Mu.reurn of'JVatura1 Hi.stoy, C'entrul Park M Z s t at 79th Street, h e m York, N Y 10024, U.S.A. and Ilefiartmenl aJ Biolog, CiQ College, Cip IJnirw~ity of',Vew York, CJ.S.A.T h c consistency index, introduced by Kluge and Farris (1969) as a measure ol'6t o f a character to a tree, has been widely and successfully employed, but might be capable of some improvement for certain applications. 'The purpose of this note is to dcwrihe two new indices, already in use in Hennig86, and to explain their interpretation.T h e consistency index, c, is defined t o be c = rnls.Irere s denotes thr amount of change in the character (for an integral character, number of' steps) required parsimoniously by the considered tree, and rn represents the minimum amount ofchange that the character may show on any trct'. Both .f and ni depeiid on the suite of' terminals used, for which reason it is assumed throughout that some particular set of terminals is treated.'I'he change, ,r, i n a character on a tree can be partitioned into observed variation, ' rn, and homoplasy (extra steps), h:T h e consistency index expresses that partition as fractions of the amount ofchangc, .\ : i 1 -c j is the fraction ofchange that must be attributed to homoplasy. T h e character fits the tree poorly to the degree that the tree requires homoplasy in the character. LYhen no homoplasy is required, the fit is perfect, and then c = 1. As rn cannot exceed J, c cannot exceed unity. If s = 0, then rn = 0, and c is taken to be unity. T h e amount ofhomoplasy might also be expressed as a fraction of possible homoplasy. This is done by the distortion coefficient, d, of Farris (1973):where g denotes the greatest amount of change that the character may require on any tree, that is, the: greatest possible value ofs, so that (gnz) is the greatest possible value of the amount of homoplasy, h. T h e complement of d, here denoted r, isIfg = rn, then .s=g, and r is taken to be unity, so that d is taken to be 0. 1 shall call r the retention index.T h e interpretation of the retention index can be seen from a simple argument. O n a tree for which .s = rn, r = 1, there is no homoplasy, and all similarities between terminals in the character are homologous. O n another tree for which s > m , some of those similarities are homoplasies. Each additional requirement for a step implies a separate ' 'l'he observed variation has frcquently been callrd the rangr of a character. 'l'hat usage is appropriatc for numerical charartcrs, but not for others, such as sequrncc sitrs or thaw having multifurcating charactcr state Irers.
