Figure 1. (a,b) Two partially resolved cladograms for 10 species (1–5, 6–10) and five areas (A–E). (c) Fully resolved consensus area cladogram for the five areas A–E. (d,e) Two area cladograms for four areas each (A,B,D,E and A,C,D,E). (f) Common ‘pruned tree’ general area cladogram for the two cladograms in (d) and (e) that removes unique and unresolved areas.

Figure 2. The principles of component analysis. (a) Area cladogram for three taxa (1–3) and four areas (A–D). Note that species 1 is widespread for areas A and B. (b) The effect of widespread taxa is that they represent unresolved nodes for further biogeographic analysis. Thus, areas A and B fall to the root of the tree and there are effectively two occurrences for species 1, although only one area can be correct (even if we do not know whether it is A or B. (c,d) Under ‘Assumption 2’ (in the sense of Nelson and Platnick, 1981) whatever is true for the relationship of species 1 in area A relative to species 2 and 3 in areas B and C, is not necessarily true of species 1 in area B relative to species 2 and 3 in areas C and D. Similarly, the converse is true, hence there are two further possibilities for component analysis. There are five possible area cladograms for each of the two statements where the missing areas B and A are placed in all of their potential positions on the primary cladograms (i.e. the filled black circles). Hence when compared to other groups of organisms there is a greater chance of finding congruence in the general areagram.

Figure 3. (a–c) Three area cladograms for three groups of three species (1–3, 4–6, 7–9) and four areas (A–D). Note that in each case there are three endemic species in one area (3–B, 5–C, 8–D), three species widespread to two areas (2–AC, 4–BD, 9–BC) and three species common to three areas (1–ABC, 6 and 7–BCD). Note too, that there are three areas to each cladogram (a – ABC, b, c – BCD) with one area ‘missing’ from each (D, A and A, respectively). (d) The most parsimonious (most defensible) general area cladogram calculated under Assumption 2 that accommodates all three area cladograms in a, b and c. Note that those areas with grey lettering in a–c represent the contributory signal in the genera area cladogram and the black letters signify noise.

Figure 4. Three-area cladograms showing different area relationships for areas A, B and C. By removing paralogy (repeated areas) by working from the tips of the cladograms to the base of each area cladogram, there is only one area relationship for all three: A(BC).

Figure 5. (a) Species cladogram for the southern beech genus, Nothofagus. Thirty species occur in five areas: Aust, Australia; SAm, South America; NZ, New Zealand; NC, New Caledonia; NG, New Guinea (figure redrawn from Linder and Crisp, 1995). (b) General area cladogram for Nothofagus (derived from the cladogram in (a)) after all paralogy has been removed, and each area represented once.