On the Mkv model with among-character rate variation

Models used in likelihood-based morphological phylogenetics often adapt molecular phylogenetics models to the specificities of morphological data. Such is the case for the widely used Mkv model, which introduces an acquisition bias correction for sampling only characters that are observed to be variable---and for models of among-character rate variation (ACRV), routinely applied by researchers to relax the equal-rates assumption of Mkv. However, the interaction between variable character acquisition bias and ACRV has never been explored before. We demonstrate that there are two distinct approaches to conditioning the likelihood on variable characters when there is ACRV, and we call them joint and marginal acquisition bias. Far from being just a trivial mathematical detail, we show that how the variable character conditional likelihood is calculated results in different assumptions about how rate variation is distributed in morphological datasets. Simulations demonstrate that tree l..., , , # On the Mkv model with among-character rate variation

[https://doi.org/10.5061/dryad.fxpnvx13g](https://doi.org/10.5061/dryad.fxpnvx13g)

## Description of the data and file structure

This compressed file archive contains all data and scripts used in the simulation study and in the empirical example included in the paper, as well as output tree files, scripts, and plots to check for MCMC convergence, and scripts for plotting results.

### Files and variables

#### File: SupplementaryDataForSubmission\_AfterRevisions.zip

**Description:** 

`data` folder: contains data files used for all analyses

* `Gekkota_Villa2023_All.nex`: Morphological data in Nexus format, used in the empirical example. Data from Villa (2023).
* `Gekkota_Villa2023_Extant.nex`: Morphological data in Nexus format, used in the empirical example. Data modified from Villa (2023) to prune out extinct taxa.
* `Sim1000Chars_TreeN_MODEL.nex`: Simulated morphological data in Nexus format, used in the simulation study. `N...,