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If the number of areas is large, it is possible to use heuristic search tools such as those employed in parsimony phylogenetics (nearest-neighbor interchange, branch and bound, etc.). In Figure 2.2(a), the distribution of species 1– 3 in area A, which is the sister in the area cladogram to the clade BCD (Figure 2.2(b)), is explained by a sequence of events involving duplication of a widespread ancestor in ABCD, extinction of the ancestor of species 1 in part of this range (BCD), successive vicariance events, and dispersal of the ancestor of species 3 and 4 to A, followed by allopatric speciation (Figure 2.2(c)).

      From the description above, it can be deduced that the most important problem in EBMs is to find the optimal cost assignments. The most common criterion is to select event costs that maximize the conservation of distribution ranges along the phylogeny (Ronquist 2003). Figure 2.1 shows that dispersal and extinction are not “phylogenetically conserved or constrained” processes because they interrupt the “vertical inheritance” of geographic ranges from ancestor to descendants. In dispersal, the colonized area B is not part of the ancestral range (Figure 2.1(c)); in extinction, part of the ancestral range (A) is lost in the right descendant (Figure 2.1(d)). Conversely, vicariance and duplication are phylogenetically constrained processes because either each descendant inherits the entire ancestral range (duplication) (Figure 2.1(b)) or the union of the two descendants’ ranges equals the ancestral range (vicariance, Figure 2.1(a)). A consequence of this cost assignment is that the frequency of dispersal and extinction events is minimized relative to vicariance and duplication in EBM reconstructions. A similar phylogenetic conservation criterion is used in parsimony-based inference to minimize homoplasies (convergence and parallelism), as evolutionary changes that are not identical by descent, that is, losses and gains of traits in unrelated lineages. In the TreeFitter reconstruction in Figure 2.2(c), extinction (e) receives a cost of 1 and dispersal (i) a cost of 2; vicariance (v) and duplication (d) are given minimum costs (0.01); the lower cost of extinction relative to dispersal is due to extirpation preserving part of the ancestral range (Figure 2.1; Sanmartín and Ronquist 2004).

Schematic illustration of event-based biogeography.

      2.2.2. Dispersal–vicariance analysis

      Figure 2.2(d) shows DIVA reconstruction for the same biogeographic scenario as in Figure 2.2(c). Notice that it is simpler than in TreeFitter, requiring only vicariance events interspersed with dispersal events. This example illustrates a difference between these two methods that is not always well understood (Wodcicki and Brooks 2005). As in cladistic biogeography, TreeFitter output is an area cladogram, whereas DIVA maps ancestral distributions and inferred biogeographic events onto the phylogeny. The constraint of hierarchical area relationships in TreeFitter means that the “redundant” distribution of species 1 and 2 in area A (Figure 2.2(a)) must be modeled as resulting from duplication within a widespread ancestor (ABCD), followed by extinction in part of the ancestral range (BCD). In DIVA, areas can be gained and lost along the branches of the phylogeny and their relationships do not need to follow a branching pattern. The overlapping distributions of species 1 and 2 are explained by dispersal to A along the internal branch, after the initial vicariance event that divided widespread ancestor 11 in ABCD (Figure 2.2(d)), and followed by a second vicariance event in widely distributed ancestor 9. DIVA is thus suited for reconstructing “reticulate” scenarios, in which area relationships are not dichotomous but resemble a network, with repeated cycles of dispersal and vicariance events. One example of such scenario is the Northern Hemisphere geological history, where the paleocontinents now forming Eurasia and North America recurrently merged and split during the last 150 Mya (Sanmartín et al. 2001). Yet, DIVA loses power and can give improbable biogeographic events when used in predominantly vicariant scenarios.

      Conversely, TreeFitter is statistically more powerful to reconstruct area relationships that fit the vicariance pattern, such as the hierarchical fragmentation of the Gondwanan supercontinent (Sanmartín and Ronquist 2004). Another difference is the treatment of duplication events. In TreeFitter, duplication of ranges involving more than one area is allowed, but only if the widespread range forms an ancestral area in the area cladogram (e.g. ABCD or BCD in Figure 2.2(c)); alternative ancestral ranges such as ACD will not be accepted. DIVA accepts any combination of areas as ancestral ranges; however, as in Fitch Parsimony, duplication can only affect single areas. As a result, and unless geological constraints are used, DIVA reconstructions do not include extinction events (Kodandaramaiah 2010).

Schematic illustration of TreeFitter reconstruction among areas of endemism in Mexico.

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