Beyond the (geometric) mean: stochastic models undermine deterministic predictions of bet hedger evolution

Bet hedging is a ubiquitous strategy for risk reduction in the face of unpredictable environmental change where a lineage lowers its variance in fitness across environments at the expense of also lowering its arithmetic mean fitness. Classically, the benefit of bet hedging has been quantified using geometric mean fitness (GMF); bet hedging is expected to evolve if and only if it has a higher GMF than the wild-type. We build upon previous research on the effect of incorporating stochasticity in phenotypic distribution, environment, and reproduction to investigate the extent to which these sources of stochasticity will impact the evolution of real-world bet hedging traits. We utilize both individual-based simulations and Markov chain numerics to demonstrate that modeling stochasticity can alter the sign of selection for the bet hedger compared to deterministic predictions. We find that bet hedging can be deleterious at small population sizes and beneficial at larger population sizes. This non-monotonic dependence of the sign of selection on population size, known as sign inversion, exists across parameter space for both conservative and diversified bet hedgers. We apply our model to published data of bet hedging strategies to show that sign inversion exists for biologically relevant parameters in two study systems: Papaver dubium, an annual poppy with variable germination phenology, and Salmonella typhimurium, a pathogenic bacteria that exhibits antibiotic persistence. Taken together, our results suggest that GMF is not enough to predict when bet hedging is adaptive.

Developing evolution-resistant drugs for COVID-19

Analyzing how mutations affect the main protease of SARS-CoV-2 may help researchers develop drugs that are effective against current and future variants of the virus.

Covalent docking and molecular dynamics simulations reveal the specificity-shifting mutations Ala237Arg and Ala237Lys in TEM beta-lactamase

The rate of modern drug discovery using experimental screening methods still lags behind the rate at which pathogens mutate, underscoring the need for fast and accurate predictive simulations of protein evolution. Multidrug-resistant bacteria evade our defenses by expressing a series of proteins, the most famous of which is the 29-kilodalton enzyme, TEM β-lactamase. Considering these challenges, we applied a covalent docking heuristic to measure the effects of all possible alanine 237 substitutions in TEM due to this codon’s importance for catalysis and effects on the binding affinities of commercially-available β-lactam compounds. In addition to the usual mutations that reduce substrate binding due to steric hindrance, we identified two distinctive specificity-shifting TEM mutations, Ala237Arg and Ala237Lys, and their respective modes of action. Notably, we discovered and verified through minimum inhibitory concentration assays that, while these mutations and their bulkier side chains lead to steric clashes that curtail ampicillin binding, these same groups foster salt bridges with the negatively-charged side-chain of the cephalosporin cefixime, widely used in the clinic to treat multi-resistant bacterial infections. To measure the stability of these unexpected interactions, we used molecular dynamics simulations and found the binding modes to be stable despite the application of biasing forces. Finally, we found that both TEM mutants also bind strongly to other drugs containing negatively-charged R-groups, such as carumonam and ceftibuten. As with cefixime, this increased binding affinity stems from a salt bridge between the compounds’ negative moieties and the positively-charged side chain of the arginine or lysine, suggesting a shared mechanism. In addition to reaffirming the power of using simulations as molecular microscopes, our results can guide the rational design of next-generation β-lactam antibiotics and bring the community closer to retaking the lead against the recurrent threat of multidrug-resistant pathogens.

Genomic clustering of fitness-affecting mutations favors the evolution of chromosomal instability

Most solid cancers are characterized by chromosomal instability (CIN)-an elevated rate of large-scale chromosomal aberrations and ploidy changes. Chromosomal instability may arise through mutations in a range of genomic integrity loci and is commonly associated with fast disease progression, poor prognosis, and multidrug resistance. However, the evolutionary forces promoting CIN-inducing alleles (hereafter, CIN mutators) during carcinogenesis remain poorly understood. Here, we develop a stochastic, individual-based model of indirect selection experienced by CIN mutators via genomic associations with fitness-affecting mutations. Because mutations associated with CIN affect large swaths of the genome and have the potential to simultaneously comprise many individual loci, we show that indirect selection on CIN mutators is critically influenced by genome organization. In particular, we find strong support for a key role played by the spatial clustering of loci with either beneficial or deleterious mutational effects. Genomic clustering of selected loci allows CIN mutators to generate favorable chromosomal changes that facilitate their rapid expansion within a neoplasm and, in turn, accelerate carcinogenesis. We then examine the distribution of oncogenic and tumor-suppressing loci in the human genome and find both to be potentially more clustered along the chromosome than expected, leading us to speculate that human genome may be susceptible to CIN hitchhiking. More quantitative data on fitness effects of individual mutations will be necessary, though, to assess the true levels of clustering in the human genome and the effectiveness of indirect selection for CIN. Finally, we use our model to examine how therapeutic strategies that increase the deleterious burden of genetically unstable cells by raising either the rate of CIN or the cost of deleterious mutations affect CIN evolution. We find that both can inhibit CIN hitchhiking and delay carcinogenesis in some circumstances, yet, in line with earlier work, we find the latter to be considerably more effective.

Migration promotes mutator alleles in subdivided populations

Mutator alleles that elevate the genomic mutation rate may invade nonrecombining populations by hitchhiking with beneficial mutations. Mutators have been repeatedly observed to take over adapting laboratory populations and have been found at high frequencies in both microbial pathogen and cancer populations in nature. Recently, we have shown that mutators are only favored by selection in sufficiently large populations and transition to being disfavored as population size decreases. This population size-dependent sign inversion in selective effect suggests that population structure may also be an important determinant of mutation rate evolution. Although large populations may favor mutators, subdividing such populations into sufficiently small subpopulations (demes) might effectively inhibit them. On the other hand, migration between small demes that otherwise inhibit hitchhiking may promote mutator fixation in the whole metapopulation. Here, we use stochastic, agent-based simulations and evolution experiments with the yeast Saccharomyces cerevisiae to show that mutators can, indeed, be favored by selection in subdivided metapopulations composed of small demes connected by sufficient migration. In fact, we show that population structure plays a previously unsuspected role in promoting mutator success in subdivided metapopulations when migration is rare.

Patterns of musculoskeletal growth and dimensional changes associated with selection and developmental plasticity in domestic and wild strain turkeys

Domestication is a type of experimental evolution in which humans have artificially selected for specific desired traits. Selected strain animals can be utilized to identify correlated responses by comparing them to the wild strain. In particular, domestic turkeys have been selected for increased body mass and high‐growth rate, most significantly over the past 60 years. Yet it remains unclear how artificial selection has affected the morphology and evolution of the musculoskeletal system as a whole. Here, we compare growth rate over 21 weeks, hind limb bone scaling across ontogeny via in vivo CT scanning, and muscle proportions in wild and domestic turkeys to identify differences in structural scaling and the potential contributions of selection and developmental plasticity to whole‐organism morphology. The domestic turkeys grew at a higher rate (0.14 kg/day vs. 0.05 kg/day) and reached over 3 times the body mass of wild birds. Comparing the proportional muscle masses in adult turkeys, only the trunk had a greater mass ratio in the domestic turkey, driven solely by M. pectoralis (2.8 times larger). The proportional increase in only breast meat and no other muscles highlights the surgical precision attainable with artificial selection. The domestic turkey femur and tibiotarsus displayed increases in polar moment of area, apparently maintaining torsional strength as body mass increased. The lack of dimensional change in the more vertically held tarsometatarsus is consistent with the pattern expected due to developmental plasticity. These results from the domestic turkey emphasize that there are morphological limits to preserving the balance between growth and function, and varying rates of trait evolution can further complicate this equilibrium.

Sign of selection on mutation rate modifiers depends on population size

The influence of population size (N) on natural selection acting on alleles that affect fitness has been understood for almost a century. As N declines, genetic drift overwhelms selection and alleles with direct fitness effects are rendered neutral. Often, however, alleles experience so-called indirect selection, meaning they affect not the fitness of an individual but the fitness distribution of its offspring. Some of the best-studied examples of indirect selection include alleles that modify aspects of the genetic system such as recombination and mutation rates. Here, we use analytics, simulations, and experimental populations of Saccharomyces cerevisiae to examine the influence of N on indirect selection acting on alleles that increase the genomic mutation rate (mutators). Mutators experience indirect selection via genomic associations with beneficial and deleterious mutations they generate. We show that, as N declines, indirect selection driven by linked beneficial mutations is overpowered by drift before drift can neutralize the cost of the deleterious load. As a result, mutators transition from being favored by indirect selection in large populations to being disfavored as N declines. This surprising phenomenon of sign inversion in selective effect demonstrates that indirect selection on mutators exhibits a profound and qualitatively distinct dependence on N.

The Influence of Higher-Order Epistasis on Biological Fitness Landscape Topography

The effect of a mutation on the organism often depends on what other mutations are already present in its genome. Geneticists refer to such mutational interactions as epistasis. Pairwise epistatic effects have been recognized for over a century, and their evolutionary implications have received theoretical attention for nearly as long. However, pairwise epistatic interactions themselves can vary with genomic background. This is called higher-order epistasis, and its consequences for evolution are much less well understood. Here, we assess the influence that higher-order epistasis has on the topography of 16 published, biological fitness landscapes. We find that on average, their effects on fitness landscape declines with order, and suggest that notable exceptions to this trend may deserve experimental scrutiny. We conclude by highlighting opportunities for further theoretical and experimental work dissecting the influence that epistasis of all orders has on fitness landscape topography and on the efficiency of evolution by natural selection.

Enzyme Efficiency but Not Thermostability Drives Cefotaxime Resistance Evolution in TEM-1 β-Lactamase

A leading intellectual challenge in evolutionary genetics is to identify the specific phenotypes that drive adaptation. Enzymes offer a particularly promising opportunity to pursue this question, because many enzymes' contributions to organismal fitness depend on a comparatively small number of experimentally accessible properties. Moreover, on first principles the demands of enzyme thermostability stand in opposition to the demands of catalytic activity. This observation, coupled with the fact that enzymes are only marginally thermostable, motivates the widely held hypothesis that mutations conferring functional improvement require compensatory mutations to restore thermostability. Here, we explicitly test this hypothesis for the first time, using four missense mutations in TEM-1 β-lactamase that jointly increase cefotaxime Minimum Inhibitory Concentration (MIC) ∼1500-fold. First, we report enzymatic efficiency (kcat/KM) and thermostability (Tm, and thence ΔG of folding) for all combinations of these mutations. Next, we fit a quantitative model that predicts MIC as a function of kcat/KM and ΔG. While kcat/KM explains ∼54% of the variance in cefotaxime MIC (∼92% after log transformation), ΔG does not improve explanatory power of the model. We also find that cefotaxime MIC rises more slowly in kcat/KM than predicted. Several explanations for these discrepancies are suggested. Finally, we demonstrate substantial sign epistasis in MIC and kcat/KM, and antagonistic pleiotropy between phenotypes, in spite of near numerical additivity in the system. Thus constraints on selectively accessible trajectories, as well as limitations in our ability to explain such constraints in terms of underlying mechanisms are observed in a comparatively "well-behaved" system.

Variability in fitness effects can preclude selection of the fittest

Evolutionary biologists often predict the outcome of natural selection on an allele by measuring its effects on lifetime survival and reproduction of individual carriers. However, alleles affecting traits like sex, evolvability, and cooperation can cause fitness effects that depend heavily on differences in the environmental, social, and genetic context of individuals carrying the allele. This variability makes it difficult to summarize the evolutionary fate of an allele based solely on its effects on any one individual. Attempts to average over this variability can sometimes salvage the concept of fitness. In other cases evolutionary outcomes can only be predicted by considering the entire genealogy of an allele, thus limiting the utility of individual fitness altogether. We describe a number of intriguing new evolutionary phenomena that have emerged in studies that explicitly model long-term lineage dynamics and discuss implications for the evolution of infectious diseases.

Genetically Determined Variation in Lysis Time Variance in the Bacteriophage φX174

Researchers in evolutionary genetics recently have recognized an exciting opportunity in decomposing beneficial mutations into their proximal, mechanistic determinants. The application of methods and concepts from molecular biology and life history theory to studies of lytic bacteriophages (phages) has allowed them to understand how natural selection sees mutations influencing life history. This work motivated the research presented here, in which we explored whether, under consistent experimental conditions, small differences in the genome of bacteriophage φX174 could lead to altered life history phenotypes among a panel of eight genetically distinct clones. We assessed the clones' phenotypes by applying a novel statistical framework to the results of a serially sampled parallel infection assay, in which we simultaneously inoculated each of a large number of replicate host volumes with ∼1 phage particle. We sequentially plated the volumes over the course of infection and counted the plaques that formed after incubation. These counts served as a proxy for the number of phage particles in a single volume as a function of time. From repeated assays, we inferred significant, genetically determined heterogeneity in lysis time and burst size, including lysis time variance. These findings are interesting in light of the genetic and phenotypic constraints on the single-protein lysis mechanism of φX174. We speculate briefly on the mechanisms underlying our results, and we discuss the potential importance of lysis time variance in viral evolution.

Adaptive Landscape by Environment Interactions Dictate Evolutionary Dynamics in Models of Drug Resistance

The adaptive landscape analogy has found practical use in recent years, as many have explored how their understanding can inform therapeutic strategies that subvert the evolution of drug resistance. A major barrier to applications of these concepts is a lack of detail concerning how the environment affects adaptive landscape topography, and consequently, the outcome of drug treatment. Here we combine empirical data, evolutionary theory, and computer simulations towards dissecting adaptive landscape by environment interactions for the evolution of drug resistance in two dimensions-drug concentration and drug type. We do so by studying the resistance mediated by Plasmodium falciparum dihydrofolate reductase (DHFR) to two related inhibitors-pyrimethamine and cycloguanil-across a breadth of drug concentrations. We first examine whether the adaptive landscapes for the two drugs are consistent with common definitions of cross-resistance. We then reconstruct all accessible pathways across the landscape, observing how their structure changes with drug environment. We offer a mechanism for non-linearity in the topography of accessible pathways by calculating of the interaction between mutation effects and drug environment, which reveals rampant patterns of epistasis. We then simulate evolution in several different drug environments to observe how these individual mutation effects (and patterns of epistasis) influence paths taken at evolutionary "forks in the road" that dictate adaptive dynamics in silico. In doing so, we reveal how classic metrics like the IC50 and minimal inhibitory concentration (MIC) are dubious proxies for understanding how evolution will occur across drug environments. We also consider how the findings reveal ambiguities in the cross-resistance concept, as subtle differences in adaptive landscape topography between otherwise equivalent drugs can drive drastically different evolutionary outcomes. Summarizing, we discuss the results with regards to their basic contribution to the study of empirical adaptive landscapes, and in terms of how they inform new models for the evolution of drug resistance.

Quantitative Description of a Protein Fitness Landscape Based on Molecular Features

Understanding the driving forces behind protein evolution requires the ability to correlate the molecular impact of mutations with organismal fitness. To address this issue, we employ here metallo-β-lactamases as a model system, which are Zn(II) dependent enzymes that mediate antibiotic resistance. We present a study of all the possible evolutionary pathways leading to a metallo-β-lactamase variant optimized by directed evolution. By studying the activity, stability and Zn(II) binding capabilities of all mutants in the preferred evolutionary pathways, we show that this local fitness landscape is strongly conditioned by epistatic interactions arising from the pleiotropic effect of mutations in the different molecular features of the enzyme. Activity and stability assays in purified enzymes do not provide explanatory power. Instead, measurement of these molecular features in an environment resembling the native one provides an accurate description of the observed antibiotic resistance profile. We report that optimization of Zn(II) binding abilities of metallo-β-lactamases during evolution is more critical than stabilization of the protein to enhance fitness. A global analysis of these parameters allows us to connect genotype with fitness based on quantitative biochemical and biophysical parameters.

The evolution of phenotypic correlations and "developmental memory"

Development introduces structured correlations among traits that may constrain or bias the distribution of phenotypes produced. Moreover, when suitable heritable variation exists, natural selection may alter such constraints and correlations, affecting the phenotypic variation available to subsequent selection. However, exactly how the distribution of phenotypes produced by complex developmental systems can be shaped by past selective environments is poorly understood. Here we investigate the evolution of a network of recurrent nonlinear ontogenetic interactions, such as a gene regulation network, in various selective scenarios. We find that evolved networks of this type can exhibit several phenomena that are familiar in cognitive learning systems. These include formation of a distributed associative memory that can "store" and "recall" multiple phenotypes that have been selected in the past, recreate complete adult phenotypic patterns accurately from partial or corrupted embryonic phenotypes, and "generalize" (by exploiting evolved developmental modules) to produce new combinations of phenotypic features. We show that these surprising behaviors follow from an equivalence between the action of natural selection on phenotypic correlations and associative learning, well-understood in the context of neural networks. This helps to explain how development facilitates the evolution of high-fitness phenotypes and how this ability changes over evolutionary time.

Should evolutionary geneticists worry about higher-order epistasis?

Natural selection drives evolving populations up the fitness landscape, the projection from nucleotide sequence space to organismal reproductive success. While it has long been appreciated that topographic complexities on fitness landscapes can arise only as a consequence of epistatic interactions between mutations, evolutionary genetics has mainly focused on epistasis between pairs of mutations. Here we propose a generalization to the classical population genetic treatment of pairwise epistasis that yields expressions for epistasis among arbitrary subsets of mutations of all orders (pairwise, three-way, etc.). Our approach reveals substantial higher-order epistasis in almost every published fitness landscape. Furthermore we demonstrate that higher-order epistasis is critically important in two systems we know best. We conclude that higher-order epistasis deserves empirical and theoretical attention from evolutionary geneticists.

Fisher's geometric model of adaptation meets the functional synthesis: data on pairwise epistasis for fitness yields insights into the shape and size of phenotype space

The functional synthesis uses experimental methods from molecular biology, biochemistry and structural biology to decompose evolutionarily important mutations into their more proximal mechanistic determinants. However these methods are technically challenging and expensive. Noting strong formal parallels between R.A. Fisher's geometric model of adaptation and a recent model for the phenotypic basis of protein evolution, we sought to use the former to make inferences into the latter using data on pairwise fitness epistasis between mutations. We present an analytic framework for classifying pairs of mutations with respect to similarity of underlying mechanism on this basis, and also show that these data can yield an estimate of the number of mutationally labile phenotypes underlying fitness effects. We use computer simulations to explore the robustness of our approach to violations of analytic assumptions and analyze several recently published datasets. This work provides a theoretical complement to the functional synthesis as well as a novel test of Fisher's geometric model.

The interface of protein structure, protein biophysics, and molecular evolution

Abstract The interface of protein structural biology, protein biophysics, molecular evolution, and molecular population genetics forms the foundations for a mechanistic understanding of many aspects of protein biochemistry. Current efforts in interdisciplinary protein modeling are in their infancy and the state-of-the art of such models is described. Beyond the relationship between amino acid substitution and static protein structure, protein function, and corresponding organismal fitness, other considerations are also discussed. More complex mutational processes such as insertion and deletion and domain rearrangements and even circular permutations should be evaluated. The role of intrinsically disordered proteins is still controversial, but may be increasingly important to consider. Protein geometry and protein dynamics as a deviation from static considerations of protein structure are also important. Protein expression level is known to be a major determinant of evolutionary rate and several considerations including selection at the mRNA level and the role of interaction specificity are discussed. Lastly, the relationship between modeling and needed high-throughput experimental data as well as experimental examination of protein evolution using ancestral sequence resurrection and in vitro biochemistry are presented, towards an aim of ultimately generating better models for biological inference and prediction.

Genome structure and the benefit of sex

We examine the behavior of sexual and asexual populations in modular multipeaked fitness landscapes and show that sexuals can systematically reach different, higher fitness adaptive peaks than asexuals. Whereas asexuals must move against selection to escape local optima, sexuals reach higher fitness peaks reliably because they create specific genetic variants that "skip over" fitness valleys, moving from peak to peak in the fitness landscape. This occurs because recombination can supply combinations of mutations in functional composites or "modules," that may include individually deleterious mutations. Thus when a beneficial module is substituted for another less-fit module by sexual recombination it provides a genetic variant that would require either several specific simultaneous mutations in an asexual population or a sequence of individual mutations some of which would be selected against. This effect requires modular genomes, such that subsets of strongly epistatic mutations are tightly physically linked. We argue that such a structure is provided simply by virtue of the fact that genomes contain many genes each containing many strongly epistatic nucleotides. We briefly discuss the connections with "building blocks" in the evolutionary computation literature. We conclude that there are conditions in which sexuals can systematically evolve high-fitness genotypes that are essentially unevolvable for asexuals.

Geographic differences in sexual reassortment in RNA phage

The genetic structure of natural bacteriophage populations is poorly understood. Recent metagenomic studies suggest that phage biogeography is characterized by frequent migration. Using virus samples mostly isolated in Southern California, we recently showed that very little population structure exists in segmented RNA phage of the Cystoviridae family due to frequent segment reassortment (sexual genetic mixis) between unrelated virus individuals. Here we use a larger genetic dataset to examine the structure of Cystoviridae phage isolated from three geographic locations in Southern New England. We document extensive natural variation in the physical sizes of RNA genome segments for these viruses. In addition, consistent with earlier findings, our phylogenetic analyses and calculations of linkage disequilibrium (LD) show no evidence of within-segment recombination in wild populations. However, in contrast to the prior study, our analysis finds that reassortment of segments between individual phage plays a lesser role among cystoviruses sampled in New England, suggesting that the evolutionary importance of genetic mixis in Cystoviridae phage may vary according to geography. We discuss possible explanations for these conflicting results across the studies, such as differing local ecology and its impact on phage growth, and geographic differences in selection against hybrid phage genotypes.

Three selections are better than one: clinal variation of thermal QTL from independent selection experiments in Drosophila

We report the results of two independent selection experiments that have exposed distinct populations of Drosophila melanogaster to different forms of thermal selection. A recombinant population derived from Arvin California and Zimbabwe isofemale lines was exposed to laboratory natural selection at two temperatures (T(AZ): 18°C and 28°C). Microsatellite mapping identified quantitative trait loci (QTL) on the X-chromosome between the replicate "Hot" and "Cold" populations. In a separate experiment, disruptive selection was imposed on an outbred California population for the "knockdown" temperature (T(KD)) in a thermal column. Microsatellite mapping of the "High" and "Low" populations also uncovered primarily X-linked QTL. Notably, a marker in the shaggy locus at band 3A was significantly differentiated in both experiments. Finer scale mapping of the 3A region has narrowed the QTL to the shaggy gene region, which contains several candidate genes that function in circadian rhythms. The same allele that was increased in frequency in the High T(KD) populations is significantly clinal in North America and is more common at the warm end of the cline (Florida vs. Maine; however, the cline was not apparent in Australia). Together, these studies show that independent selection experiments can uncover the same target of selection and that evolution in the laboratory can recapitulate putatively adaptive clinal variation in nature.

Stepwise acquisition of pyrimethamine resistance in the malaria parasite

The spread of high-level pyrimethamine resistance in Africa threatens to curtail the therapeutic lifetime of antifolate antimalarials. We studied the possible evolutionary pathways in the evolution of pyrimethamine resistance using an approach in which all possible mutational intermediates were created by site-directed mutagenesis and assayed for their level of drug resistance. The coding sequence for dihydrofolate reductase (DHFR) from the malaria parasite Plasmodium falciparum was mutagenized, and tests were carried out in Escherichia coli under conditions in which the endogenous bacterial enzyme was selectively inhibited. We studied 4 key amino acid replacements implicated in pyrimethamine resistance: N51I, C59R, S108N, and I164L. Using empirical estimates of the mutational spectrum in P. falciparum and probabilities of fixation based on the relative levels of resistance, we found that the predicted favored pathways of drug resistance are consistent with those reported in previous kinetic studies, as well as DHFR polymorphisms observed in natural populations. We found that 3 pathways account for nearly 90% of the simulated realizations of the evolution of pyrimethamine resistance. The most frequent pathway (S108N and then C59R, N51I, and I164L) accounts for more than half of the simulated realizations. Our results also suggest an explanation for why I164L is detected in Southeast Asia and South America, but not at significant frequencies in Africa.

Temporal constraints on the incorporation of regulatory mutants in evolutionary pathways

Understanding the molecular details of the sequence of events in multistep evolutionary pathways can reveal the extent to which natural selection exploits regulatory mutations affecting expression, amino acid replacements affecting the active site, amino acid replacements affecting protein folding or stability, or variations affecting gene copy number. In experimentally exploring the adaptive landscape of the evolution of resistance to beta-lactam antibiotics in enteric bacteria, we noted that a regulatory mutation that increases beta-lactamase expression by about 2-fold has a very strong tendency to be fixed at or near the end of the evolutionary pathway. This pattern contrasts with previous experiments selecting for the utilization of novel substrates, in which regulatory mutations that increase expression are often fixed early in the process. To understand the basis of the difference, we carried out experiments in which the expression of beta-lactamase was under the control of a tunable arabinose promoter. We find that the fitness effect of an increase in gene expression is highly dependent on the catalytic activity of the coding sequence. An increase in expression of an inefficient enzyme has a negligible effect on drug resistance; however, the effect of an increase in expression of an efficient enzyme is very large. The contrast in the temporal incorporation of regulatory mutants between antibiotic resistance and the utilization of novel substrates is related to the nature of the function that relates enzyme activity to fitness. A mathematical model of beta-lactam resistance is examined in detail and shown to be consistent with the observed results.

Mutational Reversions During Adaptive Protein Evolution

Adaptation is often regarded as the sequential fixation of individually, intrinsically beneficial mutations. Contrary to this expectation, we find a surprisingly large number of evolutionary trajectories on which natural selection first favors a mutation, then favors its removal, and later still favors its ultimate restoration during the course of antibiotic resistance evolution. The existence of reversion trajectories implies that natural selection may not follow the most parsimonious path separating two alleles, even during adaptation. Altogether, this discovery highlights the unusual and potentially circuitous routes natural selection can follow during adaptation.

Empirical fitness landscapes reveal accessible evolutionary paths

When attempting to understand evolution, we traditionally rely on analysing evolutionary outcomes, despite the fact that unseen intermediates determine its course. A handful of recent studies has begun to explore these intermediate evolutionary forms, which can be reconstructed in the laboratory. With this first view on empirical evolutionary landscapes, we can now finally start asking why particular evolutionary paths are taken.

Patterns and mechanisms of genetic and phenotypic differentiation in marine microbes

Microbes in the ocean dominate biogeochemical processes and are far more diverse than anticipated. Thus, in order to understand the ocean system, we need to delineate microbial populations with predictable ecological functions. Recent observations suggest that ocean communities comprise diverse groups of bacteria organized into genotypic (and phenotypic) clusters of closely related organisms. Although such patterns are similar to metazoan communities, the underlying mechanisms for microbial communities may differ substantially. Indeed, the potential among ocean microbes for vast population sizes, extensive migration and both homologous and illegitimate genetic recombinations, which are uncoupled from reproduction, challenges classical population models primarily developed for sexually reproducing animals. We examine possible mechanisms leading to the formation of genotypic clusters and consider alternative population genetic models for differentiation at individual loci as well as gene content at the level of whole genomes. We further suggest that ocean bacteria follow at least two different adaptive strategies, which constrain rates and bounds of evolutionary processes: the 'opportunitroph', exploiting spatially and temporally variable resources; and the passive oligotroph, efficiently using low nutrient concentrations. These ecological lifestyle differences may represent a fundamental divide with major consequences for growth and predation rates, genome evolution and population diversity, as emergent properties driving the division of labour within microbial communities.

Effects of intra-gene fitness interactions on the benefit of sexual recombination

Whereas spontaneous point mutation operates on nucleotides individually, sexual recombination manipulates the set of nucleotides within an allele as an essentially particulate unit. In principle, these two different scales of variation enable selection to follow fitness gradients in two different spaces: in nucleotide sequence space and allele sequence space respectively. Epistasis for fitness at these two scales, between nucleotides and between genes, may be qualitatively different and may significantly influence the advantage of mutation-based and recombination-based evolutionary trajectories respectively. We examine scenarios where the genetic sequence within a gene strongly influences the fitness effect of a mutation in that gene, whereas epistatic interactions between sites in different genes are weak or absent. We find that, in cases where beneficial alleles of a gene differ from one another at several nucleotide sites, sexual populations can exhibit enormous benefit compared with asexual populations: not only discovering fit genotypes faster than asexual populations, but also discovering high-fitness genotypes that are effectively not evolvable in asexual populations.

Darwinian evolution can follow only very few mutational paths to fitter proteins

Five point mutations in a particular beta-lactamase allele jointly increase bacterial resistance to a clinically important antibiotic by a factor of approximately 100,000. In principle, evolution to this high-resistance beta-lactamase might follow any of the 120 mutational trajectories linking these alleles. However, we demonstrate that 102 trajectories are inaccessible to Darwinian selection and that many of the remaining trajectories have negligible probabilities of realization, because four of these five mutations fail to increase drug resistance in some combinations. Pervasive biophysical pleiotropy within the beta-lactamase seems to be responsible, and because such pleiotropy appears to be a general property of missense mutations, we conclude that much protein evolution will be similarly constrained. This implies that the protein tape of life may be largely reproducible and even predictable.

Missense meanderings in sequence space: a biophysical view of protein evolution

Proteins are finicky molecules; they are barely stable and are prone to aggregate, but they must function in a crowded environment that is full of degradative enzymes bent on their destruction. It is no surprise that many common diseases are due to missense mutations that affect protein stability and aggregation. Here we review the literature on biophysics as it relates to molecular evolution, focusing on how protein stability and aggregation affect organismal fitness. We then advance a biophysical model of protein evolution that helps us to understand phenomena that range from the dynamics of molecular adaptation to the clock-like rate of protein evolution.

Widespread genetic exchange among terrestrial bacteriophages

Bacteriophages are the most numerous entities in the biosphere. Despite this numerical dominance, the genetic structure of bacteriophage populations is poorly understood. Here, we present a biogeography study involving 25 previously undescribed bacteriophages from the Cystoviridae clade, a group characterized by a dsRNA genome divided into three segments. Previous laboratory manipulation has shown that, when multiple Cystoviruses infect a single host cell, they undergo (i) rare intrasegment recombination events and (ii) frequent genetic reassortment between segments. Analyzing linkage disequilibrium (LD) within segments, we find no significant evidence of intrasegment recombination in wild populations, consistent with (i). An extensive analysis of LD between segments supports frequent reassortment, on a time scale similar to the genomic mutation rate. The absence of LD within this group of phages is consistent with expectations for a completely sexual population, despite the fact that some segments have >50% nucleotide divergence at 4-fold degenerate sites. This extraordinary rate of genetic exchange between highly unrelated individuals is unprecedented in any taxa. We discuss our results in light of the biological species concept applied to viruses.

The rank ordering of genotypic fitness values predicts genetic constraint on natural selection on landscapes lacking sign epistasis

Sewall Wright's genotypic fitness landscape makes explicit one mechanism by which epistasis for fitness can constrain evolution by natural selection. Wright distinguished between landscapes possessing multiple fitness peaks and those with only a single peak and emphasized that the former class imposes substantially greater constraint on natural selection. Here I present novel formalism that more finely partitions the universe of possible fitness landscapes on the basis of the rank ordering of their genotypic fitness values. In this report I focus on fitness landscapes lacking sign epistasis (i.e., landscapes that lack mutations the sign of whose fitness effect varies epistatically), which constitute a subset of Wright's single peaked landscapes. More than one fitness rank ordering lacking sign epistasis exists for L > 2 (where L is the number of interacting loci), and I find that a highly statistically significant effect exists between landscape membership in fitness rank-ordering partition and two different proxies for genetic constraint, even within this subset of landscapes. This statistical association is robust to population size, permitting general inferences about some of the characteristics of fitness rank orderings responsible for genetic constraint on natural selection.

Perspective: Sign epistasis and genetic constraint on evolutionary trajectories

Epistasis for fitness means that the selective effect of a mutation is conditional on the genetic background in which it appears. Although epistasis is widely observed in nature, our understanding of its consequences for evolution by natural selection remains incomplete. In particular, much attention focuses only on its influence on the instantaneous rate of changes in frequency of selected alleles via epistatic contribution to the additive genetic variance for fitness. Thus, in this framework epistasis only has evolutionary importance if the interacting loci are simultaneously segregating in the population. However, the selective accessibility of mutational trajectories to high fitness genotypes may depend on the genetic background in which novel mutations appear, and this effect is independent of population polymorphism at other loci. Here we explore this second influence of epistasis on evolution by natural selection. We show that it is the consequence of a particular form of epistasis, which we designate sign epistasis. Sign epistasis means that the sign of the fitness effect of a mutation is under epistatic control; thus, such a mutation is beneficial on some genetic backgrounds and deleterious on others. Recent experimental innovations in microbial systems now permit assessment of the fitness effects of individual mutations on multiple genetic backgrounds. We review this literature and identify many examples of sign epistasis, and we suggest that the implications of these results may generalize to other organisms. These theoretical and empirical considerations imply that strong genetic constraint on the selective accessibility of trajectories to high fitness genotypes may exist and suggest specific areas of investigation for future research.

Rapid evolutionary escape by large populations from local fitness peaks is likely in nature

Fitness interactions between loci in the genome, or epistasis, can result in mutations that are individually deleterious but jointly beneficial. Such epistasis gives rise to multiple peaks on the genotypic fitness landscape. The problem of evolutionary escape from such local peaks has been a central problem of evolutionary genetics for at least 75 years. Much attention has focused on models of small populations, in which the sequential fixation of valley genotypes carrying individually deleterious mutations operates most quickly owing to genetic drift. However, valley genotypes can also be subject to mutation while transiently segregating, giving rise to copies of the high fitness escape genotype carrying the jointly beneficial mutations. In the absence of genetic recombination, these mutations may then fix simultaneously. The time for this process declines sharply with increasing population size, and it eventually comes to dominate evolutionary behavior. Here we develop an analytic expression for N(crit), the critical population size that defines the boundary between these regimes, which shows that both are likely to operate in nature. Frequent recombination may disrupt high-fitness escape genotypes produced in populations larger than N(crit) before they reach fixation, defining a third regime whose rate again slows with increasing population size. We develop a novel expression for this critical recombination rate, which shows that in large populations the simultaneous fixation of mutations that are beneficial only jointly is unlikely to be disrupted by genetic recombination if their map distance is on the order of the size of single genes. Thus, counterintuitively, mass selection alone offers a biologically realistic resolution to the problem of evolutionary escape from local fitness peaks in natural populations.

Recombination, dominance and selection on amino acid polymorphism in the Drosophila genome: contrasting patterns on the X and fourth chromosomes

Surveys of nucleotide polymorphism and divergence indicate that the average selection coefficient on Drosophila proteins is weakly positive. Similar surveys in mitochondrial genomes and in the selfing plant Arabidopsis show that weak negative selection has operated. These differences have been attributed to the low recombination environment of mtDNA and Arabidopsis that has hindered adaptive evolution through the interference effects of linkage. We test this hypothesis with new sequence surveys of proteins lying in low recombination regions of the Drosophila genome. We surveyed >3800 bp across four proteins at the tip of the X chromosome and >3600 bp across four proteins on the fourth chromosome in 24 strains of D. melanogaster and 5 strains of D. simulans. This design seeks to study the interaction of selection and linkage by comparing silent and replacement variation in semihaploid (X chromosome) and diploid (fourth chromosome) environments lying in regions of low recombination. While the data do indicate very low rates of exchange, all four gametic phases were observed both at the tip of the X and across the fourth chromosome. Silent variation is very low at the tip of the X (thetaS = 0.0015) and on the fourth chromosome (thetaS = 0.0002), but the tip of the X shows a greater proportional loss of variation than the fourth shows relative to normal-recombination regions. In contrast, replacement polymorphism at the tip of the X is not reduced (thetaR = 0.00065, very close to the X chromosome average). MK and HKA tests both indicate a significant excess of amino acid polymorphism at the tip of the X relative to the fourth. Selection is significantly negative at the tip of the X (Nes = -1.53) and nonsignificantly positive on the fourth (Nes approximately 2.9), analogous to the difference between mtDNA (or Arabidopsis) and the Drosophila genome average. Our distal X data are distinct from regions of normal recombination where the X shows a deficiency of amino acid polymorphism relative to the autosomes, suggesting more efficient selection against recessive deleterious replacement mutations. We suggest that the excess amino acid polymorphism on the distal X relative to the fourth chromosome is due to (1) differences in the mutation rate for selected mutations on the distal X or (2) a greater relaxation of selection from stronger linkage-related interference effects on the distal X. This relaxation of selection is presumed to be greater in magnitude than the difference in efficiency of selection between X-linked vs. autosomal selection.

The rates of molecular evolution in rodent and primate mitochondrial DNA

A higher rate of molecular evolution in rodents than in primates at synonymous sites and, to a lesser extent, at amino acid replacement sites has been reported previously for most nuclear genes examined. Thus in these genes the average ratio of amino acid replacement to synonymous substitution rates in rodents is lower than in primates, an observation at odds with the neutral model of molecular evolution. Under Ohta's mildly deleterious model of molecular evolution, these observations are seen as the consequence of the combined effects of a shorter generation time (driving a higher mutation rate) and a larger effective population size (resulting in more effective selection against mildly deleterious mutations) in rodents. The present study reports the results of a maximum-likelihood analysis of the ratio of amino acid replacements to synonymous substitutions for genes encoded in mitochondrial DNA (mtDNA) in these two lineages. A similar pattern is observed: in rodents this ratio is significantly lower than in primates, again consistent only with the mildly deleterious model. Interestingly the lineage-specific difference is much more pronounced in mtDNA-encoded than in nuclear-encoded proteins, an observation which is shown to run counter to expectation under Ohta's model. Finally, accepting certain fossil divergence dates, the lineage-specific difference in amino acid replacement-to-synonymous substitution ratio in mtDNA can be partitioned and is found to be entirely the consequence of a higher mutation rate in rodents. This conclusion is consistent with a replication-dependent model of mutation in mtDNA.

Neutrality tests of conservative-radical amino acid changes in nuclear- and mitochondrially-encoded proteins

The neutralist-selectionist debate should not be viewed as a dichotomy but as a continuum. While the strictly neutral model suggests a neutralist-selectionist dichotomy, the nearly neutral model is a continuous model spanning strict neutrality through weak selection (Ns approximately 1) to deterministic selection (Ns>3). We illustrate these points with polymorphism and divergence data from a sample of 73 genes (31 mitochondrial, 36 nuclear genes from Drosophila, and six Arabidopsis data sets). In an earlier study we used the McDonald-Kreitman (MK) test to show that amino acid replacement polymorphism in animal mitochondrial genes and Arabidopsis genes show a consistent trend toward negative selection, whereas nuclear genes from Drosophila span a range from negative selection, through neutrality, to positive selection. Here we analyze a subset of these genes (13 Drosophila nuclear, ten mitochondrial, and six Arabidopsis nuclear) for polymorphism and divergence of conservative and radical amino acid replacements (a protein-based conservative-radical MK, or pMK, test). The distinct patterns of selection between the different genomes is not apparent with the pMK test. Different definitions of conservative and radical (based on amino acid polarity, volume or charge) give inconsistent results across genes. We suggest that segregating fitness difference between silent and replacement mutations are more visible to selection than are segregating fitness differences between conservative and radical amino acid mutations. New data on the variation among genes with different opportunities for positive and negative selection are as important to the continuum view of the neutralist-selectionist debate as is the distribution of selection coefficients within individual genes.

Contrasting patterns of nonneutral evolution in proteins encoded in nuclear and mitochondrial genomes

We report that patterns of nonneutral DNA sequence evolution among published nuclear and mitochondrially encoded protein-coding loci differ significantly in animals. Whereas an apparent excess of amino acid polymorphism is seen in most (25/31) mitochondrial genes, this pattern is seen in fewer than half (15/36) of the nuclear data sets. This differentiation is even greater among data sets with significant departures from neutrality (14/15 vs. 1/6). Using forward simulations, we examined patterns of nonneutral evolution using parameters chosen to mimic the differences between mitochondrial and nuclear genetics (we varied recombination rate, population size, mutation rate, selective dominance, and intensity of germ line bottleneck). Patterns of evolution were correlated only with effective population size and strength of selection, and no single genetic factor explains the empirical contrast in patterns. We further report that in Arabidopsis thaliana, a highly self-fertilizing plant with effectively low recombination, five of six published nuclear data sets also exhibit an excess of amino acid polymorphism. We suggest that the contrast between nuclear and mitochondrial nonneutrality in animals stems from differences in rates of recombination in conjunction with a distribution of selective effects. If the majority of mutations segregating in populations are deleterious, high linkage may hinder the spread of the occasional beneficial mutation.

The age of nonsynonymous and synonymous mutations in animal mtDNA and implications for the mildly deleterious theory

McDonald/Kreitman tests performed on animal mtDNA consistently reveal significant deviations from strict neutrality in the direction of an excess number of polymorphic nonsynonymous sites, which is consistent with purifying selection acting on nonsynonymous sites. We show that under models of recurrent neutral and deleterious mutations, the mean age of segregating neutral mutations is greater than the mean age of segregating selected mutations, even in the absence of recombination. We develop a test of the hypothesis that the mean age of segregating synonymous mutations equals the mean age of segregating nonsynonymous mutations in a sample of DNA sequences. The power of this age-of-mutation test and the power of the McDonald/Kreitman test are explored by computer simulations. We apply the new test to 25 previously published mitochondrial data sets and find weak evidence for selection against nonsynonymous mutations.

Comparison of 2D- and 3DFT multiple overlapping thin-slab acquisition TOF MR angiography in carotid disease

We intended to compare two-dimensional Fourier transform (2DFT) with three-dimensional Fourier transform (3DFT) multiple overlapping thin-slab acquisition (MOTSA) time-of-flight (TOF) magnetic resonance angiography for percent diameter stenosis, length of stenosis, and apparent occlusion at the carotid bifurcation. For that, 101 symptomatic patients (n = 202 carotid bifurcations) were evaluated with 3DFT MOTSA TOF and 2DFT TOF. Three observers measured the percent diameter stenosis from oblique axial multiplanar reformatted (MPR) images and length of stenosis from maximum intensity projection (MIP) images. Kappa analysis assessed interobserver agreement and the Wilcoxon signed rank test was used to compare the two MR angiographic techniques. There was a significant difference in the percent diameter stenosis (p < 0.01) and length of carotid stenosis (p < 0.01) between 2DFT and 3DFT MOTSA TOF magnetic resonance angiography. Stenosis was greater in 33% of carotid arteries and was upgraded (NASCET) in 17% of carotid arteries on the 2DFT TOF. The number of apparently occluded carotid arteries was equal with both MRA techniques. There was good agreement between the three observers (k = .50).

Streamlining outpatient geriatric assessment: essential social, environmental and economic variables

There are no known standardized instruments that encompass all of the essential elements of a streamlined outpatient geriatric assessment. A process of arriving at a consensus on essential elements of streamlined geriatric assessment in 3 domains was initiated and described. Two rounds of the Delphi technique were conducted to identify social, environmental and economic variables essential for such an assessment. Consensus among an expert panel was achieved and a list of 27 variables was reduced to 16. This result is discussed in terms of assessment context and standardizing assessment, using case examples.