The Effect of Irrelevant Characters on Bootstrap Values

Abstract

1 E-mail: hars@midway.uchicago.edu. conveniently its inverse, relevance?can be defined recursively, at least for binary characters. A binary character is relevant to a node if any of these conditions holds: (1) the character supports that node (it is free from homoplasy only on a tree con? taining that node); (2) the character is not compatible with that node (it cannot be optimized without homoplasy on a tree containing that node); or (3) the character is not compatible with a character relevant to that node (they cannot both be free from homplasy on the same tree). All other char? acters are irrelevant. The definition may be applied to ordered or unordered mul? tistate characters by translating them (for purposes of evaluation only) into additive or nonadditive binary characters (Sneath and Sokal, 1973), respectively. To provide an example of relevant char? acters, recursively defined, the trees in Fig? ure 1 were built using characters from the matrix of Table 1. If only characters 1, 2, and 3 are used (Fig. la), there is no char? acter conflict; thus (for example), charac? ters 2 and 3 are irrelevant to the node CDE.