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model, BayArea (Landis et al. 2013). It uses a Bayesian data augmentation approach in which parameters in the Q matrix are estimated by simulating outcomes (geographic range evolutionary histories) along branches in the phylogeny. This allows for a larger number of areas and geographic ranges in the model, including widespread states. Unlike DEC, there is no modeling of speciation scenarios: ranges are identically inherited by the two descendants, which also helps simplifying the model.

Schematic illustration of an Effect of decoupling biogeographic inference.

      The applications of BIB in epidemiology and phylogeography are probably some of the most popular uses of the model in the present. BIB in these fields is termed discrete trait analysis, DTA, or the “mugration” model because it equates migration to mutation events (De Maio et al. 2015). Though treating migration events as instantaneous mutations in a sequence might be acceptable at geological time scales and species levels, as was done in the original BIB (Sanmartín et al. 2008), it can be more problematic under the coalescent process; this is a model used at short-time scales and population-levels for building phylogenetic relationships (De Maio et al. 2015). Subsequent authors have extended the BIB-DTA model to allow for geographically structured populations’ conditioning under the coalescent process (De Maio et al. 2015; Muller et al. 2017).

      2.5. Expanding parametric models

      2.5.1. Time-heterogeneous models

      A similar approach was implemented in the time-stratified, “epoch” DEC model (Ree and Smith 2008; Landis 2017): the phylogeny is divided into time intervals, and each interval is assigned a different set of values that scale the baseline dispersal rate according to paleogeographic information; for example, the availability of temporal land bridges facilitating migration between continents (Buerki et al. 2011). Time-stratified DEC models can also be used in biogeographic dating (Landis 2017). Rather than assuming a single CTMC process over time, DEC is allowed to shift between different Q matrices at discrete time points, based on paleogeographic evidence. Phylogeny, molecular dating and biogeographic parameters are jointly estimated using hierarchical BI. Paleogeographic data, that is, the formation of dispersal corridors and barriers over time, is used to inform the rates of a piecewise-constant epoch DEC model, and these time-dependent CTMC probabilities are used in turn to inform estimates of species divergence times in the phylogeny; for example, species can only diverge in allopatry if a paleogeographic barrier is present (Landis 2017).

      Another exciting approach is the modeling of non-stationary CTMC models, where the equilibrium frequencies are allowed to change at discrete time points between time slices (Sanmartín 2020). Changes in area carrying capacities could result from a global extinction event that wipes out the biota of an island, decreasing its standing carrying capacity, and thus changing the stationary properties of the CTMC dispersal process. The point in time when there is a change in equilibrium frequencies and also the intensity of the extinction event (which might vary between areas) can be estimated by BI (Sanmartín 2020). Alternatively, the CTMC process may never attain equilibrium, or start with different values at root, such as in a directional CTMC process (Klofstein et al. 2015).

      2.5.2. Diversification-dependent models

      Coupling

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