Phenotypic characters are essential to study the evolution of extant and extinct life forms and to reconstruct the tree of life. Inside the cladistics theory, parsimony is used by a large majority of systematists working on phenotypic characters, whereas 3ta is much less widespread but has triggered important debates. Many important differences in the interpretation of the cladistic theory exist between these methods, e.g. meaning and treatment of reversals, character representation as 'data-matrices' in parsimony (ordered and unordered), and as rooted trees (hierarchies) in 3ta. Although 3ta has received severe criticism, mostly focused in the use of software intended to be used in parsimony, only a few empirical studies have compared these methods so far. We present the results of simulations of the evolution of phenotypic traits under a Brownian motion model to characterize differences in sensitivity between parsimony and 3ta to (1) outgroup branch length, which affects the reliability of ancestral character state estimates, (2) character state ordering scheme, and (3) ingroup branch lengths that reflect the geological age of studied taxa. Our results show that the 'nihilistic' attitude of leaving multistate characters unordered when criteria to order are available (e.g., similarity, ontogeny, etc…) can decrease resolving power of the method (by 13.4% to 29.3%) and increase the occurrence of artefactual clades (by 5% to 15.6%). Increasing outgroup branch length significantly decreases resolving power and increases artefactual resolution, at least for paleontological trees. All simulations show that ordered parsimony is always superior to 3ta in tested parameter space. These results depend on the assumption in parsimony that reversals (as implied by the Brownian motion, as in most other models) can be evidence for the support of a clade a posteriori from an analysis or a priori on simulations with a known pattern. We discuss implications of these points of view compared to the assumption inherent in 3ta (i.e., that reversals should not support a clade as other synapomorphies do) on evolutionary models.

Simulation-based and experimental studies are crucial to produce factual arguments to solve theoretical and methodological debates in phylogenetics. However, despite the large number of works that tested the relative efficiency of phylogenetic methods with various evolutionary models, the capacity of methods to manage various sources of error and homoplasy has almost never been studied. By applying ordered and unordered methods to datasets with iterative addition of errors in the ordering scheme, we show that unordered coding in parsimony is not a more cautious option. A second debate concerns how to handle reversals, especially when they are regarded as possible synapomorphies. By comparing analyses of reversible and irreversible characters, we show empirically that three-taxon analysis (3ta) manages reversals better than parsimony. For Brownian motion data, we highlight that 3ta is also more efficient than parsimony in managing random errors, which might result from taphonomic problems or any homoplasy generating events that do not follow the dichotomy reversal/ convergence, such as lateral gene transfer. We show parsimony to be more efficient with numerous character states (more than four), and 3ta to be more efficient with binary characters, both methods being equally efficient with four states per character. We finally compare methods using two empirical cases of known evolution.