Multidimensional Epistasis and the Advantage of Sex

Kondrashov and Kondrashov (2001) suggest that there is usually a disadvantage for sex in systems with multidimensional epistasis. They define systems of 'unidimensional epistasis' to be those where the fitness of a genotype is a function of the number of mutations it carries, and in contrast describe a system where the fitness of a genotype is a function of the numbers of mutations in two (or more) disjoint subsets of loci creating 'multidimensional epistasis'. In an example landscape an asexual population evolves fit genotypes about twice as fast as a sexual one. Here we examine other landscapes with multidimensional epistasis and find cases where an asexual population evolves fit genotypes 20 and 180 times slower than a sexual population

Multidimensional epistasis and the transitory advantage of sex

Identifying and quantifying the benefits of sex and recombination is a long standing problem in evolutionary theory. In particular, contradictory claims have been made about the existence of a benefit of recombination on high dimensional fitness landscapes in the presence of sign epistasis. Here we present a comparative numerical study of sexual and asexual evolutionary dynamics of haploids on tunably rugged model landscapes under strong selection, paying special attention to the temporal development of the evolutionary advantage of recombination and the link between population diversity and the rate of adaptation. We show that the adaptive advantage of recombination on static rugged landscapes is strictly transitory. At early times, an advantage of recombination arises through the possibility to combine individually occurring beneficial mutations, but this effect is reversed at longer times by the much more efficient trapping of recombining populations at local fitness peaks. These findings are explained by means of well established results for a setup with only two loci. In accordance with the Red Queen hypothesis the transitory advantage can be prolonged indefinitely in fluctuating environments, and it is maximal when the environment fluctuates on the same time scale on which trapping at local optima typically occurs.Comment: 34 pages, 9 figures and 8 supplementary figures; revised and final versio

Exploring the effect of sex on empirical fitness landscapes

The nature of epistasis has important consequences for the evolutionary significance of sex and recombination. Recent efforts to find negative epistasis as a source of negative linkage disequilibrium and associated long-term advantage to sex have yielded little support. Sign epistasis, where the sign of the fitness effects of alleles varies across genetic backgrounds, is responsible for the ruggedness of the fitness landscape, with several unexplored implications for the evolution of sex. Here, we describe fitness landscapes for two sets of strains of the asexual fungus Aspergillus niger involving all combinations of five mutations. We find that 30% of the single-mutation fitness effects are positive despite their negative effect in the wild-type strain and that several local fitness maxima and minima are present. We then compare adaptation of sexual and asexual populations on these empirical fitness landscapes by using simulations. The results show a general disadvantage of sex on these rugged landscapes, caused by the breakdown by recombination of genotypes on fitness peaks. Sex facilitates movement to the global peak only for some parameter values on one landscape, indicating its dependence on the landscape’s topography. We discuss possible reasons for the discrepancy between our results and the reports of faster adaptation of sexual population

Predicting the Evolution of Sex on Complex Fitness Landscapes

Most population genetic theories on the evolution of sex or recombination are based on fairly restrictive assumptions about the nature of the underlying fitness landscapes. Here we use computer simulations to study the evolution of sex on fitness landscapes with different degrees of complexity and epistasis. We evaluate predictors of the evolution of sex, which are derived from the conditions established in the population genetic literature for the evolution of sex on simpler fitness landscapes. These predictors are based on quantities such as the variance of Hamming distance, mean fitness, additive genetic variance, and epistasis. We show that for complex fitness landscapes all the predictors generally perform poorly. Interestingly, while the simplest predictor, ΔVarHD, also suffers from a lack of accuracy, it turns out to be the most robust across different types of fitness landscapes. ΔVarHD is based on the change in Hamming distance variance induced by recombination and thus does not require individual fitness measurements. The presence of loci that are not under selection can, however, severely diminish predictor accuracy. Our study thus highlights the difficulty of establishing reliable criteria for the evolution of sex on complex fitness landscapes and illustrates the challenge for both theoretical and experimental research on the origin and maintenance of sexual reproduction

The causes of epistasis

[EN] Since Bateson's discovery that genes can suppress the phenotypic effects of other genes, gene interactions-called epistasis-have been the topic of a vast research effort. Systems and developmental biologists study epistasis to understand the genotype-phenotype map, whereas evolutionary biologists recognize the fundamental importance of epistasis for evolution. Depending on its form, epistasis may lead to divergence and speciation, provide evolutionary benefits to sex and affect the robustness and evolvability of organisms. That epistasis can itself be shaped by evolution has only recently been realized. Here, we review the empirical pattern of epistasis, and some of the factors that may affect the form and extent of epistasis. Based on their divergent consequences, we distinguish between interactions with or without mean effect, and those affecting the magnitude of fitness effects or their sign. Empirical work has begun to quantify epistasis in multiple dimensions in the context of metabolic and fitness landscape models. We discuss possible proximate causes (such as protein function and metabolic networks) and ultimate factors (including mutation, recombination, and the importance of natural selection and genetic drift). We conclude that, in general, pleiotropy is an important prerequisite for epistasis, and that epistasis may evolve as an adaptive or intrinsic consequence of changes in genetic robustness and evolvability.We thank Fons Debets, Ryszard Korona, Alexey Kondrashov, Joachim Krug, Sijmen Schoustra and an anonymous reviewer for constructive comments, and funds from the European Union Seventh Framework Programme (FP7/2007-2013) under grant agreement 225167 (eFLUX), a visitor grant from Research School Production Ecology and Resource Conservation for S.F.E., and NSF grant DEB-0844355 for T.F.C.De Visser, JAGM.; Cooper, TF.; Elena Fito, SF. (2011). 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The contribution of statistical physics to evolutionary biology

Evolutionary biology shares many concepts with statistical physics: both deal with populations, whether of molecules or organisms, and both seek to simplify evolution in very many dimensions. Often, methodologies have undergone parallel and independent development, as with stochastic methods in population genetics. We discuss aspects of population genetics that have embraced methods from physics: amongst others, non-equilibrium statistical mechanics, travelling waves, and Monte-Carlo methods have been used to study polygenic evolution, rates of adaptation, and range expansions. These applications indicate that evolutionary biology can further benefit from interactions with other areas of statistical physics, for example, by following the distribution of paths taken by a population through time.Comment: 18 pages, 3 figures, glossary. Accepted in Trend in Ecology and Evolution (to appear in print in August 2011

Emergenesis: Genetic traits that may not run in familes.

Traits that are influenced by a configuration--rather than by a simple sum-- of polymorphic genes may not be seen to be genetic unless one studies monozygotic twins (who share all their genes and thus all gene configurations) because such “emergenic” traits will tend not to run in families. Personal idiosyncrasies that have been found to be surprisingly concordant among MZ twins separated in infancy and reared apart may be emergenic traits. More speculatively, important human traits like leadership, genius in its many manfestations, being an eflective therapist or parent, as well as certain psychopathological syndromes, may also be emergenic. These ideas re-emphasize the importance of the role played in human aflairs by genetic variation

Addressing Issues in the Detection of Gene-Environment Interaction Through the Study of Conduct Disorder

This work addresses issues in the study of gene-environment interaction (GxE) through research of conduct disorder (CD) among adolescents and extends the recent report of significant GxE and subsequent replication studies. A sub-sample of 1,299 individual participants/649 twin pairs and their parents from the Virginia Twin Study of Adolescent and Behavioral Development was used for whom Monoamine Oxidase A (MAOA) genotype, diagnosis of CD, maternal antisocial personality symptoms, and household neglect were obtained. This dissertation (1) tested for GxE by gender using MAOA and childhood adversity using multiple approaches to CD measurement and model assessment, (2) determined whether other mechanisms would explain differences in GxE by gender and (3) identified and assessed other genes and environments related to the interaction MAOA and childhood adversity. Using a multiple regression approach, a main effect of the low/low MAOA genotype remained after controlling other risk factors in females. However, the effects of GxE were modest and were removed by transforming the environmental measures. In contrast, there was no significant effect of the low activity MAOA allele in males although significant GxE was detected and remained after transformation. The sign of the interaction for males was opposite from females, indicating genetic sensitivity to childhood adversity may differ by gender. Upon further investigation, gender differences in GxE were due to genotype-sex interaction and may involve MAOA. A Markov Chain Monte Carlo approach including a genetic Item Response Theory modeled CD as a trait with continuous liability, since false detection of GxE may result from measurement. In males and females, the inclusion of GxE while controlling for the other covariates was appropriate, but was little improvement in model fit and effect sizes of GxE were small. Other candidate genes functioning in the serotonin and dopamine neurotransmitter systems were tested for interaction with MAOA to affect risk for CD. Main genetic effects of dopamine transporter genotype and MAOA in the presence of comorbidity were detected. No epistatic effects were detected. The use of random forests systematically assessed the environment and produced several interesting environments that will require more thoughtful consideration before incorporation into a model testing GxE

Universality classes of interaction structures for NK fitness landscapes

Kauffman's NK-model is a paradigmatic example of a class of stochastic models of genotypic fitness landscapes that aim to capture generic features of epistatic interactions in multilocus systems. Genotypes are represented as sequences of $L$ binary loci. The fitness assigned to a genotype is a sum of contributions, each of which is a random function defined on a subset of $k \le L$ loci. These subsets or neighborhoods determine the genetic interactions of the model. Whereas earlier work on the NK model suggested that most of its properties are robust with regard to the choice of neighborhoods, recent work has revealed an important and sometimes counter-intuitive influence of the interaction structure on the properties of NK fitness landscapes. Here we review these developments and present new results concerning the number of local fitness maxima and the statistics of selectively accessible (that is, fitness-monotonic) mutational pathways. In particular, we develop a unified framework for computing the exponential growth rate of the expected number of local fitness maxima as a function of $L$, and identify two different universality classes of interaction structures that display different asymptotics of this quantity for large $k$. Moreover, we show that the probability that the fitness landscape can be traversed along an accessible path decreases exponentially in $L$ for a large class of interaction structures that we characterize as locally bounded. Finally, we discuss the impact of the NK interaction structures on the dynamics of evolution using adaptive walk models.Comment: 61 pages, 9 figure