Consensus functions and patterns in molecular sequences.

In recent years, methods of consensus, developed for the solution of problems in the social sciences, have become widely used in molecular biology. We study a method of consensus originally due to Waterman et al. (Waterman, Galas and Arratis. 1984. Pattern recognition in several sequences: consensus and alignment. Bull. math. Biol. 46, 515-527) which is used to identify patterns or features in a molecular sequence where a pattern can vary in position within a given window. We show that some well-known consensus methods of the social sciences, the median and the mean, are special cases of this method for certain choices of the parameters used in it and give a precise account of the parameters for which these special cases arise. We also show that the specific parameters used in the method of Waterman et al. make their method equivalent to the media procedure which is widely used in the social sciences.