a | In comparisons among orthologous proteins from a given set of species, convergent substitutions at a particular site refer to independent changes from different ancestral amino acids to the same derived amino acid. In this case, there was a change from G (the ancestral state) to T (the derived state) in one species, and a change from A to T in another species. The convergent substitutions are denoted by red bold lines. b | Parallel substitutions at a site refer to independent changes from the same ancestral amino acid to the same derived amino acid. In this case, changes from A to T occurred in two different species. The parallel substitutions are denoted by red bold lines. In sets of closely related species, parallelism is generally more common than convergence simply because — at any given site — close relatives will be more likely to share the same ancestral state prior to the occurrence of independent substitutions.

Substitutions at the indicated sites in Na⁺,K⁺-ATPase α1 subunit (ATPα1) are implicated in cardenolide-binding in insect taxa that feed on Apocynaceae. Names of insect orders are shown on the far right. Numbered columns correspond to sites that are implicated in cardenolide-binding based on experimental evidence. Grey sites correspond to sites that may have a role in cardenolide-binding based on structural considerations. Dots denote identity with the consensus sequence. Outgroup sequences of vertebrate Na⁺,K⁺-ATPase α1 subunit (ATP1A1; a homologue of ATPα1) from several taxa (sheep, pig and spiny dogfish) are shown for reference. Letters in red boxes represent amino acid replacements whose functional effects have been experimentally characterized. Underlined letters are substitutions that require at least two nonsynoymous substitutions relative to the ancestral sequence. Orange-shaded rows correspond to specialists that are known to sequester cardenolides. Grey-shaded rows represent species that either are not known to sequester cardenolides and/or are nonspecialists that are only occasionally found on Apocynaceae. Green circles represent inferred duplications of the gene encoding ATPα1. Numbers at the bottom of the figure correspond to the number of inferred substitutions associated with use of Apocynaceae. Red boxes at the bottom of the figure correspond to parallel substitutions (observed in more than one independent lineage). Blue boxes correspond to unique substitutions (observed in only one lineage). Note that a preponderance of parallel substitutions occurs only in taxa that possess a single copy of the gene encoding ATPα1. In those taxa that possess two duplicate copies, a greater number of unique (nonshared) substitutions have occurred. It may be that the possession of two functionally redundant paralogues alleviates pleiotropic constraints, so a broader spectrum of function-altering mutations can contribute to adaptation. A. nerii, Aphis nerii; A. pisum, Acyrthosiphon pisum; B. mori, Bombyx mori; B. tabaci, Bemisia tabaci; B. trivittata, Boisea trivittata; C. auratus, Chrysochus auratus; C. castaneus, Cyrtepistomus castaneus; C. lectularius, Cimex lectularius; C. tenera, Cycnia tenera; D. citri, Diaphorina citri; D. eresimus, Danaus eresimus; D. gilippus, Danaus gilippus; D. plexippus, Danaus plexippus; E. egle, Euchaetes egle; H. melpomene, Heliconius melpomene; L. archippus, Limenitis archippus; L. caryae, Lophocampa caryae; L. clivicollis, Labidomera clivicollis; L. halia, Lycorea halia; L. kalmii, Lygaeus kalmii; M. robiniae, Megacyllene robiniae; O. aries, Ovis aries; O. faciatus, Oncopeltus fasciatus; P. chalceus, Pogonus chalceus; P. glaucus, Papilio glaucus; P. versicolora, Plagiodera versicolora; R. lineaticollis, Rhyssomatus lineaticollis; S. acanthias, Squalus acanthias; S. scrofa, Sus scrofa; T. castaneum, Tribolium castaneum; T. legitima, Trichordestra legitima; T. tetrophthalmus, Tetraopes tetrophthalmus. Adapted from Zhen, Y., Aardema, M. L., Medina, E. M., Schumer, M. & Andolfatto, P. Parallel molecular evolution in an herbivore community. Science 337, 1634–1637 (2012). Reprinted with permission from the American Association for the Advancement of Science.

Horizontal rows correspond to each of the 20 possible amino acids at each site in a protein. a | At each site, the currently predominant amino acid (shown in bold outline) confers high fitness. b | The single-position fitness landscape of site 7, shown in isolation. c | Temporal change in the single-position fitness landscape. The relative fitness levels of different amino acids at the position change through time owing to changes in the genetic background (that is, substitutions at other sites) and/or changes in the environment. The depicted changes in fitness are modelled as a Poisson process. Adapted from Bazykin, G. A. Changing preferences: deformation of single position amino acid fitness landscapes and evolution of proteins. Biology Letters (2015) 11, 20150315, by permission of the Royal Society.

As a result of nonlinearity in the relationship between phenotype and fitness, mutations with additive effects on phenotype can have epistatic effects on fitness. In this hypothetical example, the same mutation is introduced into three genotypes (labelled a, b and c on the figure) that have different phenotypes. The mutation has the same phenotypic effect (Δp = 1) on each of the three backgrounds, but the change in fitness (Δw) is different in each case. The mutation increases fitness in genotypes a and b (although the magnitude of the increment is different) and it reduces fitness in genotype c. Adapted from REF. .