying the allele frequencies and homozygous effects at each locus, and an additional factor measuring the strength of the n-th order epistatic interaction. The variance/covariance components in an infinitely large panmictic population (ancestral components) were compared with their expected values at equilibrium over replicates randomly derived from the base population, after t bottlenecks of size N (derived components). Formulae were obtained giving the derived components (and the between-line variance) as functions of the ancestral ones (alternatively, in terms of allele frequencies and effects) and the corresponding inbreeding coefficient F(t). The n-th order derived component of the genetic variance/covariance is continuously eroded by inbreeding, but the remaining components may increase initially until a critical F(t) value is attained, which is inversely related to the order of the pertinent component, and subsequently decline to zero. These changes can be assigned to the between-line variances/covariances of gene substitution and epistatic effects induced by drift. Numerical examples indicate that: (1) the derived additive variance/covariance component will generally exceed its ancestral value unless epistasis is weak; (2) the derived epistatic variance/covariance components will generally exceed their ancestral values unless allele frequencies are extreme; (3) for systems showing equal ancestral additive and total non-additive variance/covariance components, those including a smaller number of epistatic loci may generate a larger excess in additive variance/covariance after bottlenecks than others involving a larger number of loci, provided that F(t) is low. Our results indicate that it is unlikely that the rate of evolution may be significantly accelerated after population bottlenecks, in spite of occasional increments of the derived additive variance over its ancestral value.     

MODELING THE GENETIC BASIS OF HETEROSIS: TESTS OF ALTERNATIVE HYPOTHESES

Houle (1994) showed that marker-associated heterosis due to general inbreeding depression could not be distinguished from direct overdominance at the marker locus by examining mean genotypic fitnesses, in the one-locus case. Indeed, both hypotheses equally fit the same regression model, referred to as the “adaptive distance model” (Smouse 1986). I here extend the analysis to several loci and to the relationship between marker genotype and variance in fitness. Several predictions differ between the overdominance and inbreeding hypotheses: (1) all locus-specific effects are equal under inbreeding, whereas they are not under overdominance; (2) the adaptive distance model has an increasingly low fit when the number of loci increases, under inbreeding, whereas it always explains the whole variance in fitness under overdominance; (3) a negative relationship is predicted between mean fitness and the variance in fitness, under inbreeding, which is not predicted under overdominance. Some statistical tests are derived from these predictions, that help to identify the genetic basis of heterosis. Simulations show that the power of these tests allows their application to real datasets.     

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.     

A Monte Carlo algorithm for computing the IBD matrices using incomplete marker information

Identity-By-Descent (IBD) is a general measurement of the relationship between two groups of genes. If the two groups consist of two homologous genes, one from each individual, the IBD is called the coancestry between the two individuals. Coancestry is an important concept in both population and quantitative genetics. It is the probability that both genes are copies of the same gene in the genealogy. The average coancestry value at a random locus in a population reflects the level of population diversity, effective population size, the level of inbreeding and other attributes. Coancestry is also the building block for the covariance structure used to estimate the additive genetic variance component for a quantitative trait. There are many other types of IBD matrices, depending on the natures of the genes included in each group, and these IBD matrices vary from locus to locus. Molecular markers distributed along the genome provide information that can be used to infer these locus-specific IBD matrices. As a result, we can estimate and test the variance components of a quantitative trait contributed by these loci using the inferred IBD matrices. In this study, we develop the concept of locus-specific epistatic IBD matrices and a Monte Carlo method to infer these IBD matrices. The method is suitable for large pedigrees with arbitrary complexity and various levels of missing marker information. With these locus-specific IBD matrices, we are ready to search for quantitative trait loci along the genome in complicated pedigrees.     

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.     

Quantitative Trait Loci Differentiating the Outbreeding Mimulus Guttatus from the Inbreeding M. Platycalyx

Theoretical predictions about the evolution of selfing depend on the genetic architecture of loci controlling selfing (monogenic vs. polygenic determination, large vs. small effect of alleles, dominance vs. recessiveness), and studies of such architecture are lacking. We inferred the genetic basis of mating system differences between the outbreeding Mimulus guttatus and the inbreeding M. platycalyx by quantitative trait locus (QTL) mapping using random amplified polymorphic DNA and isozyme markers. One to three QTL were detected for each of five mating system characters, and each QTL explained 7.6-28.6% of the phenotypic variance. Taken together, QTL accounted for up to 38% of the variation in mating system characters, and a large proportion of variation was unaccounted for. Inferred QTL often affected more than one trait, contributing to the genetic correlation between those traits. These results are consistent with the hypothesis that quantitative variation in plant mating system characters is primarily controlled by loci with small effect.     

Features of genetic variability in microsatellite DNA loci in the French Bulldog dog breed

Genetic variability in microsatellite markers PEZ1, PEZ3, PEZ6, PEZ8, FHC2010, and FHC2054 from a panel recommended by the International Society for Animal Genetics has been assessed for a micropopulation of dogs of the French Bulldog breed. The number and size of alleles, the number of alleles per locus, the effective number of alleles, the polymorphism index, expected and actual heterozygosity, and Wright’s fixation index have been determined to characterize each locus investigated. Deficit of heterozygous genotypes was observed in the micropopulation investigated, which is indicative of inbreeding. The relationship between the degree of homozygosity for six microsatellite loci and the degree of inbreeding has been analyzed. The results obtained point at a trend for increase of the relative abundance of homozygous loci upon an increase in the inbreeding coefficient of individuals.     

A test for deviation from island-model population structure

The neutral island model forms the basis for several estimation models that relate patterns of genetic structure to microevolutionary processes. Estimates of gene flow are often based on this model and may be biased when the model's assumptions are violated. An appropriate test for violations is to compare FST scores for individual loci to a null distribution based on the average FST taken over multiple loci. A parametric bootstrap method is described here based on Wright's beta-distribution to generate null distributions of FST for each locus. These null distributions account for error introduced by sampling populations, individuals and loci, and also biological sources of error, including variable alleles/locus and inbreeding. Confidence limits can be obtained directly from these distributions. Significant deviations from the island model may be the result of selection, deviations from the island model's migration pattern, nonequilibrium conditions, or other deviations from island-model assumptions. Only strong biases are likely to be detected because of the inherently large sampling variation of FST. Nevertheless, a coefficient, Nb, describing bias in the spread of the beta-distribution in units comparable to the gene flow parameter, Nm, can be obtained for each locus. In samples from populations of the butterfly Coenonympha tullia, the loci Idh-1, Mdh-1, Pgi and Pgm showed significantly lower FST than expected.     

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.     

Isolation and characterization of 23 microsatellite loci in the hen flea Ceratophyllus gallinae

Nineteen dinucleotide, two trinucleotide and two tetranucleotide microsatellite loci developed for the hen flea Ceratophyllus gallinae are presented. Twenty fleas were screened at each locus. Loci were polymorphic (three to nine alleles per locus). These markers will provide a system to study population segregation and diversity, gene flow, dispersal and inbreeding.     

Isolation and characterization of 16 microsatellite loci in the Great Tit Parus major

Six dinucleotide, three trinucleotide and seven tetranucleotide microsatellite loci developed for the great tit Parus major are presented. Thirty individual birds were screened at each locus. Loci were polymorphic (four to 19 alleles per locus). These markers provide a system to study paternity, genetic diversity in natural populations, gene flow, dispersal and inbreeding.     

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.     

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.     

Calculation of the inbreeding coefficient

Wright's rule for calculating the inbreeding coefficient for an arbitrary pedigree is proven for both autosomal and X-linked loci.Supported by NSF Grant PHY-84-16691     

Complex medico-genetic study of the population of western Siberia. III. Distribution of phenotypes and gene frequencies in the northern Khanty population

Distribution of phenotypes and gene frequencies for 5 polymorphic loci as well as frequencies of incidence of some anthroposcopic parameters in five subpopulations of the North Khanty population is presented. A comparative analysis was performed for the traits studied among the people of Finno-Ugric group and of North Asia. Wahlund's variance values point to significant subdivision of the population in question. Disruption of the Hardy-Weinberg equilibrium for haptoglobin locus was observed in two subpopulations. Estimates of inbreeding coefficients obtained by different ways (from gene frequencies, genealogy and isonymy) are compared.     

Inbreeding depression and the evolution of dispersal rates: a multilocus model

Inbreeding depression is one of the possible reasons organisms disperse. In this article, we present a two-locus model for the evolution of dispersal in the presence of inbreeding depression. The first locus codes for a modifier of the migration rate, while the second locus is a selected locus generating inbreeding depression. We express the change in frequency of the migration modifier as a function of allele frequencies and genetic associations and then use a quasi-equilibrium assumption to express genetic associations as functions of allele frequencies. Our model disentangles two effects of inbreeding depression: it gives an advantage to migrant individuals because their offspring are on average less homozygous, but it also decreases the degree of population structure, thus decreasing the strength of kin selection for dispersal. We then extend our model to include an infinite number of selected loci. When the cost of dispersal is not too high, the model predictions are confirmed by multilocus simulation results and show that inbreeding depression can have a substantial effect on the dispersal rate. For high costs of dispersal, we observe discrepancies between the model and the simulations, probably caused by associations among selected loci, which are neglected in the analysis.     

The effect of epistasis on the excess of the additive and nonadditive variances after population bottlenecks

The effect of population bottlenecks on the components of the genetic variance generated by two neutral independent epistatic loci has been studied theoretically (VA, additive; VD, dominant; VAA, additive x additive; VAD, additive x dominant; VDD; dominant x dominant components of variance). Nonoverdominance and overdominance models were considered, covering all possible types of marginal gene action at the single locus level. The variance components in an infinitely large panmictic population (ancestral components) were compared with their expected values at equilibrium, after t consecutive bottlenecks of equal size N (derived components). Formulae were obtained in terms of allele frequencies and effects at each locus and the corresponding epistatic value. An excess of VA after bottlenecks can be assigned to two sources: (1) the spatiotemporal changes in the marginal average effects of gene substitution alpha(i), which are equal to zero only for additive gene action within and between loci; and (2) the covariance between alpha2(i) and the heterozygosity at the loci involved, which is generated by dominance, with or without epistasis. Numerical examples were analyzed, indicating that an increase in VA after bottlenecks will only occur if its ancestral value is minimal or very small. For the nonoverdominance model with weak reinforcing epistasis, that increase has been detected only for extreme frequencies of the negative allele at one or both loci. With strong epistasis, however, this result can be extended to a broad range of intermediate frequencies. With no epistasis, the same qualitative results were found, indicating that dominance can be considered as the primary cause of an increase in VA following bottlenecks. In parallel, the derived total nonadditive variance exceeded its ancestral value (V(NA) = V(D) + V(AA) + V(AD) + V(DD)) for a range of combinations of allele frequencies covering those for an excess of VA and for very large frequencies of the negative allele at both loci. For the overdominance model, an increase in V(A) and V(NA) was respectively observed for equilibrium (intermediate) frequencies at one or both loci or for extreme frequencies at both loci. For all models, the magnitude of the change of V(A) and V(NA) was inversely related to N and t. At low levels of inbreeding, the between-line variance was not affected by the type of gene action. For the models considered, the results indicate that it is unlikely that the rate of evolution may be accelerated after population bottlenecks, in spite of occasional increments of the derived V(A) over its ancestral value.