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HOMOPLASY AND THE CHOICE AMONG CLADOGRAMS
Author(s) -
Goloboff Pablo A.
Publication year - 1991
Publication title -
cladistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.323
H-Index - 92
eISSN - 1096-0031
pISSN - 0748-3007
DOI - 10.1111/j.1096-0031.1991.tb00035.x
Subject(s) - cladogram , mathematics , consistency (knowledge bases) , consistency index , statistic , tree (set theory) , congruence (geometry) , set (abstract data type) , statistics , cladistics , combinatorics , measure (data warehouse) , hierarchy , discrete mathematics , biology , phylogenetic tree , computer science , data mining , geometry , biochemistry , materials science , rheology , gene , economics , market economy , composite material , programming language
Cladistic data are more decisive when the possible trees differ more in tree length. When all the possible dichotomous trees have the same length, no one tree is better supported than the others, and the data are completely undecisive . From a rule for recursively generating undecisive matrices for different numbers of taxa, formulas to calculate consistency, rescaled consistency and retention indices in undecisive matrices are derived. The least decisive matrices are not the matrices with the lowest possible consistency, rescaled consistency or retention indices (on the most parsimonious trees); those statistics do not directly vary with decisiveness. Decisiveness can be measured with a newly proposed statistic, DD = S̄ − S )/( S̄ − S ) (where S = length of the most parsimonious cladogram, S̄ = mean length of all the possible cladograms for the data set and M = observed variation). For any data set, S̄ can be calculated exactly with simple formulas; it depends on the types of characters present, and not on their congruence. Despite some recent assertions to the contrary, the consistency index is an appropriate measure of homoplasy (= deviation from hierarchy). The retention index seems more appropriate for comparing the fit of different trees for the same data set.