Generalized hidden Markov models for phylogenetic comparative datasets

Abstract

Hidden Markov models (HMMs) have emerged as an important tool for understanding the evolution of characters that take on discrete states. Their flexibility and biological sensibility make them appealing for many phylogenetic comparative applications. Previously available packages placed unnecessary limits on the number of observed and hidden states that can be considered when estimating transition rates and inferring ancestral states on a phylogeny. To address these issues, we expanded the capabilities of the R package corHMM to handle n‐state and n‐character problems and provide users with a streamlined set of functions to create custom HMMs for any biological question of arbitrary complexity. We show that increasing the number of observed states increases the accuracy of ancestral state reconstruction. We also explore the conditions for when an HMM is most effective, finding that an HMM is an appropriate model when the degree of rate heterogeneity is moderate to high. Finally, we demonstrate the importance of these generalizations by reconstructing the phyllotaxy of the ancestral angiosperm flower. Partially contradicting previous results, we find the most likely state to be a whorled perianth, whorled androecium, whorled gynoecium. The difference between our analysis and previous studies was that our modelling explicitly allowed for the correlated evolution of several flower characters.

Phylogenetic signal and rate of evolutionary change in language structures

“…From the computational side, poor reconstruction is an effect of the interaction between the evolutionary rate and the values at the tips: if the model itself is not sure about the ancestral state, like the ‘equal rates’ model, it lets more information flow into the ancestral state. With the ‘all rates differ’ model, the reconstruction is less susceptible to slight differences in tip values [ 52 , p. 476]. We will take feature TE027 ‘Can 1PL marker be augmented by a collective plural marker?’ as an illustrative example for the interaction between the model assumptions and the tips (see figure 10 for the distribution of the feature on the tree and the reconstructed ancestral states).…”

Evolutionary history of mental glands in turtles reveals a single origin in an aquatic ancestor and recurrent losses independent of macrohabitat

“…All remaining turtle species, including taxa not belonging to these three families with semiaquatic lifestyles (such as for example some side-necked and kinosternid species), were coded as aquatic (Table S1). We inferred ancestral states for MG and macrohabitat using the corHMM function in the corHMM v2.5 R package 89,90 . This function calculates the maximum likelihood estimates of transition rates between states and then uses these values for determining state probabilities for internal nodes of the tree, and can also incorporate "hidden" rate changes across a phylogeny 91 .…”

“…The three models described above assume that the process generating the different states at the tips and ancestral nodes is homogenous across all branches of a phylogenetic tree, which may be a major simplification of biological reality. The generalized hidden Markov model 90 , 91 implemented in corHMM v2.5 relaxes this assumption by allowing more than one process to affect trait evolution across a phylogeny. This is achieved by constructing > 1 rate categories (i.e.…”

“…Next, we asked whether gland status and macrohabitat are correlated in turtles. We used the corHMM function in the corHMM v2.5 package to fit different models of evolution for the two categorical traits 50 , 90 , 93 . For two binary characters (X, Y) with states 0 and 1, a maximum of 8 different transition parameters can be defined (disallowing for simultaneous changes in both variables), in a continuous-time Markov chain.…”

Ecological selectivity and the evolution of mammalian substrate preference across the K–Pg boundary

“…Hidden Markov models (HMMs) have emerged as a powerful tool for assessing the possibility that unobserved rate heterogeneity can have an outsized influence on reconstructing the evolutionary history of discrete characters (Beaulieu & O'Meara, 2016;Beaulieu et al, 2013;Boyko & Beaulieu, 2021). In comparison with time-homogeneous models, which assume that specified character transition rates do not evolve, HMMs provide an elegant solution for evaluating the hypothesis that the mode of character evolution has evolved throughout a clade's evolutionary history.…”