Generalized Hidden Markov Models for Phylogenetic Comparative Datasets

Abstract

1. Hidden Markov models (HMM) 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. 2. 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. 3. 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. 4. 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 outperforms a Markov model when the degree of rate heterogeneity is moderate to high. 5. Finally, we demonstrate the importance of these generalizations by reconstructing the morphology of the ancestral angiosperm flower. Exactly opposite to previous results, we find the most likely state to be a spiral perianth, spiral androecium, whorled gynoecium. The difference between our analysis and previous studies was that our modeling allowed for the correlated evolution of several flower characters.

Potential survival of some, but not all, diversification methods

“…Good science will involve comparing different reasonable models to the data, not just comparing our slightly more complex model of interest with slightly simpler models. Much of our work on hidden rate models (e.g., Beaulieu et al 2013;Beaulieu and O'Meara 2016;Caetano et al 2018;Boyko and Beaulieu 2021) is motivated by this desire to give our preferred models an actual chance to lose against other models in the hope that we learn from this.…”

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).…”

Distilling complex evolutionary histories with shiftPlot

“…We originally formulated shiftPlot as a tool to visualize results directly from corHMM (Boyko & Beaulieu, 2021), an R package used for fitting hidden Markov models of discrete character evolution. However, since the package generally requires minimal inputs (a phylogeny and associated node states), it functions across platforms to address the general issue of overly complex phylogenetic data presentations.…”