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Dispersal–vicariance analysis (Ronquist 1997), implemented in the software DIVA, is arguably the most popular event-based method. DIVA resembles character-state reconstruction methods employed in phylogenetic inference to map the evolution of a trait, such as the optimization algorithm of Fitch Parsimony. Given a tree and associated geographic ranges, ancestral distributions are mapped (optimized) along internal nodes by finding the sequence of biogeographic events that minimizes the total cost of the reconstruction. A major difference with Fitch Parsimony is that, while phylogenetic inference assumes single-state ancestors, DIVA allows ancestors present in two or more states, that is, widespread ancestral ranges formed by two or more discrete areas. This difference implies that DIVA optimization is more complex than Fitch’s because it needs to include both anagenetic and cladogenetic events of range evolution. Changes in distribution range along the branches of the phylogeny (anagenetic change) are optimized as dispersal (range expansion: A to AB) or extinction (range contraction: AB to B) events. Range evolution at cladogenetic (speciation) nodes can involve duplication, if the ancestor occupies a single area (A/A), or vicariance, if a widespread ancestral range is divided into non-overlapping subsets (A/B). DIVA uses a slightly less complex cost-matrix than TreeFitter: dispersal and extinction are assigned a cost of 1, and duplication and vicariance, a cost of zero.

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).

Figure 2.3. TreeFitter reconstruction among areas of endemism in Mexico based on Marshall and Liebherr (2000)’s large insect dataset. Inset top: area cladogram obtained with Brooks Parsimony Analysis, a cladistic method. Main: area cladogram obtained with TreeFitter; “stars” represent conflicting nodes. The first division in the area cladogram involves the Transvolcanic Arch in BF and the Isthmus of Teuantepec in TF. Geological evidence indicates that disjunctions across the Isthmus are older than those involving the Transvolcanic Arch (Mastretta-Yanes et al. 2015). Also, biogeographic relationships across the Transvolcanic Arch are supported only by widespread species, which could be explained by dispersal. Conversely, the Isthmus of Teuantepec relationship in the TF cladogram is supported only by ancestral nodes, that is, inherited ranges, suggesting shared history

A main contribution of EBMs to historical biogeography was to demonstrate that dispersal, if constrained by abiotic factors such as wind strength or the direction of ocean currents, could be a pattern-generating process, in the same manner as vicariance is. “Concerted, directional” dispersal driven by the eastward moving West Wind Drift explains shared biogeographic patterns across southern hemisphere plant lineages (Sanmartín et al. 2007). Statistical testing of competing hypotheses is another contribution of EBMs. Frequencies of event types can be compared between the empirical phylogeny and a distribution of simulated phylogenies generated by randomizing geographic ranges among terminals. Significant differences indicate that biogeographic events are phylogenetically conserved (Sanmartín 2012). These randomization tests are common in parsimony-based optimization, which lacks an underlying probabilistic model (Faith and Cranston 1991); the discriminatory power of such tests, however, is questioned (Peres-Neto and Marques 2000).

While EBMs have now been superseded by parametric probabilistic approaches that integrate the time dimension (see below), they remain popular in fields where molecular data is not available, such as paleontology (Prieto-Marquez 2010; Upchurch et al. 2015). Treefitter is also used in host–parasite coevolution studies (Quinn et al. 2013). Using large datasets of phylogenetic and distributional data, event-based methods have been used to test broad-scale dispersal and vicariance hypotheses (Sanmartín et al. 2001; Donoghue and Smith 2004; Sanmartín and Ronquist 2004; Bremer and Jansen 2006). Figure 2.3 shows an example of this kind of analysis.