PLOTTING FREQUENCY DISTRIBUTIONS OF PHYLOGENETIC GROUPINGS FOUND AMONG SETS OF MOST PARSIMONIOUS TREES.

Abstract

\If any d a ta sets used in phylogenetic ana lysis yield more than one mos t pa rsimonious tree (\i!PT). Indeed , when a la rge num ber of taxa a re exam ined and mul tistate unordered characters a re used , severa thousand M PTs can be produced. T he nature a nd ex tent of the va riat ion in tree st ructure a mong MPTs is often difficult to summarize . T his note is in tended to bring attention to a g ra phical method tha t makes the task less cumbersome. The method is a lso proposed as a useful ped agogical tool. Th e method is stra ightforwa rd . C lades are ra nked in descending o rder acco rding to the freq uency with which they occur in a set of M PTs. T he ra nked clad es a re then plo tted against their respec tive frequencies. T he resul tant ra nked frequency profi le, hereafter referred to as the hiera rchic signa l, cha rac terizes topological variation withi n the MPT set. T he method is illustra ted using MPTs d erived from an a llozyme stud y of 37 carcha rhinid sha rk species (Naylor, submitted ). Seventeen loci conta ini ng 201 a ll eles we re scored . Loc were treated as cha racte rs while a ll eles within loci were trea ted as unordered cha racter states. 32 767 most pa rsimonious trees were genera ted using the heuristic sea rch procedure (TBR ) of the computer progra m PAU P 3.0 (Swofford , 1990) . [This number of trees (2 1 5 I ) represents the maximum tha t can be genera ted in any single run using Pi U P 3.0. I t a lmost cer tainly does not represent a ll of the most parsimonious trees that a rise from this pa rticula r data se t.] i frequency plot of the clades found among the 32 767 MPTs was generated [Fig. I (A)] by ta king advantage of the 'show dot plo t of g roup freq uencies' option ofPAU P 3.0. T he da ta were then subjected to successive we ighting (Farris, 1969) using the rescaled consistency index (Fa rris, 1989) to determine new weights a t each ite ration . Weights stabili zed a fter three heuristic search itera tions producing a new se t of21 145 trees. The clades present a mong the successively weigh ted MPTs were compared with those found in the origina se t of MPTs. The frequency histogram of the clad es fo und aft er successive weighting is shown in Fig. I (B). Gra phica lly the effect of successive weighting on this d a ta se t can be seen a t a glance. The pla teau region of the sigmoida l distribu tion is extended while the ta il region is truncated . T his corresponds to a n increase in the number of clad es found in high frequencies with a concomitant dec rease in the number of clades found in low frequencies. Ths histogram method also provides insight into the workings of strict (Nelson, 1979; R ohlf, 1982) a nd majority rule (M argush a nd M cM orris, 198 1) consensus trees. Strict consensus trees summari ze onl y those groupings that a re found in 100% of MPTs, whereas majority rule consensus trees summa rize groupings tha t a re found in more tha n 50% ofMPTs. Thus, for the sha rk d a ta above the histogram conveys an immediate sense