Supplementary material and supplementary data files for: Handling logical character dependency in phylogenetic inference: Extensive performance testing of assumptions and solutions using simulated and empirical data

Logical character dependency is a major conceptual and methodological
problem in phylogenetic inference of morphological datasets, as it
violates the assumption of character independence that is common to all
phylogenetic methods. It is more frequently observed in higher-level
phylogenies or in datasets characterizing major evolutionary transitions,
as these represent parts of the tree of life where (primary) anatomical
characters either originate or disappear entirely. As a result, secondary
traits related to these primary characters become “inapplicable” across
all sampled taxa in which that character is absent. Various solutions have
been explored over the last three decades to handle character dependency,
such as alternative character coding schemes and, more recently, new
algorithmic implementations. However, the accuracy of the proposed
solutions, or the impact of character dependency across distinct
optimality criteria, has never been directly tested using standard
performance measures. Here, we utilize simple and complex simulated
morphological datasets analyzed under different maximum parsimony
optimization procedures and Bayesian inference to test the accuracy of
various coding and algorithmic solutions to character dependency. This is
complemented by empirical analyses using a recoded dataset on
palaeognathid birds. We find that in small, simulated datasets, absent
coding performs better than other popular coding strategies available
(contingent and multistate), whereas in more complex simulations (larger
datasets controlled for different tree structure and character
distribution models) contingent coding is favored more frequently. Under
contingent coding, a recently proposed weighting algorithm produces the
most accurate results for maximum parsimony. However, Bayesian inference
outperforms all parsimony-based solutions to handle character dependency
due to fundamental differences in their optimization procedures—a simple
alternative that has been long overlooked. Yet, we show that the more
primary characters bearing secondary (dependent) traits there are in a
dataset, the harder it is to estimate the true phylogenetic tree,
regardless of the optimality criterion, owing to a considerable expansion
of the tree parameter space.