Detecting evolutionary trends from molecular data. 1. Some measures of compositional nonrandomness.

The measures of compositional nonrandomness to be discussed as to their physical significance and to their power of detecting evolutionary significant variations are (see article)(pi a priori probability for amino acid i, ni its number of occurrences in a protein of length L). As a concrete example, the pi are here supposed to represent equal frequencies of all non-stop codons. For each quantity, four levels are defined: The base level, with optimal (i.e. minimal nonrandomness) composition, admitting non-integer values of ni; the integer level with optimal integer composition; the noise level, represented by a typical random cain; and the real protein level. On all these levels, S, which is the measure with the most direct physical sense, shows the smoothest behavior with the smallest relative fluctuations and thus the highest resolution.