David Waxman

Sympatric speciation by sexual conflict

It is well established that sexual conflict can drive an endless coevolutionary chase between the sexes potentially leading to genetic divergence of isolated populations and allopatric speciation. We present a simple mathematical model that shows that sexual conflict over mating rate can result in two other general regimes. First, rather than “running away” from males, females can diversify genetically into separate groups, effectively “trapping” the males in the middle at a state characterized by reduced mating success. Female diversification brings coevolutionary chase to the end. Second, under certain conditions, males respond to female diversification by diversifying themselves. This response results in the formation of reproductively isolated clusters of genotypes that emerge sympatrically.

20 Questions on Adaptive Dynamics

Adaptive Dynamics is an approach to studying evolutionary change when fitness is density or frequency dependent. Modern papers identifying themselves as using this approach first appeared in the 1990s, and have greatly increased up to the present. However, because of the rather technical nature of many of the papers, the approach is not widely known or understood by evolutionary biologists. In this review we aim to remedy this situation by outlining the methodology and then examining its strengths and weaknesses. We carry this out by posing and answering 20 key questions on Adaptive Dynamics. We conclude that Adaptive Dynamics provides a set of useful approximations for studying various evolutionary questions. However, as with any approximate method, conclusions based on Adaptive Dynamics are valid only under some restrictions that we discuss.

Explaining the geographic distributions of sexual and asexual populations

Examination of the geographic distributions of sexual organisms and their asexual, or parthenogenetic, competitors reveals certain consistent patterns. These patterns are called geographic parthenogenes is. For example, if we compare sexual organisms with closely related asexuals, we find that, in the Northern Hemisphere, there is a strong tendency for the asexuals to occur further to the north. One researcher to document this pattern is Bierzychudek, who examined 43 cases (drawn from 10 genera) where the geographic distributions of a sexual plant and a closely related asexual are known. In 76% of these cases, the asexual plants range was more northerly than the range of the sexual. Some of the remaining cases probably fit with this pattern, but more data must be obtained before this suggestion can be confirmed. Asexuals also tend to occur at high altitudes, and in marginal, resource-poor environments. We have constructed a mathematical model of a habitat that stretches from south to north in the Northern Hemisphere. Our computer simulations based on this model support the idea that a single basic process may account for much of what is known about geographic parthenogenesis. This process involves the movement of individuals from areas in which they are well adapted to areas where they are poorly adapted.

Pleiotropic scaling of gene effects and the 'cost of complexity'.

As perceived by Darwin, evolutionary adaptation by the processes of mutation and selection is difficult to understand for complex features that are the product of numerous traits acting in concert, for example the eye or the apparatus of flight. Typically, mutations simultaneously affect multiple phenotypic characters. This phenomenon is known as pleiotropy. The impact of pleiotropy on evolution has for decades been the subject of formal analysis. Some authors have suggested that pleiotropy can impede evolutionary progress (a so-called ‘cost of complexity’). The plausibility of various phenomena attributed to pleiotropy depends on how many traits are affected by each mutation and on our understanding of the correlation between the number of traits affected by each gene substitution and the size of mutational effects on individual traits. Here we show, by studying pleiotropy in mice with the use of quantitative trait loci (QTLs) affecting skeletal characters, that most QTLs affect a relatively small subset of traits and that a substitution at a QTL has an effect on each trait that increases with the total number of traits affected. This suggests that evolution of higher organisms does not suffer a ‘cost of complexity’ because most mutations affect few traits and the size of the effects does not decrease with pleiotropy.

MODULARITY AND THE COST OF COMPLEXITY

Abstract. In this work we consider the geometrical model of R. A. Fisher, in which individuals are characterized by a number of phenotypic characters under optimizing selection. Recent work on this model by H. A. Orr has demonstrated that as the number of characters increases, there is a significant reduction in the rate of adaptation. Orr has dubbed this a “cost of complexity.” Although there is little evidence as to whether such a cost applies in the natural world, we suggest that the prediction is surprising, at least naively. With this in mind, we examine the robustness of Orrs prediction by modifiying the model in various ways that might reduce or remove the cost. In particular, we explore the suggestion that modular pleiotropy, in which mutations affect only a subset of the traits, could play an important role. We conclude that although modifications of the model can mitigate the cost to a limited extent, Orrs finding is robust.

Fisher’s Microscope and Haldane’s Ellipse

Fisher’s geometrical model was introduced to study the phenotypic size of mutations contributing to adaptation. However, as pointed out by Haldane, the model involves a simplified picture of the action of natural selection, and this calls into question its generality. In particular, Fisher’s model assumes that each trait contributes independently to fitness. Here, we show that Haldane’s concerns may be incorporated into Fisher’s model solely by allowing the intensity of selection to vary between traits. We further show that this generalization may be achieved by introducing a single, intuitively defined quantity that describes the phenotype prior to adaptation. Comparing the process of adaptation under the original and generalized models, we show that the generalization may bias results toward either larger or smaller mutations. The applicability of Fisher’s model is then discussed.

Mutation and sex in a competitive world

How do deleterious mutations interact to affect fitness? The answer to this question has substantial implications for a variety of important problems in population biology, including the evolution of sex, the rate of adaptation and the conservation of small populations. Here we analyse a mathematical model of competition for food in which deleterious mutations affect competitive ability. We show that, if individuals usually compete in small groups, then competition can easily lead to a type of genetic interaction known as synergistic epistasis. This means that a deleterious mutation is most damaging in a genome that already has many other deleterious mutations. We also show that competition in small groups can produce a large advantage for sexual populations, both in mean fitness and in ability to resist invasion by asexual lineages. One implication of our findings is that experimental efforts to demonstrate synergistic epistasis may not succeed unless the experiments are redesigned to make them much more naturalistic.

What's wrong with a little sex?

In many species, most (or all) offspring are produced by sexual means. However, theory suggests that selection should often favour the evolution of species in which a small fraction of offspring are produced sexually, and the rest are produced asexually. Here, we present the analysis of a model that may help to resolve this paradox. We show that, when heterozygote advantage is in force, members of species in which sex is rare will tend to produce poorly adapted offspring when they mate. This problem should be less severe in species where most offspring are produced by sexual means. As a consequence, once the rate of sexual reproduction becomes sufficiently rare, the benefits of sex may vanish, leading to the evolution of obligate asexuality. Substantial benefits of sexual reproduction may tend to accrue only if a large proportion of offspring are produced sexually. We suggest that similar findings are likely in the case of epistatic interactions between loci.

A Unified Treatment of the Probability of Fixation when Population Size and the Strength of Selection Change Over Time

The fixation probability is determined when population size and selection change over time and differs from Kimura’s result, with long-term implications for a population. It is found that changes in population size are not equivalent to the corresponding changes in selection and can result in less drift than anticipated.

Divergence and Polymorphism Under the Nearly Neutral Theory of Molecular Evolution

The nearly neutral theory attributes most nucleotide substitution and polymorphism to genetic drift acting on weakly selected mutants, and assumes that the selection coefficients for these mutants are drawn from a continuous distribution. This means that parameter estimation can require numerical integration, and this can be computationally costly and inaccurate. Furthermore, the leading parameter dependencies of important quantities can be unclear, making results difficult to understand. For some commonly used distributions of mutant effects, we show how these problems can be avoided by writing equations in terms of special functions. Series expansion then allows for their rapid calculation and, also, illuminates leading parameter dependencies. For example, we show that if mutants are gamma distributed, the neutrality index is largely independent of the effective population size. However, we also show that such results are not robust to misspecification of the functional form of distribution. Some implications of these findings are then discussed.