Comparison of the Full Distribution of Fitness Effects of New Amino Acid Mutations Across Great Apes

Biases in ARG-Based Inference of Historical Population Size in Populations Experiencing Selection

Inferring the demographic history of populations provides fundamental insights into species dynamics and is essential for developing a null model to accurately study selective processes. However, background selection and selective sweeps can produce genomic signatures at linked sites that mimic or mask signals associated with historical population size change. While the theoretical biases introduced by the linked effects of selection have been well established, it is unclear whether ancestral recombination graph (ARG)-based approaches to demographic inference in typical empirical analyses are susceptible to misinference due to these effects. To address this, we developed highly realistic forward simulations of human and Drosophila melanogaster populations, including empirically estimated variability of gene density, mutation rates, recombination rates, purifying, and positive selection, across different historical demographic scenarios, to broadly assess the impact of selection on demographic inference using a genealogy-based approach. Our results indicate that the linked effects of selection minimally impact demographic inference for human populations, although it could cause misinference in populations with similar genome architecture and population parameters experiencing more frequent recurrent sweeps. We found that accurate demographic inference of D. melanogaster populations by ARG-based methods is compromised by the presence of pervasive background selection alone, leading to spurious inferences of recent population expansion, which may be further worsened by recurrent sweeps, depending on the proportion and strength of beneficial mutations. Caution and additional testing with species-specific simulations are needed when inferring population history with non-human populations using ARG-based approaches to avoid misinference due to the linked effects of selection.

An efficient and robust ABC approach to infer the rate and strength of adaptation

Inferring the effects of positive selection on genomes remains a critical step in characterizing the ultimate and proximate causes of adaptation across species, and quantifying positive selection remains a challenge due to the confounding effects of many other evolutionary processes. Robust and efficient approaches for adaptation inference could help characterize the rate and strength of adaptation in nonmodel species for which demographic history, mutational processes, and recombination patterns are not currently well-described. Here, we introduce an efficient and user-friendly extension of the McDonald-Kreitman test (ABC-MK) for quantifying long-term protein adaptation in specific lineages of interest. We characterize the performance of our approach with forward simulations and find that it is robust to many demographic perturbations and positive selection configurations, demonstrating its suitability for applications to nonmodel genomes. We apply ABC-MK to the human proteome and a set of known virus interacting proteins (VIPs) to test the long-term adaptation in genes interacting with viruses. We find substantially stronger signatures of positive selection on RNA-VIPs than DNA-VIPs, suggesting that RNA viruses may be an important driver of human adaptation over deep evolutionary time scales.

Shared evolutionary processes shape landscapes of genomic variation in the great apes

For at least the past 5 decades, population genetics, as a field, has worked to describe the precise balance of forces that shape patterns of variation in genomes. The problem is challenging because modeling the interactions between evolutionary processes is difficult, and different processes can impact genetic variation in similar ways. In this paper, we describe how diversity and divergence between closely related species change with time, using correlations between landscapes of genetic variation as a tool to understand the interplay between evolutionary processes. We find strong correlations between landscapes of diversity and divergence in a well-sampled set of great ape genomes, and explore how various processes such as incomplete lineage sorting, mutation rate variation, GC-biased gene conversion and selection contribute to these correlations. Through highly realistic, chromosome-scale, forward-in-time simulations, we show that the landscapes of diversity and divergence in the great apes are too well correlated to be explained via strictly neutral processes alone. Our best fitting simulation includes both deleterious and beneficial mutations in functional portions of the genome, in which 9% of fixations within those regions is driven by positive selection. This study provides a framework for modeling genetic variation in closely related species, an approach which can shed light on the complex balance of forces that have shaped genetic variation.

The impact of non-neutral synonymous mutations when inferring selection on non-synonymous mutations

The distribution of fitness effects (DFE) describes the proportions of new mutations that have different effects on reproductive fitness. Accurate measurements of the DFE are important because the DFE is a fundamental parameter in evolutionary genetics and has implications for our understanding of other phenomena like complex disease or inbreeding depression. Current computational methods to infer the DFE for nonsynonymous mutations from natural variation first estimate demographic parameters from synonymous variants to control for the effects of demography and background selection. Then, conditional on these parameters, the DFE is then inferred for nonsynonymous mutations. This approach relies on the assumption that synonymous variants are neutrally evolving. However, some evidence points toward synonymous mutations having measurable effects on fitness. To test whether selection on synonymous mutations affects inference of the DFE of nonsynonymous mutations, we simulated several possible models of selection on synonymous mutations using SLiM and attempted to recover the DFE of nonsynonymous mutations using Fit∂a∂i, a common method for DFE inference. Our results show that the presence of selection on synonymous variants leads to incorrect inferences of recent population growth. Furthermore, under certain parameter combinations, inferences of the DFE can have an inflated proportion of highly deleterious nonsynonymous mutations. However, this bias can be eliminated if the correct demographic parameters are used for DFE inference instead of the biased ones inferred from synonymous variants. Our work demonstrates how unmodeled selection on synonymous mutations may affect downstream inferences of the DFE.

Half a Century of Controversy: The Neutralist/Selectionist Debate in Molecular Evolution

The neutral and nearly neutral theories, introduced more than 50 yr ago, have raised and still raise passionate discussion regarding the forces governing molecular evolution and their relative importance. The debate, initially focused on the amount of within-species polymorphism and constancy of the substitution rate, has spread, matured, and now underlies a wide range of topics and questions. The neutralist/selectionist controversy has structured the field and influences the way molecular evolutionary scientists conceive their research.

Using Computational Simulations to Model Deleterious Variation and Genetic Load in Natural Populations

AbstractDeleterious genetic variation is abundant in wild populations, and understanding the ecological and conservation implications of such variation is an area of active research. Genomic methods are increasingly used to quantify the impacts of deleterious variation in natural populations; however, these approaches remain limited by an inability to accurately predict the selective and dominance effects of mutations. Computational simulations of deleterious variation offer a complementary tool that can help overcome these limitations, although such approaches have yet to be widely employed. In this perspective article, we aim to encourage ecological and conservation genomics researchers to adopt greater use of computational simulations to aid in deepening our understanding of deleterious variation in natural populations. We first provide an overview of the components of a simulation of deleterious variation, describing the key parameters involved in such models. Next, we discuss several approaches for validating simulation models. Finally, we compare and validate several recently proposed deleterious mutation models, demonstrating that models based on estimates of selection parameters from experimental systems are biased toward highly deleterious mutations. We describe a new model that is supported by multiple orthogonal lines of evidence and provide example scripts for implementing this model (https://github.com/ckyriazis/simulations_review).

Between but Not Within-Species Variation in the Distribution of Fitness Effects

New mutations provide the raw material for evolution and adaptation. The distribution of fitness effects (DFE) describes the spectrum of effects of new mutations that can occur along a genome, and is, therefore, of vital interest in evolutionary biology. Recent work has uncovered striking similarities in the DFE between closely related species, prompting us to ask whether there is variation in the DFE among populations of the same species, or among species with different degrees of divergence, that is whether there is variation in the DFE at different levels of evolution. Using exome capture data from six tree species sampled across Europe we characterized the DFE for multiple species, and for each species, multiple populations, and investigated the factors potentially influencing the DFE, such as demography, population divergence, and genetic background. We find statistical support for the presence of variation in the DFE at the species level, even among relatively closely related species. However, we find very little difference at the population level, suggesting that differences in the DFE are primarily driven by deep features of species biology, and those evolutionarily recent events, such as demographic changes and local adaptation, have little impact.

Inference of the distribution of fitness effects of mutations is affected by single nucleotide polymorphism filtering methods, sample size and population structure

The distribution of fitness effects (DFE) of new mutations has been of interest to evolutionary biologists since the concept of mutations arose. Modern population genomic data enable us to quantify the DFE empirically, but few studies have examined how data processing, sample size and cryptic population structure might affect the accuracy of DFE inference. We used simulated and empirical data (from Arabidopsis lyrata) to show the effects of missing data filtering, sample size, number of single nucleotide polymorphisms (SNPs) and population structure on the accuracy and variance of DFE estimates. Our analyses focus on three filtering methods-downsampling, imputation and subsampling-with sample sizes of 4-100 individuals. We show that (1) the choice of missing-data treatment directly affects the estimated DFE, with downsampling performing better than imputation and subsampling; (2) the estimated DFE is less reliable in small samples (<8 individuals), and becomes unpredictable with too few SNPs (<5000, the sum of 0- and 4-fold SNPs); and (3) population structure may skew the inferred DFE towards more strongly deleterious mutations. We suggest that future studies should consider downsampling for small data sets, and use samples larger than 4 (ideally larger than 8) individuals, with more than 5000 SNPs in order to improve the robustness of DFE inference and enable comparative analyses.

An efficient and robust ABC approach to infer the rate and strength of adaptation

Inferring the effects of positive selection on genomes remains a critical step in characterizing the ultimate and proximate causes of adaptation across species, and quantifying positive selection remains a challenge due to the confounding effects of many other evolutionary processes. Robust and efficient approaches for adaptation inference could help characterize the rate and strength of adaptation in non-model species for which demographic history, mutational processes, and recombination patterns are not currently well-described. Here, we introduce an efficient and user-friendly extension of the McDonald-Kreitman test (ABC-MK) for quantifying long-term protein adaptation in specific lineages of interest. We characterize the performance of our approach with forward simulations and find that it is robust to many demographic perturbations and positive selection configurations, demonstrating its suitability for applications to non-model genomes. We apply ABC-MK to the human proteome and a set of known Virus Interacting Proteins (VIPs) to test the long-term adaptation in genes interacting with viruses. We find substantially stronger signatures of positive selection on RNA-VIPs than DNA-VIPs, suggesting that RNA viruses may be an important driver of human adaptation over deep evolutionary time scales.

Quantifying the fraction of new mutations that are recessive lethal

The presence and impact of recessive lethal mutations have been widely documented in diploid outcrossing species. However, precise estimates of the proportion of new mutations that are recessive lethal remain limited. Here, we evaluate the performance of Fit∂a∂i, a commonly used method for inferring the distribution of fitness effects (DFE), in the presence of lethal mutations. Using simulations, we demonstrate that in both additive and recessive cases, inference of the deleterious nonlethal portion of the DFE is minimally affected by a small proportion (<10%) of lethal mutations. Additionally, we demonstrate that while Fit∂a∂i cannot estimate the fraction of recessive lethal mutations, Fit∂a∂i can accurately infer the fraction of additive lethal mutations. Finally, as an alternative approach to estimate the proportion of mutations that are recessive lethal, we employ models of mutation-selection-drift balance using existing genomic parameters and estimates of segregating recessive lethals for humans and Drosophila melanogaster. In both species, the segregating recessive lethal load can be explained by a very small fraction (<1%) of new nonsynonymous mutations being recessive lethal. Our results refute recent assertions of a much higher proportion of mutations being recessive lethal (4%-5%), while highlighting the need for additional information on the joint distribution of selection and dominance coefficients.

Deleterious Variation in Natural Populations and Implications for Conservation Genetics

Deleterious mutations decrease reproductive fitness and are ubiquitous in genomes. Given that many organisms face ongoing threats of extinction, there is interest in elucidating the impact of deleterious variation on extinction risk and optimizing management strategies accounting for such mutations. Quantifying deleterious variation and understanding the effects of population history on deleterious variation are complex endeavors because we do not know the strength of selection acting on each mutation. Further, the effect of demographic history on deleterious mutations depends on the strength of selection against the mutation and the degree of dominance. Here we clarify how deleterious variation can be quantified and studied in natural populations. We then discuss how different demographic factors, such as small population size, nonequilibrium population size changes, inbreeding, and gene flow, affect deleterious variation. Lastly, we provide guidance on studying deleterious variation in nonmodel populations of conservation concern.

The critically endangered vaquita is not doomed to extinction by inbreeding depression

In cases of severe wildlife population decline, a key question is whether recovery efforts will be impeded by genetic factors, such as inbreeding depression. Decades of excess mortality from gillnet fishing have driven Mexico's vaquita porpoise (Phocoena sinus) to ~10 remaining individuals. We analyzed whole-genome sequences from 20 vaquitas and integrated genomic and demographic information into stochastic, individual-based simulations to quantify the species' recovery potential. Our analysis suggests that the vaquita's historical rarity has resulted in a low burden of segregating deleterious variation, reducing the risk of inbreeding depression. Similarly, genome-informed simulations suggest that the vaquita can recover if bycatch mortality is immediately halted. This study provides hope for vaquitas and other naturally rare endangered species and highlights the utility of genomics in predicting extinction risk.

Evolution of prudent predation in complex food webs

Prudent predators catch sufficient prey to sustain their populations but not as much as to undermine their populations' survival. The idea that predators evolve to be prudent has been dismissed in the 1970s, but the arguments invoked then are untenable in the light of modern evolution theory. The evolution of prudent predation has repeatedly been demonstrated in two-species predator-prey metacommunity models. However, the vigorous population fluctuations that these models predict are not widely observed. Here we show that in complex model food webs prudent predation evolves as a result of consumer-mediated ('apparent') competitive exclusion of resources, which disadvantages aggressive consumers and does not generate such fluctuations. We make testable predictions for empirical signatures of this mechanism and its outcomes. Then we discuss how these predictions are borne out across freshwater, marine and terrestrial ecosystems. Demonstrating explanatory power of evolved prudent predation well beyond the question of predator-prey coexistence, the predicted signatures explain unexpected declines of invasive alien species, the shape of stock-recruitment relations of fish, and the clearance rates of pelagic consumers across the latitudinal gradient and 15 orders of magnitude in body mass. Specific research to further test this theory is proposed.

What does the distribution of fitness effects of new mutations reflect? Insights from plants

The distribution of fitness effects (DFE) of new mutations plays a central role in molecular evolution. It is therefore crucial to be able to estimate it accurately from genomic data and to understand the factors that shape it. After a rapid overview of available methods to characterize the fitness effects of mutations, we review what is known on the factors affecting them in plants. Available data indicate that life history traits (e.g. mating system and longevity) have a major effect on the DFE. By contrast, the impact of demography within species appears to be more limited. These results remain to be confirmed, and methods to estimate the joint evolution of demography, life history traits, and the DFE need to be developed.

Demographic history and patterns of molecular evolution from whole genome sequencing in the radiation of Galapagos giant tortoises

Whole genome sequencing provides deep insights into the evolutionary history of a species, including patterns of diversity, signals of selection, and historical demography. When applied to closely related taxa with a wealth of background knowledge, population genomics provides a comparative context for interpreting population genetic summary statistics and comparing empirical results with the expectations of population genetic theory. The Galapagos giant tortoises (Chelonoidis spp.), an iconic rapid and recent radiation, offer such an opportunity. Here, we sequenced whole genomes from three individuals of the 12 extant lineages of Galapagos giant tortoise and estimate diversity measures and reconstruct changes in coalescent rate over time. We also compare the number of derived alleles in each lineage to infer how synonymous and nonsynonymous mutation accumulation rates correlate with population size and life history traits. Remarkably, we find that patterns of molecular evolution are similar within individuals of the same lineage, but can differ significantly among lineages, reinforcing the evolutionary distinctiveness of the Galapagos giant tortoise species. Notably, differences in mutation accumulation among lineages do not align with simple population genetic predictions, suggesting that the drivers of purifying selection are more complex than is currently appreciated. By integrating results from earlier population genetic and phylogeographic studies with new findings from the analysis of whole genomes, we provide the most in-depth insights to date on the evolution of Galapagos giant tortoises, and identify discrepancies between expectation from population genetic theory and empirical data that warrant further scrutiny.

Reconstructing the History of Variation in Effective Population Size along Phylogenies

The nearly neutral theory predicts specific relations between effective population size (Ne) and patterns of divergence and polymorphism, which depend on the shape of the distribution of fitness effects (DFE) of new mutations. However, testing these relations is not straightforward, owing to the difficulty in estimating Ne. Here, we introduce an integrative framework allowing for an explicit reconstruction of the phylogenetic history of Ne, thus leading to a quantitative test of the nearly neutral theory and an estimation of the allometric scaling of the ratios of nonsynonymous over synonymous polymorphism (πN/πS) and divergence (dN/dS) with respect to Ne. As an illustration, we applied our method to primates, for which the nearly neutral predictions were mostly verified. Under a purely nearly neutral model with a constant DFE across species, we find that the variation in πN/πS and dN/dS as a function of Ne is too large to be compatible with current estimates of the DFE based on site frequency spectra. The reconstructed history of Ne shows a 10-fold variation across primates. The mutation rate per generation u, also reconstructed over the tree by the method, varies over a 3-fold range and is negatively correlated with Ne. As a result of these opposing trends for Ne and u, variation in πS is intermediate, primarily driven by Ne but substantially influenced by u. Altogether, our integrative framework provides a quantitative assessment of the role of Ne and u in modulating patterns of genetic variation, while giving a synthetic picture of their history over the clade.

Hunting for beneficial mutations: conditioning on SIFT scores when estimating the distribution of fitness effect of new mutations

The Distribution of Fitness Effects (DFE) of new mutations is a key parameter of molecular evolution. The DFE can in principle be estimated by comparing the Site Frequency Spectra (SFS) of putatively neutral and functional polymorphisms. Unfortunately the DFE is intrinsically hard to estimate, especially for beneficial mutations since these tend to be exceedingly rare. There is therefore a strong incentive to find out whether conditioning on properties of mutations that are independent of the SFS could provide additional information. In the present study, we developed a new measure based on SIFT scores. SIFT scores are assigned to nucleotide sites based on their level of conservation across a multi species alignment: the more conserved a site, the more likely mutations occurring at this site are deleterious and the lower the SIFT score. If one knows the ancestral state at a given site, one can assign a value to new mutations occurring at the site based on the change of SIFT score associated with the mutation. We called this new measure δ. We show that properties of the DFE as well as the flux of beneficial mutations across classes covary with δ and, hence, that SIFT scores are informative when estimating the fitness effect of new mutations. In particular, conditioning on SIFT scores can help to characterize beneficial mutations.

Inferring genome-wide correlations of mutation fitness effects between populations

The effect of a mutation on fitness may differ between populations depending on environmental and genetic context, but little is known about the factors that underlie such differences. To quantify genome-wide correlations in mutation fitness effects, we developed a novel concept called a joint distribution of fitness effects (DFE) between populations. We then proposed a new statistic w to measure the DFE correlation between populations. Using simulation, we showed that inferring the DFE correlation from the joint allele frequency spectrum is statistically precise and robust. Using population genomic data, we inferred DFE correlations of populations in humans, Drosophila melanogaster, and wild tomatoes. In these species, we found that the overall correlation of the joint DFE was inversely related to genetic differentiation. In humans and D. melanogaster, deleterious mutations had a lower DFE correlation than tolerated mutations, indicating a complex joint DFE. Altogether, the DFE correlation can be reliably inferred, and it offers extensive insight into the genetics of population divergence.

Purifying Selection in Corvids Is Less Efficient on Islands

Theory predicts that deleterious mutations accumulate more readily in small populations. As a consequence, mutation load is expected to be elevated in species where life-history strategies and geographic or historical contingencies reduce the number of reproducing individuals. Yet, few studies have empirically tested this prediction using genome-wide data in a comparative framework. We collected whole-genome sequencing data for 147 individuals across seven crow species (Corvus spp.). For each species, we estimated the distribution of fitness effects of deleterious mutations and compared it with proxies of the effective population size N_e. Island species with comparatively smaller geographic range sizes had a significantly increased mutation load. These results support the view that small populations have an elevated risk of mutational meltdown, which may contribute to the higher extinction rates observed in island species.

How Much Does Ne Vary Among Species?

Genetic drift is an important evolutionary force of strength inversely proportional to Ne , the effective population size. The impact of drift on genome diversity and evolution is known to vary among species, but quantifying this effect is a difficult task. Here we assess the magnitude of variation in drift power among species of animals via its effect on the mutation load - which implies also inferring the distribution of fitness effects of deleterious mutations. To this aim, we analyze the nonsynonymous (amino-acid changing) and synonymous (amino-acid conservative) allele frequency spectra in a large sample of metazoan species, with a focus on the primates vs. fruit flies contrast. We show that a Gamma model of the distribution of fitness effects is not suitable due to strong differences in estimated shape parameters among taxa, while adding a class of lethal mutations essentially solves the problem. Using the Gamma + lethal model and assuming that the mean deleterious effects of nonsynonymous mutations is shared among species, we estimate that the power of drift varies by a factor of at least 500 between large-Ne and small-Ne species of animals, i.e., an order of magnitude more than the among-species variation in genetic diversity. Our results are relevant to Lewontin's paradox while further questioning the meaning of the Ne parameter in population genomics.

Inferring Parameters of the Distribution of Fitness Effects of New Mutations When Beneficial Mutations Are Strongly Advantageous and Rare

Characterizing the distribution of fitness effects (DFE) for new mutations is central in evolutionary genetics. Analysis of molecular data under the McDonald-Kreitman test has suggested that adaptive substitutions make a substantial contribution to between-species divergence. Methods have been proposed to estimate the parameters of the distribution of fitness effects for positively selected mutations from the unfolded site frequency spectrum (uSFS). Such methods perform well when beneficial mutations are mildly selected and frequent. However, when beneficial mutations are strongly selected and rare, they may make little contribution to standing variation and will thus be difficult to detect from the uSFS. In this study, I analyze uSFS data from simulated populations subject to advantageous mutations with effects on fitness ranging from mildly to strongly beneficial. As expected, frequent, mildly beneficial mutations contribute substantially to standing genetic variation and parameters are accurately recovered from the uSFS. However, when advantageous mutations are strongly selected and rare, there are very few segregating in populations at any one time. Fitting the uSFS in such cases leads to underestimates of the strength of positive selection and may lead researchers to false conclusions regarding the relative contribution adaptive mutations make to molecular evolution. Fortunately, the parameters for the distribution of fitness effects for harmful mutations are estimated with high accuracy and precision. The results from this study suggest that the parameters of positively selected mutations obtained by analysis of the uSFS should be treated with caution and that variability at linked sites should be used in conjunction with standing variability to estimate parameters of the distribution of fitness effects in the future.

Is adaptation limited by mutation? A timescale-dependent effect of genetic diversity on the adaptive substitution rate in animals

Whether adaptation is limited by the beneficial mutation supply is a long-standing question of evolutionary genetics, which is more generally related to the determination of the adaptive substitution rate and its relationship with species effective population size (Ne) and genetic diversity. Empirical evidence reported so far is equivocal, with some but not all studies supporting a higher adaptive substitution rate in large-Ne than in small-Ne species. We gathered coding sequence polymorphism data and estimated the adaptive amino-acid substitution rate ωa, in 50 species from ten distant groups of animals with markedly different population mutation rate θ. We reveal the existence of a complex, timescale dependent relationship between species adaptive substitution rate and genetic diversity. We find a positive relationship between ωa and θ among closely related species, indicating that adaptation is indeed limited by the mutation supply, but this was only true in relatively low-θ taxa. In contrast, we uncover no significant correlation between ωa and θ at a larger taxonomic scale, suggesting that the proportion of beneficial mutations scales negatively with species' long-term Ne.

Impact of Mutation Rate and Selection at Linked Sites on DNA Variation across the Genomes of Humans and Other Homininae

DNA diversity varies across the genome of many species. Variation in diversity across a genome might arise from regional variation in the mutation rate, variation in the intensity and mode of natural selection, and regional variation in the recombination rate. We show that both noncoding and nonsynonymous diversity are positively correlated to a measure of the mutation rate and the recombination rate and negatively correlated to the density of conserved sequences in 50 kb windows across the genomes of humans and nonhuman homininae. Interestingly, we find that although noncoding diversity is equally affected by these three genomic variables, nonsynonymous diversity is mostly dominated by the density of conserved sequences. The positive correlation between diversity and our measure of the mutation rate seems to be largely a direct consequence of regions with higher mutation rates having more diversity. However, the positive correlation with recombination rate and the negative correlation with the density of conserved sequences suggest that selection at linked sites also affect levels of diversity. This is supported by the observation that the ratio of the number of nonsynonymous to noncoding polymorphisms is negatively correlated to a measure of the effective population size across the genome. We show these patterns persist even when we restrict our analysis to GC-conservative mutations, demonstrating that the patterns are not driven by GC biased gene conversion. In conclusion, our comparative analyses describe how recombination rate, gene density, and mutation rate interact to produce the patterns of DNA diversity that we observe along the hominine genomes.

Variation of the adaptive substitution rate between species and within genomes

The importance of adaptive mutations in molecular evolution is extensively debated. Recent developments in population genomics allow inferring rates of adaptive mutations by fitting a distribution of fitness effects to the observed patterns of polymorphism and divergence at sites under selection and sites assumed to evolve neutrally. Here, we summarize the current state-of-the-art of these methods and review the factors that affect the molecular rate of adaptation. Several studies have reported extensive cross-species variation in the proportion of adaptive amino-acid substitutions (α) and predicted that species with larger effective population sizes undergo less genetic drift and higher rates of adaptation. Disentangling the rates of positive and negative selection, however, revealed that mutations with deleterious effects are the main driver of this population size effect and that adaptive substitution rates vary comparatively little across species. Conversely, rates of adaptive substitution have been documented to vary substantially within genomes. On a genome-wide scale, gene density, recombination and mutation rate were observed to play a role in shaping molecular rates of adaptation, as predicted under models of linked selection. At the gene level, it has been reported that the gene functional category and the macromolecular structure substantially impact the rate of adaptive mutations. Here, we deliver a comprehensive review of methods used to infer the molecular adaptive rate, the potential drivers of adaptive evolution and how positive selection shapes molecular evolution within genes, across genes within species and between species.