Evolved attitudes to risk and the demand for equity.

The equity premium puzzle refers to the observation that people invest far less in the stock market than is implied by measures of their risk aversion in other contexts. Here, we argue that light on this puzzle can be shed by the hypothesis that human risk attitudes were at least partly shaped by our evolutionary history. In particular, a simple evolutionary model shows that natural selection will, over the long haul, favor a greater aversion to aggregate than to idiosyncratic risk. We apply this model-via both a static model of portfolio choice and a dynamic model that allows for intertemporal tradeoffs-to show that an aversion to aggregate risk that is derived from biology may help explain the equity premium puzzle. The type of investor favored in our model would indeed invest less in equities than other common observations of risk-taking behavior from outside the stock market would imply, while engaging in reasonable tradeoffs over time.

The Population Genetics of Evolutionary Rescue in Diploids: X Chromosomal versus Autosomal Rescue.

Most population genetic theory assumes that populations adapt to an environmental change without a change in population size. However, environmental changes might be so severe that populations decline in size and, without adaptation, become extinct. This "evolutionary rescue" scenario differs from traditional models of adaptation in that rescue involves a race between adaptation and extinction. While most previous work has usually focused on models of evolutionary rescue in haploids, here we consider diploids. In many species, diploidy introduces a novel feature into adaptation: adaptive evolution might occur either on sex chromosomes or on autosomes. Previous studies of nonrescue adaptation revealed that the relative rates of adaptation on the X chromosome versus autosomes depend on the dominance of beneficial mutations, reflecting differences in effective population size and the efficacy of selection. Here, we extend these results to evolutionary rescue and find that, given equal-sized chromosomes, there is greater parameter space in which the X is more likely to contribute to adaptation than the autosomes relative to standard nonrescue models. We also discuss how subtle effects of dominance can increase the chance of evolutionary rescue in diploids when absolute heterozygote fitness is close to 1. These effects do not arise in standard nonrescue models.

Measures of the efficiency of natural selection during gene substitution.

Natural selection is not perfectly efficient: it does not cause the instantaneous substitution of a beneficial mutation. Instead, substitution takes time, reflecting the statistical consequences of fitness differences over some number of generations. In this note, I suggest two measures of the efficiency of natural selection during gene substitution. I compare these measures against both ideal (instantaneous) and failed evolution. I also compare these measures to Haldane's cost of natural selection.

The population genetics of evolutionary rescue.

Evolutionary rescue occurs when a population that is threatened with extinction by an environmental change adapts to the change sufficiently rapidly to survive. Here we extend the mathematical theory of evolutionary rescue. In particular, we model evolutionary rescue to a sudden environmental change when adaptation involves evolution at a single locus. We consider adaptation using either new mutations or alleles from the standing genetic variation that begin rare. We obtain several results: i) the total probability of evolutionary rescue from either new mutation or standing variation; ii) the conditions under which rescue is more likely to involve a new mutation versus an allele from the standing genetic variation; iii) a mathematical description of the U-shaped curve of total population size through time, conditional on rescue; and iv) the time until the average population size begins to rebound as well as the minimal expected population size experienced by a rescued population. Our analysis requires taking into account a subtle population-genetic effect (familiar from the theory of genetic hitchhiking) that involves "oversampling" of those lucky alleles that ultimately sweep to high frequency. Our results are relevant to conservation biology, experimental microbial evolution, and medicine (e.g., the dynamics of antibiotic resistance).

The population genetics of beneficial mutations.

The population genetic study of advantageous mutations has lagged behind that of deleterious and neutral mutations. But over the past two decades, a number of significant developments, both theoretical and empirical, have occurred. Here, I review two of these developments: the attempt to determine the distribution of fitness effects among beneficial mutations and the attempt to determine their average dominance. Considering both theory and data, I conclude that, while considerable theoretical progress has been made, we still lack sufficient data to draw confident conclusions about the distribution of effects or the dominance of beneficial mutations.

Darwin and Darwinism: the (alleged) social implications of the origin of species.

Most scientific theories, even revolutionary ones, change the practice of a particular science but have few consequences for culture or society at large. But Darwinism, it has often been said, is different in this respect. Since the publication of The Origin of Species, many have claimed that Darwinism has a number of profound social implications. Here, I briefly consider three of these: the economic, the political, and the religious. I suggest that, for the most part, these supposed implications have been misconstrued or exaggerated. Indeed, it is reasonably clear that the chain of implication sometimes primarily ran in the opposite direction-from, for instance, economics and political theory to Darwinism.

The population genetics of adaptation: multiple substitutions on a smooth fitness landscape.

Much recent work in the theoretical study of adaptation has focused on the so-called strong selection-weak mutation (SSWM) limit, wherein adaptation is due to new mutations of definite selective advantage. This work, in turn, has focused on the first step (substitution) during adaptive evolution. Here we extend this theory to allow multiple steps during adaptation. We find analytic solutions to the probability that adaptation follows a certain path during evolution as well as the probability that adaptation arrives at a given genotype regardless of the path taken. We also consider the probability of parallel adaptation and the proportion of the total increase in fitness caused by the first substitution. Our key assumption is that there is no epistasis among beneficial mutations.

Fitness and its role in evolutionary genetics.

Although the operation of natural selection requires that genotypes differ in fitness, some geneticists may find it easier to understand natural selection than fitness. Partly this reflects the fact that the word 'fitness' has been used to mean subtly different things. In this Review I distinguish among these meanings (for example, individual fitness, absolute fitness and relative fitness) and explain how evolutionary geneticists use fitness to predict changes in the genetic composition of populations through time. I also review the empirical study of fitness, emphasizing approaches that take advantage of recent genetic and genomic data, and I highlight important unresolved problems in understanding fitness.

A single gene causes both male sterility and segregation distortion in Drosophila hybrids.

A central goal of evolutionary biology is to identify the genes and evolutionary forces that cause speciation, the emergence of reproductive isolation between populations. Despite the identification of several genes that cause hybrid sterility or inviability-many of which have evolved rapidly under positive Darwinian selection-little is known about the ecological or genomic forces that drive the evolution of postzygotic isolation. Here, we show that the same gene, Overdrive, causes both male sterility and segregation distortion in F1 hybrids between the Bogota and U.S. subspecies of Drosophila pseudoobscura. This segregation distorter gene is essential for hybrid sterility, a strong reproductive barrier between these young taxa. Our results suggest that genetic conflict may be an important evolutionary force in speciation.

A general extreme value theory model for the adaptation of DNA sequences under strong selection and weak mutation.

Recent theoretical studies of the adaptation of DNA sequences assume that the distribution of fitness effects among new beneficial mutations is exponential. This has been justified by using extreme value theory and, in particular, by assuming that the distribution of fitnesses belongs to the Gumbel domain of attraction. However, extreme value theory shows that two other domains of attraction are also possible: the Fréchet and Weibull domains. Distributions in the Fréchet domain have right tails that are heavier than exponential, while distributions in the Weibull domain have right tails that are truncated. To explore the consequences of relaxing the Gumbel assumption, we generalize previous adaptation theory to allow all three domains. We find that many of the previously derived Gumbel-based predictions about the first step of adaptation are fairly robust for some moderate forms of right tails in the Weibull and Fréchet domains, but significant departures are possible, especially for predictions concerning multiple steps in adaptation.

Population extinction and the genetics of adaptation.

Theories of adaptation typically ignore the effect of environmental change on population size. But some environmental challenges--challenges to which populations must adapt--may depress absolute fitness below 1, causing populations to decline. Under this scenario, adaptation is a race; beneficial alleles that adapt a population to the new environment must sweep to high frequency before the population becomes extinct. We derive simple, though approximate, solutions to the probability of successful adaptation (population survival) when adaptation involves new mutations, the standing genetic variation, or a mixture of the two. Our results show that adaptation to such environmental challenges can be difficult when relying on new mutations at one or a few loci, and populations will often decline to extinction.

Absolute fitness, relative fitness, and utility.

It is well known that (1) natural selection typically favors an allele with both a large mean fitness and a small variance in fitness; and (2) investors typically prefer a portfolio with both a large mean return and a small variance in returns. In the case of investors, this mean-variance trade-off reflects risk aversion; in the case of evolution, the mathematics is straightforward but the result is harder to intuit. In particular, it is harder to understand where, in the mathematics of natural selection, risk aversion arises. Here I present a result that suggests a simple answer to this question. Although my answer is essentially identical to one offered previously, my path to it differs somewhat from previous approaches. Some may find this new approach easier to intuit.

A religion for Darwinians?

A review of Philip Kitcher's book, Living with Darwinism: evolution, design, and the future of faith.

A mission to convert.

Primarily a review of Richard Dawkins' book, The God delusion (Boston: Houghton Mifflin, 2006).

Speciation in Drosophila: from phenotypes to molecules.

Study of the genetics of speciation--and especially of the genetics of intrinsic postzygotic isolation-has enjoyed remarkable progress over the last 2 decades. Indeed progress has been so rapid that one might be tempted to ask if the genetics of postzygotic isolation is now wrapped up. Here we argue that the genetics of speciation is far from complete. In particular, we review 2 topics where recent work has revealed major surprises: 1) the role of meiotic drive in hybrid sterility and 2) the role of gene transposition in speciation. These surprises, and others like them, suggest that evolutionary biologists may understand less about the genetic basis of speciation than seemed likely a few years ago.

Gene transposition as a cause of hybrid sterility in Drosophila.

We describe reproductive isolation caused by a gene transposition. In certain Drosophila melanogaster-D. simulans hybrids, hybrid male sterility is caused by the lack of a single-copy gene essential for male fertility, JYAlpha. This gene is located on the fourth chromosome of D. melanogaster but on the third chromosome of D. simulans. Genomic and molecular analyses show that JYAlpha transposed to the third chromosome during the evolutionary history of the D. simulans lineage. Because of this transposition, a fraction of hybrids completely lack JYAlpha and are sterile, representing reproductive isolation without sequence evolution.

The population genetics of adaptation on correlated fitness landscapes: the block model.

Several recent theoretical studies of the genetics of adaptation have focused on the mutational landscape model, which considers evolution on rugged fitness landscapes (i.e., ones having many local optima). Adaptation in this model is characterized by several simple results. Here I ask whether these results also hold on correlated fitness landscapes, which are smoother than those considered in the mutational landscape model. In particular, I study the genetics of adaptation in the block model, a tunably rugged model of fitness landscapes. Considering the scenario in which adaptation begins from a high fitness wild-type DNA sequence, I use extreme value theory and computer simulations to study both single adaptive steps and entire adaptive walks. I show that all previous results characterizing single steps in adaptation in the mutational landscape model hold at least approximately on correlated landscapes in the block model; many entire-walk results, however, do not.

The distribution of fitness effects among beneficial mutations in Fisher's geometric model of adaptation.

Recent models of adaptation at the DNA sequence level assume that the fitness effects of new mutations show certain statistical properties. In particular, these models assume that the distribution of fitness effects among new mutations is in the domain of attraction of the so-called Gumbel-type extreme value distribution. This assumption has not, however, been justified on any biological or theoretical grounds. In this note, I study random mutation in one of the simplest models of mutation and adaptation-Fisher's geometric model. I show that random mutation in this model yields a distribution of mutational effects that belongs to the Gumbel type. I also show that the distribution of fitness effects among rare beneficial mutations in Fisher's model is asymptotically exponential. I confirm these analytic findings with exact computer simulations. These results provide some support for the use of Gumbel-type extreme value theory in studies of adaptation and point to a surprising connection between recent phenotypic- and sequence-based models of adaptation: in both, the distribution of fitness effects among rare beneficial mutations is approximately exponential.