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Macroevolution posed difficulties for Darwin and later theorists because species' phenotypes frequently change abruptly, or experience long periods of stasis, both counter to the theory of incremental change or gradualism. We introduce a statistical model that accommodates this uneven evolutionary landscape by estimating two kinds of historical change: directional changes that shift the mean phenotype along the branches of a phylogenetic tree, and evolvability changes that alter a clade's ability to explore its trait-space. In mammals, we find that both processes make substantial independent contributions to explaining macroevolution, and are rarely linked. 'Watershed' moments of increased evolvability greatly outnumber reductions in evolutionary potentials, and large or abrupt phenotypic shifts are explicable statistically as biased random walks, allowing macroevolutionary theory to engage with the language and concepts of gradualist microevolution. Our findings recast macroevolutionary phenomena, illustrating the necessity of accounting for a variety of evolutionary processes simultaneously., (© 2022. The Author(s).)

The fossil record is the best evidence of the characteristics of extinct species, but only a narrow range of traits fossilize or survive the fossilization process. Lacking fossil or other evidence about the past, ancestral states can be reconstructed. Three pieces of information are combined when reconstructing ancestral states: extant or known trait values (data); the evolutionary history, linking the species of interest (phylogeny); and the evolutionary model of trait change. These reconstructed ancestral states can be interpreted as our best guess as to the route evolution took, given the distribution of the trait across species, the relationships among them, and our model of evolution. Because the information we use to reconstruct the past is often not known without error, uncertainty about their true values should be accounted for when reconstructing ancestral states. In this chapter we describe how ancestral states can be reconstructed using a Bayesian framework implemented in the software BayesTraits to account for uncertainty in the phylogenetic tree and the model of evolution., (© 2022. The Author(s), under exclusive license to Springer Science+Business Media, LLC, part of Springer Nature.)