Although epistasis is at the center of the Fisher-Wright debate, biologists not involved in the controversy are often unaware that there are actually two different formal definitions of epistasis. We compare concepts of genetic independence in the two theoretical traditions of evolutionary genetics, population genetics and quantitative genetics, and show how independence of gene action (represented by the multiplicative model of population genetics) can be different from the absence of gene interaction (represented by the linear additive model of (...) quantitative genetics). The two formulations converge with weak selection but not with strong selection or, for multiple loci, when the aggregated interaction terms are not negligible. As a result of the different formulations of gene interaction, the presence or absence of linkage disequilibrium,/D/, does not necessarily indicate the presence or absence of fitness epistasis. Indeed, linkage disequilibrium is generated in ‘additive’ models in quantitative genetics whenever two (or more) loci experience simultaneous selection. As a research strategy, it is often practical, for theoretical or experimental reasons, to minimize gene interaction by assuming independence of gene action in regard to fitness, or by assuming linear additive effects of multiple loci on a phenotype. However, minimizing the role of epistasis in theoretical investigations hinders our understanding of the origins of diversity and the evolution of complex phenotypes. (shrink)

Pleiotropy, in which one mutation causes multiple phenotypes, has traditionally been seen as a deviation from the conventional observation in which one gene affects one phenotype. Epistasis, or gene–gene interaction, has also been treated as an exception to the Mendelian one gene–one phenotype paradigm. This simplified perspective belies the pervasive complexity of biology and hinders progress toward a deeper understanding of biological systems. We assert that epistasis and pleiotropy are not isolated occurrences, but ubiquitous and inherent properties of (...) biomolecular networks. These phenomena should not be treated as exceptions, but rather as fundamental components of genetic analyses. A systems level understanding of epistasis and pleiotropy is, therefore, critical to furthering our understanding of human genetics and its contribution to common human disease. Finally, graph theory offers an intuitive and powerful set of tools with which to study the network bases of these important genetic phenomena. (shrink)

Epistasis plays an important role in the genetic architecture of common human diseases and can be viewed from two perspectives, biological and statistical, each derived from and leading to different assumptions and research strategies. Biological epistasis is the result of physical interactions among biomolecules within gene regulatory networks and biochemical pathways in an individual such that the effect of a gene on a phenotype is dependent on one or more other genes. In contrast, statistical epistasis is defined (...) as deviation from additivity in a mathematical model summarizing the relationship between multilocus genotypes and phenotypic variation in a population. The goal of this essay is to review definitions and examples of biological and statistical epistasis and to explore the relationship between the two. Specifically, we present and discuss the following two questions in the context of human health and disease. First, when does statistical evidence of epistasis in human populations imply underlying biomolecular interactions in the etiology of disease? Second, when do biomolecular interactions produce patterns of statistical epistasis in human populations?Answers to these two reciprocal questions will provide an important framework for using genetic information to improve our ability to diagnose, prevent and treat common human diseases. We propose that systems biology will provide the necessary information for addressing these questions and that model systems such as bacteria, yeast and digital organisms will be a useful place to start. BioEssays 27:637–646, 2005. © 2005 Wiley Periodicals, Inc. (shrink)

Recent studies have revealed an astonishing diversity of sex chromosomes in many vertebrate lineages, prompting questions about the mechanisms of sex chromosome turnover. While there is considerable population genetic theory about the evolutionary forces promoting sex chromosome replacement, this theory has not yet been integrated with our understanding of the molecular and developmental genetics of sex determination. Here, we review recent data to examine four questions about how the structure of gene networks influences the evolution of sex determination. We argue (...) that patterns of epistasis, arising from the structure of genetic networks, may play an important role in regulating the rates and patterns of sex chromosome replacement. (shrink)

Discussion of the cognitive division of labor has usually made very little contact with relevant materials from other disciplines, including theoretical biology, management science, and design theory. This article draws on these materials to consider some unavoidable conundrums faced by any attempt to present a particular way of dividing tasks among a labor team as the uniquely rational way of doing this, given the interdependence of the underlying evaluative standards by which the products of a system of division of labor (...) will be judged. Divisions of labor will typically cut across these interdependencies in ways which leave the outcomes of a process of labor hostage to path dependencies and suboptimalities. Some attempts to avoid these results are shown to be unsuccessful. All these difficulties are compounded by the fact that, in many cases, the division of labor has to be constructed over a ground of values that is itself being constructed simultaneously with the products which they are invoked to assess. Key Words: risk spreading • interdependency • NK fitness landscapes • complexity • epistasis • Kuhn • modularity • path dependency. (shrink)

Graphical AbstractSquamates may be an attractive group in which to study the influence of sex chromosomes on speciation rates because of the repeated evolution of heterogamety (both XY and ZW), as well as an apparently large number of taxa with environmental sex-determination.

The genomes of virtually all sexually reproducing species contain transposable elements. Although active elements generally transpose more rapidly than they are inactivated by mutation or excision, their number can be kept in check by purifying selection if its effectiveness becomes disproportionately greater as their copy number increases. In sexually reproducing species, such synergistic selection can result from ectopic crossing-over or from homologous recombination under negative epistasis. In addition, there may be controls on transposon activity that are associated with meiosis. (...) Because a sexual lineage that abandons sex must lack such mechanisms, it may be driven to extinction by the unchecked proliferation of deleterious transposons inherited from its sexual progenitor. An important component of the evolutionary advantage of sex over asex may therefore lie in the ability of sex, despite facilitating the spread of deleterious elements within interbreeding populations, also to restrain their intragenomic proliferation. BioEssays 27:76–85, 2005. © 2004 Wiley Periodicals, Inc. (shrink)

This paper gives a detailed narrative of a controversial empirical research in postwar population genetics, the analysis of the cytological polymorphisms of an Australian grasshopper, Moraba scurra. This research intertwined key technical developments in three research areas during the 1950s and 1960s: it involved Dobzhansky’s empirical research program on cytological polymorphisms, the mathematical theory of natural selection in two-locus systems, and the building of reliable estimates of natural selection in the wild. In the mid-1950s the cytologist Michael White discovered an (...) interesting case of epistasis in populations of Moraba scurra. These observations received a wide diffusion when theoretical population geneticist Richard Lewontin represented White’s data on adaptive topographies. These topographies connected the information on the genetic structure of these grasshopper populations with the formal framework of theoretical population genetics. As such, they appeared at the time as the most successful application of two-locus models of natural selection to an empirical study system. However, this connection generated paradoxical results: in the landscapes, all grasshopper populations were located on a ridge while they were expected to reach a peak. This puzzling result fueled years of research and triggered a controversy attracting contributors from Australia, the United States and the United Kingdom. While the original problem seemed, at first, purely empirical, the subsequent controversy affected the main mathematical tools used in the study of two-gene systems under natural selection. Adaptive topographies and their underlying mathematical structure, Wright’s mean fitness equations, were submitted to close scrutiny. Suspicion eventually shifted to the statistical machinery used in data analysis, reflecting the crucial role of statistical inference in applied population genetics. In the 1950s and 1960s, population geneticists were not simply in search for new generalizations about the evolutionary process and for new evidence about genetic variation: struggling against statistical artifacts, they were searching for reliable tests and descriptors to analyze their data. (shrink)

Systems involving many interacting variables are at the heart of the natural and social sciences. Causal language is pervasive in the analysis of such systems, especially when insight into their behavior is translated into policy decisions. This is exemplified by economics, but to an increasing extent also by biology, due to the advent of sophisticated tools to identify the genetic basis of many diseases. It is argued here that a regularity notion of causality can only be meaningfully defined for systems (...) with linear interactions among their variables. For the vastly more important class of nonlinear systems, no such notion is likely to exist. This thesis is developed with examples of dynamical systems taken mostly from mathematical biology. It is discussed with particular reference to the problem of causal inference in complex genetic systems, systems for which often only statistical characterizations exist. (shrink)

In this paper, we perform theoretical analysis and experiments on the Simplex Crossover (SPX), which we have proposed. Real-coded GAs are expected to be a powerful function optimization technique for real-world applications where it is often hard to formulate the objective function. However, we believe there are two problems which will make such applications difficult; 1) performance of real-coded GAs depends on the coordinate system used to express the objective function, and 2) it costs much labor to adjust parameters so (...) that the GAs always find an optimum point efficiently. The result of our theoretical analysis and experiments shows that a performance of SPX is independent of linear coordinate transformation and that SPX always optimizes various test function efficiently when theoretical value for expansion rate, which is a parameter of SPX, is applied. We also show that BLX-α is equivalent to degenerate form of SPX. Experiments show that we have something misunderstood effect of epistasis on performance degradation of real-coded GAs. (shrink)

Genetic variation in fitness is the fundamental prerequisite for adaptive evolutionary change. If there is no variation in survival and reproduction or if this variation has no genetic basis, then the composition of a population will not evolve over time. Consequently, the factors influencing genetic variation in fitness have received close attention from evolutionary biologists. One key factor is the mode of reproduction. Indeed, it has long been thought that sex enhances fitness variation and that this explains the ubiquity of (...) sexual reproduction among eukaryotes. Nevertheless, theoretical studies have demonstrated that sex need not always increase genetic variation in fitness. In particular, if fitness interactions among beneficial alleles (epistasis) are positive, sex can reduce genetic variance in fitness. Empirical data have been sorely needed to settle the issue of whether sex does enhance fitness variation. A recent flurry of studies1-4 has demonstrated that sex and recombination do dramatically increase genetic variation in fitness and consequently the rate of adaptive evolution. Interpreted in light of evolutionary theory, these studies rule out positive in these experiments epistasis as a major source of genetic associations. Further studies are needed, however, to tease apart other possible sources. BioEssays 25:533–537, 2003. © 2003 Wiley Periodicals, Inc. (shrink)

This chapter analyzes the revolutionary impact of genomic science on the study of evolution, and addresses the issues that modern evolutionary biology has either learned or needs to grapple with in the age of genomics. It suggests that transposable elements are genomic constituents which can result in novel genes or gene functions. The chapter proposes that although epigenetic changes remain compatible with the Modern Synthesis, dissecting the details could possibly result in new insights into the dynamics of the evolutionary process (...) which are not currently considered. It shows that the nature of epistasis is increasingly gaining prominence, and offers new avenues of research into the genetic architecture of evolutionary change. (shrink)

How much bacterial evolution occurs in our intestines and which factors control it are currently burning questions. The formation of new ecotypes, some of which capable of coexisting for long periods of time, is highly likely in our guts. Horizontal gene transfer driven by temperate phages that can perform lysogeny is also widespread in mammalian intestines. Yet, the roles of mutation and especially lysogeny as key drivers of gut bacterial adaptation remain poorly understood. The mammalian gut contains hundreds of bacterial (...) species, each with many strains and ecotypes, whose abundance varies along the lifetime of a host. A continuous high input of mutations and horizontal gene transfer events mediated by temperate phages drives that diversity. Future experiments to study the interaction between mutations that cause adaptation in microbiomes and lysogenic events with different costs and benefits will be key to understand the dynamic microbiomes of mammals. Also see the video abstract here: https://youtu.be/Zjqsiyb5Pk0. (shrink)

The beanbag genetics controversy can be traced from the dispute between Fisher and Wright, through Mayr''s influential promotion of the issue, to the contemporary units of selection debate. It centers on the claim that genic models of natural selection break down in the face of epistatic interactions among genes during phenotypic development. This claim is explored from both a conceptual and a quantitative point of view, and is shown to be defective on both counts.Firstly, an analysis of the controversy''s theoretical (...) origins demonstrates that this claim derives from a misinterpretation of the conceptual foundations of Fisher''s genetical theory of natural selection, and confounds his fundamentally different concepts of the average excess and average effect of a gene. Secondly, an extension of the genic approach is proposed which models the dynamics of selection among epistatically interacting complexes of many genes. Paradoxically, this preliminary, but fundamentally genic model provides quantitative support for some controversial qualitative claims regarding the evolutionary consequences of strong gene interactions made by opponents of genic selectionism, including Mayr''s theory of peripartric speciation. These findings foster hope that the proposed approach may eventually nudge the beanbag controversy out of its conceptual trenches into a more empirically oriented dialogue. (shrink)