Ancestral state reconstruction is a phylogenetic comparative method that involves estimating the unknown trait values of hypothetical ancestral taxa at internal nodes of a phylogenetic tree. Ancestral state reconstruction has long been, and continues to remain, among the most popular analyses in phylogenetic comparative research. In this review, I illustrate the theory and practice of ancestral state reconstruction for both discretely and continuously-valued phenotypic traits. For discrete characters, I focus on the Mk model and describe the distinction between marginal and joint reconstruction, as well as between local vs. global estimation. For continuous traits, I describe ancestral state reconstruction under a model of Brownian motion evolution. I highlight several use cases of ancestral state reconstruction via a set of empirical examples, ranging from diel activity pattern in primates, to environmental tolerance in lizards. Finally, I discuss and explore the statistical properties of ancestral state estimation as well as its limitations. By illustrating ancestral reconstruction under the hidden-rates and threshold models (for discrete traits), and bounded Brownian motion (for continuous characters), I demonstrate the considerable sensitivity of ancestral reconstruction to model misspecification. Although ancestral state reconstruction is virtually certain to retain its popularity into the future, I conclude by recommending considerable caution and circumspection in the use and interpretation of ancestral reconstruction in empirical evolutionary research.
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