Directionality in the evolution of influenza A haemagglutinin

Evolutionary repeatability of emergent properties of ecological communities

Most species belong to ecological communities where their interactions give rise to emergent community-level properties, such as diversity and productivity. Understanding and predicting how these properties change over time has been a major goal in ecology, with important practical implications for sustainability and human health. Less attention has been paid to the fact that community-level properties can also change because member species evolve. Yet, our ability to predict long-term eco-evolutionary dynamics hinges on how repeatably community-level properties change as a result of species evolution. Here, we review studies of evolution of both natural and experimental communities and make the case that community-level properties at least sometimes evolve repeatably. We discuss challenges faced in investigations of evolutionary repeatability. In particular, only a handful of studies enable us to quantify repeatability. We argue that quantifying repeatability at the community level is critical for approaching what we see as three major open questions in the field: (i) Is the observed degree of repeatability surprising? (ii) How is evolutionary repeatability at the community level related to repeatability at the level of traits of member species? (iii) What factors affect repeatability? We outline some theoretical and empirical approaches to addressing these questions. Advances in these directions will not only enrich our basic understanding of evolution and ecology but will also help us predict eco-evolutionary dynamics. This article is part of the theme issue 'Interdisciplinary approaches to predicting evolutionary biology'.

Ongoing global and regional adaptive evolution of SARS-CoV-2

Understanding the trends in severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) evolution is paramount to control the COVID-19 pandemic. We analyzed more than 300,000 high-quality genome sequences of SARS-CoV-2 variants available as of January 2021. The results show that the ongoing evolution of SARS-CoV-2 during the pandemic is characterized primarily by purifying selection, but a small set of sites appear to evolve under positive selection. The receptor-binding domain of the spike protein and the region of the nucleocapsid protein associated with nuclear localization signals (NLS) are enriched with positively selected amino acid replacements. These replacements form a strongly connected network of apparent epistatic interactions and are signatures of major partitions in the SARS-CoV-2 phylogeny. Virus diversity within each geographic region has been steadily growing for the entirety of the pandemic, but analysis of the phylogenetic distances between pairs of regions reveals four distinct periods based on global partitioning of the tree and the emergence of key mutations. The initial period of rapid diversification into region-specific phylogenies that ended in February 2020 was followed by a major extinction event and global homogenization concomitant with the spread of D614G in the spike protein, ending in March 2020. The NLS-associated variants across multiple partitions rose to global prominence in March to July, during a period of stasis in terms of interregional diversity. Finally, beginning in July 2020, multiple mutations, some of which have since been demonstrated to enable antibody evasion, began to emerge associated with ongoing regional diversification, which might be indicative of speciation.

Detecting genetic interactions using parallel evolution in experimental populations

Eukaryotic genomes contain thousands of genes organized into complex and interconnected genetic interaction networks. Most of our understanding of how genetic variation affects these networks comes from quantitative-trait loci mapping and from the systematic analysis of double-deletion (or knockdown) mutants, primarily in the yeast Saccharomyces cerevisiae. Evolve and re-sequence experiments are an alternative approach for identifying novel functional variants and genetic interactions, particularly between non-loss-of-function mutations. These experiments leverage natural selection to obtain genotypes with functionally important variants and positive genetic interactions. However, no systematic methods for detecting genetic interactions in these data are yet available. Here, we introduce a computational method based on the idea that variants in genes that interact will co-occur in evolved genotypes more often than expected by chance. We apply this method to a previously published yeast experimental evolution dataset. We find that genetic targets of selection are distributed non-uniformly among evolved genotypes, indicating that genetic interactions had a significant effect on evolutionary trajectories. We identify individual gene pairs with a statistically significant genetic interaction score. The strongest interaction is between genes TRK1 and PHO84, genes that have not been reported to interact in previous systematic studies. Our work demonstrates that leveraging parallelism in experimental evolution is useful for identifying genetic interactions that have escaped detection by other methods. This article is part of the theme issue 'Convergent evolution in the genomics era: new insights and directions'.

H1N1 seasonal influenza virus evolutionary rate changed over time

It was previously shown that the seasonal H1N1 influenza virus antigenic drift occurred at a slower rate than the seasonal H3N2 virus during the first decade of the 21th century. It was hypothesized that the slower antigenic evolution led to a decrease in average ages of infection, which in turn resulted in lower level of global viral circulation. It is unclear what caused the difference between the two viruses, but a plausible explanation may be related to the fact that the H1N1 virus had been in human population for much longer than the H3N2 virus. This would suggest that H1N1 antigenic drift in an earlier period may have been different from a more recent period. To test this hypothesis, we analyzed seasonal H1N1 influenza sequences during various time periods. In comparison to more recent H1N1 virus, the older H1N1 virus during the first half of the 20th century showed evidences of higher nonsynnonymous/synonymous ration (dN/dS) in its hemagglutinin (HA) gene. We compared amino acid sequence changes in the HA epitopes for each outbreak season and found that there were less changes in later years. Amino acid sequence diversity in the epitopes as measured by sequence entropy became smaller for each passing decade. These suggest that there might be some limit to the antigenic drift. The longer an influenza virus has drifted in human population, the less flexibility it may become. With less flexibility to adapt and escape the host immunity, the virus may have to rely more on younger naïve population.

Changing preferences: deformation of single position amino acid fitness landscapes and evolution of proteins

The fitness landscape-the function that relates genotypes to fitness-and its role in directing evolution are a central object of evolutionary biology. However, its huge dimensionality precludes understanding of even the basic aspects of its shape. One way to approach it is to ask a simpler question: what are the properties of a function that assigns fitness to each possible variant at just one particular site-a single position fitness landscape-and how does it change in the course of evolution? Analyses of genomic data from multiple species and multiple individuals within a species have proved beyond reasonable doubt that fitness functions of positions throughout the genome do themselves change with time, thus shaping protein evolution. Here, I will briefly review the literature that addresses these dynamics, focusing on recent genome-scale analyses of fitness functions of amino acid sites, i.e. vectors of fitnesses of 20 individual amino acid variants at a given position of a protein. The set of amino acids that confer high fitness at a particular position changes with time, and the rate of this change is comparable with the rate at which a position evolves, implying that this process plays a major role in evolutionary dynamics. However, the causes of these changes remain largely unclear.

A genotype network reveals homoplastic cycles of convergent evolution in influenza A (H3N2) haemagglutinin

Networks of evolving genotypes can be constructed from the worldwide time-resolved genotyping of pathogens like influenza viruses. Such genotype networks are graphs where neighbouring vertices (viral strains) differ in a single nucleotide or amino acid. A rich trove of network analysis methods can help understand the evolutionary dynamics reflected in the structure of these networks. Here, I analyse a genotype network comprising hundreds of influenza A (H3N2) haemagglutinin genes. The network is rife with cycles that reflect non-random parallel or convergent (homoplastic) evolution. These cycles also show patterns of sequence change characteristic for strong and local evolutionary constraints, positive selection and mutation-limited evolution. Such cycles would not be visible on a phylogenetic tree, illustrating that genotype network analysis can complement phylogenetic analyses. The network also shows a distinct modular or community structure that reflects temporal more than spatial proximity of viral strains, where lowly connected bridge strains connect different modules. These and other organizational patterns illustrate that genotype networks can help us study evolution in action at an unprecedented level of resolution.

Measuring edge importance: a quantitative analysis of the stochastic shielding approximation for random processes on graphs

Mathematical models of cellular physiological mechanisms often involve random walks on graphs representing transitions within networks of functional states. Schmandt and Galán recently introduced a novel stochastic shielding approximation as a fast, accurate method for generating approximate sample paths from a finite state Markov process in which only a subset of states are observable. For example, in ion-channel models, such as the Hodgkin-Huxley or other conductance-based neural models, a nerve cell has a population of ion channels whose states comprise the nodes of a graph, only some of which allow a transmembrane current to pass. The stochastic shielding approximation consists of neglecting fluctuations in the dynamics associated with edges in the graph not directly affecting the observable states. We consider the problem of finding the optimal complexity reducing mapping from a stochastic process on a graph to an approximate process on a smaller sample space, as determined by the choice of a particular linear measurement functional on the graph. The partitioning of ion-channel states into conducting versus nonconducting states provides a case in point. In addition to establishing that Schmandt and Galán's approximation is in fact optimal in a specific sense, we use recent results from random matrix theory to provide heuristic error estimates for the accuracy of the stochastic shielding approximation for an ensemble of random graphs. Moreover, we provide a novel quantitative measure of the contribution of individual transitions within the reaction graph to the accuracy of the approximate process.

Intrasubtype reassortments cause adaptive amino acid replacements in H3N2 influenza genes

Reassortments and point mutations are two major contributors to diversity of Influenza A virus; however, the link between these two processes is unclear. It has been suggested that reassortments provoke a temporary increase in the rate of amino acid changes as the viral proteins adapt to new genetic environment, but this phenomenon has not been studied systematically. Here, we use a phylogenetic approach to infer the reassortment events between the 8 segments of influenza A H3N2 virus since its emergence in humans in 1968. We then study the amino acid replacements that occurred in genes encoded in each segment subsequent to reassortments. In five out of eight genes (NA, M1, HA, PB1 and NS1), the reassortment events led to a transient increase in the rate of amino acid replacements on the descendant phylogenetic branches. In NA and HA, the replacements following reassortments were enriched with parallel and/or reversing replacements; in contrast, the replacements at sites responsible for differences between antigenic clusters (in HA) and at sites under positive selection (in NA) were underrepresented among them. Post-reassortment adaptive walks contribute to adaptive evolution in Influenza A: in NA, an average reassortment event causes at least 2.1 amino acid replacements in a reassorted gene, with, on average, 0.43 amino acid replacements per evolving post-reassortment lineage; and at least ~9% of all amino acid replacements are provoked by reassortments.

Components of selection in the evolution of the influenza virus: linkage effects beat inherent selection

The influenza virus is an important human pathogen, with a rapid rate of evolution in the human population. The rate of homologous recombination within genes of influenza is essentially zero. As such, where two alleles within the same gene are in linkage disequilibrium, interference between alleles will occur, whereby selection acting upon one allele has an influence upon the frequency of the other. We here measured the relative importance of selection and interference effects upon the evolution of influenza. We considered time-resolved allele frequency data from the global evolutionary history of the haemagglutinin gene of human influenza A/H3N2, conducting an in-depth analysis of sequences collected since 1996. Using a model that accounts for selection-caused interference between alleles in linkage disequilibrium, we estimated the inherent selective benefit of individual polymorphisms in the viral population. These inherent selection coefficients were in turn used to calculate the total selective effect of interference acting upon each polymorphism, considering the effect of the initial background upon which a mutation arose, and the subsequent effect of interference from other alleles that were under selection. Viewing events in retrospect, we estimated the influence of each of these components in determining whether a mutant allele eventually fixed or died in the global viral population. Our inherent selection coefficients, when combined across different regions of the protein, were consistent with previous measurements of dN/dS for the same system. Alleles going on to fix in the global population tended to be under more positive selection, to arise on more beneficial backgrounds, and to avoid strong negative interference from other alleles under selection. However, on average, the fate of a polymorphism was determined more by the combined influence of interference effects than by its inherent selection coefficient.

Success in life is the product of many factors. Inherent ability often underlies great achievement. But other factors may play their part. The circumstances a child is born into may help or hinder his or her progress. Later events also have their effect; a life may be influenced by a lucky break, or an unforeseen disaster. In this work, we examine the factors underlying success for mutations in the HA gene of human influenza virus A/H3N2, defining success as the attainment of a high frequency in the global population. We examined the history of the gene from 1968 until 2010. For each observed mutation, a mathematical model was used to estimate the inherent benefit or disadvantage it conferred to the virus. We calculated the advantageousness or otherwise of the background upon which it arose, and the subsequent effect of interference from other mutations under selection. We found that successful mutations tended to have an advantageous background, and were subsequently fortunate in avoiding negative events throughout their lifetime. Beneficial mutations were more likely to be successful. But a mutation's chances of success were influenced more by circumstances of birth and subsequent events, than by its inherent effect on the virus.

Integrating sequence variation and protein structure to identify sites under selection

We present a novel method to identify sites under selection in protein-coding genes. Our method combines the traditional Goldman-Yang model of coding-sequence evolution with the information obtained from the 3D structure of the evolving protein, specifically the relative solvent accessibility (RSA) of individual residues. We develop a random-effects likelihood sites model in which rate classes are RSA dependent. The RSA dependence is modeled with linear functions. We demonstrate that our RSA-dependent model provides a significantly better fit to molecular sequence data than does a traditional, RSA-independent model. We further show that our model provides a natural, RSA-dependent neutral baseline for the evolutionary rate ratio ω = dN/dS Sites that deviate from this neutral baseline likely experience selection pressure for function. We apply our method to the influenza proteins hemagglutinin and neuraminidase. For hemagglutinin, our method recovers positively selected sites near the sialic acid-binding site and negatively selected sites that may be important for trimerization. For neuraminidase, our method recovers the oseltamivir resistance site and otherwise suggests that few sites deviate from the neutral baseline. Our method is broadly applicable to any protein sequences for which structural data are available or can be obtained via homology modeling or threading.

Clonal interference in the evolution of influenza

The seasonal influenza A virus undergoes rapid evolution to escape human immune response. Adaptive changes occur primarily in antigenic epitopes, the antibody-binding domains of the viral hemagglutinin. This process involves recurrent selective sweeps, in which clusters of simultaneous nucleotide fixations in the hemagglutinin coding sequence are observed about every 4 years. Here, we show that influenza A (H3N2) evolves by strong clonal interference. This mode of evolution is a red queen race between viral strains with different beneficial mutations. Clonal interference explains and quantifies the observed sweep pattern: we find an average of at least one strongly beneficial amino acid substitution per year, and a given selective sweep has three to four driving mutations on average. The inference of selection and clonal interference is based on frequency time series of single-nucleotide polymorphisms, which are obtained from a sample of influenza genome sequences over 39 years. Our results imply that mode and speed of influenza evolution are governed not only by positive selection within, but also by background selection outside antigenic epitopes: immune adaptation and conservation of other viral functions interfere with each other. Hence, adapting viral proteins are predicted to be particularly brittle. We conclude that a quantitative understanding of influenza's evolutionary and epidemiological dynamics must be based on all genomic domains and functions coupled by clonal interference.

Alignment free characterization of the influenza-A hemagglutinin genes by the ISSCOR method

Analyses and visualizations by the ISSCOR method of the influenza virus hemagglutinin genes of three different A-subtypes revealed some rather striking temporal (for A/H3N3), and spatial relationships (for A/H5N1) between groups of individual gene subsets. The application to the A/H1N1 set revealed also relationships between the seasonal H1, and the swine-like novel 2009 H1v variants in a quick and unambiguous manner. Based on these examples we consider the application of the ISSCOR method for analysis of large sets of homologous genes as a worthwhile addition to a toolbox of genomics-it allows a rapid diagnostics of trends, and possibly can even aid an early warning of newly emerging epidemiological threats.

Gnarled-trunk evolutionary model of influenza A virus hemagglutinin

Human influenza A viruses undergo antigenic changes with gradual accumulation of amino acid substitutions on the hemagglutinin (HA) molecule. A strong antigenic mismatch between vaccine and epidemic strains often requires the replacement of influenza vaccines worldwide. To establish a practical model enabling us to predict the future direction of the influenza virus evolution, relative distances of amino acid sequences among past epidemic strains were analyzed by multidimensional scaling (MDS). We found that human influenza viruses have evolved along a gnarled evolutionary pathway with an approximately constant curvature in the MDS-constructed 3D space. The gnarled pathway indicated that evolution on the trunk favored multiple substitutions at the same amino acid positions on HA. The constant curvature was reasonably explained by assuming that the rate of amino acid substitutions varied from one position to another according to a gamma distribution. Furthermore, we utilized the estimated parameters of the gamma distribution to predict the amino acid substitutions on HA in subsequent years. Retrospective prediction tests for 12 years from 1997 to 2009 showed that 70% of actual amino acid substitutions were correctly predicted, and that 45% of predicted amino acid substitutions have been actually observed. Although it remains unsolved how to predict the exact timing of antigenic changes, the present results suggest that our model may have the potential to recognize emerging epidemic strains.

Detecting past positive selection through ongoing negative selection

Detecting positive selection is a challenging task. We propose a method for detecting past positive selection through ongoing negative selection, based on comparison of the parameters of intraspecies polymorphism at functionally important and selectively neutral sites where a nucleotide substitution of the same kind occurred recently. Reduced occurrence of recently replaced ancestral alleles at functionally important sites indicates that negative selection currently acts against these alleles and, therefore, that their replacements were driven by positive selection. Application of this method to the Drosophila melanogaster lineage shows that the fraction of adaptive amino acid replacements remained approximately 0.5 for a long time. In the Homo sapiens lineage, however, this fraction drops from approximately 0.5 before the Ponginae–Homininae divergence to approximately 0 after it. The proposed method is based on essentially the same data as the McDonald–Kreitman test but is free from some of its limitations, which may open new opportunities, especially when many genotypes within a species are known.

Prevalence of epistasis in the evolution of influenza A surface proteins

The surface proteins of human influenza A viruses experience positive selection to escape both human immunity and, more recently, antiviral drug treatments. In bacteria and viruses, immune-escape and drug-resistant phenotypes often appear through a combination of several mutations that have epistatic effects on pathogen fitness. However, the extent and structure of epistasis in influenza viral proteins have not been systematically investigated. Here, we develop a novel statistical method to detect positive epistasis between pairs of sites in a protein, based on the observed temporal patterns of sequence evolution. The method rests on the simple idea that a substitution at one site should rapidly follow a substitution at another site if the sites are positively epistatic. We apply this method to the surface proteins hemagglutinin and neuraminidase of influenza A virus subtypes H3N2 and H1N1. Compared to a non-epistatic null distribution, we detect substantial amounts of epistasis and determine the identities of putatively epistatic pairs of sites. In particular, using sequence data alone, our method identifies epistatic interactions between specific sites in neuraminidase that have recently been demonstrated, in vitro, to confer resistance to the drug oseltamivir; these epistatic interactions are responsible for widespread drug resistance among H1N1 viruses circulating today. This experimental validation demonstrates the predictive power of our method to identify epistatic sites of importance for viral adaptation and public health. We conclude that epistasis plays a large role in shaping the molecular evolution of influenza viruses. In particular, sites with , which would normally not be identified as positively selected, can facilitate viral adaptation through epistatic interactions with their partner sites. The knowledge of specific interactions among sites in influenza proteins may help us to predict the course of antigenic evolution and, consequently, to select more appropriate vaccines and drugs.

Epistasis describes non-additive interactions among genetic sites: the consequence of a mutation at one site may depend on the status of the genome at other sites. In an extreme case, a mutation may have no effect if it arises on one genetic background, but a strong effect on another background. Epistatic mutations in viruses and bacteria that live under severe conditions, such as antibiotic treatments or immune pressure, often allow pathogens to develop drug resistance or escape the immune system. In this paper we develop a new phylogenetic method for detecting epistasis, and we apply this method to the surface proteins of the influenza A virus, which are important targets of the immune system and drug treatments. The authors identify and characterize hundreds of epistatic mutations in these proteins. Among those identified, we find the specific epistatic mutations that were recently shown, experimentally, to confer resistance to the drug Tamiflu. The results of this study may help to predict the course of influenza's antigenic evolution and to select more appropriate vaccines and drugs.

Natural selection and the genetics of adaptation in threespine stickleback

Growing knowledge of the molecular basis of adaptation in wild populations is expanding the study of natural selection. We summarize ongoing efforts to infer three aspects of natural selection--mechanism, form and history--from the genetics of adaptive evolution in threespine stickleback that colonized freshwater after the last ice age. We tested a mechanism of selection for reduced bony armour in freshwater by tracking genotype and allele frequency changes at an underlying major locus (Ectodysplasin) in transplanted stickleback populations. We inferred disruptive selection on genotypes at the same locus in a population polymorphic for bony armour. Finally, we compared the distribution of phenotypic effect sizes of genes underlying changes in body shape with that predicted by models of adaptive peak shifts following colonization of freshwater. Studies of the effects of selection on genes complement efforts to identify the molecular basis of adaptive differences, and improve our understanding of phenotypic evolution.

Use of phylogenetics in the molecular epidemiology and evolutionary studies of viral infections

Since DNA sequencing techniques first became available almost 30 years ago, the amount of nucleic acid sequence data has increased enormously. Phylogenetics, which is widely applied to compare and analyze such data, is particularly useful for the analysis of genes from rapidly evolving viruses. It has been used extensively to describe the molecular epidemiology and transmission of the human immunodeficiency virus (HIV), the origins and subsequent evolution of the severe acute respiratory syndrome (SARS)-associated coronavirus (SCoV), and, more recently, the evolving epidemiology of avian influenza as well as seasonal and pandemic human influenza viruses. Recent advances in phylogenetic methods can infer more in-depth information about the patterns of virus emergence, adding to the conventional approaches in viral epidemiology. Examples of this information include estimations (with confidence limits) of the actual time of the origin of a new viral strain or its emergence in a new species, viral recombination and reassortment events, the rate of population size change in a viral epidemic, and how the virus spreads and evolves within a specific population and geographical region. Such sequence-derived information obtained from the phylogenetic tree can assist in the design and implementation of public health and therapeutic interventions. However, application of many of these advanced phylogenetic methods are currently limited to specialized phylogeneticists and statisticians, mainly because of their mathematical basis and their dependence on the use of a large number of computer programs. This review attempts to bridge this gap by presenting conceptual, technical, and practical aspects of applying phylogenetic methods in studies of influenza, HIV, and SCoV. It aims to provide, with minimal mathematics and statistics, a practical overview of how phylogenetic methods can be incorporated into virological studies by clinical and laboratory specialists.

Evolution: like any other science it is predictable

Evolutionary biology rejoices in the diversity of life, but this comes at a cost: other than working in the common framework of neo-Darwinian evolution, specialists in, for example, diatoms and mammals have little to say to each other. Accordingly, their research tends to track the particularities and peculiarities of a given group and seldom enquires whether there are any wider or deeper sets of explanations. Here, I present evidence in support of the heterodox idea that evolution might look to a general theory that does more than serve as a tautology ('evolution explains evolution'). Specifically, I argue that far from its myriad of products being fortuitous and accidental, evolution is remarkably predictable. Thus, I urge a move away from the continuing obsession with Darwinian mechanisms, which are entirely uncontroversial. Rather, I emphasize why we should seek explanations for ubiquitous evolutionary convergence, as well as the emergence of complex integrated systems. At present, evolutionary theory seems to be akin to nineteenth-century physics, blissfully unaware of the imminent arrival of quantum mechanics and general relativity. Physics had its Newton, biology its Darwin: evolutionary biology now awaits its Einstein.

The role of genomics in tracking the evolution of influenza A virus

Influenza A virus causes annual epidemics and occasional pandemics of short-term respiratory infections associated with considerable morbidity and mortality. The pandemics occur when new human-transmissible viruses that have the major surface protein of influenza A viruses from other host species are introduced into the human population. Between such rare events, the evolution of influenza is shaped by antigenic drift: the accumulation of mutations that result in changes in exposed regions of the viral surface proteins. Antigenic drift makes the virus less susceptible to immediate neutralization by the immune system in individuals who have had a previous influenza infection or vaccination. A biannual reevaluation of the vaccine composition is essential to maintain its effectiveness due to this immune escape. The study of influenza genomes is key to this endeavor, increasing our understanding of antigenic drift and enhancing the accuracy of vaccine strain selection. Recent large-scale genome sequencing and antigenic typing has considerably improved our understanding of influenza evolution: epidemics around the globe are seeded from a reservoir in East-Southeast Asia with year-round prevalence of influenza viruses; antigenically similar strains predominate in epidemics worldwide for several years before being replaced by a new antigenic cluster of strains. Future in-depth studies of the influenza reservoir, along with large-scale data mining of genomic resources and the integration of epidemiological, genomic, and antigenic data, should enhance our understanding of antigenic drift and improve the detection and control of antigenically novel emerging strains.

Models of coding sequence evolution

Probabilistic models of sequence evolution are in widespread use in phylogenetics and molecular sequence evolution. These models have become increasingly sophisticated and combined with statistical model comparison techniques have helped to shed light on how genes and proteins evolve. Models of codon evolution have been particularly useful, because, in addition to providing a significant improvement in model realism for protein-coding sequences, codon models can also be designed to test hypotheses about the selective pressures that shape the evolution of the sequences. Such models typically assume a phylogeny and can be used to identify sites or lineages that have evolved adaptively. Recently some of the key assumptions that underlie phylogenetic tests of selection have been questioned, such as the assumption that the rate of synonymous changes is constant across sites or that a single phylogenetic tree can be assumed at all sites for recombining sequences. While some of these issues have been addressed through the development of novel methods, others remain as caveats that need to be considered on a case-by-case basis. Here, we outline the theory of codon models and their application to the detection of positive selection. We review some of the more recent developments that have improved their power and utility, laying a foundation for further advances in the modeling of coding sequence evolution.