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EBMs have now been superseded by parametric probabilistic approaches that integrate the time dimension (see below), they remain popular in fields where molecular data is not available, such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

      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 uncertainty: only those trees containing the node of interest (X) will be used in the estimation of ancestral-range marginal probabilities.

Schematic illustration of accounting for phylogenetic uncertainty.

      Nylander et al. (2008) demonstrated that accounting for phylogenetic uncertainty may also reduce biogeographic uncertainty: that is, for a given node, some ancestral ranges that were equally optimal in DIVA will be associated with higher marginal probabilities in the Bayes-DIVA analysis; in Figure 2.4, the ancestral range for node X that receives the highest marginal probability is A.

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