A formula for maximum possible steps in multistate characters: isolating matrix parameter effects on measures of evolutionary convergence

To identify a biological signal in the distribution of homoplasy, it is first necessary to isolate non-biological factors affecting its measurement. The number of states per character in a phylogenetic data matrix may indicate evolutionary flexibility and, consequently, the likelihood of recurrent evolution. However, we show here that the number of states per character limits the maximum number of steps that may be inferred using parsimony. A formula is provided for the maximum number of steps that may be taken by a character with a given number of states and taxa. We show that as more character states are included the maximum proportion of steps that can be attributed to homoplasy falls, and the greatest amount of homoplasy measurable with the consistency index declines.