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Quantitative assessment of serial brain sections provides an objective measure of neurological events at cellular and molecular levels but is difficult to implement in experimental neuroscience laboratories because of variation from person-to-person and the time required for analysis. Whole slide imaging (WSI) technology, recently introduced for pathological diagnoses, offers an electronic environment and a variety of computational tools for performing high-throughput histological analysis and managing the associated information. In our study, we applied various algorithms to quantify histologic changes associated with brain injury and compared the results to manual assessment. WSI showed a high degree of concordance with manual quantitation by Pearson correlation and strong agreement using Bland-Altman plots in: (i) cortical necrosis in cresyl-violet-stained brain sections of mice after focal cerebral ischemia; (ii) intracerebral hemorrhage in ischemic mouse brains for automated annotation of the small regions, rather than whole hemisphere of the tissue sections; (iii) Iba1-immunoreactive cell density in the adjacent and remote brain regions of mice subject to controlled cortical impact (CCI); and (iv) neuronal degeneration by silver staining after CCI. These results show that WSI, when appropriately applied and carefully validated, is a highly efficient and unbiased tool to locate and identify neuropathological features, delineate affected regions and histologically quantify these events.

Traumatic brain injury (TBI) is a leading cause of death and long-term disability. Following the initial insult, severe TBI progresses to a secondary injury phase associated with biochemical and cellular changes. The secondary injury is thought to be responsible for the development of many of the neurological deficits observed after TBI and also provides a window of opportunity for therapeutic intervention. Matrix metalloproteinase-9 (MMP-9 or gelatinase B) expression is elevated in neurological diseases and its activation is an important factor in detrimental outcomes including excitotoxicity, mitochondrial dysfunction and apoptosis, and increases in inflammatory responses and astrogliosis. In this study, we used an experimental mouse model of TBI to examine the role of MMP-9 and the therapeutic potential of SB-3CT, a mechanism-based gelatinase selective inhibitor, in ameliorating the secondary injury. We observed that activation of MMP-9 occurred within one day following TBI, and remained elevated for 7 days after the initial insult. SB-3CT effectively attenuated MMP-9 activity, reduced brain lesion volumes and prevented neuronal loss and dendritic degeneration. Pharmacokinetic studies revealed that SB-3CT and its active metabolite, p-OH SB-3CT, were rapidly absorbed and distributed to the brain. Moreover, SB-3CT treatment mitigated microglial activation and astrogliosis after TBI. Importantly, SB-3CT treatment improved long-term neurobehavioral outcomes, including sensorimotor function, and hippocampus-associated spatial learning and memory. These results demonstrate that MMP-9 is a key target for therapy to attenuate secondary injury cascades and that this class of mechanism-based gelatinase inhibitor-with such desirable pharmacokinetic properties-holds considerable promise as a potential pharmacological treatment of TBI.

Abstract Background Predicted increases in stream temperature due to climate change will have a number of direct and indirect impacts on stream biota. A potential intervention for mitigating stream temperature rise is the use of wooded riparian zones to increase shade and reduce direct warming through solar radiation. To assess the effectiveness of this intervention, we conducted a systematic review of the available evidence for the effects of wooded riparian zones on stream temperature. Methods We searched literature databases and conducted relevant web searches. Inclusion criteria were: subject - any stream in a temperate climate; intervention - presence of trees in the riparian zone; comparator - absence of trees in the riparian zone; outcome measure - stream temperature. Included studies were sorted into 3 groups based on the scale of the intervention and design of the study. Two groups were taken forward for synthesis; Group 1 studies comparing water temperature in streams with and without buffer strips/riparian cover and Group 2 comparisons of stream temperatures in open and forested landscapes. Temperature data were extracted and quantitative synthesis performed using a random effects meta-analysis on the differences in mean and maximum temperature. Results Ten studies were included in each of Groups 1 and 2. Results for both groups suggest that riparian wooded zones lower spring and summer stream temperatures. Lowering of maximum is greater than lowering of mean temperature. Further analysis of environmental variables that might modify the effects of the intervention was not possible using the limited set of studies. Conclusions Wooded riparian zones can reduce stream temperatures, particularly in terms of maximum temperatures. Because temperature is known to affect fish, amphibian and invertebrate life history, the reported effect sizes are likely to have a biological significance for the stream biotic community. Consequently investment in creation of wooded riparian zones might provide benefits in terms of mitigating some of the ecological effects of climate change on water temperature. Considerable uncertainty lies in the environmental variables that may modify the cooling effect of wooded riparian zones, and therefore it is not possible to identify when the use of this intervention for cooling would be most valuable.

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., Competing Interests: The authors declare no competing interest.

Background: Clinical practice guidelines (CPGs) have been associated with improved patient outcomes. We aimed to evaluate institutional CPG adherence and hypothesized that adherence would be associated with fewer complications in pediatric appendicitis., Methods: A retrospective review was conducted of pediatric (<18 y) appendicitis patients who underwent appendectomy (6/1/2017-5/30/2018). Patients were managed using an institutional pediatric appendicitis CPG. The primary outcome was CPG adherence, defined as receipt of preoperative antibiotics at diagnosis, surgical prophylaxis before incision, and, in perforated/gangrenous appendicitis, continued postoperative antibiotics, and prescription for discharge antibiotics. Univariate and multivariate analyzes were performed., Results: Among 399 patients, the baseline characteristics were similar between CPG-adherent and nonadherent patients. Overall CPG adherence was low at 55% (n = 221). Only 58% of patients received preoperative antibiotics per protocol (n = 233). Patients with simple appendicitis were more likely to proceed to surgery without receiving any preoperative antibiotics (35% vs. 21%, P = 0.004). Surgical prophylaxis compliance was high at 97% (n = 389). CPG violation was associated with reoperation (n = 5 versus 0, P = 0.02). After adjusting for age and admission white blood cell count, the association between CPG adherence and postoperative surgical site infection or intra-abdominal abscess remained nonsignificant (OR: 1.2, 95% CI: 0.5-2.5)., Conclusions: Despite a long-standing pediatric appendicitis CPG, adherence with antibiotic components of the CPG was poor. CPG violation was significantly associated with reoperation, but was not associated with other postoperative complications. Regular audits of CPG adherence are necessary to ascertain reasons for noncompliance and identify ways to improve adherence., (Copyright © 2020 Elsevier Inc. All rights reserved.)

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.

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., (Copyright © 2019 Elsevier Ltd. All rights reserved.)

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).

Competing Interests: The authors have declared that no competing interests exist.

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.

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.

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.

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.

Natural selection might drive the evolution of postzygotic reproductive isolation even when allopatric populations adapt to identical environments, an idea first suggested by Muller (1942). Here, we analyze this scenario mathematically, focusing on the evolution of a Dobzhansky-Muller incompatibility (DMI) between populations. Our results identify a potential problem with Muller's scenario: adaptation to identical environments can often involve substitution of the same alleles, precluding formation of a hybrid incompatibility. We show that the probability of evolving a DMI falls as selection coefficients among beneficial alleles become less similar. The reason is that if one locus is under much stronger selection than the other, that locus is much more likely to experience a substitution first in both populations. This precludes the development of a DMI, which requires different substitutions in the two populations.

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.

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.

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.

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

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.

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

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.

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.

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.

Fisher and Muller's theory that recombination speeds adaptation by eliminating competition among beneficial mutations has proved a popular explanation for the advantage of sex. Recent theoretical studies have attempted to quantify the speed of adaptation under the Fisher-Muller model, partly in an attempt to understand the role of "clonal interference" in microbial experimental evolution. We reexamine adaptation in sexuals vs. asexuals, using a model of DNA sequence evolution. In this model, a modest number of sites can mutate to beneficial alleles and the fitness effects of these mutations are unequal. We study (1) transition probabilities to different beneficial mutations; (2) waiting times to the first and the last substitutions of beneficial mutations; and (3) trajectories of mean fitness through time. We find that some of these statistics are surprisingly similar between sexuals and asexuals. These results highlight the importance of the choice of substitution model in assessing the Fisher-Muller advantage of sex.

Recent studies of the genetics of speciation in Drosophila have focused on two problems: (i) identifying and characterizing the genes that cause reproductive isolation, and (ii) determining the evolutionary forces that drove the divergence of these "speciation genes." Here, I review this work. I conclude that speciation genes correspond to ordinary loci having normal functions within species. These genes fall into several functional classes, although a role in transcriptional regulation could prove particularly common. More important, speciation genes are typically very rapidly evolving, and this divergence is often driven by positive Darwinian selection. Finally, I review recent work in Drosophila pseudoobscura on the possible role of meiotic drive in the evolution of the genes that cause postzygotic isolation.

We show that, contrary to claims in the literature, "sterile" males resulting from the cross of the Bogota and USA subspecies of Drosophila pseudoobscura are weakly fertile. Surprisingly, these hybrid males produce almost all daughters when crossed to females of any genotype (pure Bogota, pure USA, hybrid F1). Several lines of evidence suggest that this sex ratio distortion is caused by sex chromosome segregation distortion in hybrid males. We genetically analyze this normally cryptic segregation distortion and show that it involves several regions of the Bogota X chromosome that show strong epistatic interactions with each other. We further show that segregation distortion is normally masked within the Bogota subspecies by autosomal suppressors. Our analysis shows that the genetic basis of hybrid segregation distortion is similar to that of hybrid male sterility between the same subspecies. Indeed the severity of segregation distortion is correlated with the severity of sterility among hybrids. We discuss the possibility that hybrid sterility in this paradigmatic case of incipient speciation is caused by segregation distortion.

Theoretical work on adaptation has lagged behind experimental. But two classes of adaptation model have been partly explored. One is phenotypic and the other DNA sequence based. I briefly consider an example of each--Fisher's geometric model and Gillespie's mutational landscape model, respectively--reviewing recent results. Despite their fundamental differences, these models give rise to several strikingly similar results. I consider possible reasons for this congruence. I also emphasize what predictions do and, as important, do not follow from these models.

Theoretical studies of adaptation have exploded over the past decade. This work has been inspired by recent, surprising findings in the experimental study of adaptation. For example, morphological evolution sometimes involves a modest number of genetic changes, with some individual changes having a large effect on the phenotype or fitness. Here I survey the history of adaptation theory, focusing on the rise and fall of various views over the past century and the reasons for the slow development of a mature theory of adaptation. I also discuss the challenges that face contemporary theories of adaptation.

How often will natural selection drive parallel evolution at the DNA sequence level? More precisely, what is the probability that selection will cause two populations that live in identical environments to substitute the same beneficial mutation? Here I show that, under fairly general conditions, the answer is simple: if a wild-type sequence can mutate to n different beneficial mutations, replicate populations will on average fix the same mutation with probability P = 2/(n + 1). This probability, which is derived using extreme value theory, is independent of most biological details, including the length of the gene in question and the precise distribution of fitness effects among alleles. I conclude that the probability of parallel evolution under natural selection is nearly twice as large as that under neutrality.

We study levels of X-linked vs. autosomal diversity using a model developed to analyze the hitchhiking effect. Repeated bouts of hitchhiking are thought to lower X-linked diversity for two reasons: first, because sojourn times of beneficial mutations are shorter on the X, and second, because adaptive substitutions may be more frequent on the X. We investigate whether each of these effects does, in fact, cause reduced X-linked diversity under hitchhiking. We study the strength of the hitchhiking effect on the X vs. autosomes when there is no recombination and under two different recombination schemes. When recombination occurs in both sexes, X-linked vs. autosomal diversity is reduced by hitchhiking under a broad range of conditions, but when there is no recombination in males, as in Drosophila, the required conditions are considerably more restrictive.

Until recently, the genes that cause reproductive isolation remained black boxes. Consequently, evolutionary biologists were unable to answer several questions about the identities and characteristics of "speciation genes". Over the past few years, however, evolutionary geneticists have finally succeeded in isolating several such genes, providing our first glimpse at factors that are thought to be representative of those underlying the origin of species. Evolutionary analysis of these genes suggests that speciation results from positive Darwinian selection within species. Molecular evolutionary study of the genes causing reproductive isolation may represent an important new phase in the study of speciation.

Speciation--the splitting of one species into two--occurs by the evolution of any of several forms of reproductive isolation between taxa, including the intrinsic sterility and inviability of hybrids. Abundant evidence shows that these hybrid fitness problems are caused by incompatible interactions between loci: new alleles that become established in one species are sometimes functionally incompatible with alleles at interacting loci from another species. However, almost nothing is known about the genes involved in such hybrid incompatibilities or the evolutionary forces that drive their divergence. Here we identify a gene that causes epistatic inviability in hybrids between two fruitfly species, Drosophila melanogaster and D. simulans. Our population genetic analysis reveals that this gene--which encodes a nuclear pore protein--evolved by positive natural selection in both species' lineages. These results show that a lethal hybrid incompatibility has evolved as a by-product of adaptive protein evolution.

We know little about the distribution of fitness effects among new beneficial mutations, a problem that partly reflects the rarity of these changes. Surprisingly, though, population genetic theory allows us to predict what this distribution should look like under fairly general assumptions. Using extreme value theory, I derive this distribution and show that it has two unexpected properties. First, the distribution of beneficial fitness effects at a gene is exponential. Second, the distribution of beneficial effects at a gene has the same mean regardless of the fitness of the present wild-type allele. Adaptation from new mutations is thus characterized by a kind of invariance: natural selection chooses from the same spectrum of beneficial effects at a locus independent of the fitness rank of the present wild type. I show that these findings are reasonably robust to deviations from several assumptions. I further show that one can back calculate the mean size of new beneficial mutations from the observed mean size of fixed beneficial mutations.

I consider the adaptation of a DNA sequence when mutant fitnesses are drawn randomly from a probability distribution. I focus on "gradient" adaptation in which the population jumps to the best mutant sequence available at each substitution. Given a random starting point, I derive the distribution of the number of substitutions that occur during adaptive walks to a locally optimal sequence. I show that the mean walk length is a constant:L = e-1, where e approximately 2.72. I argue that this result represents a limit on what is possible under any form of adaptation. No adaptive algorithm on any fitness landscape can arrive at a local optimum in fewer than a mean of L = e-1 steps when starting from a random sequence. Put differently, evolution must try out at least e wild-type sequences during an average bout of adaptation.

I describe several patterns characterizing the genetics of adaptation at the DNA level. Following Gillespie (1983, 1984, 1991), I consider a population presently fixed for the ith best allele at a locus and study the sequential substitution of favorable mutations that results in fixation of the fittest DNA sequence locally available. Given a wild type sequence that is less than optimal, I derive the fitness rank of the next allele typically fixed by natural selection as well as the mean and variance of the jump in fitness that results when natural selection drives a substitution. Looking over the whole series of substitutions required to reach the best allele, I show that the mean fitness jumps occurring throughout an adaptive walk are constrained to a twofold window of values, assuming only that adaptation begins from a reasonably fit allele. I also show that the first substitution and the substitution of largest effect account for a large share of the total fitness increase during adaptation. I further show that the distribution of selection coefficients fixed throughout such an adaptive walk is exponential (ignoring mutations of small effect), a finding reminiscent of that seen in Fisher's geometric model of adaptation. Last, I show that adaptation by natural selection behaves in several respects as the average of two idealized forms of adaptation, perfect and random.

We analyzed the genetic basis of postzygotic isolation between the Bogota and USA subspecies of Drosophila pseudoobscura. These subspecies diverged very recently (perhaps as recently as 155,000 to 230,000 years ago) and are partially reproductively isolated: Bogota and USA show very little prezygotic isolation but form sterile F1 males in one direction of the hybridization. We dissected the basis of this hybrid sterility and reached four main conclusions. First, postzygotic isolation appears to involve a modest number of genes: we found large chromosome regions that have no effect on hybrid fertility. Second, although apparently few in number, the factors causing hybrid sterility show a remarkably complex pattern of epistatic interaction. Hybrids suffer no hybrid sterility until they carry the "right" allele (Bogota vs. USA) at at least four loci. We describe the complete pattern of interactions between all chromosome regions known to affect hybrid fertility. Third, hybrid sterility is caused mainly by X-autosomal incompatibilities. Fourth, hybrid sterility does not involve a maternal effect, despite earlier claims to the contrary. In general, our results suggest that fewer genes are required for the appearance of hybrid sterility than implied by previous studies of older pairs of Drosophila species. Indeed, a maximum likelihood analysis suggests that roughly 15 hybrid male steriles separate the Bogota and USA subspecies. Only a subset of these would act in F1 hybrids.

Hybrid sterility and inviability often result from the accumulation of substitutions that, while functional on their normal genetic backgrounds, cause a loss of fitness when brought together in hybrids. Previous theory has shown that such Dobzhansky-Muller incompatibilities should accumulate at least as fast as the square of the number of substitutions separating two species, the so-called snowball effect. Here we explicitly describe the stochastic accumulation of these incompatibilities as a function of time. The accumulation of these incompatibilities involves three levels of stochasticity: (1) the number of substitutions separating two allopatric lineages at a given time; (2) the number of incompatibilities resulting from these substitutions; and (3) the fitness effects of individual incompatibilities. Previous analyses ignored the stochasticity of molecular evolution (level 1) as well as that due to the variable effects of incompatibilities (level 3). Here we approximate the full stochastic process characterizing the accumulation of hybrid incompatibilities between pairs of loci. We derive the distribution of the number of incompatibilities as a function of divergence time between allopatric taxa as well as the distribution of waiting times to speciation by postzygotic isolation. We provide simple approximations for the mean and variance of these waiting times. These results let us estimate. albeit crudely, the probability, p, that two diverged sites from different species will contribute to hybrid sterility or inviability. Our analyses of data from Drosophila and Bombina suggest that p is generally very small, on the order of 10(-6) or less.

We consider populations that adapt to a sudden environmental change by fixing alleles found at mutation-selection balance. In particular, we calculate probabilities of fixation for previously deleterious alleles, ignoring the input of new mutations. We find that "Haldane's sieve"--the bias against the establishment of recessive beneficial mutations--does not hold under these conditions. Instead probabilities of fixation are generally independent of dominance. We show that this result is robust to patterns of sex expression for both X-linked and autosomal loci. We further show that adaptive evolution is invariably slower at X-linked than autosomal loci when evolution begins from mutation-selection balance. This result differs from that obtained when adaptation uses new mutations, a finding that may have some bearing on recent attempts to distinguish between hitchhiking and background selection by contrasting the molecular population genetics of X-linked vs. autosomal loci. Last, we suggest a test to determine whether adaptation used new mutations or previously deleterious alleles from the standing genetic variation.

New species arise as reproductive isolation evolves between diverging populations. Here we review recent work in the genetics of postzygotic reproductive isolation-the sterility and inviability of species hybrids. Over the last few years, research has taken two new directions. First, we have begun to learn a good deal about the population genetic forces driving the evolution of postzygotic isolation. It has, for instance, become increasingly clear that conflict-driven processes, like sexual selection and meiotic drive, may contribute to the evolution of hybrid sterility. Second, we have begun to learn something about the identity and molecular characteristics of the actual genes causing hybrid problems. Although molecular genetic data are limited, early findings suggest that "speciation genes" correspond to loci having normal functions within species and that these loci sometimes diverge as a consequence of evolution in gene regulation.

I study the population genetics of adaptation in asexuals. I show that the rate of adaptive substitution in an asexual species or nonrecombining chromosome region is a bell-shaped function of the mutation rate: at some point, increasing the mutation rate decreases the rate of substitution. Curiously, the mutation rate that maximizes the rate of adaptation depends solely on the strength of selection against deleterious mutations. In particular, adaptation is fastest when the genomic rate of mutation, U, equals the harmonic mean of selection coefficients against deleterious mutations, where we assume that selection for favorable alleles is milder than that against deleterious ones. This simple result is independent of the shape of the distribution of effects among favorable and deleterious mutations, population size, and the action of clonal interference. In the course of this work, I derive an approximation to the probability of fixation of a favorable mutation in an asexual genome or nonrecombining chromosome region in which both favorable and deleterious mutations occur.

Several hybrid rescue mutations-alleles that restore the viability of normally lethal hybrids-have been discovered in Drosophila melanogaster and its relatives. Here we analyze one of these genes, Hybrid male rescue (Hmr), asking two questions about its role in hybrid inviability. (1) Does the wild-type allele from D. melanogaster (Hmr(mel)) cause hybrid embryonic inviability? (2) Does Hmr(mel) cause hybrid larval inviability? Our results show that the wild-type product of Hmr is neither necessary nor sufficient for hybrid embryonic inviability. Hmr(mel) does, however, appear to lower the viability of hybrid larvae. The data further suggest (though do not prove) that Hmr(mel) acts as a gain-of-function poison in hybrids. These findings support previous claims that hybrid embryonic and larval lethalities are genetically distinct and suggest that Hmr(mel) is at least one of the proximate causes of hybrid larval inviability.

The sterility and inviability of species hybrids can be explained by between-locus "Dobzhansky-Muller" incompatibilities: alleles that are fit on their "normal" genetic backgrounds sometimes lower fitness when brought together in hybrids. We present a model of two-locus incompatibilities that distinguishes among three types of hybrid interactions: those between heterozygous loci (H(0)), those between a heterozygous and a homozygous (or hemizygous) locus (H(1)), and those between homozygous loci (H(2)). We predict the relative fitnesses of hybrid genotypes by calculating the expected numbers of each type of incompatibility. We use this model to study Haldane's rule and the large effect of X chromosomes on postzygotic isolation. We show that the severity of H(0) vs. H(1) incompatibilities is key to understanding Haldane's rule, while the severity of H(1) vs. H(2) incompatibilities must also be considered to explain large X effects. Large X effects are not inevitable in backcross analyses but rather-like Haldane's rule-may often reflect the recessivity of alleles causing postzygotic isolation. We also consider incompatibilities involving the Y (or W) chromosome and maternal effects. Such incompatibilities are common in Drosophila species crosses, and their consequences in male- vs. female-heterogametic taxa may explain the pattern of exceptions to Haldane's rule.