Brownian motion in cladistics
Under the conditions examined in our simulations, ordered parsimony performed best, thus confirming our first hypothesis. Simulating characters on a phylogeny has the advantage that the reference phylogeny is known without error. However, the Brownian motion, evolutionary model that is widely used in simulations of evolution, and which we used here, impacts upon the results, and reflects theoretical assumptions. Under Brownian motion, character evolution is stochastic and unpredictable, as are many historical events, but follows a general pattern that reflects the phylogeny, which can be inferred by analyzing character state data. Here, because of the generation of discretized continuous characters, the distribution of character states is unimodal (S6). They are intrinsically ordered and thus represent morphoclines. Brownian motion, like most other models of molecular evolution, such as GTR+I+Г (Tavaré, 1986) or the speciational model, is not directional (i.e., it implies no trends). Thus, the relationships between character states can be represented by unrooted trees (Fig. 1A). Brownian motion thus leads to an intrinsically ordered and unpolarized modeling (when the root condition is not specified in the simulation, as is the case here), contrary to models implying trends or irreversible evolution, which are intrinsically polarized. Under Brownian motion, the probability for a character state 0 to evolve into 1 is greater than the probability for 0 to evolve into 2 in a short time; it was thus expected to favour ordered parsimony over unordered parsimony, and to a lesser extent, 3ta. However, this model, one of the simplest, seems applicable to various characters, such as ontogenetic sequence data (Poe and Wake, 2004; Poe, 2006).