Epistasis-Induced Evolutionary Plateaus in Selection Responses.

Understanding and predicting evolution is a central challenge in both population and quantitative genetics. The amount of genetic variance for quantitative traits available in a population conditions the particular way in which this population will (or will not) evolve under natural or artificial selection. Here, we explore the potential of gene-gene interactions (epistasis) to induce evolutionary plateaus at which evolutionary change virtually collapses for a number of generations, followed by the release of previously cryptic genetic variation. First, we demonstrate theoretically that a wide range of epistatic interactions has the potential to generate temporary decelerations in the course of response to selection. Second, we perform simulations to show that such microevolutionary plateaus may occur in selection responses under empirically based assumptions. Finally, we show that such events can be traced in artificial selection experiments, thus providing further empirical evidence for this phenomenon.

Dissection of cell cycle-dependent dynamics of Dnmt1 by FRAP and diffusion-coupled modeling.

DNA methyltransferase 1 (Dnmt1) reestablishes methylation of hemimethylated CpG sites generated during DNA replication in mammalian cells. Two subdomains, the proliferating cell nuclear antigen (PCNA)-binding domain (PBD) and the targeting sequence (TS) domain, target Dnmt1 to the replication sites in S phase. We aimed to dissect the details of the cell cycle-dependent coordinated activity of both domains. To that end, we combined super-resolution 3D-structured illumination microscopy and fluorescence recovery after photobleaching (FRAP) experiments of GFP-Dnmt1 wild type and mutant constructs in somatic mouse cells. To interpret the differences in FRAP kinetics, we refined existing data analysis and modeling approaches to (i) account for the heterogeneous and variable distribution of Dnmt1-binding sites in different cell cycle stages; (ii) allow diffusion-coupled dynamics; (iii) accommodate multiple binding classes. We find that transient PBD-dependent interaction directly at replication sites is the predominant specific interaction in early S phase (residence time Tres ≤ 10 s). In late S phase, this binding class is taken over by a substantially stronger (Tres ∼22 s) TS domain-dependent interaction at PCNA-enriched replication sites and at nearby pericentromeric heterochromatin subregions. We propose a two-loading-platform-model of additional PCNA-independent loading at postreplicative, heterochromatic Dnmt1 target sites to ensure faithful maintenance of densely methylated genomic regions.

Corrigendum: Gene-environment interaction in the era of precision medicine-filling the potholes rather than starting to build a new road.

[This corrects the article DOI: 10.3389/fgene.2020.00921.].

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.

Identification of X-linked quantitative trait loci affecting cold tolerance in Drosophila melanogaster and fine mapping by selective sweep analysis.

Drosophila melanogaster is a cosmopolitan species that colonizes a great variety of environments. One trait that shows abundant evidence for naturally segregating genetic variance in different populations of D. melanogaster is cold tolerance. Previous work has found quantitative trait loci (QTL) exclusively on the second and the third chromosomes. To gain insight into the genetic architecture of cold tolerance on the X chromosome and to compare the results with our analyses of selective sweeps, a mapping population was derived from a cross between substitution lines that solely differed in the origin of their X chromosome: one originates from a European inbred line and the other one from an African inbred line. We found a total of six QTL for cold tolerance factors on the X chromosome of D. melanogaster. Although the composite interval mapping revealed slightly different QTL profiles between sexes, a coherent model suggests that most QTL overlapped between sexes, and each explained around 5-14% of the genetic variance (which may be slightly overestimated). The allelic effects were largely additive, but we also detected two significant interactions. Taken together, this provides evidence for multiple QTL that are spread along the entire X chromosome and whose effects range from low to intermediate. One detected transgressive QTL influences cold tolerance in different ways for the two sexes. While females benefit from the European allele increasing their cold tolerance, males tend to do better with the African allele. Finally, using selective sweep mapping, the candidate gene CG16700 for cold tolerance colocalizing with a QTL was identified.

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.

How to perform meaningful estimates of genetic effects.

Although the genotype-phenotype map plays a central role both in Quantitative and Evolutionary Genetics, the formalization of a completely general and satisfactory model of genetic effects, particularly accounting for epistasis, remains a theoretical challenge. Here, we use a two-locus genetic system in simulated populations with epistasis to show the convenience of using a recently developed model, NOIA, to perform estimates of genetic effects and the decomposition of the genetic variance that are orthogonal even under deviations from the Hardy-Weinberg proportions. We develop the theory for how to use this model in interval mapping of quantitative trait loci using Halley-Knott regressions, and we analyze a real data set to illustrate the advantage of using this approach in practice. In this example, we show that departures from the Hardy-Weinberg proportions that are expected by sampling alone substantially alter the orthogonal estimates of genetic effects when other statistical models, like F2 or G2A, are used instead of NOIA. Finally, for the first time from real data, we provide estimates of functional genetic effects as sets of effects of natural allele substitutions in a particular genotype, which enriches the debate on the interpretation of genetic effects as implemented both in functional and in statistical models. We also discuss further implementations leading to a completely general genotype-phenotype map.

Gene-Environment Interaction in the Era of Precision Medicine - Filling the Potholes Rather Than Starting to Build a New Road.

Gene-environment interaction is a key part of evolutionary biology, animal, and plant breeding, and a number of health sciences, like epidemiology and precision medicine. However, bottlenecks in models of gene-environment interaction have recently been made manifest, particularly in the field of medicine and, consequently, specific improvements have been explicitly requested-namely, an implementation of gene-environment interaction satisfactorily disentangled from gene-environment correlation. The present paper meets those demands by providing mathematical developments that implement classical models of genetic effects and bring them up to date with the prospects current available data bestow. These developments are shown to overcome the limitations of previous proposals through the analysis of illustrative examples on disease susceptibility, with special attention paid to precision medicine. Indeed, a number of misconceptions about the application of models of genetic/environmental effects to precision medicine are here identified and clarified. The theory here provided is argued to strengthen, in particular, the methodology required for high-precision characterization of strain virulence in the study of the COVID-19 pandemic.

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.

Effects of epistasis and the evolution of genetic architecture: exact results for a 2-locus model.

We study a two-locus model of a quantitative trait with a continuum-of alleles and multilinear epistasis that evolves under mutation, selection, and genetic drift. We derive analytical results based on the so-called House of Gauss approximation for the genetic variance, the mean phenotype, and the mutational variance in the balance of the evolutionary forces. The analytical work is complemented by extensive individual-based computer simulations. We find that (1) analytical results are accurate in a large parameter space; (2) epistasis always reduces the equilibrium genetic variance, as predicted in earlier studies that exclude drift; (3) large-scale stochastic fluctuations and non-equilibrium phenomena like adaptive inertia can strongly influence the evolution of the genetic architecture of the trait.

Orthogonal Decomposition of the Genetic Variance for Epistatic Traits Under Linkage Disequilibrium-Applications to the Analysis of Bateson-Dobzhansky-Müller Incompatibilities and Sign Epistasis.

The one-century-old theory of orthogonal genetic variance decomposition originated the field of quantitative genetics and has kept on being improved ever since. Recently, serious concerns about the possibility of attaining a satisfactory implementation of genetic variance decomposition with linkage disequilibrium (LD) and epistasis have been raised. In this paper we dissipate such doubts by completing the classical theory of variance decomposition into additive, dominance and epistasis components with LD. We apply that theory to the analysis of the genotype-to-phenotype maps of two cases of particular evolutionary interest-Bateson-Dobzhansky-Müller incompatibilities and sign epistasis. For the first case we show how negative LD and reduction of heterozygotes may contribute to maintain genetic variability after secondary contact. For the second case we show that LD transforms the set of frequencies leading to an evolutionary plateau into a ridge. Our theoretical developments reassuringly reflect the complexity LD conveys to genetic systems throughout novel properties-as compared with systems under linkage equilibrium. We argue that such particularities might have actually contributed to cause confusion about the feasibility of developing this methodology. In any case, the theory we provide in this paper enables new perspectives in both evolutionary and quantitative genetics studies.

A unified model for functional and statistical epistasis and its application in quantitative trait Loci analysis.

Interaction between genes, or epistasis, is found to be common and it is a key concept for understanding adaptation and evolution of natural populations, response to selection in breeding programs, and determination of complex disease. Currently, two independent classes of models are used to study epistasis. Statistical models focus on maintaining desired statistical properties for detection and estimation of genetic effects and for the decomposition of genetic variance using average effects of allele substitutions in populations as parameters. Functional models focus on the evolutionary consequences of the attributes of the genotype-phenotype map using natural effects of allele substitutions as parameters. Here we provide a new, general and unified model framework: the natural and orthogonal interactions (NOIA) model. NOIA implements tools for transforming genetic effects measured in one population to the ones of other populations (e.g., between two experimental designs for QTL) and parameters of statistical and functional epistasis into each other (thus enabling us to obtain functional estimates of QTL), as demonstrated numerically. We develop graphical interpretations of functional and statistical models as regressions of the genotypic values on the gene content, which illustrates the difference between the models--the constraint on the slope of the functional regression--and when the models are equivalent. Furthermore, we use our theoretical foundations to conceptually clarify functional and statistical epistasis, discuss the advantages of NOIA over previous theory, and stress the importance of linking functional and statistical models.

Evolution of genetic architecture under directional selection.

We investigate the multilinear epistatic model under mutation-limited directional selection. We confirm previous results that only directional epistasis, in which genes on average reinforce or diminish each other's effects, contribute to the initial evolution of mutational effects. Thus, either canalization or decanalization can occur under directional selection, depending on whether positive or negative epistasis is prevalent. We then focus on the evolution of the epistatic coefficients themselves. In the absence of higher-order epistasis, positive pairwise epistasis will tend to weaken relative to additive effects, while negative pairwise epistasis will tend to become strengthened. Positive third-order epistasis will counteract these effects, while negative third-order epistasis will reinforce them. More generally, gene interactions of all orders have an inherent tendency for negative changes under directional selection, which can only be modified by higher-order directional epistasis. We identify three types of nonadditive quasi-equilibrium architectures that, although not strictly stable, can be maintained for an extended time: (1) nondirectional epistatic architectures; (2) canalized architectures with strong epistasis; and (3) near-additive architectures in which additive effects keep increasing relative to epistasis.

Models of general frequency-dependent selection and mating-interaction effects and the analysis of selection patterns in Drosophila inversion polymorphisms.

We investigate mechanisms of balancing selection by extending two deterministic models of selection in a one-locus two-allele genetic system to allow for frequency-dependent fitnesses. Specifically we extend models of constant selection to allow for general frequency-dependent fitness functions for sex-dependent viabilities and multiplicative fertilities, while non-multiplicative mating-dependent components remain constant. We compute protected polymorphism conditions that take the form of harmonic means involving both the frequency- and the mating-dependent parameters. This allows for a direct comparison of the equilibrium properties of the frequency-dependent models with those of the constant models and for an analysis of equilibrium of the general model of constant fertility. We then apply the theory to analyze the maintenance of inversion polymorphisms in Drosophila subobscura and D. pseudoobscura, for which data on empirical fitness component estimates are available in the literature. Regression on fitness estimates obtained at different starting frequencies enables us to implement explicit fitness functions in the models and therefore to perform complete studies of equilibrium and stability for particular sets of data. The results point to frequency dependence of fitness components as the main mechanism responsible for the maintenance of the inversion polymorphisms considered, particularly in relation to heterosis, although we also discuss the contribution of other selection mechanisms.

On the partitioning of genetic variance with epistasis.

The decomposition of genetic variance into additive, dominance, and epistatic components is a common procedure in quantitative genetics. Yet, the interpretation of this variance partition is not trivial, especially concerning nonadditive components. In this chapter, we compile various uses of variance partitioning from published analyses, new simulations, and theoretical examples. We show ways in which advanced genetic modeling facilitates the analysis of data through variance partitioning, focusing on the natural and orthogonal interactions (NOIA) model. We also discuss how epistasis and epistatic variance may influence the outcome of selection, a topic that is still a matter of debate among quantitative and evolutionary geneticists.

Corrigendum for "Dissecting genetic effects with imprinting".

[This corrects the article DOI: 10.3389/fevo.2014.00051.][This corrects the article on p. 198 in vol. 5, PMID: 25071828.].

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.

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.

Within-niche constant selection of Drosophila inversions?

Extensive and fruitful work is being devoted for more than 70 years to elucidate the fine points of the maintenance of inversion polymorphisms of the genus Drosophila. Recent studies have resumed selection in heterogeneous environments (or niches) as a major underlying mechanism for these balanced polymorphisms. In those studies, constant selection within niches is assumed throughout although this assumption is since long known not to hold. In the present communication it is sustained that the results in those studies are robust in the face of this fact. To that end, this communication deals with a particular long-lasting question within this topic-whether the minimal model of constant viability selection (MCV, assuming frequency-, sex-, and stage-independent adaptive values) suffices to reproduce the trajectories of frequencies of Drosophila chromosomal arrangements observed in experimental populations along generations under homogeneous environments. Fitness estimates are here obtained from published trajectories of frequencies using a maximum likelihood approach, and relevant literature is revised in the light of these new analyses, pointing to an affirmative answer to that question.

Clarifying the Relationship between Average Excesses and Average Effects of Allele Substitutions.

Fisher's concepts of average effects and average excesses are at the core of the quantitative genetics theory. Their meaning and relationship have regularly been discussed and clarified. Here we develop a generalized set of one locus two-allele orthogonal contrasts for average excesses and average effects, based on the concept of the effective gene content of alleles. Our developments help understand the average excesses of alleles for the biallelic case. We dissect how average excesses relate to the average effects and to the decomposition of the genetic variance.