A mixability theory for the role of sex in evolution

Dynamic diversity is the answer to proxy failure

We argue that a diverse and dynamic pool of agents mitigates proxy failure. Proxy modularity plays a key role in the ongoing production of diversity. We review examples from a range of scales.

Cultural niche construction with application to fertility control: A model for education and social transmission of contraceptive use

The evolution of a cultural trait may be affected by niche construction, or changes in the selective environment of that trait due to the inheritance of other cultural traits that make up a cultural background. This study investigates the evolution of a cultural trait, such as the acceptance of the idea of contraception, that is both vertically and horizontally transmitted within a homogeneous social network. Individuals may conform to the norm, and adopters of the trait have fewer progeny than others. In addition, adoption of this trait is affected by a vertically transmitted aspect of the cultural background, such as the preference for high or low levels of education. Our model shows that such cultural niche construction can facilitate the spread of traits with low Darwinian fitness while providing an environment that counteracts conformity to norms. In addition, niche construction can facilitate the 'demographic transition' by making reduced fertility socially accepted.

Problem of Domain/Building Block Preservation in the Evolution of Biological Macromolecules and Evolutionary Computation

Structurally and functionally isolated domains in biological macromolecular evolution, both natural and artificial, are largely similar to "schemata", building blocks (BBs), in evolutionary computation (EC). The problem of preserving in subsequent evolutionary searches the already found domains / BBs is well known and quite relevant in biology as well as in EC. Both biology and EC are seeing parallel and independent development of several approaches to identifying and preserving previously identified domains / BBs. First, we notice the similarity of DNA shuffling methods in synthetic biology and multi-parent recombination algorithms in EC. Furthermore, approaches to computer identification of domains in proteins that are being developed in biology can be aligned with BB identification methods in EC. Finally, approaches to chimeric protein libraries optimization in biology can be compared to evolutionary search methods based on probabilistic models in EC. We propose to validate the prospects of mutual exchange of ideas and transfer of algorithms and approaches between evolutionary systems biology and EC in these three principal directions. A crucial aim of this transfer is the design of new advanced experimental techniques capable of solving more complex problems of in vitro evolution.

Distributed algorithms from arboreal ants for the shortest path problem

Colonies of the arboreal turtle ant create networks of trails that link nests and food sources on the graph formed by branches and vines in the canopy of the tropical forest. Ants put down a volatile pheromone on the edges as they traverse them. At each vertex, the next edge to traverse is chosen using a decision rule based on the current pheromone level. There is a bidirectional flow of ants around the network. In a previous field study, it was observed that the trail networks approximately minimize the number of vertices, thus solving a variant of the popular shortest path problem without any central control and with minimal computational resources. We propose a biologically plausible model, based on a variant of the reinforced random walk on a graph, which explains this observation and suggests surprising algorithms for the shortest path problem and its variants. Through simulations and analysis, we show that when the rate of flow of ants does not change, the dynamics converges to the path with the minimum number of vertices, as observed in the field. The dynamics converges to the shortest path when the rate of flow increases with time, so the colony can solve the shortest path problem merely by increasing the flow rate. We also show that to guarantee convergence to the shortest path, bidirectional flow and a decision rule dividing the flow in proportion to the pheromone level are necessary, but convergence to approximately short paths is possible with other decision rules.

Making the most of potential: potential games and genotypic convergence

We consider genotypic convergence of populations and show that under fixed fitness asexual and haploid sexual populations attain monomorphic convergence (even under genetic linkage between loci) to basins of attraction with locally exponential convergence rates; the same convergence obtains in single locus diploid sexual reproduction but to polymorphic populations. Furthermore, we show that there is a unified theory underlying these convergences: all of them can be interpreted as instantiations of players in a potential game implementing a multiplicative weights updating algorithm to converge to equilibrium, making use of the Baum-Eagon Theorem. To analyse varying environments, we introduce the concept of 'virtual convergence', under which, even if fixation is not attained, the population nevertheless achieves the fitness growth rate it would have had under convergence to an optimal genotype. Virtual convergence is attained by asexual, haploid sexual and multi-locus diploid reproducing populations, even if environments vary arbitrarily. We also study conditions for true monomorphic convergence in asexually reproducing populations in varying environments.

From genotypes to organisms: State-of-the-art and perspectives of a cornerstone in evolutionary dynamics

Understanding how genotypes map onto phenotypes, fitness, and eventually organisms is arguably the next major missing piece in a fully predictive theory of evolution. We refer to this generally as the problem of the genotype-phenotype map. Though we are still far from achieving a complete picture of these relationships, our current understanding of simpler questions, such as the structure induced in the space of genotypes by sequences mapped to molecular structures, has revealed important facts that deeply affect the dynamical description of evolutionary processes. Empirical evidence supporting the fundamental relevance of features such as phenotypic bias is mounting as well, while the synthesis of conceptual and experimental progress leads to questioning current assumptions on the nature of evolutionary dynamics-cancer progression models or synthetic biology approaches being notable examples. This work delves with a critical and constructive attitude into our current knowledge of how genotypes map onto molecular phenotypes and organismal functions, and discusses theoretical and empirical avenues to broaden and improve this comprehension. As a final goal, this community should aim at deriving an updated picture of evolutionary processes soundly relying on the structural properties of genotype spaces, as revealed by modern techniques of molecular and functional analysis.

Asymmetric Evolvability Leads to Specialization without Trade-Offs

AbstractMany organisms are specialized, and these narrow niches are often explained with trade-offs-the inability for one organism to express maximal performance in two or more environments. However, evidence is lacking that trade-offs are sufficient to explain specialists. Several lines of theoretical inquiry suggest that populations can specialize without explicit trade-offs, as a result of relaxed selection in generalists for their performance in rare environments. Here, I synthesize and extend these approaches, showing that emergent asymmetries in evolvability can push a population toward specialization in the absence of trade-offs and in the presence of substantial ecological costs of specialism. Simulations are used to demonstrate how adaptation to a more common environment interferes with adaptation to a less common but otherwise equal alternative environment and that this interference is greatly exacerbated at low recombination rates. This adaptive process of specialization can effectively trap populations in a suboptimal niche. These modeling results predict that transient differences in evolvability across traits during a single episode of adaptation could have long-term consequences for a population's niche.

The power of randomization by sex in multilocus genetic evolution

Background

Many hypotheses have been proposed for how sexual reproduction may facilitate an increase in the population mean fitness, such as the Fisher-Muller theory, Muller’s ratchet and others. According to the recently proposed mixability theory, however, sexual recombination shifts the focus of natural selection away from favoring particular genetic combinations of high fitness towards favoring alleles that perform well across different genetic combinations. Mixability theory shows that, in finite populations, because sex essentially randomizes genetic combinations, if one allele performs better than another across the existing combinations of alleles, that allele will likely also perform better overall across a vast space of untested potential genotypes. However, this superiority has been established only for a single-locus diploid model.

Results

We show that, in both haploids and diploids, the power of randomization by sex extends to the multilocus case, and becomes substantially stronger with increasing numbers of loci. In addition, we make an explicit comparison between the sexual and asexual cases, showing that sexual recombination is the cause of the randomization effect.

Conclusions

That the randomization effect applies to the multilocus case and becomes stronger with increasing numbers of loci suggests that it holds under realistic conditions. One may expect, therefore, that in nature the ability of an allele to perform well in interaction with existing genetic combinations is indicative of how well it will perform in a far larger space of potential combinations that have not yet materialized and been tested. Randomization plays a similar role in a statistical test, where it allows one to draw an inference from the outcome of the test in a small sample about its expected outcome in a larger space of possibilities—i.e., to generalize. Our results are relevant to recent theories examining evolution as a learning process.

Reviewers

This article was reviewed by David Ardell and Brian Golding.

Cultural adaptation is maximised when intelligent individuals rarely think for themselves

Humans are remarkable in their reliance on cultural inheritance, and the ecological success this has produced. Nonetheless, we lack a thorough understanding of how the cognitive underpinnings of cultural transmission affect cultural adaptation across diverse tasks. Here, we use an agent-based simulation to investigate how different learning mechanisms (both social and asocial) interact with task structure to affect cultural adaptation. Specifically, we compared learning through refinement, recombination or both, in tasks of different difficulty, with learners of different asocial intelligence. We find that for simple tasks all learning mechanisms are roughly equivalent. However, for hard tasks, performance was maximised when populations consisted of highly intelligent individuals who nonetheless rarely innovated and instead recombined existing information. Our results thus show that cumulative cultural adaptation relies on the combination of individual intelligence and 'blind' population-level processes, although the former may be rarely used. The counterintuitive requirement that individuals be highly intelligent, but rarely use this intelligence, may help resolve the debate over the role of individual intelligence in cultural adaptation.

Primordial sex facilitates the emergence of evolution

Compartments are ubiquitous throughout biology, and they have very likely played a crucial role at the origin of life. Here we assume that a protocell, which is a compartment enclosing functional components, requires N such components in order to be evolvable. We calculate the timescale in which a minimal evolvable protocell is produced. We show that when protocells fuse and share information, the timescales polynomially in N By contrast, in the absence of fusion, the worst-case scenario is exponential in N We discuss the implications of this result for the origin of life and other biological processes.

Computational Complexity as an Ultimate Constraint on Evolution

Experiments show that evolutionary fitness landscapes can have a rich combinatorial structure due to epistasis. For some landscapes, this structure can produce a computational constraint that prevents evolution from finding local fitness optima-thus overturning the traditional assumption that local fitness peaks can always be reached quickly if no other evolutionary forces challenge natural selection. Here, I introduce a distinction between easy landscapes of traditional theory where local fitness peaks can be found in a moderate number of steps, and hard landscapes where finding local optima requires an infeasible amount of time. Hard examples exist even among landscapes with no reciprocal sign epistasis; on these semismooth fitness landscapes, strong selection weak mutation dynamics cannot find the unique peak in polynomial time. More generally, on hard rugged fitness landscapes that include reciprocal sign epistasis, no evolutionary dynamics-even ones that do not follow adaptive paths-can find a local fitness optimum quickly. Moreover, on hard landscapes, the fitness advantage of nearby mutants cannot drop off exponentially fast but has to follow a power-law that long-term evolution experiments have associated with unbounded growth in fitness. Thus, the constraint of computational complexity enables open-ended evolution on finite landscapes. Knowing this constraint allows us to use the tools of theoretical computer science and combinatorial optimization to characterize the fitness landscapes that we expect to see in nature. I present candidates for hard landscapes at scales from single genes, to microbes, to complex organisms with costly learning (Baldwin effect) or maintained cooperation (Hankshaw effect). Just how ubiquitous hard landscapes (and the corresponding ultimate constraint on evolution) are in nature becomes an open empirical question.

Sex: The power of randomization

In evolutionary biology, randomness has been perceived as a force that, in and of itself, is capable of inventing: mutation creates new genetic information at random across the genome which leads to phenotypic change, which is then subject to selection. However, in science in general and in computer science in particular, the widespread use of randomness takes a different form. Here, randomization allows for the breaking of pattern, as seen for example in its removal of biases (patterns) by random sampling or random assignment to conditions. Combined with various forms of evaluation, this breaking of pattern becomes an extraordinarily powerful tool, as also seen in many randomized algorithms in computer science. Here we show that this power of randomness is harnessed in nature by sex and recombination. In a finite population, and under the assumption of interactions between genetic variants, sex and recombination allow selection to test how well an allele will perform in a sample of combinations of interacting genetic partners drawn at random from all possible such combinations; consequently, even a small number of tests of genotypes such as takes place in a finite population favors alleles that will most likely perform well in a vast number of yet unrealized genetic combinations. This power of randomization is not manifest in asexual populations.

Synergy from reproductive division of labor and genetic complexity drive the evolution of sex

Computer experiments that mirror the evolutionary dynamics of sexual and asexual organisms as they occur in nature were used to test features proposed to explain the evolution of sexual recombination. Results show that this evolution is better described as a network of interactions between possible sexual forms, including diploidy, thelytoky, facultative sex, assortation, bisexuality, and division of labor between the sexes, rather than a simple transition from parthenogenesis to sexual recombination. Diploidy was shown to be fundamental for the evolution of sex; bisexual reproduction emerged only among anisogamic diploids with a synergistic division of reproductive labor; and facultative sex was more likely to evolve among haploids practicing assortative mating. Looking at the evolution of sex as a complex system through individual-based simulations explains better the diversity of sexual strategies known to exist in nature, compared to classical analytical models.

Diatom flagellar genes and their expression during sexual reproduction in Leptocylindrus danicus

Background

Flagella have been lost in the vegetative phase of the diatom life cycle, but they are still present in male gametes of centric species, thereby representing a hallmark of sexual reproduction. This process, besides maintaining and creating new genetic diversity, in diatoms is also fundamental to restore the maximum cell size following its reduction during vegetative division. Nevertheless, sexual reproduction has been demonstrated in a limited number of diatom species, while our understanding of its different phases and of their genetic control is scarce.

Results

In the transcriptome of Leptocylindrus danicus, a centric diatom widespread in the world’s seas, we identified 22 transcripts related to the flagella development and confirmed synchronous overexpression of 6 flagellum-related genes during the male gamete formation process. These transcripts were mostly absent in the closely related species L. aporus, which does not have sexual reproduction. Among the 22 transcripts, L. danicus showed proteins that belong to the Intra Flagellar Transport (IFT) subcomplex B as well as IFT-A proteins, the latter previously thought to be absent in diatoms. The presence of flagellum-related proteins was also traced in the transcriptomes of several other centric species. Finally, phylogenetic reconstruction of the IFT172 and IFT88 proteins showed that their sequences are conserved across protist species and have evolved similarly to other phylogenetic marker genes.

Conclusion

Our analysis describes for the first time the diatom flagellar gene set, which appears to be more complete and functional than previously reported based on the genome sequence of the model centric diatom, Thalassiosira pseudonana. This first recognition of the whole set of diatom flagellar genes and of their activation pattern paves the way to a wider recognition of the relevance of sexual reproduction in individual species and in the natural environment.

Electronic supplementary material

The online version of this article (10.1186/s12864-017-4210-8) contains supplementary material, which is available to authorized users.

How evolution learns to generalise: Using the principles of learning theory to understand the evolution of developmental organisation

One of the most intriguing questions in evolution is how organisms exhibit suitable phenotypic variation to rapidly adapt in novel selective environments. Such variability is crucial for evolvability, but poorly understood. In particular, how can natural selection favour developmental organisations that facilitate adaptive evolution in previously unseen environments? Such a capacity suggests foresight that is incompatible with the short-sighted concept of natural selection. A potential resolution is provided by the idea that evolution may discover and exploit information not only about the particular phenotypes selected in the past, but their underlying structural regularities: new phenotypes, with the same underlying regularities, but novel particulars, may then be useful in new environments. If true, we still need to understand the conditions in which natural selection will discover such deep regularities rather than exploiting ‘quick fixes’ (i.e., fixes that provide adaptive phenotypes in the short term, but limit future evolvability). Here we argue that the ability of evolution to discover such regularities is formally analogous to learning principles, familiar in humans and machines, that enable generalisation from past experience. Conversely, natural selection that fails to enhance evolvability is directly analogous to the learning problem of over-fitting and the subsequent failure to generalise. We support the conclusion that evolving systems and learning systems are different instantiations of the same algorithmic principles by showing that existing results from the learning domain can be transferred to the evolution domain. Specifically, we show that conditions that alleviate over-fitting in learning systems successfully predict which biological conditions (e.g., environmental variation, regularity, noise or a pressure for developmental simplicity) enhance evolvability. This equivalence provides access to a well-developed theoretical framework from learning theory that enables a characterisation of the general conditions for the evolution of evolvability.

A striking feature of evolving organisms is their ability to acquire novel characteristics that help them adapt in new environments. The origin and the conditions of such ability remain elusive and is a long-standing question in evolutionary biology. Recent theory suggests that organisms can evolve designs that help them generate novel features that are more likely to be beneficial. Specifically, this is possible when the environments that organisms are exposed to share common regularities. However, the organisms develop robust designs that tend to produce what had been selected in the past and might be inflexible for future environments. The resolution comes from a recent theory introduced by Watson and Szathmáry that suggests a deep analogy between learning and evolution. Accordingly, here we utilise learning theory to explain the conditions that lead to more evolvable designs. We successfully demonstrate this by equating evolvability to the way humans and machines generalise to previously-unseen situations. Specifically, we show that the same conditions that enhance generalisation in learning systems have biological analogues and help us understand why environmental noise and the reproductive and maintenance costs of gene-regulatory connections can lead to more evolvable designs.

How Crossover Speeds up Building Block Assembly in Genetic Algorithms

We reinvestigate a fundamental question: How effective is crossover in genetic algorithms in combining building blocks of good solutions? Although this has been discussed controversially for decades, we are still lacking a rigorous and intuitive answer. We provide such answers for royal road functions and OneMax, where every bit is a building block. For the latter, we show that using crossover makes every ([Formula: see text]+[Formula: see text]) genetic algorithm at least twice as fast as the fastest evolutionary algorithm using only standard bit mutation, up to small-order terms and for moderate [Formula: see text] and [Formula: see text]. Crossover is beneficial because it can capitalize on mutations that have both beneficial and disruptive effects on building blocks: crossover is able to repair the disruptive effects of mutation in later generations. Compared to mutation-based evolutionary algorithms, this makes multibit mutations more useful. Introducing crossover changes the optimal mutation rate on OneMax from [Formula: see text] to [Formula: see text]. This holds both for uniform crossover and k-point crossover. Experiments and statistical tests confirm that our findings apply to a broad class of building block functions.

Sexual reproduction with variable mating systems can resist asexuality in a rock-paper-scissors dynamics

While sex can be advantageous for a lineage in the long term, we still lack an explanation for its maintenance with the twofold cost per generation. Here we model an infinite diploid population where two autosomal loci determine, respectively, the reproductive mode, sexual versus asexual and the mating system, polygynous (costly sex) versus monogamous (assuming equal contribution of parents to offspring, i.e. non-costly sex). We show that alleles for costly sex can spread when non-costly sexual modes buffer the interaction between asexual and costly sexual strategies, even without twofold benefit of recombination with respect to asexuality. The three interacting strategies have intransitive fitness relationships leading to a rock-paper-scissors dynamics, so that alleles for costly sex cannot be eliminated by asexuals in most situations throughout the parameter space. Our results indicate that sexual lineages with variable mating systems can resist the invasion of asexuals and allow for long-term effects to accumulate, thus providing a solution to the persisting theoretical question of why sex was not displaced by asexuality along evolution.

Towards an ecological understanding of morphological evolution

The roots of modern evo-devo can be traced back to the comparative anatomy of the 19th century. Inheriting from this tradition, the field has maintained a mechanistic approach to understanding the origins of distinct animal morphologies. While this focus has produced a valuable body of work, we argue here that a fuller understanding of why species diverge morphologically must be centered on the selective forces driving divergence, and these forces ultimately reside in the ecological context in which organisms live and reproduce. We discuss reasons why we expect many morphological novelties to evolve largely secondarily to, and often as a by-product of, primary selection on life-history traits. By shifting the focus to proximate evolutionary causes, our perspective necessarily prioritises selection experiments as a means of empirical testing. We outline experimental approaches designed to dissect the role of ecological variables in the evolution of animal development and morphology, and we show how methods and advances in fields as diverse as population genomics and ecological stoichiometry can contribute to progress in this direction.

Evolutionary genetic bases of longevity and senescence

Senescence, as a time-dependent developmental process, affects all organisms at every stage in their development and growth. During this process, genetic, epigenetic and environmental factors are known to introduce a wide range of variation for longevity among individuals. As an important life-history trait, longevity shows ontogenetic relationships with other complex traits, and hence may be viewed as a composite trait. Factors that influence the origin and maintenance of diversity of life are ultimately governed by Darwinian processes. Here we review evolutionary genetic mechanisms underlying longevity and senescence in humans from a life-history and genotype-epigenetic-phenotype (G-E-P) map prospective. We suggest that synergistic and cascading effects of cis-ruptive mechanisms in the genome, and epigenetic disruptive processes in relation to environmental factors may lead to sequential slippage in the G-E-P space. These mechanisms accompany age, stage and individual specific senescent processes, influenced by positive pleiotropy of certain genes, superior genome integrity, negative-frequency dependent selection and other factors that universally regulate rarity in nature. Finally we interpret life span as an inherent property of self-organizing systems that, accordingly, maintain species-specific limits for the entire complex of fitness traits. We conclude that Darwinian approaches provide unique opportunities to discover the biological bases of longevity as well as devise individual specific medical or other interventions toward improving health span.

Confidence sharing: an economic strategy for efficient information flows in animal groups

Social animals may share information to obtain a more complete and accurate picture of their surroundings. However, physical constraints on communication limit the flow of information between interacting individuals in a way that can cause an accumulation of errors and deteriorated collective behaviors. Here, we theoretically study a general model of information sharing within animal groups. We take an algorithmic perspective to identify efficient communication schemes that are, nevertheless, economic in terms of communication, memory and individual internal computation. We present a simple and natural algorithm in which each agent compresses all information it has gathered into a single parameter that represents its confidence in its behavior. Confidence is communicated between agents by means of active signaling. We motivate this model by novel and existing empirical evidences for confidence sharing in animal groups. We rigorously show that this algorithm competes extremely well with the best possible algorithm that operates without any computational constraints. We also show that this algorithm is minimal, in the sense that further reduction in communication may significantly reduce performances. Our proofs rely on the Cramér-Rao bound and on our definition of a Fisher Channel Capacity. We use these concepts to quantify information flows within the group which are then used to obtain lower bounds on collective performance. The abstract nature of our model makes it rigorously solvable and its conclusions highly general. Indeed, our results suggest confidence sharing as a central notion in the context of animal communication.

Cooperative groups are abundant on all scales of the biological world. Despite much empirical evidence on a wide variety of natural communication schemes, there is still a growing need for rigorous tools to quantify and understand the information flows involved. Here, we borrow techniques from information theory and theoretical distributed computing to study information sharing within animal groups. We consider a group of individuals that integrate personal and social information to obtain improved knowledge of their surroundings. We rigorously show that communication between such individuals can be compressed into simple messages that contain an opinion and a corresponding confidence parameter. While this algorithm is extremely efficient, further reduction in communication capacity may greatly hamper collective performances.

Quantifying protein modularity and evolvability: a comparison of different techniques

Modularity increases evolvability by reducing constraints on adaptation and by allowing preexisting parts to function in new contexts for novel uses. Protein evolution provides an excellent context to study the causes and consequences of biological modularity. In order to address such questions, however, an index for protein modularity is necessary. This paper proposes a simple index for protein modularity-"module density"-which is the number of evolutionarily independent modules that compose a protein divided by the number of amino acids in the protein. The decomposition of proteins into constituent modules can be accomplished by either of two classes of methods. The first class of methods relies on "suppositional" criteria to assign amino acids to modules, whereas the second class of methods relies on "coevolutionary" criteria for this task. One simple and practical method from the first class consists of approximating the number of modules in a protein as the number of regular secondary structure elements (i.e., helices and sheets). Methods based on coevolutionary criteria require more elaborate data, but they have the advantage of being able to specify modules without prior assumptions about why they exist. Given the increasing availability of datasets sampling protein mutational spectra (e.g., from comparative genomics, experimental evolution, and computational prediction), methods based on coevolutionary criteria will likely become more promising in the near future. The ability to meaningfully quantify protein modularity via simple indices has the potential to aid future efforts to understand protein evolutionary rate determinants, improve molecular evolution models and engineer novel proteins.

Does sex speed up evolutionary rate and increase biodiversity?

Most empirical and theoretical studies have shown that sex increases the rate of evolution, although evidence of sex constraining genomic and epigenetic variation and slowing down evolution also exists. Faster rates with sex have been attributed to new gene combinations, removal of deleterious mutations, and adaptation to heterogeneous environments. Slower rates with sex have been attributed to removal of major genetic rearrangements, the cost of finding a mate, vulnerability to predation, and exposure to sexually transmitted diseases. Whether sex speeds or slows evolution, the connection between reproductive mode, the evolutionary rate, and species diversity remains largely unexplored. Here we present a spatially explicit model of ecological and evolutionary dynamics based on DNA sequence change to study the connection between mutation, speciation, and the resulting biodiversity in sexual and asexual populations. We show that faster speciation can decrease the abundance of newly formed species and thus decrease long-term biodiversity. In this way, sex can reduce diversity relative to asexual populations, because it leads to a higher rate of production of new species, but with lower abundances. Our results show that reproductive mode and the mechanisms underlying it can alter the link between mutation, evolutionary rate, speciation and biodiversity and we suggest that a high rate of evolution may not be required to yield high biodiversity.

The role of sex in driving genetic variation and the speed at which new species emerge has been debated for over a century. There is experimental and theoretical evidence that sex increases genetic variation and the speed at which new species emerge, although evidence that sex reduces variation and slows the formation of new species also exists. Surprisingly, given the link between sex and genetic variation, little work has been done on the impact of sex on biodiversity. In the present theoretical study we show that a faster evolutionary rate can decrease the abundance of newly formed species and thus decrease long-term biodiversity. This leads to the paradoxical result that sexual reproduction can increase genetic variation but reduce species diversity. These results suggest that reducing the rate of appearance of genetic variation and the speed at which new species emerge may increase biodiversity in the long-term. This unexpected link between reproductive mode, the speed of evolution and biodiversity suggests that a high evolutionary rate may not be required to yield a large number of species in natural ecosystems.

Order-preserving principles underlying genotype-phenotype maps ensure high additive proportions of genetic variance

In quantitative genetics, the degree of resemblance between parents and offspring is described in terms of the additive variance (V(A)) relative to genetic (V(G)) and phenotypic (V(P)) variance. For populations with extreme allele frequencies, high V(A)/V(G) can be explained without considering properties of the genotype-phenotype (GP) map. We show that randomly generated GP maps in populations with intermediate allele frequencies generate far lower V(A)/V(G) values than empirically observed. The main reason is that order-breaking behaviour is ubiquitous in random GP maps. Rearrangement of genotypic values to introduce order-preservation for one or more loci causes a dramatic increase in V(A)/V(G). This suggests the existence of order-preserving design principles in the regulatory machinery underlying GP maps. We illustrate this feature by showing how the ubiquitously observed monotonicity of dose-response relationships gives much higher V(A)/V(G) values than a unimodal dose-response relationship in simple gene network models.

An analytical contrast between fitness maximization and selection for mixability

It has been recently shown numerically that sex enables selection for alleles that perform well across different genetic contexts, i.e., selection for mixability. Here we capture this result analytically in a simple case. This serves a dual purpose. First, it provides a clear distinction between fitness maximization and selection for mixability. Second, it points out a limitation of the traditional analytical approach as applied to mixability.

Genetic architecture and the evolution of sex

Theoretical investigations of the advantages of sex have tended to treat the genetic architecture of organisms as static and have not considered that genetic architecture might coevolve with reproductive mode. As a result, some potential advantages of sex may have been missed. Using a gene network model, we recently showed that recombination imposes selection for robustness to mutation and that negative epistasis can evolve as a by-product of this selection. These results motivated a detailed exploration of the mutational deterministic hypothesis, a hypothesis in which the advantage of sex depends critically on epistasis. We found that sexual populations do evolve higher mean fitness and lower genetic load than asexual populations at equilibrium, and, under moderate stabilizing selection and large population size, these equilibrium sexual populations resist invasion by asexuals. However, we found no evidence that these long- and short-term advantages to sex were explained by the negative epistasis that evolved in our experiments. The long-term advantage of sex was that sexual populations evolved a lower deleterious mutation rate, but this property was not sufficient to account for the ability of sexual populations to resist invasion by asexuals. The ability to resist asexual invasion was acquired simultaneously with an increase in recombinational robustness that minimized the cost of sex. These observations provide the first direct evidence that sexual reproduction does indeed select for conditions that favor its own maintenance. Furthermore, our results highlight the importance of considering a dynamic view of the genetic architecture to understand the evolution of sex and recombination.

Genetic linkage and natural selection

The prevalence of recombination in eukaryotes poses one of the most puzzling questions in biology. The most compelling general explanation is that recombination facilitates selection by breaking down the negative associations generated by random drift (i.e. Hill-Robertson interference, HRI). I classify the effects of HRI owing to: deleterious mutation, balancing selection and selective sweeps on: neutral diversity, rates of adaptation and the mutation load. These effects are mediated primarily by the density of deleterious mutations and of selective sweeps. Sequence polymorphism and divergence suggest that these rates may be high enough to cause significant interference even in genomic regions of high recombination. However, neither seems able to generate enough variance in fitness to select strongly for high rates of recombination. It is plausible that spatial and temporal fluctuations in selection generate much more fitness variance, and hence selection for recombination, than can be explained by uniformly deleterious mutations or species-wide selective sweeps.

Redundancy and the evolution of cis-regulatory element multiplicity

The promoter regions of many genes contain multiple binding sites for the same transcription factor (TF). One possibility is that this multiplicity evolved through transitional forms showing redundant cis-regulation. To evaluate this hypothesis, we must disentangle the relative contributions of different evolutionary mechanisms to the evolution of binding site multiplicity. Here, we attempt to do this using a model of binding site evolution. Our model considers binding sequences and their interactions with TFs explicitly, and allows us to cast the evolution of gene networks into a neutral network framework. We then test some of the model's predictions using data from yeast. Analysis of the model suggested three candidate nonadaptive processes favoring the evolution of cis-regulatory element redundancy and multiplicity: neutral evolution in long promoters, recombination and TF promiscuity. We find that recombination rate is positively associated with binding site multiplicity in yeast. Our model also indicated that weak direct selection for multiplicity (partial redundancy) can play a major role in organisms with large populations. Our data suggest that selection for changes in gene expression level may have contributed to the evolution of multiple binding sites in yeast. We conclude that the evolution of cis-regulatory element redundancy and multiplicity is impacted by many aspects of the biology of an organism: both adaptive and nonadaptive processes, both changes in cis to binding sites and in trans to the TFs that interact with them, both the functional setting of the promoter and the population genetic context of the individuals carrying them.

TFs regulate gene expression by binding to specific sequences in the promoter regions of their target genes. Promoters often contain multiple copies of the same TF binding sites. How does this multiplicity evolve? One possibility is that individuals with multiple, redundant binding sites have higher fitness. However, nonadaptive processes are also likely to be important. Here, we develop a mathematical model of the evolution of TF binding sites to help us disentangle how different evolutionary mechanisms contribute to the evolution of binding site redundancy and multiplicity. We show that recombination is expected to promote the evolution of multiple binding sites. This prediction is corroborated by genome-wide data from yeast. Another important factor in the evolution of multiplicity predicted in our analysis is TF promiscuity, that is, the ability of a TF to bind to multiple sequences. In addition, our analysis indicated that direct selection can have large effects on the evolution of redundancy and multiplicity. Data from yeast identified selection for changes in expression level as a candidate mechanism for the evolution of multiple binding sites. We conclude that, although selection may play a major role in the evolution of multiplicity in regulatory regions, nonadaptive forces can also lead to high levels of multiplicity.

Sex, mixability, and 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.