Discrete characters may be characterized as either binary (coded into two mutually exclusive alternative states) or as multistate (a transformation series of three or more discrete states). The alternative states of a binary character are generally (although not necessarily) explicit hypotheses of the primitive and derived (advanced) states of a single evolutionary transformation event, such as the origin (or loss) of a novel feature. A multistate character is a more complex intellectual device with many more interpretations of meaning. Multistate characters may be presented as many stages of a long-term phyloge-netic trend (e.g., larger relative brain size, larger body size) or as independent alternative trends from a common ancestral plan (e.g., large brains evolving from enlargement of the cerebellum in chondrichthyans vs. the telencephalon in mammals). An ordered transformation series models a preconceived phylogenetic sequence of changes, such that in the series 1-2-3, state 3 is only permitted to be derived from state 2. In an unordered transformation series, state 3 may be derived from either of states 1 or 2. Following a similar logic, reversals (e.g., from 2 to 1) may be allowed, penalized, or prohibited, depending on the preconceptions of the investigator. Of course, building a priori conceptions of order or reversibility into an analysis of character state change precludes the use of that analysis as an independent test of those assumptions. To summarize this section, treating all characters as unpolarized and unordered means that all transitions among states are regarded as equally probable.
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