PACT: an efficient and powerful algorithm for generating area cladograms

Aim To introduce and describe the functioning of a new algorithm, phylogenetic analysis for comparing trees (PACT), for generating area cladograms that provide accurate representation of information contained in taxon-area cladograms. Methods PACT operates in the following steps. Convert all phylogenies to taxon-area cladograms. Convert all taxon-area cladograms to Venn diagrams. Choose any taxon-area cladogram from the set of taxon-area cladograms to be analysed and determine its elements. This will be the template area cladogram. Select a second taxon-area cladogram. Determine its elements. Document which elements in the second tree occur in the template tree (denoted by 'Y') and which do not (denoted by 'N'). Each 'Y' indicates a match with previous pattern and these are combined. Each 'N' is a new element and is attached to the template area cladogram at the node where it is linked with a Y. This requires two rules: (1) 'Y + Y = Y' (combine common elements) as long as they are connected at the same node; and (2) 'Y + N = YN' (add novel elements to the template area cladogram at the node where they first appear). Once the novel elements in the second taxon-area cladogram have been added to the template area cladogram, see if any of them can be further combined. This requires three additional rules: (1) 'Y(Y- = Y(Y-' (do not combine Y's if they are attached at different nodes on the template area cladogram); (2) 'Y + YN = YN' (Y is part of group YN); and (3) 'YN + YN = YNN' (Y is the same for each, but each N is different). Repeat for all available taxon-area cladograms. Results Three exemplars demonstrate that PACT provides the most accurate area cladograms for vicariance-driven biotic diversification, dispersal-driven biotic diversification and taxon pulse-driven biotic diversification. PACT can also be used as an a priori method of biogeographical analysis. Main conclusions PACT embodies all the strong points and none of the weaknesses of previously proposed methods of historical biogeography. It is most useful as an a posteriori method, but it is also superior to all previous a priori methods because it does not specify costs, or weights or probabilities, or likelihoods of particular biogeographical processes a priori and is thus sensitive to clade-specific historical contingencies.