Phylogenetic analysis of characters with dependencies under maximum likelihood

The dependencies between characters used in phylogenetic analysis (e.g., inapplicabilities, functional dependencies) can be taken into account by using combinations of character states as possible ancestral morphotypes, and using appropriate rates of transformation between such morphotypes. As every morphotype represents a permissible combination of the original character states, this allows for easily ruling out specific combinations of character states, and taking into account changes that are either less or more likely to co-occur, or to occur in certain contexts. For inapplicable characters, Goloboff et al. (2021) used morphotypes but proposed obtaining transition probabilities between morphotypes from products of transition probabilities of the original characters and factors to incorporate dependencies. The product of transition probabilities is shown here to be flawed (failing the time-continuity requirement of phylogenetic Markov models, essential for statistical consistency und..., , , # Phylogenetic analysis of characters with dependencies under maximum likelihood

[https://doi.org/10.5061/dryad.p8cz8wb03](https://doi.org/10.5061/dryad.p8cz8wb03)

This package contains the Supplementary Materials, with additional technical details and discussion on implementation, plus test datasets and scripts.

## Description of the data and file structure

All the materials needed to reproduce the datasets used in the simulations reported in the paper are in a single file, called **Materials.zip**. The contents of this ZIP file are: 

a)  **SupplementaryMaterials.txt**, containing technical details and implementation notes (complementing the descriptions and discussion in the main text). This supplementary material explains methods for modeling dependent morphological characters in phylogenetics using maximum likelihood. It compares two approaches to calculating transition probabilities—probability products versus rate matrix exponentiation—and supports the latter for consistency....,