Abstract
Modeling discrete phenotypic traits for either ancestral character state reconstruction or morphology-based phylogenetic inference suffers from ambiguities of character coding, homology assessment, dependencies, and selection of adequate models. These drawbacks occur because trait evolution is driven by two key processes—hierarchical and hidden—which are not accommodated simultaneously by the available phylogenetic methods. The hierarchical process refers to the dependencies between anatomical body parts, while the hidden process refers to the evolution of gene regulatory networks (GRNs) underlying trait development. Herein, I demonstrate that these processes can be efficiently modeled using structured Markov models (SMM) equipped with hidden states, which resolves the majority of the problems associated with discrete traits. Integration of SMM with anatomy ontologies can adequately incorporate the hierarchical dependencies, while the use of the hidden states accommodates hidden evolution of GRNs and substitution rate heterogeneity. I assess the new models using simulations and theoretical synthesis. The new approach solves the long-standing “tail color problem,” in which the trait is scored for species with tails of different colors or no tails. It also presents a previously unknown issue called the “two-scientist paradox,” in which the nature of coding the trait and the hidden processes driving the trait’s evolution are confounded; failing to account for the hidden process may result in a bias, which can be avoided by using hidden state models. All this provides a clear guideline for coding traits into characters. This article gives practical examples of using the new framework for phylogenetic inference and comparative analysis.
Highlights
The hierarchical process refers to the dependencies between anatomical body parts, while the hidden process refers to the evolution of gene regulatory networks (GRNs) underlying trait development
I demonstrate that these processes can be efficiently modeled using structured Markov models (SMM) equipped with hidden states, which resolves the majority of the problems associated with discrete traits
While both processes are at first glance dissimilar, they are interacting—modeling a hierarchical process often requires equipping a SMM with elements of a HMM; at the same time modeling hidden processes requires structuring HMM using SMM techniques
Summary
An observation of some feature(s) of a phenotype. A formalized coding of a trait (observation) into a character string (i.e., character) that consists of two or more entities called “character states”; “character” is used as a synonym of “discrete-state Markov model”. If rates in the rate matrix, and values of the initial vector are identically and independently distributed (i.i.d.), which does not rule out the possibility they are different, the amalgamated DNA character is nearly lumpable under any possible partitioning scheme This occurs because the i.i.d. condition produces an aggregated chain whose error, in approximating the original rates, is insignificant as the number of the original states increases, while the number of the aggregated states decreases (Supplementary Appendix S5 available on Dryad). The states ar and ab correspond to the same observation specifying the absence of the tail since tail color cannot be observed when the tail is absent These matrices, as might be expected, cannot be reduced to a three-state matrix with states {a,r,b} under any values of their rate parameters because they are not lumpable under the partitioning scheme {{ar, ab}, {pr}, {pb}} (Supplementary Appendix S6 available on Dryad). The schemes #2 and #3 fail to provide biologically logical character optimization, and the scheme #4 does not include
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