Identifying quantitative trait locus by genetic background interactions in association studies

Association studies are designed to identify main effects of alleles across a potentially wide range of genetic backgrounds. To control for spurious associations, effects of the genetic background itself are often incorporated into the linear model, either in the form of subpopulation effects in the case of structure or in the form of genetic relationship matrices in the case of complex pedigrees. In this context epistatic interactions between loci can be captured as an interaction effect between the associated locus and the genetic background. In this study I developed genetic and statistical models to tie the locus by genetic background interaction idea back to more standard concepts of epistasis when genetic background is modeled using an additive relationship matrix. I also simulated epistatic interactions in four-generation randomly mating pedigrees and evaluated the ability of the statistical models to identify when a biallelic associated locus was epistatic to other loci. Under additive-by-additive epistasis, when interaction effects of the associated locus were quite large (explaining 20% of the phenotypic variance), epistasis was detected in 79% of pedigrees containing 320 individuals. The epistatic model also predicted the genotypic value of progeny better than a standard additive model in 78% of simulations. When interaction effects were smaller (although still fairly large, explaining 5% of the phenotypic variance), epistasis was detected in only 9% of pedigrees containing 320 individuals and the epistatic and additive models were equally effective at predicting the genotypic values of progeny. Epistasis was detected with the same power whether the overall epistatic effect was the result of a single pairwise interaction or the sum of nine pairwise interactions, each generating one ninth of the epistatic variance. The power to detect epistasis was highest (94%) at low QTL minor allele frequency, fell to a minimum (60%) at minor allele frequency of about 0.2, and then plateaued at about 80% as alleles reached intermediate frequencies. The power to detect epistasis declined when the linkage disequilibrium between the DNA marker and the functional polymorphism was not complete.     

Misspecification in Mixed-Model-Based Association Analysis

Additive genetic variance in natural populations is commonly estimated using mixed models, in which the covariance of the genetic effects is modeled by a genetic similarity matrix derived from a dense set of markers. An important but usually implicit assumption is that the presence of any nonadditive genetic effect increases only the residual variance and does not affect estimates of additive genetic variance. Here we show that this is true only for panels of unrelated individuals. In the case that there is genetic relatedness, the combination of population structure and epistatic interactions can lead to inflated estimates of additive genetic variance.     

The role of epistasis in the manifestation of heterosis: a systems-oriented approach

Heterosis is widely used in breeding, but the genetic basis of this biological phenomenon has not been elucidated. We postulate that additive and dominance genetic effects as well as two-locus interactions estimated in classical QTL analyses are not sufficient for quantifying the contributions of QTL to heterosis. A general theoretical framework for determining the contributions of different types of genetic effects to heterosis was developed. Additive x additive epistatic interactions of individual loci with the entire genetic background were identified as a major component of midparent heterosis. On the basis of these findings we defined a new type of heterotic effect denoted as augmented dominance effect di* that comprises the dominance effect at each QTL minus half the sum of additive x additive interactions with all other QTL. We demonstrate that genotypic expectations of QTL effects obtained from analyses with the design III using testcrosses of recombinant inbred lines and composite-interval mapping precisely equal genotypic expectations of midparent heterosis, thus identifying genomic regions relevant for expression of heterosis. The theory for QTL mapping of multiple traits is extended to the simultaneous mapping of newly defined genetic effects to improve the power of QTL detection and distinguish between dominance and overdominance.     

Exploratory behavior undergoes genotype–age interactions in a wild bird

Animal personality traits are often heritable and plastic at the same time. Indeed, behaviors that reflect an individual's personality can respond to environmental factors or change with age. To date, little is known regarding personality changes during a wild animals' lifetime and even less about stability in heritability of behavior across ages. In this study, we investigated age‐related changes in the mean and in the additive genetic variance of exploratory behavior, a commonly used measure of animal personality, in a wild population of great tits. Heritability of exploration is reduced in adults compared to juveniles, with a low genetic correlation across these age classes. A random regression animal model confirmed the occurrence of genotype–age interactions (G×A) in exploration, causing a decrease in additive genetic variance before individuals become 1 year old, and a decline in cross‐age genetic correlations between young and increasingly old individuals. Of the few studies investigating G×A in behaviors, this study provides rare evidence for this phenomenon in an extensively studied behavior. We indeed demonstrate that heritability and cross‐age genetic correlations in this behavior are not stable over an individual's lifetime, which can affect its potential response to selection. Because G×A is likely to be common in behaviors and have consequences for our understanding of the evolution of animal personality, more attention should be turned to this phenomenon in the future work.     

A general definition of the heritable variation that determines the potential of a population to respond to selection

Genetic selection is a major force shaping life on earth. In classical genetic theory, response to selection is the product of the strength of selection and the additive genetic variance in a trait. The additive genetic variance reflects a population's intrinsic potential to respond to selection. The ordinary additive genetic variance, however, ignores the social organization of life. With social interactions among individuals, individual trait values may depend on genes in others, a phenomenon known as indirect genetic effects. Models accounting for indirect genetic effects, however, lack a general definition of heritable variation. Here I propose a general definition of the heritable variation that determines the potential of a population to respond to selection. This generalizes the concept of heritable variance to any inheritance model and level of organization. The result shows that heritable variance determining potential response to selection is the variance among individuals in the heritable quantity that determines the population mean trait value, rather than the usual additive genetic component of phenotypic variance. It follows, therefore, that heritable variance may exceed phenotypic variance among individuals, which is impossible in classical theory. This work also provides a measure of the utilization of heritable variation for response to selection and integrates two well-known models of maternal genetic effects. The result shows that relatedness between the focal individual and the individuals affecting its fitness is a key determinant of the utilization of heritable variance for response to selection.     

A study of heterogeneity of environmental variance for slaughter weight in pigs

This work presents an analysis of heterogeneity of environmental variance for slaughter weight (175 days) in pigs. This heterogeneity is associated with systematic and additive genetic effects. The model also postulates the presence of additive genetic effects affecting the mean and environmental variance. The study reveals the presence of genetic variation at the level of the mean and the variance, but an absence of correlation, or a small negative correlation, between both types of additive genetic effects. In addition, we show that both, the additive genetic effects on the mean and those on environmental variance have an important influence upon the future economic performance of selected individuals.     

Genetic parameters in a rubber tree population: heritabilities,genotype-by-environment interactions and multi-trait correlations

Rubber tree breeding programs are mainly driven by selection of individuals with high yield and quality of rubber. Data from 51 open-pollinated progenies tested on six sites in Brazil were analyzed over several traits to estimate the following: genetic parameters such as narrow-sense heritability and additive genetic variance in single- and multi-site analyses, type B correlations to determine the relevance of genotype-by-environment interactions and its effects on alternative selection strategies, additive genetic repeatability correlation for rubber yield based on three consecutive yearly measurements, and type A correlations to evaluate trait-to-trait genetic associations for all measured traits. Average rubber yield (RYm) showed an estimated narrow-sense heritability of 0.31, with an estimated type B correlation of 0.84, indicating low levels of genotype-by-environment interaction. The trait survival and number of latex vessel rings (RG) showed larger genotype-by-environment interaction and the lowest heritabilites. High to moderate type B correlation was found for most traits, with a value of 0.85 between diameter (or girth) and RYm; therefore, it is possible to achieve interesting rubber yield genetic gains (over 3 years of measurements) from indirect selection based on diameter at age 2.     

Both additivity and epistasis control the genetic variation for fruit quality traits in tomato

The effect of a gene involved in the variation of a quantitative trait may change due to epistatic interactions with the overall genetic background or with other genes through digenic interactions. The classical populations used to map quantitative trait loci (QTL) are poorly efficient to detect epistasis. To assess the importance of epistasis in the genetic control of fruit quality traits, we compared 13 tomato lines having the same genetic background except for one to five chromosome fragments introgressed from a distant line. Six traits were assessed: fruit soluble solid content, sugar content and titratable acidity, fruit weight, locule number and fruit firmness. Except for firmness, a large part of the variation of the six traits was under additive control, but interactions between QTL leading to epistasis effects were common. In the lines cumulating several QTL regions, all the significant epistatic interactions had a sign opposite to the additive effects, suggesting less than additive epistasis. Finally the re-examination of the segregating population initially used to map the QTL confirmed the extent of epistasis, which frequently involved a region where main effect QTL have been detected in this progeny or in other studies.     

A new approach to the study of genetic variability of complex characters

A new approach to multivariate genetic analysis of complex organismal traits is developed. It is based on examination of the distribution of parental strains and the F1 and F2 hybrids in a multidimensional space, and the determination of the directions corresponding to heterozygosity, epistatic and additive gene effects. The effect of heterozygosity includes variability produced by interaction between and within heterozygous loci. The additive gene effects and the remaining epistatic interactions between the homozygous loci can be visualized separately from the effects of heterozygosity by an appropriate projection of the points in multidimensional space. In all, 20 morphological, physiological and behavioural characters and 21 craniometric measures were studied in crosses between two laboratory rat strains. Linear combinations of craniometric and of morphophysiological characters with a high narrow-sense heritability could be identified. These combinations characterized the organismal stress response, which had been selected for in one of the strains. The prospects for the practical application of the new approach and also for the evaluation of the contribution of the genetic diversity to phenotypic variability in animals in natural populations are discussed.     

Epistasis Is a Major Determinant of the Additive Genetic Variance in Mimulus guttatus

The influence of genetic interactions (epistasis) on the genetic variance of quantitative traits is a major unresolved problem relevant to medical, agricultural, and evolutionary genetics. The additive genetic component is typically a high proportion of the total genetic variance in quantitative traits, despite that underlying genes must interact to determine phenotype. This study estimates direct and interaction effects for 11 pairs of Quantitative Trait Loci (QTLs) affecting floral traits within a single population of Mimulus guttatus. With estimates of all 9 genotypes for each QTL pair, we are able to map from QTL effects to variance components as a function of population allele frequencies, and thus predict changes in variance components as allele frequencies change. This mapping requires an analytical framework that properly accounts for bias introduced by estimation errors. We find that even with abundant interactions between QTLs, most of the genetic variance is likely to be additive. However, the strong dependency of allelic average effects on genetic background implies that epistasis is a major determinant of the additive genetic variance, and thus, the population’s ability to respond to selection.     

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.     

Quantitative Genetics of DROSOPHILA MELANOGASTER. I. Sexual Dimorphism in Genetic Parameters for Wing Traits

Sexual dimorphism in genetic parameters is examined for wing dimensions of Drosophila melanogaster. Data are fit to a quantitative genetic model where phenotypic variance is a linear function of additive genetic autosomal variance (common to both sexes), additive genetic X-linked variances distinct for each sex, variance due to common rearing environment of families, residual environmental variance, random error variance due to replication, and variance due to measurement error and developmental asymmetry (left vs. right sides). Polygenic dosage compensation and its effect on genetic variances and covariances between sexes is discussed. Variance estimates for wing length and other wing dimensions highly correlated with length support the hypothesis that the Drosophila system of dosage compensation will cause male X-linked genetic variance to be substantially larger than female X-linked variance. Results for various wing dimensions differ, suggesting that the level of dosage compensation may differ for different traits. Genetic correlations between sexes for the same trait are presented. Total additive genetic correlations are near unity for most wing traits; this indicates that selection in the same direction in both sexes would have a minor effect on changing the magnitude of difference between sexes. Additive X-linked correlations suggest some genotype x sex interactions for X-linked effects.     

Inferring the trajectory of genetic variance in the course of artificial selection

A method is proposed to infer genetic parameters within a cohort, using data from all individuals in an experiment. An application is the study of changes in additive genetic variance over generations, employing data from all generations. Inferences about the genetic variance in a given generation are based on its marginal posterior distribution, estimated via Markov chain Monte Carlo methods. As defined, the additive genetic variance within the group is directly related to the amount of selection response to be expected if parents are chosen within the group. Results from a simulated selection experiment are used to illustrate properties of the method. Four sets of data are analysed: directional selection with and without environmental trend, and random selection, with and without environmental trend. In all cases, posterior credibility intervals of size 95% assign relatively high density to values of the additive genetic variance and heritability in the neighbourhood of the true values. Properties and generalizations of the method are discussed.     

Evolution of tolerance: the genetic basis of a host's resistance against parasite manipulation

Despite considerable theoretical advances in the evolutionary biology of host–parasite systems, our knowledge of host–parasite coevolution in natural systems is often limited. Among the reasons for the lag of experimental insight behind theory is that the parasite's virulence is not a simple trait that is controlled by the parasite's genes. Rather, virulence can be expressed in several traits due to the subtle interactions between the host and the parasite. Furthermore, the host might evolve tolerance to the parasite if there is sufficient genetic variance to reduce the detrimental effect of the parasite on these traits. We studied the traits underlying virulence and the genetic potential to evolve tolerance to infection in the host–parasite system Aedes aegypti – Brachiola algerae . We reared the mosquitoes in a half-sib design, exposed half of the individuals in each full-sib family to the parasite and measured several life history traits – juvenile mortality, age at pupation and adult size – of infected and uninfected individuals. Virulence was due in large part to a delay of the mosquito's age at pupation by about 10%. Although this imposes strong selection pressure on the mosquito to resist the parasite, all of the mosquitoes were infected, implying a lack of resistance. Furthermore, although additive genetic variance was present for other traits, we found no indication of additive genetic variation for the age at pupation, nor for the delay of pupation due to infection, implying no potential for the evolution of tolerance. Overall, the results suggest that in this host–parasite system, the host has little evolutionary control over the expression of the parasite's virulence.     

A dynamic and complex network regulates the heterosis of yield-correlated traits in rapeseed (Brassica napus L.)

Although much research has been conducted, the genetic architecture of heterosis remains ambiguous. To unravel the genetic architecture of heterosis, a reconstructed F(2) population was produced by random intercross among 202 lines of a double haploid population in rapeseed (Brassica napus L.). Both populations were planted in three environments and 15 yield-correlated traits were measured, and only seed yield and eight yield-correlated traits showed significant mid-parent heterosis, with the mean ranging from 8.7% (branch number) to 31.4% (seed yield). Hundreds of QTL and epistatic interactions were identified for the 15 yield-correlated traits, involving numerous variable loci with moderate effect, genome-wide distribution and obvious hotspots. All kinds of mode-of-inheritance of QTL (additive, A; partial-dominant, PD; full-dominant, D; over-dominant, OD) and epistatic interactions (additive × additive, AA; additive × dominant/dominant × additive, AD/DA; dominant × dominant, DD) were observed and epistasis, especially AA epistasis, seemed to be the major genetic basis of heterosis in rapeseed. Consistent with the low correlation between marker heterozygosity and mid-parent heterosis/hybrid performance, a considerable proportion of dominant and DD epistatic effects were negative, indicating heterozygosity was not always advantageous for heterosis/hybrid performance. The implications of our results on evolution and crop breeding are discussed.     

The effects of pathogen infection and mutation on life-history characters in Arabidopsis thaliana

The nature of the interaction among deleterious mutations is important to models in many areas of evolutionary biology. In addition, interactions between genetic and environmental factors may affect the predictions of such models. Individuals of unknown genotypes of Arabidopsis thaliana, ecotype Marburg, were exposed to five levels of chemical (EMS) mutagenesis and three levels of Pseudomonas syringae infection. Survival, growth and flowering characteristics of each individual were measured. The logarithm of fitness is expected to be a linear function of mutation number if mutations act independently. Furthermore, the expected number of mutations should be approximately a linear function of time of exposure to mutagen. Therefore, nonlinear effects of mutagen exposure on the logarithm of fitness characters would suggest epistasis between mutations. Similarly, if pathogen infection and mutation act independently of each other, their effects should be additive on a log scale. Statistical interactions between these factors would suggest they do not act independently; particularly, if highly mutated individuals suffer more when infected than do less mutated individuals, this suggests that pathogens and mutations act synergistically. Pseudomonas-infected individuals were shown to have an increased probability of flowering under conditions of short day length, but to ultimately produce fewer flowers than uninfected individuals. This suggests a plastic response to stress and, despite that response, an ultimately deleterious effect of infection on fitness. Leaf rosette growth was negatively and linearly related to the expected number of mutations, and the effects of mutation on different life-cycle stages appeared to be uncorrelated. No significant interactions between pathogen and mutation main effects were found. These results suggest that mutations act multiplicatively with each other and with pathogen infection in determining individual fitness.     

Foraging behaviour influences the outcome of predator–predator interactions

Abstract.  1. Interactions among predators may influence the total efficiency of a predator complex. The effect of intra- and interspecific interactions of the generalist predators Orthotylus marginalis (Heteroptera: Miridae) and Anthocoris nemorum (Heteroptera: Anthocoridae) was investigated in a laboratory experiment. Outcomes of the interactions were determined by comparing predation rates on eggs and larvae of the blue willow beetle Phratora vulgatissima of single individuals with those of two individuals of the same or different species.
2. A non-additive, antagonistic effect on predation rates due to intraspecific interactions was found between individuals of A. nemorum . No such effect was found in O. marginalis . These results are as expected as a consequence of differences in behaviour of the two predator species: A. nemorum is a much more active and mobile predator than O. marginalis .
3. Contrary to expectation, interspecific interactions between A. nemorum and O. marginalis did not affect the total predation rate.
4. An observation from the field corroborated the results obtained in the laboratory study; there was no negative relationship between the densities of the two predator species, indicating that the two species do not interact negatively in the field at their natural densities.
5. It is concluded that the additive effect of multiple predator species is of potential value in biological control.     

Nonadditive effects of group membership can lead to additive group phenotypes for anti-predator behaviour of guppies, Poecilia reticulata

Nonadditive effects of group membership are generated when individuals respond differently to the same social environment and may alter predictions about how behavioural evolution will occur. Despite this importance, the relationship between an individual's behaviour in two different social contexts and how reciprocal interactions among individuals within groups influence group behaviour are poorly understood. Guppy anti-predator behaviour can be used to explore how individuals behaviourally respond to changes in social context. Individuals from two strains were tested for response to a model predator alone and in groups to evaluate how individuals alter their behaviour in response to social context and how group phenotype relates to individual behaviour. Nonadditive effects of group membership were detected for a number of behaviours, revealing that the effect of being in a group differed among individuals. These nonadditive effects, however, yielded an additive group phenotype. That is, the average behaviour of the group was equal to the average of its parts, for all behaviours in both strains. Such an additive group phenotype may have resulted because all individuals within a group respond to the specific social environment provided by the other members of their group.     

THE COSTS AND BENEFITS OF TOLERANCE TO COMPETITION IN IPOMOEA PURPUREA,THE COMMON MORNING GLORY

Tolerance to competition has been hypothesized to reduce the negative impact of plant–plant competition on fitness. Although competitive interactions are a strong selective force, an analysis of net selection on tolerance to competition is absent in the literature. Using 55 full/half‐sibling families from 18 maternal lines in the crop weed Ipomoea purpurea, we measured fitness and putative tolerance traits when grown with and without competition in an agricultural field. We tested for the presence of genetic variation for tolerance to competition and determined if there were costs and benefits of this trait. We also assessed correlations between tolerance and potential tolerance traits. We uncovered a fitness benefit of tolerance in the presence of competition and a cost in its absence. We failed to detect evidence of additive genetic variation underlying tolerance, but did uncover the presence of a significant maternal‐line effect for tolerance, which suggests its evolutionary trajectory is not easily predicted. The cost of tolerance is likely due to later initiation of flowering of tolerant individuals in the absence of competition, whereas relative growth rate was found to positively covary with tolerance in the presence of competition, and can thus be considered a tolerance trait.     

A semiparametric response surface model for assessing drug interaction

Summary .   When multiple drugs are administered simultaneously, investigators are often interested in assessing whether the drug combinations are synergistic, additive, or antagonistic. Existing response surface models are not adequate to capture the complex patterns of drug interactions. We propose a two-component semiparametric response surface model with a parametric function to describe the additive effect of a combination dose and a nonparametric function to capture the departure from the additive effect. The nonparametric function is estimated using the technique developed in thin plate splines, and the pointwise bootstrap confidence interval for this function is constructed. The proposed semiparametric model offers an effective way of formulating the additive effect while allowing the flexibility of modeling a departure from additivity. Example and simulations are given to illustrate that the proposed model provides an excellent estimation for different patterns of interactions between two drugs.