A Conditional Probability of Reconstruction Measure for Internal Cladogram Branches

The conditional probability of reconstruction is a measure of the robustness of cladogram internodes and, unlike Bremer support and bootstrapping values, directly gauges probability. The new method compares the three putative branch lengths (the optimal and two alternatives) obtained through branch recalculation after nearest neighbor interchange and recalculation under constraint. With rooted trees, one switches the two free lineages attached at the distal end of an internal branch withthe basallineage.Probabilisticreconstruction ofabranch for smalldatasets(e.g., morphological) isdeenedashavingnocontrarysupportforthetwoalternativebranchesand, whensufecientdataare available (e.g., molecular studies), as meeting a selected conedence limit in chi-squared analysis. The exactprobabilitythattheinternalbranchisreconstructedisthesameasthepreselectedconedencelevel metwithchi-squaredanalysis;alternatively,itisasimplecalculationofthelengthoftheoptimalbranch dividedbythesumofthelengthsofallthreeputativebranches.Thisnewmeasureofrobustnessallows calculation of summary probabilities of subclade and tree reconstruction. The measure is conditional on a particular data set and optimization method but may also compare support from coneicting gene trees. Examples are provided by a morphological data set (the bryophyte Didymodon) and a molecular data set (primates). (Branch length; chi-squared; Didymodon; multiple gene trees; primates; probabilistic reconstruction; support) Although optimality methods maximize phylogenetic information, such information may be coneicting or (in the case of mor- phological data) paltry, and relative support for the optimal versus alternative but some- what longer trees is not easily measured. Parsimonymethodsclearlyeliminategrossly unreasonable trees in terms of total length, but generally an additional support mea- sure is necessary to distinguish the optimal tree from the many reasonable but less op- timal solutions if the result is to be useful and reliable (Zander, 1998a). The methodol- ogy of parsimony analysis allows measure- ment, in terms of length, of alternative inter- nal branches that are suboptimal to those in the shortest tree—the shorter the alternative branches(thefewertheputativesynapomor- phies), the less the contradiction to the op- timal branch. In recent literature, measures of support for internal branches are gener- allylimitedtobootstrapping(BS)andBremer support (BR; the decay index). These, how- ever,arenotthefamiliarconedencevaluesor probability measures of other biological dis- ciplines and are difecult to interpret as mea- sures of reliability of the reconstruction. The number of alternative branches to be assayed for coneict may be reduced by de- composing a cladogram into a set of triplets of alternative positions of subclades arising from any one internal branch (internode), the unrooted four-taxon tree being the sim- plest, most general case of this. In particular, in a rooted tree, the three free subclades of anyinternalbranchmay beinterchangedun- der constraint, switching either of the two that terminate the internode with that at the base of the internode. To recalcu- late branch lengths by this nearest neigh- bor interchange, one may either use con- straint trees with a parsimony program such as PAUP (Swofford, 1998) or simply move branches in MacClade (Maddison and Maddison, 1999) with the same optimiza- tion settings. Recalculation thus results in three branch length values that may be com- pared: the length of the optimal internode in the shortest tree and the lengths of the two alternative internodes. Here I advance the rationale that if the two closest alter- natives (i.e., the most reasonable for that optimization) to the optimal internode are foundtohave no statistically signiecantcon- eict with the optimal branch, the optimal branch may be considered a probabilistic reconstruction—given that particular data set,optimality method,weighting, and other assumptions—andisthusa"conditional"re-