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The latest exciting developments in parametric biogeography have been in the direction of implementing “state-dependent speciation and extinction (SSE) models”, in which there is a causal relationship between range evolution and lineage diversification (Maddison et al. 2007, Goldberg et al. 2011; FitzJohn 2012). As explained above, BIB and DEC do not include a speciation parameter in the stochastic CTMC process that governs geographic evolution. This is unrealistic since diversification and range evolution clearly interact: for example, the dispersal of a species into a new region may result in increased speciation rates due to lower competition or access to novel environmental resources (Moore and Donoghue 2007). Moreover, unlike the DEC model, SSE models provide a complete parametric description of biogeographic evolution, since speciation is a rate parameter in the CTMC process. In the geological state-dependent speciation and extinction model (GeoSSE; Goldberg et al. 2011), the Q matrix includes parameters for anagenetic range expansion and range contraction or extinction, as well as parameters for lineage speciation within single areas (S_A, S_B) or within a widespread range (S_AB). There is also a parameter for lineage extinction within single areas (E_A, E_B): for widespread ranges, this is modeled as the sum of extinction events in single areas. All these parameters are time-dependent. The SSE counterpart of DEC+J is the ClaSSE model (Goldberg and Igic 2012), which allows changes in states to occur not only along branches (anagenetic) but also at speciation nodes (cladogenetic): this “founder-speciation” event is governed by its own time-dependent rate parameter in the Q matrix.

Coupling diversification with range evolution, as in GeoSSE and ClaSSE, allows statistical testing of classical hypotheses, such as whether widespread ranges lead to higher speciation rates (Goldberg et al. 2011) or whether extinction rates are dependent on area size or environmental heterogeneity (Meseguer et al. 2015). A shortcoming of SSE models is their computational complexity. The stationary distributions and parameter probabilities in SSE models are estimated through numerical integration, rather than analytically by matrix exponentiation as in DEC. One attractive avenue forward to tackle these computationally intractable models is the probabilistic programming language (PPL) framework (Ronquist et al. 2020).