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.
2.3. From parsimony-based to semiparametric approaches
Event-based methods were based on explicit process models and therefore represented a considerable advance over cladistic methods in terms of statistical power. However, they still have several limitations. The cost of events, for example, cannot be estimated from the data but must be fixed a priori using ad hoc criteria such as the phylogenetic conservation of ancestral ranges. As explained above, through dispersal and extinction, the descendants come to occupy a different range than the ancestor, so these two processes are underestimated (“minimized”) in event-based reconstructions (Sanmartín 2012). Another constraint imposed by the use of parsimony is that biogeographic reconstructions are inferred on cladograms with no branch lengths or time information. This makes it difficult to discriminate between shared distribution history and biogeographic “pseudocongruence”, that is, shared patterns that are spatially but not temporally congruent (Page 1993; Donoghue and Moore 2003) and between competing dispersal and vicariance explanations: in vicariance, the appearance of the barrier within the ancestral range is the trigger for allopatric speciation, while in dispersal, the barrier predates geographic change (Chapter 1). Finally, parsimony-based inference ignores two sources of error associated with reconstructing trait evolution: “phylogenetic uncertainty” – ancestral areas are reconstructed over a single topology, the most parsimonious tree, assuming there is no uncertainty in phylogenetic relationships – and “reconstruction uncertainty”, where only the minimum-cost (most parsimonious) reconstructions are evaluated, even though alternative reconstructions could be almost as likely, or even more likely if additional information is considered (Ronquist 2004).
Incorporating phylogenetic uncertainty in EBMs is relatively straightforward: run the analysis over a distribution of trees that represent the level of clade support in the phylogeny; this distribution can be obtained from bootstrap pseudoreplication or a Bayesian posterior probability distribution. Non-bifurcating nodes (polytomies) and nodes with low clade support can then be associated with low support for ancestral ranges. In Nylander et al.’s (2008) Bayes-DIVA method, DIVA parsimony-based reconstructions are averaged over a distribution of trees representing the posterior probability obtained from a Bayesian phylogenetic analysis. Figure 2.4 gives an example. Node “X” is a highly supported clade including three species distributed in areas C, B and A. Phylogenetic relationships in the rest of the tree are uncertain and vary over the Bayesian sample of trees, including the potential sister-group. For example, the stem or parent node of X (“Y” in Figure 2.4) has as the other descendant: “D” in tree 1, “E” in tree 2 and “F(ED)” in tree 3. Each of these tree topologies has a different posterior probability (PP) value. Because in Bayesian inference (BI), the frequency with which a tree is sampled in the analysis is proportional to its posterior probability (Ronquist 2004), the nodal ancestral area reconstructions in Bayes-DIVA can be interpreted as “marginal probabilities” (i.e. the different wedges in the pie chart in Figure 2.4). In other words, averaging DIVA reconstructions over a Bayesian sample of trees gives us estimates of ancestral ranges at nodes that are marginalized over the variation in the remainder tree topology. Notice that DIVA does not integrate branch length information, so the only parameter that is marginalized is the tree topology; in this sense, Bayes-DIVA can be considered an empirical Bayesian method (Nylander et al. 2008). It is also a semiparametric model since it contains a parametric (Bayesian phylogenetic inference) and a nonparametric (parsimony biogeographic inference) component. Another important distinction is given by tree 4: Pagel et al.’s (2004) definition of a “floating node”. Trees containing different definitions (bipartitions) of node X (tree 4, PP = 0.10) are excluded from the marginal estimations for that node in Bayes-DIVA: that is, the wedges in the pie chart sum to 0.90 (Figure 2.4). In other words, Bayes-DIVA uses a node-to-node approach in accounting for phylogenetic
