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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).
Figure 2.2. Event-based biogeography. a) An organism phylogeny with six species (1–6) distributed in four areas (A–D). b) Area cladogram depicting relationships among areas of endemism. c) TreeFitter reconstruction: total cost = 3.04. d) DIVA reconstruction, total cost = 2.0. Notice that TreeFitter and DIVA provide a full description of ancestral ranges and explanatory events but differ in the treatment of duplication (see the text). Symbols: vicariance (circle), duplication (rhombus), dispersal (arrow or cross) and extinction (short line). For a color version of this figure, see www.iste.co.uk/guilbert/biogeography.zip
2.2.2. Dispersal–vicariance analysis
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,