Character space restrictions and boundary conditions in the evolution of quantitative multistate characters.

The effects of restrictions of available character space on the mean morphological distance between living members of evolutionary phylads are examined by Monte Carlo simulation. The approach involves specifying the degree to which ancestor-descendant species may differ and limiting the range of attainable character states within a phylad. Morphological evolution is modeled as a Markovian process involving quantitative multistate characters. States for a given character are allowed to evolve at timedependent or speciation-dependent rates. The final distributions of morphological distance for a given trait among members of a phylad depend on the number of species in the phylad, the rate and pattern of evolution of new character states, and the existence of boundary conditions indicating possible selective constraints on the trait. When morphological change is proportional to time, increasing restrictions on character evolution tend to (a) lower mean distance between species and (b) leave the ratio of mean distances (B,/D, ) in species-rich vs. species-poor phylads of comparable evolutionary age near one. When change is proportional to rate of speciation, similar restrictions tend to (a) limit mean distance only in phylads in which the number of speciations exceeds the range of attainable character states and (b) permit D,/i& to be considerably greater than one, except in extreme cases. Implications of these results for the current phyletic gradualism-rectangular evolution controversy are considered.