Multilocus interactions restrict gene introgression in interspecific populations of polyploid Gossypium (cotton)

Abstract.— Experimental advanced-generation backcross populations contain individuals with genomic compositions similar to those resulting from interspecific hybridization in nature. By applying a detailed restriction fragment length polymorphism (RFLP) map to 3662 BC₃F₂ plants derived from 24 different BC₁ individuals of a cross between Gossypium hirsutum and G. barbadense , large and widespread deficiencies of donor ( G. barbadense ) chromatin were found, and seven independent chromosomal regions were entirely absent. This skewed chromatin transmission is best accounted for by multilocus epistatic interactions affecting chromatin transmission. The observed frequencies of two-locus genotypes were significantly different from Mendelian expectations about 26 times more often than could be explained by chance ( P ≤ 0.01). For identical pairs of loci, different two-locus genotypes occurred in excess in different BC₃ families, implying the existence of higher-order interlocus interactions beyond the resolution of these data. Some G. barbadense markers occurred more frequently than expected by chance, indicating that genomic interactions do not always favor host chromatin. A preponderance of interspecific allelic interactions involved one locus each in the two different subgenomes of (allotetraploid) Gossypium , thus supporting several other lines of evidence suggesting that intersubgenomic interactions contribute to unique features that distinguish tetraploid cotton from its diploid ancestors.     

The Impact of Macroscopic Epistasis on Long-Term Evolutionary Dynamics

Genetic interactions can strongly influence the fitness effects of individual mutations, yet the impact of these epistatic interactions on evolutionary dynamics remains poorly understood. Here we investigate the evolutionary role of epistasis over 50,000 generations in a well-studied laboratory evolution experiment in Escherichia coli. The extensive duration of this experiment provides a unique window into the effects of epistasis during long-term adaptation to a constant environment. Guided by analytical results in the weak-mutation limit, we develop a computational framework to assess the compatibility of a given epistatic model with the observed patterns of fitness gain and mutation accumulation through time. We find that a decelerating fitness trajectory alone provides little power to distinguish between competing models, including those that lack any direct epistatic interactions between mutations. However, when combined with the mutation trajectory, these observables place strong constraints on the set of possible models of epistasis, ruling out many existing explanations of the data. Instead, we find that the data are consistent with a “two-epoch” model of adaptation, in which an initial burst of diminishing-returns epistasis is followed by a steady accumulation of mutations under a constant distribution of fitness effects. Our results highlight the need for additional DNA sequencing of these populations, as well as for more sophisticated models of epistasis that are compatible with all of the experimental data.     

GENETIC ARCHITECTURE AND POSTZYGOTIC REPRODUCTIVE ISOLATION: EVOLUTION OF BATESON–DOBZHANSKY–MULLER INCOMPATIBILITIES IN A POLYGENIC MODEL

The Bateson–Dobzhansky–Muller model predicts that postzygotic isolation evolves due to the accumulation of incompatible epistatic interactions, but few studies have quantified the relationship between genetic architecture and patterns of reproductive divergence. We examined how the direction and magnitude of epistatic interactions in a polygenic trait under stabilizing selection influenced the evolution of hybrid incompatibilities. We found that populations evolving independently under stabilizing selection experienced suites of compensatory allelic changes that resulted in genetic divergence between populations despite the maintenance of a stable, high‐fitness phenotype. A small number of loci were then incompatible with multiple alleles in the genetic background of the hybrid and the identity of these incompatibility loci changed over the evolution of the populations. For F₁ hybrids, reduced fitness evolved in a window of intermediate strengths of epistatic interactions, but F₂ and backcross hybrids evolved reduced fitness across weak and moderate strengths of epistasis due to segregation variance. Strong epistatic interactions constrained the allelic divergence of parental populations and prevented the development of reproductive isolation. Because many traits with varying genetic architectures must be under stabilizing selection, our results indicate that polygenetic drift is a plausible hypothesis for the evolution of postzygotic reproductive isolation.     

Epistatic Adaptive Evolution of Human Color Vision

Establishing genotype-phenotype relationship is the key to understand the molecular mechanism of phenotypic adaptation. This initial step may be untangled by analyzing appropriate ancestral molecules, but it is a daunting task to recapitulate the evolution of non-additive (epistatic) interactions of amino acids and function of a protein separately. To adapt to the ultraviolet (UV)-free retinal environment, the short wavelength-sensitive (SWS1) visual pigment in human (human S1) switched from detecting UV to absorbing blue light during the last 90 million years. Mutagenesis experiments of the UV-sensitive pigment in the Boreoeutherian ancestor show that the blue-sensitivity was achieved by seven mutations. The experimental and quantum chemical analyses show that 4,008 of all 5,040 possible evolutionary trajectories are terminated prematurely by containing a dehydrated nonfunctional pigment. Phylogenetic analysis further suggests that human ancestors achieved the blue-sensitivity gradually and almost exclusively by epistasis. When the final stage of spectral tuning of human S1 was underway 45–30 million years ago, the middle and long wavelength-sensitive (MWS/LWS) pigments appeared and so-called trichromatic color vision was established by interprotein epistasis. The adaptive evolution of human S1 differs dramatically from orthologous pigments with a major mutational effect used in achieving blue-sensitivity in a fish and several mammalian species and in regaining UV vision in birds. These observations imply that the mechanisms of epistatic interactions must be understood by studying various orthologues in different species that have adapted to various ecological and physiological environments.     

Random Amplified Polymorphic DNA Diversity among Surface and Subterranean Populations of Asellus aquaticus (Crustacea: Isopoda)

The ecological and evolutionary processes leading to isolation and adaptation of cave animals compared to their surface ancestors are not yet unequivocally understood. In this study the genetic relations of four cave and three surface population of the freshwater crustacean Asellus aquaticus in the Karst region of SW Slovenia and NE Italy were assessed using RAPDs as genetic markers. The results suggest that specialized populations from two caves invaded their subterranean habitat independently, and that their morphological similarity is a result of convergent evolution. Another, less specialized cave population seems to originate from a later colonization of a cave system already inhabited by a more specialized population, but the two populations do not interbreed. This series of temporally and spatially independent invasions has generated a diversity hotspot of non-interbreeding populations of a ubiquitous freshwatercrustacean, which is uniform over most of its range. Genetic variability estimated by the percentage of polymorphic RAPD fragments was similar (86–91%) in most cave and surface populations. Substantially lower values (as low as 49%) were found in two cave populations affected by heavy pollution. Two a priori groupings of populations, traditional subspecies and hydrologically connected groups, were rejected as not significant by means of nested analysis of molecular variance (AMOVA). On the other hand, groupings revealed by UPGMA clustering displayed a significant component of among-group variance. An analysis of gene flow between populations using estimated migration rates confirmed these findings.     

Reduction in the metabolic levels due to phenotypic plasticity in the Pyrenean newt,Calotriton asper,during cave colonization

According to theories on cave adaptation, cave organisms are expected to develop a lower metabolic rate compared to surface organisms as an adaptation to food scarcity in the subterranean environments. To test this hypothesis, we compared the oxygen consumption rates of the surface and subterranean populations of a surface‐dwelling species, the newt Calotriton asper, occasionally found in caves. In this study, we designed a new experimental setup in which animals with free movement were monitored for several days in a respirometer. First, we measured the metabolic rates of individuals from the surface and subterranean populations, both maintained for eight years in captivity in a natural cave. We then tested individuals from these populations immediately after they were caught and one year later while being maintained in the cave. We found that the surface individuals that acclimated to the cave significantly reduced their oxygen consumption, whereas individuals from the subterranean population maintained in the cave under a light/dark cycle did not significantly modify their metabolic rates. Second, we compared these metabolic rates to those of an obligate subterranean salamander (Proteus anguinus), a surface aquatic Urodel (Ambystoma mexicanum), and a fish species (Gobio occitaniae) as references for surface organisms from different phyla. As predicted, we found differences between the subterranean and surface species, and the metabolic rates of surface and subterranean C. asper populations were between those of the obligate subterranean and surface species. These results suggest that the plasticity of the metabolism observed in surface C. asper was neither directly due to food availability in our experiments nor the light/dark conditions, but due to static temperatures. Moreover, we suggest that this adjustment of the metabolic level at a temperature close to the thermal optimum may further allow individual species to cope with the food limitations of the subterranean environment.     

Evolution in caves: Darwin’s ‘wrecks of ancient life’ in the molecular era

Cave animals have historically attracted the attention of evolutionary biologists because of their bizarre ‘regressive’ characters and convergent evolution. However, understanding of their biogeographic and evolutionary history, including mechanisms of speciation, has remained elusive. In the last decade, molecular data have been obtained for subterranean taxa and their surface relatives, which have allowed some of the classical debates on the evolution of cave fauna to be revisited. Here, we review some of the major studies, focusing on the contribution of phylogeography in the following areas: biogeographic history and the relative roles of dispersal and vicariance, colonization history, cryptic species diversity and modes of speciation of cave animals. We further consider the limitations of current research and prospects for the future. Phylogeographic studies have confirmed that cave species are often cryptic, with highly restricted distributions, but have also shown that their divergence and potential speciation may occur despite the presence of gene flow from surface populations. Significantly, phylogeographic studies have provided evidence for speciation and adaptive evolution within the confines of cave environments, questioning the assumption that cave species evolved directly from surface ancestors. Recent technical developments involving ‘next generation’ DNA sequencing and theoretical developments in coalescent and population modelling are likely to revolutionize the field further, particularly in the study of speciation and the genetic basis of adaptation and convergent evolution within subterranean habitats. In summary, phylogeographic studies have provided an unprecedented insight into the evolution of these unique fauna, and the future of the field should be inspiring and data rich.     

Parallel morphological evolution and habitat‐dependent sexual dimorphism in cave‐ vs. surface populations of the Asellus aquaticus (Crustacea: Isopoda: Asellidae) species complex

Studying parallel evolution (repeated, independent evolution of similar phenotypes in similar environments) is a powerful tool to understand environment‐dependent selective forces. Surface‐dwelling species that repeatedly and independently colonized caves provide unique models for such studies. The primarily surface‐dwelling Asellus aquaticus species complex is a good candidate to carry out such research, because it colonized several caves in Europe. By comparing 17 functional morphological traits between six cave and nine surface populations of the A. aquaticus species complex, we investigated population divergence in morphology and sexual dimorphism. We found habitat‐dependent population divergence in 10 out of 17 traits, likely reflecting habitat‐driven changes in selection acting on sensory systems, feeding, grooming, and antipredator mechanisms. Sexual dimorphism was present in 15 traits, explained by sexual selection acting on male traits important in male–male agonistic behavior or mate guarding and fecundity selection acting on female traits affecting offspring number and nursing. In eight traits, the degree of sexual dimorphism was habitat dependent. We conclude that cave‐related morphological changes are highly trait‐ and function‐specific and that the strength of sexual/fecundity selection strongly differs between cave and surface habitats. The considerable population variation within habitat type warrants further studies to reveal cave‐specific adaptations besides the parallel patterns.     

The Evolution of Epigean and Stygobitic Species of Koonunga Sayce, 1907 (Syncarida: Anaspidacea) in Southern Australia,with the Description of Three New Species

Three new species of Koonunga were discovered in surface and subterranean waters in southern Australia, and were defined using mtDNA analyses and morphology. The new species are: Koonunga hornei Leijs & King; K. tatiaraensis Leijs & King and K. allambiensis Leijs & King. Molecular clock analyses indicate that the divergence times of the species are older than the landscape that they currently inhabit. Different scenarios explaining this apparent discrepancy are discussed in the context of the palaeography of the area. A freshwater epigean origin for Koonunga is considered the most likely hypothesis, whereby some lineages made the transition to the subterranean environment within the last few million years influenced by significant climatic cooling/drying. We discuss the possibility that one stygobitic lineage secondarily regained some of its body pigmentation as adaptation to increased photic conditions after cave collapse and forming of cenotes during the last glacial maximum.     

Genome Wide Association for Addiction: Replicated Results and Comparisons of Two Analytic Approaches

Background

Vulnerabilities to dependence on addictive substances are substantially heritable complex disorders whose underlying genetic architecture is likely to be polygenic, with modest contributions from variants in many individual genes. “Nontemplate” genome wide association (GWA) approaches can identity groups of chromosomal regions and genes that, taken together, are much more likely to contain allelic variants that alter vulnerability to substance dependence than expected by chance.

Methodology/Principal Findings

We report pooled “nontemplate” genome-wide association studies of two independent samples of substance dependent vs control research volunteers (n = 1620), one European-American and the other African-American using 1 million SNP (single nucleotide polymorphism) Affymetrix genotyping arrays. We assess convergence between results from these two samples using two related methods that seek clustering of nominally-positive results and assess significance levels with Monte Carlo and permutation approaches. Both “converge then cluster” and “cluster then converge” analyses document convergence between the results obtained from these two independent datasets in ways that are virtually never found by chance. The genes identified in this fashion are also identified by individually-genotyped dbGAP data that compare allele frequencies in cocaine dependent vs control individuals.

Conclusions/Significance

These overlapping results identify small chromosomal regions that are also identified by genome wide data from studies of other relevant samples to extents much greater than chance. These chromosomal regions contain more genes related to “cell adhesion” processes than expected by chance. They also contain a number of genes that encode potential targets for anti-addiction pharmacotherapeutics. “Nontemplate” GWA approaches that seek chromosomal regions in which nominally-positive associations are found in multiple independent samples are likely to complement classical, “template” GWA approaches in which “genome wide” levels of significance are sought for SNP data from single case vs control comparisons.     

Mutations in Global Regulators Lead to Metabolic Selection during Adaptation to Complex Environments

Adaptation to ecologically complex environments can provide insights into the evolutionary dynamics and functional constraints encountered by organisms during natural selection. Adaptation to a new environment with abundant and varied resources can be difficult to achieve by small incremental changes if many mutations are required to achieve even modest gains in fitness. Since changing complex environments are quite common in nature, we investigated how such an epistatic bottleneck can be avoided to allow rapid adaptation. We show that adaptive mutations arise repeatedly in independently evolved populations in the context of greatly increased genetic and phenotypic diversity. We go on to show that weak selection requiring substantial metabolic reprogramming can be readily achieved by mutations in the global response regulator arcA and the stress response regulator rpoS. We identified 46 unique single-nucleotide variants of arcA and 18 mutations in rpoS, nine of which resulted in stop codons or large deletions, suggesting that subtle modulations of ArcA function and knockouts of rpoS are largely responsible for the metabolic shifts leading to adaptation. These mutations allow a higher order metabolic selection that eliminates epistatic bottlenecks, which could occur when many changes would be required. Proteomic and carbohydrate analysis of adapting E. coli populations revealed an up-regulation of enzymes associated with the TCA cycle and amino acid metabolism, and an increase in the secretion of putrescine. The overall effect of adaptation across populations is to redirect and efficiently utilize uptake and catabolism of abundant amino acids. Concomitantly, there is a pronounced spread of more ecologically limited strains that results from specialization through metabolic erosion. Remarkably, the global regulators arcA and rpoS can provide a “one-step” mechanism of adaptation to a novel environment, which highlights the importance of global resource management as a powerful strategy to adaptation.     

Eyeless Mexican Cavefish Save Energy by Eliminating the Circadian Rhythm in Metabolism

The eyed surface form and eyeless cave form of the Mexican tetra Astyanax mexicanus experience stark differences in the daily periodicities of light, food and predation, factors which are likely to have a profound influence on metabolism. We measured the metabolic rate of Pachón cave and surface fish at a fixed swimming speed under light/dark and constant dark photoperiods. In constant darkness surface forms exhibited a circadian rhythm in metabolism with an increase in oxygen demand during the subjective daytime, whereas cave forms did not. The lack of circadian rhythm in metabolism leads to a 27% energy savings for Pachón cave fish compared to surface fish when comparing both forms in their natural photoperiods. When surface forms were tested under constant dark conditions they expended 38% more energy than cave forms under equivalent conditions. Elimination of the circadian rhythm in metabolism may be a general feature of animals that live in perpetually dark food-limited environments such as caves or the deep sea.     

Population genetics of grotto sculpin (Cottus specus), a new cave-adapted fish species

The grotto sculpin (Cottus specus) is a troglomorphic fish endemic to cave systems in Perry County, Missouri. These fish are state-threatened and were recently listed as federally endangered under the Endangered Species Act (ESA). Due to the unstable nature of the cave environment, grotto sculpins are highly susceptible to pollution via agricultural and waste runoff. Here we provide a summary of population genetic diversity within the range of the grotto sculpin. Samples from twenty-one cave, surface, and resurgence sites within and surrounding the Bois Brule drainage in Perry County, southeast Missouri, USA were collected and sequence data from the mitochondrial control were analyzed using analysis of molecular variance, maximum likelihood, parsimony, and Bayesian techniques. We found a substantial degree of divergence from surface populations of Midlands and Black River banded sculpin races (7.7–8.0 %). Within the Bois Brule drainage, two distinct lineages of grotto sculpin were identified which correspond with northern and southern cave system boundaries and may represent independent cave invasions.     

Long-term adaptation of epistatic genetic networks

Gene networks are likely to govern most traits in nature. Mutations at these genes often show functional epistatic interactions that lead to complex genetic architectures and variable fitness effects in different genetic backgrounds. Understanding how epistatic genetic systems evolve in nature remains one of the great challenges in evolutionary biology. Here we combine an analytical framework with individual-based simulations to generate novel predictions about long-term adaptation of epistatic networks. We find that relative to traits governed by independently evolving genes, adaptation with epistatic gene networks is often characterized by longer waiting times to selective sweeps, lower standing genetic variation, and larger fitness effects of adaptive mutations. This may cause epistatic networks to either adapt more slowly or more quickly relative to a nonepistatic system. Interestingly, epistatic networks may adapt faster even when epistatic effects of mutations are on average deleterious. Further, we study the evolution of epistatic properties of adaptive mutations in gene networks. Our results show that adaptive mutations with small fitness effects typically evolve positive synergistic interactions, whereas adaptive mutations with large fitness effects evolve positive synergistic and negative antagonistic interactions at approximately equal frequencies. These results provide testable predictions for adaptation of traits governed by epistatic networks and the evolution of epistasis within networks.     

Chest Radiographic Patterns and the Transmission of Tuberculosis: Implications for Automated Systems

BackgroundComputer-aided detection to identify and diagnose pulmonary tuberculosis is being explored. While both cavitation on chest radiograph and smear-positivity on microscopy are independent risk factors for the infectiousness of pulmonary tuberculosis it is unknown which radiographic pattern, were it detectable, would provide the greatest public health benefit; i.e. reduced transmission. Herein we provide that evidence.Objectives1) to determine whether pulmonary tuberculosis in a high income, low incidence country is more likely to present with “typical” adult-type pulmonary tuberculosis radiographic features and 2) to determine whether those with “typical” radiographic features are more likely than those without such features to transmit the organism and/or cause secondary cases.MethodsOver a three-year period beginning January 1, 2006 consecutive adults with smear-positive pulmonary tuberculosis in the Province of Alberta, Canada, were identified and their pre-treatment radiographs scored by three independent readers as “typical” (having an upper lung zone predominant infiltrate, with or without cavitation but no discernable adenopathy) or “atypical” (all others). Each patient’s pre-treatment bacillary burden was carefully documented and, during a 30-month transmission window, each patient’s transmission events were recorded. Mycobacteriology, radiology and transmission were compared in those with “typical” versus “atypical” radiographs.FindingsA total of 97 smear-positive pulmonary tuberculosis cases were identified, 69 (71.1%) with and 28 (28.9%) without “typical” chest radiographs. “Typical” cases were more likely to have high bacillary burdens and cavitation (Odds Ratios and 95% Confidence Intervals: 2.75 [1.04–7.31] and 9.10 [2.51–32.94], respectively). Typical cases were also responsible for most transmission events—78% of tuberculin skin test conversions (p<0.002) and 95% of secondary cases in reported close contacts (p<0.01); 94% of secondary cases in “unreported” contacts (p<0.02).ConclusionAs a group, smear-positive pulmonary tuberculosis patients with typical radiographic features constitute the greatest public health risk. This may have implications for automated detection systems.     

Environment Determines Epistatic Patterns for a ssDNA Virus

Despite the accumulation of substantial quantities of information about epistatic interactions among both deleterious and beneficial mutations in a wide array of experimental systems, neither consistent patterns nor causal explanations for these interactions have yet emerged. Furthermore, the effects of mutations depend on the environment in which they are characterized, implying that the environment may also influence epistatic interactions. Recent work with beneficial mutations for the single-stranded DNA bacteriophage ID11 demonstrated that interactions between pairs of mutations could be understood by means of a simple model that assumes that mutations have additive phenotypic effects and that epistasis arises through a nonlinear phenotype–fitness map with a single intermediate optimum. To determine whether such a model could also explain changes in epistatic patterns associated with changes in environment, we measured epistatic interactions for these same mutations under conditions for which we expected to find the wild-type ID11 at different distances from its phenotypic optimum by assaying fitnesses at three different temperatures: 33°, 37°, and 41°. Epistasis was present and negative under all conditions, but became more pronounced as temperature increased. We found that the additive-phenotypes model explained these patterns as changes in the parameters of the phenotype–fitness map, but that a model that additionally allows the phenotypes to vary across temperatures performed significantly better. Our results show that ostensibly complex patterns of fitness effects and epistasis across environments can be explained by assuming a simple structure for the genotype–phenotype relationship.     

Phylogeography of cave pseudoscorpions in southern Australia

Aim  To investigate molecular phylogenetic divergence and historical biogeography of the cave-dwelling pseudoscorpion genus Protochelifer.
Location  Caves and nearby epigean habitats in southern Australia were sampled from western Victoria, Naracoorte Caves, Flinders Ranges, Kangaroo Island, Nullarbor Plain and south-west Western Australia.
Methods  Allozyme electrophoresis (57 individuals) and a 569-base-pair section of the mtDNA COI gene (22 individuals) were used to reconstruct phylogenetic relationships among four cave species and three epigean species from 13 locations.
Results  Phylogenetic reconstruction using the allozyme and mtDNA sequence data revealed a similar topology, showing recent speciation of several Protochelifer populations in caves from Naracoorte to the Nullarbor Plain. Naracoorte Caves contained a single species, Protochelifer naracoortensis , found in four separate caves, while all other cave species appear to be restricted to single caves.
Main conclusions  At a local scale, as indicated by the four Naracoorte caves, dispersal is thought to occur via micro- and mesocaverns, and possibly by phoresy using insect or bat vectors. With current data we are unable to determine if cavernicolous species of Protochelifer have arisen from a single cave colonization event followed by phoretic dispersal on bats to other caves, or multiple cave-invasion events from independent epigean ancestors. Genetic heterogeneity among Protochelifer populations from Nullarbor caves suggest that P. cavernarum , the only species presently recorded from this region, is likely to constitute a species complex requiring further study to fully resolve its relationships.     

Adaptive introgression of the beta-globin cluster in two Andean waterfowl

Introgression of beneficial alleles has emerged as an important avenue for genetic adaptation in both plant and animal populations. In vertebrates, adaptation to hypoxic high-altitude environments involves the coordination of multiple molecular and cellular mechanisms, including selection on the hypoxia-inducible factor (HIF) pathway and the blood-O₂ transport protein hemoglobin (Hb). In two Andean duck species, a striking DNA sequence similarity reflecting identity by descent is present across the ~20 kb β-globin cluster including both embryonic (HBE) and adult (HBB) paralogs, though it was yet untested whether this is due to independent parallel evolution or adaptive introgression. In this study, we find that identical amino acid substitutions in the β-globin cluster that increase Hb-O₂ affinity have likely resulted from historical interbreeding between high-altitude populations of two different distantly-related species. We examined the direction of introgression and discovered that the species with a deeper mtDNA divergence that colonized high altitude earlier in history (Anas flavirostris) transferred adaptive genetic variation to the species with a shallower divergence (A. georgica) that likely colonized high altitude more recently possibly following a range shift into a novel environment. As a consequence, the species that received these β-globin variants through hybridization might have adapted to hypoxic conditions in the high-altitude environment more quickly through acquiring beneficial alleles from the standing, hybrid-origin variation, leading to faster evolution.Subject terms: Evolutionary genetics, Evolutionary biology     

Deleterious Passengers in Adapting Populations

Most new mutations are deleterious and are eventually eliminated by natural selection. But in an adapting population, the rapid amplification of beneficial mutations can hinder the removal of deleterious variants in nearby regions of the genome, altering the patterns of sequence evolution. Here, we analyze the interactions between beneficial “driver” mutations and linked deleterious “passengers” during the course of adaptation. We derive analytical expressions for the substitution rate of a deleterious mutation as a function of its fitness cost, as well as the reduction in the beneficial substitution rate due to the genetic load of the passengers. We find that the fate of each deleterious mutation varies dramatically with the rate and spectrum of beneficial mutations and the deleterious substitution rate depends nonmonotonically on the population size and the rate of adaptation. By quantifying this dependence, our results allow us to estimate which deleterious mutations will be likely to fix and how many of these mutations must arise before the progress of adaptation is significantly reduced.