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.     

Pleiotropy, epistasis and new QTL: the genetic architecture of honey bee foraging behavior

The regulation of division of labor in social insects, particularly in the honey bee (Apis mellifera L.), has received considerable attention from a number of biological subdisciplines, including quantitative and behavioral genetics, because of the high complexity of the behavioral traits involved. The foraging choices of honey bee workers can be accurately quantified, and previous studies have made the foraging behavior of honey bees one of the best studied naturally occurring behavioral phenotypes. Three quantitative trait loci (QTL) have been identified that influence a set of foraging variables, including the concentration of nectar collected and the amount of pollen and nectar brought back to the hive. This study extends previous genetic investigations and represents the most comprehensive investigation of the genetic architecture of these foraging variables. We examined the effects of markers for the three established QTL and for one further candidate gene (Amfor), in two reciprocal backcross populations. These populations were also used to carry out two new QTL mapping studies, with over 400 Amplified Fragment Length Polymorphism (AFLP) markers in each. We detected a variety of effects of the genetic markers for the established QTL and the candidate gene, which were mostly epistatic in nature. A few new QTL could be detected with a variety of mapping techniques. Our results add complexity to the genetic architecture of the foraging behavior of the honey bee. Specifically, we support the hypotheses that pln1, pln2, pln3, and Amfor are involved in the regulation of foraging behavior in the honey bee and add some new factors that deserve further study in the future.     

Modeling epistasis of quantitative trait loci using Cockerham's model

We use the orthogonal contrast scales proposed by Cockerham to construct a genetic model, called Cockerham's model, for studying epistasis between genes. The properties of Cockerham's model in modeling and mapping epistatic genes under linkage equilibrium and disequilibrium are investigated and discussed. Because of its orthogonal property, Cockerham's model has several advantages in partitioning genetic variance into components, interpreting and estimating gene effects, and application to quantitative trait loci (QTL) mapping when compared to other models, and thus it can facilitate the study of epistasis between genes and be readily used in QTL mapping. The issues of QTL mapping with epistasis are also addressed. Real and simulated examples are used to illustrate Cockerham's model, compare different models, and map for epistatic QTL. Finally, we extend Cockerham's model to multiple loci and discuss its applications to QTL mapping.     

On the evolution of epistasis III: the haploid case with mutation

Whether interaction between genes is better represented by synergistic or antagonistic epistasis has been a focus of experimental research in bacterial population genetics. Our previous research on evolution of modifiers of epistasis in diploid systems has indicated that the strength of positive or negative epistasis should increase provided linkage disequilibrium is maintained. Here we study a modifier of epistasis in fitness between two loci in a haploid system. Epistasis is modified in the neighborhood of a mutation-selection balance. We show that when linkage in the three-locus system is tight, an increase in the frequency of a modifier allele that induces either more negative or more positive epistasis is possible. Epistasis here can be measured on either an additive or multiplicative scale.     

A genetic model for the evolution of the glycosphingolipids

The glycosphingolipids have been found in many animal tissues, but the complexity of their molecular structure varies considerably among the different phyla. Relatively simple structures have been found in invertebrate species, while the most complex have been demonstrated in brain tissue of modern fishes and amphibians. The data on the phylogenetic distribution of the glycosphingolipids has been interpreted to indicate that a significant number of gene duplications, involving many different structural genes, may have occurred during a few specific periods of vertebrate evolution. The transition from invertebrate to jawless vertebrate, the divergence of rays and skates from true sharks, the advent of modern bony fishes and the transition from aquatic to terrestrial vertebrates, each could have veen accompained by duplications of genes involved in the synthesis and degradation of glycosphingolipids. The evolutionary study of such a multi-enzyme system may be one means to detect alterations in the genome as a whole. The apparent correspondence in time of these gene duplications involved in glycosphingolipid metabolism and periods of rapid vertebrate evolution which may have been accompanied by significant increases in the amount of cellular DNA suggests that such changes may have occurred via the mechanism of tetraploidization.     

Modeling genetic architecture: a multilinear theory of gene interaction

The map from genotype to phenotype is an exceedingly complex function of central importance in biology. In this work we derive and analyze a mathematically tractable model of the genotype-phenotype map that allows for any order of gene interaction. By assuming that the alterations of the effect of a gene substitution due to changes in the genetic background can be described as a linear transformation, we show that the genotype-phenotype map is a sum of linear and multilinear terms of operationally defined "reference" effects at each locus. The "multilinear" model is used to study the effect of epistasis on quantitative genetic variation, on the response to selection, and on genetic canalization. It is shown how the model can be used to estimate the strength of "functional" epistasis from a variety of genetic experiments.     

Words as alleles: connecting language evolution with Bayesian learners to models of genetic drift

Scientists studying how languages change over time often make an analogy between biological and cultural evolution, with words or grammars behaving like traits subject to natural selection. Recent work has exploited this analogy by using models of biological evolution to explain the properties of languages and other cultural artefacts. However, the mechanisms of biological and cultural evolution are very different: biological traits are passed between generations by genes, while languages and concepts are transmitted through learning. Here we show that these different mechanisms can have the same results, demonstrating that the transmission of frequency distributions over variants of linguistic forms by Bayesian learners is equivalent to the Wright–Fisher model of genetic drift. This simple learning mechanism thus provides a justification for the use of models of genetic drift in studying language evolution. In addition to providing an explicit connection between biological and cultural evolution, this allows us to define a ‘neutral’ model that indicates how languages can change in the absence of selection at the level of linguistic variants. We demonstrate that this neutral model can account for three phenomena: the s-shaped curve of language change, the distribution of word frequencies, and the relationship between word frequencies and extinction rates.     

Transposable element-medicated evolution of sex: A population genetic model

For a population made up of individuals capable of sexual as well as asexual modes of reproduction, conditions for the spread of a transposable element are explored using a one-locus, two-haplotype model. The analysis is then extended to include the possibility that the transposable element can modulate the probability of sexual reproduction, thus casting Hickey’s (1982,Genetics 101: 519–531) suggestion in a population genetics framework. The model explicitly includes the cost of sexual reproduction, fitness disadvantage to the transposable element, probability of transposition, and the predisposition for sexual reproduction in the presence and absence of the transposable element. The model predicts several kinds of outcome, including initial frequency dependence and stable polymorphism. More importantly, it is seen that for a wide range of parameter values, the transposable element can go to fixation. Therefore it is able to convert the population from a predominantly asexual to a predominantly sexual mode of reproduction. Viewed in conjunction with recent results implicating short stretches of apparently non-coding DNA in sex determination (McCoubreyet al. 1988,Science 242: 1146–1151), the model hints at the important role this mechanism could have played in the evolution of sexuality.     

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.     

Modeling the evolution of a classic genetic switch

Background  

The regulatory network underlying the yeast galactose-use pathway has emerged as a model system for the study of regulatory network evolution. Evidence has recently been provided for adaptive evolution in this network following a whole genome duplication event. An ancestral gene encoding a bi-functional galactokinase and co-inducer protein molecule has become subfunctionalized as paralogous genes (GAL1 and GAL3) in Saccharomyces cerevisiae, with most fitness gains being attributable to changes in cis-regulatory elements. However, the quantitative functional implications of the evolutionary changes in this regulatory network remain unexplored.     

Prevalence of epistasis in the evolution of influenza A surface proteins

The surface proteins of human influenza A viruses experience positive selection to escape both human immunity and, more recently, antiviral drug treatments. In bacteria and viruses, immune-escape and drug-resistant phenotypes often appear through a combination of several mutations that have epistatic effects on pathogen fitness. However, the extent and structure of epistasis in influenza viral proteins have not been systematically investigated. Here, we develop a novel statistical method to detect positive epistasis between pairs of sites in a protein, based on the observed temporal patterns of sequence evolution. The method rests on the simple idea that a substitution at one site should rapidly follow a substitution at another site if the sites are positively epistatic. We apply this method to the surface proteins hemagglutinin and neuraminidase of influenza A virus subtypes H3N2 and H1N1. Compared to a non-epistatic null distribution, we detect substantial amounts of epistasis and determine the identities of putatively epistatic pairs of sites. In particular, using sequence data alone, our method identifies epistatic interactions between specific sites in neuraminidase that have recently been demonstrated, in vitro, to confer resistance to the drug oseltamivir; these epistatic interactions are responsible for widespread drug resistance among H1N1 viruses circulating today. This experimental validation demonstrates the predictive power of our method to identify epistatic sites of importance for viral adaptation and public health. We conclude that epistasis plays a large role in shaping the molecular evolution of influenza viruses. In particular, sites with , which would normally not be identified as positively selected, can facilitate viral adaptation through epistatic interactions with their partner sites. The knowledge of specific interactions among sites in influenza proteins may help us to predict the course of antigenic evolution and, consequently, to select more appropriate vaccines and drugs.     

A model of evolution for accumulating genetic information

By taking into account recent knowledge of multigene families and other repetitive DNA sequences, a model of evolution by gene duplication for accumulating genetic information is studied. Genetic information is defined as the sum of distinct functions that the gene family can perform. A coefficient, "genetic diversity" is defined and used in this study, that is highly correlated with genetic information. Initially, a multigene family with a few gene copies is assumed, and natural selection starts to work on this gene family to increase genetic diversity contained in the gene family. As an important mechanism, unequal crossing-over is incorporated. Together with mutation, it is responsible for supplying genetic variability among individuals for selection to work. A specific model, in which individuals with less genetic diversity are selectively disadvantageous, has been studied in detail. Through approximate theoretical analysis and extensive Monte Carlo studies, it has been shown that the system is an extremely efficient way to accumulate genetic information. For attaining one gene, the genetic load is much smaller under this model than under the traditional model of natural selection. The model may be applied to the process of origin of multigene families with diverse copy members such as those of immunoglobulin or cytochrome P450. In general, the process of creating new genes by duplication might be somewhere between the present and the traditional models.     

On the evolution of epistasis I: diploids under selection

One interpretation of recent literature on the evolution of phenotypic modularity is that evolution should act to decrease the degree of interaction between genes that contribute to different phenotypes. This issue is addressed directly here using a fitness scheme determined by two genetic loci and a third locus which modifies a measure of statistical interaction between the fitnesses due to the first two. The equilibrium structure of such an epistasis-modifying locus is studied. It is shown that under well-specified conditions a modifying allele that increases epistasis succeeds. In other words, genetic interactions tend to become stronger. It is speculated that this occurs because the mean fitness in such models is locally increasing as a function of the degree of epistasis.     

A multilocus model of the genetic architecture of autoimmune thyroid disorder, with clinical implications

We report here a preliminary model of the genetic architecture of Autoimmune Thyroid Disorder (AITD). Using a flexible class of mathematical modeling techniques, applied to an established set of data and supplemented with information both from candidate-gene and genome-wide-association studies and from basic bioinformatics, we find strong statistical support for a model in which AITD is the result of "hits" along three distinct genetic pathways: affected individuals have (1) a genetic susceptibility to clinical AITD, along with (2) a separate predisposition to develop the autoantibodies characteristic of AITD, and they also have (3) a predisposition to develop high levels of autoantibodies once they occur. Genes underlying each of these factors then appear to interact with one another to cause clinical AITD. We also find that a genetic variant in CTLA4 that increases risk for AITD in some people might actually protect against AITD in others, depending on which additional risk variants an individual carries. Our data show that the use of statistical methods for the incorporation of information from multiple sources, combined with careful modeling of distinct intermediate phenotypes, can provide insights into the genetic architecture of complex diseases. This model has several clinical implications, which we believe will prove relevant to other complex diseases as well.     

Beyond the phenotypic gambit: molecular behavioural ecology and the evolution of genetic architecture

Most studies of behaviour examine traits whose proximate causes include sensory input and neural decision-making, but conflict and collaboration in biological systems began long before brains or sensory systems evolved. Many behaviours result from non-neural mechanisms such as direct physical contact between recognition proteins or modifications of development that coincide with altered behaviour. These simple molecular mechanisms form the basis of important biological functions and can enact organismal interactions that are as subtle, strategic and interesting as any. The genetic changes that underlie divergent molecular behaviours are often targets of selection, indicating that their functional variation has important fitness consequences. These behaviours evolve by discrete units of quantifiable phenotypic effect (amino acid and regulatory mutations, often by successive mutations of the same gene), so the role of selection in shaping evolutionary change can be evaluated on the scale at which heritable phenotypic variation originates. We describe experimental strategies for finding genes that underlie biochemical and developmental alterations of behaviour, survey the existing literature highlighting cases where the simplicity of molecular behaviours has allowed insight to the evolutionary process and discuss the utility of a genetic knowledge of the sources and spectrum of phenotypic variation for a deeper understanding of how genetic and phenotypic architectures evolve.     

Two-locus epistasis with sexually antagonistic selection: a genetic Parrondo's paradox

An example is provided where, with antagonistic selection and epistatic interaction of alleles at two loci, an autosomal allele can rise in frequency, persist in the population, and even continue to fixation, despite having an apparently lower average fitness than the alternative allele, in a process similar to Parrondo's paradox.     

The evolution of genetic architecture under frequency-dependent disruptive selection

We propose a model to analyze a quantitative trait under frequency-dependent disruptive selection. Selection on the trait is a combination of stabilizing selection and intraspecific competition, where competition is maximal between individuals with equal phenotypes. In addition, there is a density-dependent component induced by population regulation. The trait is determined additively by a number of biallelic loci, which can have different effects on the trait value. In contrast to most previous models, we assume that the allelic effects at the loci can evolve due to epistatic interactions with the genetic background. Using a modifier approach, we derive analytical results under the assumption of weak selection and constant population size, and we investigate the full model by numerical simulations. We find that frequency-dependent disruptive selection favors the evolution of a highly asymmetric genetic architecture, where most of the genetic variation is concentrated on a small number of loci. We show that the evolution of genetic architecture can be understood in terms of the ecological niches created by competition. The phenotypic distribution of a population with an adapted genetic architecture closely matches this niche structure. Thus, evolution of the genetic architecture seems to be a plausible way for populations to adapt to regimes of frequency-dependent disruptive selection. As such, it should be seen as a potential evolutionary pathway to discrete polymorphisms and as a potential alternative to other evolutionary responses, such as the evolution of sexual dimorphism or assortative mating.     

A hyperspace model to decipher the genetic architecture of developmental processes: allometry meets ontogeny

To better utilize limited resources for their survival and reproduction, all organisms undergo developmental changes in both body size and shape during ontogeny. The genetic analysis of size change with increasing age, i.e., growth, has received considerable attention in quantitative developmental genetic studies, but the genetic architecture of ontogenetic changes in body shape and its associated allometry have been poorly understood partly due to the lack of analytical tools. In this article, we attempt to construct a multivariate statistical framework for studying the genetic regulation of ontogenetic growth and shape. We have integrated biologically meaningful mathematical functions of growth curves and developmental allometry into the estimation process of genetic mapping aimed at identifying individual quantitative trait loci (QTL) for phenotypic variation. This model defined with high dimensions can characterize the ontogenetic patterns of genetic effects of QTL over the lifetime of an organism and assess the interplay between genetic actions/interactions and phenotypic integration. The closed forms for the residual covariance matrix and its determinant and inverse were derived to overcome the computational complexity typical of our high-dimensional model. We used a worked example to validate the utility of this model. The implications of this model for genetic research of evo-devo are discussed.