Estimation of genetic effects and genotype-phenotype maps

Estimating directional epistasis

Epistasis, i.e., the fact that gene effects depend on the genetic background, is a direct consequence of the complexity of genetic architectures. Despite this, most of the models used in evolutionary and quantitative genetics pay scant attention to genetic interactions. For instance, the traditional decomposition of genetic effects models epistasis as noise around the evolutionarily-relevant additive effects. Such an approach is only valid if it is assumed that there is no general pattern among interactions—a highly speculative scenario. Systematic interactions generate directional epistasis, which has major evolutionary consequences. In spite of its importance, directional epistasis is rarely measured or reported by quantitative geneticists, not only because its relevance is generally ignored, but also due to the lack of simple, operational, and accessible methods for its estimation. This paper describes conceptual and statistical tools that can be used to estimate directional epistasis from various kinds of data, including QTL mapping results, phenotype measurements in mutants, and artificial selection responses. As an illustration, I measured directional epistasis from a real-life example. I then discuss the interpretation of the estimates, showing how they can be used to draw meaningful biological inferences.

MAPfastR: quantitative trait loci mapping in outbred line crosses

MAPfastR is a software package developed to analyze quantitative trait loci data from inbred and outbred line-crosses. The package includes a number of modules for fast and accurate quantitative trait loci analyses. It has been developed in the R language for fast and comprehensive analyses of large datasets. MAPfastR is freely available at: http://www.computationalgenetics.se/?page_id=7

Modelling of genetic interactions improves prediction of hybrid patterns--a case study in domestic fowl

A major challenge in complex trait genetics is to unravel how multiple loci and environmental factors together cause phenotypic diversity. Both first (F(1)) and second (F(2)) generation hybrids often display phenotypes that deviate from what is expected under intermediate inheritance. We have here studied two chicken F(2) populations generated by crossing divergent chicken lines to assess how epistatic loci, identified in earlier quantitative trait locus (QTL) studies, contribute to hybrid deviations from the mid-parent phenotype. Empirical evidence suggests that the average phenotypes of the intercross birds tend to be lower than the midpoint between the parental means in both crosses. Our results confirm that epistatic interactions, despite a relatively small contribution to the phenotypic variance, play an important role in the deviation of hybrid phenotypes from the mid-parent values (i.e. multi-locus hybrid genotypes lead to lower rather than higher body weights). To a lesser extent, dominance also appears to contribute to the mid-parent deviation, at least in one of the crosses. This observation coincides with the hypothesis that hybridization tends to break up co-adapted gene complexes, i.e. generate Bateson-Dobzhansky-Muller incompatibilities.

Monotonicity is a key feature of genotype-phenotype maps

It was recently shown that monotone gene action, i.e., order-preservation between allele content and corresponding genotypic values in the mapping from genotypes to phenotypes, is a prerequisite for achieving a predictable parent-offspring relationship across the whole allele frequency spectrum. Here we test the consequential prediction that the design principles underlying gene regulatory networks are likely to generate highly monotone genotype-phenotype maps. To this end we present two measures of the monotonicity of a genotype-phenotype map, one based on allele substitution effects, and the other based on isotonic regression. We apply these measures to genotype-phenotype maps emerging from simulations of 1881 different 3-gene regulatory networks. We confirm that in general, genotype-phenotype maps are indeed highly monotonic across network types. However, regulatory motifs involving incoherent feedforward or positive feedback, as well as pleiotropy in the mapping between genotypes and gene regulatory parameters, are clearly predisposed for generating non-monotonicity. We present analytical results confirming these deep connections between molecular regulatory architecture and monotonicity properties of the genotype-phenotype map. These connections seem to be beyond reach by the classical distinction between additive and non-additive gene action.

Current applications of models of genetic effects with interactions across the genome

Models of genetic effects integrate the action of genes, regulatory regions and interactions among alleles across the genome. Such theoretical frameworks are critical for applied studies in at least two ways. First, discovering genetic networks with specific effects underlying traits in populations requires the development of models that implement those effects as parameters-adjusting the implementation of epistasis parameters in genetic models has for instance been a requirement for properly testing for epistasis in gene-mapping studies. Second, studying the properties and implications of models of genetic effects that involve complex genetic networks has proven to be valuable, whether those networks have been revealed for particular organisms or inferred to be of interest from theoretical works and simulations. Here I review the current state of development and recent applications of models of genetic effects. I focus on general models aiming to depict complex genotype-to-phenotype maps and on applications of them to networks of interacting loci.

Multiallelic models of genetic effects and variance decomposition in non-equilibrium populations

Quantitative genetics stems from the theoretical models of genetic effects, which are re-parameterizations of the genotypic values into parameters of biological (genetic) relevance. Different formulations of genetic effects are adequate to address different subjects. We thus need to generalize and unify them under a common framework for enabling researchers to easily transform genetic effects between different biological meanings. The Natural and Orthogonal Interactions (NOIA) model of genetic effects has been developed to achieve this aim. Here, we further implement the statistical formulation of NOIA with multiple alleles under Hardy-Weinberg departures (HWD). We show that our developments are straightforwardly connected to the decomposition of the genetic variance and we point out several emergent properties of multiallelic quantitative genetic models, as compared to the biallelic ones. Further, NOIA entails a natural extension of one-locus developments to multiple epistatic loci under linkage equilibrium. Therefore, we present an extension of the orthogonal decomposition of the genetic variance to multiple epistatic, multiallelic loci under HWD. We illustrate this theory with a graphical interpretation and an analysis of published data on the human acid phosphatase (ACP1) polymorphism.

Order-preserving principles underlying genotype-phenotype maps ensure high additive proportions of genetic variance

In quantitative genetics, the degree of resemblance between parents and offspring is described in terms of the additive variance (V(A)) relative to genetic (V(G)) and phenotypic (V(P)) variance. For populations with extreme allele frequencies, high V(A)/V(G) can be explained without considering properties of the genotype-phenotype (GP) map. We show that randomly generated GP maps in populations with intermediate allele frequencies generate far lower V(A)/V(G) values than empirically observed. The main reason is that order-breaking behaviour is ubiquitous in random GP maps. Rearrangement of genotypic values to introduce order-preservation for one or more loci causes a dramatic increase in V(A)/V(G). This suggests the existence of order-preserving design principles in the regulatory machinery underlying GP maps. We illustrate this feature by showing how the ubiquitously observed monotonicity of dose-response relationships gives much higher V(A)/V(G) values than a unimodal dose-response relationship in simple gene network models.

Mapping QTLs with main and epistatic effects underlying grain yield and heading time in soft winter wheat

There is increasing awareness that epistasis plays a role for the determination of complex traits. This study employed an association mapping approach in a large panel of 455 diverse European elite soft winter wheat lines. The genotypes were evaluated in multi-environment trials and fingerprinted with SSR markers to dissect the underlying genetic architecture of grain yield and heading time. A linear mixed model was applied to assess marker-trait associations incorporating information of covariance among relatives. Our findings indicate that main effects dominate the control of grain yield in wheat. In contrast, the genetic architecture underlying heading time is controlled by main and epistatic effects. Consequently, for heading time it is important to consider epistatic effects towards an increased selection gain in marker-assisted breeding.

Epistatic effect between ACACA and FABP2 gene on abdominal fat traits in broilers

Epistasis is generally defined as the interaction between two or more genes or their mRNA or protein products to influence a single trait. Experimental evidence suggested that epistasis could be important in the determination of the genetic architecture of complex traits in domestic animals. Acetyl-coenzyme A carboxylase alpha (ACACA) and fatty acid binding protein 2 (FABP2) are both key factors of lipogenesis and transport. They may play a crucial role in the weight variability of abdominal adipose tissue in the growing chicken. In this study, the polymorphisms of c.2292G>A in ACACA and c.-561A>C in FABP2 were detected among individuals from two broiler lines which were divergently selected for abdominal fat content. Epistasis between the two SNPs on abdominal fat weight (AFW) and abdominal fat percentage (AFP) was analyzed. The additive x additive epistatic components between these two SNPs were found significant or suggestively significant on both AFW and AFP in lean lines of the 9th and 10th generation; whereas, it was not significantly associated with either AFW or AFP in fat lines. At the same time, there were not any other significant epistatic components found in both generations or in both lines. Significant epistatic effects between these two SNPs found only in the lean lines could partly be due to the fact that the abdominal fat traits in these two experimental lines have been greatly modified by strong artificial selection. The results suggested that the epistasis mode may be different between the lean and fat chicken lines. Our results could be helpful in further understanding the genetic interaction between candidate genes contributing to phenotypic variation of abdominal fat content in broilers.

A modelling framework for the analysis of artificial-selection time series

Artificial-selection experiments constitute an important source of empirical information for breeders, geneticists and evolutionary biologists. Selected characters can generally be shifted far from their initial state, sometimes beyond what is usually considered as typical inter-specific divergence. A careful analysis of the data collected during such experiments may thus reveal the dynamical properties of the genetic architecture that underlies the trait under selection. Here, we propose a statistical framework describing the dynamics of selection-response time series. We highlight how both phenomenological models (which do not make assumptions on the nature of genetic phenomena) and mechanistic models (explaining the temporal trends in terms of e.g. mutations, epistasis or canalization) can be used to understand and interpret artificial-selection data. The practical use of the models and their implementation in a software package are demonstrated through the analysis of a selection experiment on the shape of the wing in Drosophila melanogaster.

Evolution of pleiotropy: epistatic interaction pattern supports a mechanistic model underlying variation in genotype-phenotype map

The genotype-phenotype (GP) map consists of developmental and physiological mechanisms mapping genetic onto phenotypic variation. It determines the distribution of heritable phenotypic variance on which selection can act. Comparative studies of morphology as well as of gene regulatory networks show that the GP map itself evolves, yet little is known about the actual evolutionary mechanisms involved. The study of such mechanisms requires exploring the variation in GP maps at the population level, which presently is easier to quantify by statistical genetic methods rather than by regulatory network structures. We focus on the evolution of pleiotropy, a major structural aspect of the GP map. Pleiotropic genes affect multiple traits and underlie genetic covariance between traits, often causing evolutionary constraints. Previous quantitative genetic studies have demonstrated population-level variation in pleiotropy in the form of loci, at which genotypes differ in the genetic covariation between traits. This variation can potentially fuel evolution of the GP map under selection and/or drift. Here, we propose a developmental mechanism underlying population genetic variation in covariance and test its predictions. Specifically, the mechanism predicts that the loci identified as responsible for genetic variation in pleiotropy are involved in trait-specific epistatic interactions. We test this prediction for loci affecting allometric relationships between traits in an advanced intercross between inbred mouse strains. The results consistently support the prediction. We further find a high degree of sign epistasis in these interactions, which we interpret as an indication of adaptive gene complexes within the diverged parental lines.

Directionality of epistasis in a murine intercross population

Directional epistasis describes a situation in which epistasis consistently increases or decreases the effect of allele substitutions, thereby affecting the amount of additive genetic variance available for selection in a given direction. This study applies a recent parameterization of directionality of epistasis to empirical data. Data stems from a QTL mapping study on an intercross between inbred mouse (Mus musculus) strains LG/J and SM/J, originally selected for large and small body mass, respectively. Results show a negative average directionality of epistasis for body-composition traits, predicting a reduction in additive allelic effects and in the response to selection for increased size. Focusing on average modification of additive effect of single loci, we find a more complex picture, whereby the effects of some loci are enhanced consistently across backgrounds, while effects of other loci are decreased, potentially contributing to either enhancement or reduction of allelic effects when selection acts at single loci. We demonstrate and discuss how the interpretation of the overall measurement of directionality depends on the complexity of the genotype-phenotype map. The measure of directionality changes with the power of scale in a predictable way; however, its expected effect with respect to the modification of additive genetic effects remains constant.

Controlling false positives in the mapping of epistatic QTL

This study addresses the poorly explored issue of the control of false positive rate (FPR) in the mapping of pair-wise epistatic quantitative trait loci (QTL). A nested test framework was developed to (1) allow pre-identified QTL to be used directly to detect epistasis in one-dimensional genome scans, (2) to detect novel epistatic QTL pairs in two-dimensional genome scans and (3) to derive genome-wide thresholds through permutation and handle multiple testing. We used large-scale simulations to evaluate the performance of both the one- and two-dimensional approaches in mapping different forms and levels of epistasis and to generate profiles of FPR, power and accuracy to inform epistasis mapping studies. We showed that the nested test framework and genome-wide thresholds were essential to control FPR at the 5% level. The one-dimensional approach was generally more powerful than the two-dimensional approach in detecting QTL-associated epistasis and identified nearly all epistatic pairs detected from the two-dimensional approach. However, only the two-dimensional approach could detect epistatic QTL with weak main effects. Combining the two approaches allowed effective mapping of different forms of epistasis, whereas using the nested test framework kept the FPR under control. This approach provides a good search engine for high-throughput epistasis analyses.

Genetic architecture of tameness in a rat model of animal domestication

A common feature of domestic animals is tameness-i.e., they tolerate and are unafraid of human presence and handling. To gain insight into the genetic basis of tameness and aggression, we studied an intercross between two lines of rats (Rattus norvegicus) selected over >60 generations for increased tameness and increased aggression against humans, respectively. We measured 45 traits, including tameness and aggression, anxiety-related traits, organ weights, and levels of serum components in >700 rats from an intercross population. Using 201 genetic markers, we identified two significant quantitative trait loci (QTL) for tameness. These loci overlap with QTL for adrenal gland weight and for anxiety-related traits and are part of a five-locus epistatic network influencing tameness. An additional QTL influences the occurrence of white coat spots, but shows no significant effect on tameness. The loci described here are important starting points for finding the genes that cause tameness in these rats and potentially in domestic animals in general.

Dissection of the genetic architecture of body weight in chicken reveals the impact of epistasis on domestication traits

In this contribution, we study the genetic mechanisms leading to differences in the observed growth patterns of domesticated White Leghorn chickens and their wild ancestor the red jungle fowl. An epistatic QTL analysis for several body-weight measures from hatch to adulthood confirms earlier findings that polymorphisms at >15 loci contribute to body-weight determination in an F(2) intercross between these populations and that many loci are involved in complex genetic interactions. Here, we use a new genetic model to decompose the genetic effects of this multilocus epistatic genetic network. The results show how the functional modeling of genetic effects provides new insights into how genetic interactions in a large set of loci jointly contribute to phenotypic expression. By exploring the functional effects of QTL alleles, we show that some alleles can display temporal shifts in the expression of genetic effects due to their dependencies on the genetic background. Our results demonstrate that the effects of many genes are dependent on genetic interactions with other loci and how their involvement in the domestication process relies on these interactions.