BackgroundThe modern evolutionary synthesis leaves unresolved some of the most fundamental, long-standing questions in evolutionary biology: What is the role of sex in evolution? How does complex adaptation evolve? How can selection operate effectively on genetic interactions? More recently, the molecular biology and genomics revolutions have raised a host of critical new questions, through empirical findings that the modern synthesis fails to explain: for example, the discovery of de novo genes; the immense constructive role of transposable elements in evolution; genetic variance and biochemical activity that go far beyond what traditional natural selection can maintain; perplexing cases of molecular parallelism; and more.Presentation of the hypothesisHere I address these questions from a unified perspective, by means of a new mechanistic view of evolution that offers a novel connection between selection on the phenotype and genetic evolutionary change (while relying, like the traditional theory, on natural selection as the only source of feedback on the fit between an organism and its environment). I hypothesize that the mutation that is of relevance for the evolution of complex adaptation—while not Lamarckian, or “directed” to increase fitness—is not random, but is instead the outcome of a complex and continually evolving biological process that combines information from multiple loci into one. This allows selection on a fleeting combination of interacting alleles at different loci to have a hereditary effect according to the combination’s fitness.Testing and implications of the hypothesisThis proposed mechanism addresses the problem of how beneficial genetic interactions can evolve under selection, and also offers an intuitive explanation for the role of sex in evolution, which focuses on sex as the generator of genetic combinations. Importantly, it also implies that genetic variation that has appeared neutral through the lens of traditional theory can actually experience selection on interactions and thus has a much greater adaptive potential than previously considered. Empirical evidence for the proposed mechanism from both molecular evolution and evolution at the organismal level is discussed, and multiple predictions are offered by which it may be tested.ReviewersThis article was reviewed by Nigel Goldenfeld (nominated by Eugene V. Koonin), Jürgen Brosius and W. Ford Doolittle.

Even the most seasoned students of evolution, starting with Darwin himself, have occasionally expressed amazement that the mechanism of natural selection has produced the whole of Life as we see it around us. There is a computational way to articulate the same amazement: "What algorithm could possibly achieve all this in a mere three and a half billion years?" In this paper we propose an answer: We demonstrate that in the regime of weak selection, the standard equations of population genetics describing natural selection in the presence of sex become identical to those of a repeated game between genes played according to multiplicative weight updates (MWUA), an algorithm known in computer science to be surprisingly powerful and versatile. MWUA maximizes a tradeoff between cumulative performance and entropy, which suggests a new view on the maintenance of diversity in evolution.coordination games | learning algorithms P recisely how does selection change the composition of the gene pool from generation to generation? The field of population genetics has developed a comprehensive mathematical framework for answering this and related questions (1). Our analysis in this paper focuses particularly on the regime of weak selection, now a widely used assumption (2, 3). Weak selection assumes that the differences in fitness between genotypes are small relative to the recombination rate, and consequently, through a result due to Nagylaki et al. (4) (see also ref. 1, section II.6.2), evolution proceeds near linkage equilibrium, a regime where the probability of occurrence of a certain genotype involving various alleles is simply the product of the probabilities of each of its alleles. Based on this result, we show that evolution in the regime of weak selection can be formulated as a repeated game, where the recombining loci are the players, the alleles in those loci are the possible actions or strategies available to each player, and the expected payoff at each generation is the expected fitness of an organism across the genotypes that are present in the population. Moreover, and perhaps most importantly, we show that the equations of population genetic dynamics are mathematically equivalent to positing that each locus selects a probability distribution on alleles according to a particular rule which, in the context of the theory of algorithms, game theory, and machine learning, is known as the multiplicative weight updates algorithm (MWUA). MWUA is known in computer science as a simple but surprisingly powerful algorithm (see ref. 5 for a survey). Moreover, there is a dual view of this algorithm: each locus may be seen as selecting its new allele distribution at each generation so as to maximize a certain convex combination of (i) cumulative expected fitness and (ii) the entropy of its distribution on alleles. This connection between evolution, game theory, and algorithms seems to us rife with productive insights; for example, the dual view just mentioned sheds new light on the maintenance of diversity in evolution.Game t...

How does new genetic information arise? Traditional thinking holds that mutation happens by accident and then spreads in the population by either natural selection or random genetic drift. There have been at least two fundamental conceptual problems with imagining an alternative. First, it seemed that the only alternative is a mutation that responds “smartly” to the immediate environment; but in complex multicellulars, it is hard to imagine how this could be implemented. Second, if there were mechanisms of mutation that “knew” what genetic changes would be favored in a given environment, this would have only begged the question of how they acquired that particular knowledge to begin with. This paper offers an alternative that avoids these problems. It holds that mutational mechanisms act on information that is in the genome, based on considerations of simplicity, parsimony, elegance, etc. (which are different than fitness considerations). This simplification process, under the performance pressure exerted by selection, not only leads to the improvement of adaptations but also creates elements that have the capacity to serve in new contexts they were not originally selected for. Novelty, then, arises at the system level from emergent interactions between such elements. Thus, mechanistically driven mutation neither requires Lamarckian transmission nor closes the door on novelty, because the changes it implements interact with one another globally in surprising and beneficial ways. Finally, I argue, for example, that genes used together are fused together; that simplification leads to complexity; and that evolution and learning are conceptually linked.

The question of what role sex plays in evolution is still open despite decades of research. It has often been assumed that sex should facilitate the increase in fitness. Hence, the fact that it may break down highly favorable genetic combinations has been seen as a problem. Here, we consider an alternative approach. We define a measure that represents the ability of alleles to perform well across different combinations and, using numerical iterations within a classical population-genetic framework, show that selection in the presence of sex favors this ability in a highly robust manner. We also show that the mechanism responsible for this effect has been out of the purview of previous theory, because it operates during the evolutionary transient, and that the breaking down of favorable genetic combinations is an integral part of it. Implications of these results and more to evolutionary theory are discussed.recombination ͉ modularity ͉ fitness robustness ͉ evolvability ͉ epistasis T heories on the role of sex in evolution have often been led by the assumption that sex should facilitate the increase in population mean fitness, w (1). At the same time, it has been recognized that sex may break down highly favorable combinations of genes, which impedes the increase in fitness (2, 3). Thus, in a prominent review of sex theory, Barton and Charlesworth (4) wrote to the effect that the breaking down of highly favorable gene combinations has been one of the most obvious difficulties in understanding sex.Here, we examine the role of sex in evolution from a different angle. We develop a measure, M , which represents the genomewide ability of alleles to perform well across different combinations. Using numerical iterations within a classical population-genetic framework, we find that sex favors the increase in M in a highly robust manner. Furthermore, we expose the mechanism underlying this effect and find that it operates during the evolutionary transient, which has been studied relatively little. We also find that the breaking down of highly favorable gene combinations is an integral part of this mechanism. Therefore, if the role of sex involves selection not for the best combinations of genes, as would be registered by w , but for genes that are favorable in many different combinations, as is registered by M , then the breaking down of highly favorable combinations does not necessarily pose a problem.A precedent to our work can be found in the work of Crow and Kimura (5), who suggested briefly, based on intuition, that sex favored ''good mixers.'' However, they did not develop this intuition, and in fact considered the breaking down of highly favorable gene combinations to be a disadvantage of sex. In line with their choice of words, we call M the ''average mixability'' of alleles in the genome.Theoretical treatments normally assume that genes make separate contributions to fitness. For example, in the case of two loci, the fitness w ij of a haploid genotype consisting of allele i at the first locus and allele j at the ...

While it is known that the mutation rate varies across the genome, previous estimates were based on averaging across various numbers of positions. Here we describe a method to measure the origination rates of target mutations at target base positions and apply it to a 6-bp region in the human hemoglobin subunit beta (HBB) gene and to the identical, paralogous hemoglobin subunit delta (HBD) region in sperm cells from both African and European donors. The HBB region of interest (ROI) includes the site of the hemoglobin S (HbS) mutation, which protects against malaria, is common in Africa and has served as a classic example of adaptation by random mutation and natural selection. We found a significant correspondence between de novo mutation rates and past observations of alleles in carriers, showing that mutation rates vary substantially in a mutation-specific manner that contributes to the site frequency spectrum. We also found that the overall point mutation rate is significantly higher in Africans than in Europeans in the HBB region studied. Finally, the rate of the 20A→T mutation, called the 'HbS mutation' when it appears in HBB, is significantly higher than expected from the genome-wide average for this mutation type. Nine instances were observed in the African HBB ROI, where it is of adaptive significance, representing at least three independent originations; no instances were observed elsewhere. Further studies will be needed to examine mutation rates at the single-mutation resolution across these and other loci and organisms and to uncover the molecular mechanisms responsible.

Many behaviors have been attributed to internal conflict within the animal and human mind. However, internal conflict has not been reconciled with evolutionary principles, in that it appears maladaptive relative to a seamless decision-making process. We study this problem through a mathematical analysis of decisionmaking structures. We find that, under natural physiological limitations, an optimal decision-making system can involve ''selfish'' agents that are in conflict with one another, even though the system is designed for a single purpose. It follows that conflict can emerge within a collective even when natural selection acts on the level of the collective only.bounded rationality ͉ collective decision making ͉ computational complexity ͉ levels of selection ͉ modularity

The assumption that different genetic elements can make separate contributions to the same quantitative trait was originally made in order to reconcile biometry and Mendelism and ever since has been used in population genetics, specifically for the trait of fitness. Here we show that sex is responsible for the existence of separate genetic effects on fitness and, more generally, for the existence of a hierarchy of genetic evolutionary modules. Using the tools developed in the process, we also demonstrate that in terms of their fitness effects, separation and fusion of genes are associated with the increase and decrease of the recombination rate between them, respectively. Implications for sex and evolution theory are discussed.recombination | epistasis | additive effects | fitness | genetic architecture S ex has been called "the queen of problems in evolutionary biology" largely because its functional significance has not been determined (1). In a recent paper, a new approach to this problem was proposed: mixability theory (2). It was shown formally that sex enables selection for alleles that perform well across different genetic contexts (henceforth, "selection for mixability"). Furthermore, it was argued qualitatively that selection for mixability is responsible for the existence of separate, identifiable contributions by genes to fitness (2). Separate contributions to fitness are a defining characteristic of evolutionary modules-modules that serve different adaptive functions and that are expected to reduce evolutionary tradeoffs between adaptations (3, 4). Thus, a connection was hypothesized between sex, separate contributions to fitness, and genetic modularity (2, 5), the last of which has become widely appreciated for its importance to evolution as a result of the genomic era (3, 6).In this article, two major limitations of mixability theory are overcome. First, although mixability theory has so far considered only the gene as a potential evolutionary module (2), the study of genetic modularity is concerned largely with the existence of sets of closely interacting (but not necessarily linked) genes, with weak interactions between these sets (3, 6). Here, we show that sex causes the existence of evolutionary modules consisting of such sets of genes. In addition, we show that the modularity characteristics of strong interactions within sets, weak interactions between sets, and multiple use of lower-level modules in higher-level modules (3, 6) arise together in evolutionary modules directly from the interaction of sex and natural selection.Second, the argument that sex causes separate genetic effects on fitness (2) followed qualitatively from the results of mixability theory and, due to its importance, warrants a rigorous demonstration. Here, such a demonstration is provided.The implications of the argument on separate effects relate to the foundations of evolutionary theory. For evolution to have occurred by small, cumulative steps, Darwin proposed that natural selection acted on continuous variation. But as...

We study the population genetics of Evolution in the important special case of weak selection, in which all fitness values are assumed to be close to one another. We show that in this regime natural selection is tantamount to the multiplicative updates game dynamics in a coordination game between genes. Importantly, the utility maximized in this game, as well as the amount by which each allele is boosted, is precisely the allele's mixability, or average fitness, a quantity recently proposed in [12] as a novel concept that is crucial in understanding natural selection under sex, thus providing a rigorous demonstration of that insight. We also prove that the equilibria in two-person coordination games can have large supports, and thus genetic diversity does not suffer much at equilibrium. Establishing large supports involves answering through a novel technique the following question: what is the probability that for a random square matrix A both systems Ax = 1 and A T y = 1 have positive solutions? Both the question and the technique may be of broader interest.