LITMIR.BIZ

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uses Markov-Chain Monte Carlo (MCMC) simulations and BI to estimate ancestral ranges and rates of biogeographic parameters alongside phylogenetic parameters, such as the tree topology, rates of molecular evolution and branch lengths; the input data are DNA sequences and tip distributions of the study species (Sanmartín et al. 2008). The DEC model was originally implemented in an ML framework (Ree and Smith 2008) and later extended to BI (Landis et al. 2013), but it is typically applied to a phylogeny with fixed topology and branch lengths. Though they both use CTMC processes to model range evolution, BIB and DEC models are slightly different (Figure 2.5). BIB (Figure 2.5(a)) implements a simpler character evolutionary model, in which ancestors can only occupy single areas (A or B) and range evolution along the branches if governed by a CTMC process with only one type of parameter equivalent to range switching or instantaneous dispersal; the Q matrix describes the instantaneous transition from one area as a jump dispersal event (p = A to B). At the speciation events in the phylogeny, the single-area ancestral range is inherited entirely and identically by the two descendants (A/A); in other words, there is no need to include a cladogenetic component in the BIB model because the ancestral range is not altered through speciation (Figure 2.5(a)).

DEC implements a more complex ancestral-state reconstruction model (Figure 2.5(b)), allowing for ranges in the Q matrix to comprise two or more discrete areas (i.e. widespread states, AB). Therefore, the model requires an additional cladogenetic component describing the different ways (range inheritance scenarios) by which a widespread ancestral range is divided between the two descendants. In Figure 2.5(b), this involves vicariance, range division into non-overlapping subsets (A/B), but other possible range inheritance scenarios are “peripheral isolate speciation” (Ree et al. 2005), in which one descendant inherits the whole ancestral range and the other descendant inherits only one area (AB/B), or “widespread sympatry”, in which the two descendants inherit the widespread ancestral range (AB/AB; Landis et al. 2013). In the original ML implementation of DEC (Ree and Smith 2008), all these range inheritance scenarios are assigned equal relative likelihoods or “weights”. In the BI implementation (Landis 2017), different prior probabilities can be assigned to the speciation modes. There are other DEC-derived models (DIVALIKE, BAYAREALIKE, Maztke 2014) which differ on the type of range inheritance scenarios allowed for widespread ranges. Like BIB, DEC implements anagenetic evolution as a CTMC process. Instantaneous transitions between geographic states are governed by two parameters (Figure 2.5(b)): range expansion, where an additional area is added to the current range (D_AB = A to AB), and range contraction, with the removal of an area from the ancestral range (E_B = AB to B). Notice that instantaneous transitions between single-area states are not allowed in DEC. Moving between single areas requires going through a widespread state in which the ancestor is present in both areas (Figure 2.5(b)). This can be observed in the Q matrix, with zero rate values for direct transitions between A and B (Figure 2.5(b)). A transition from A to B requires two consecutive instantaneous events: range expansion from A to AB and range contraction from AB to B.

      Figure 2.6 illustrates, with a real biogeographic problem, some of the differences between BIB and DEC. In sum, the BIB model allows only anagenetic changes along branches in the phylogeny and constrains ancestors to occur in single areas, whereas DEC includes both anagenetic and cladogenetic range evolution; in fact, DEC is the parametric counterpart of DIVA (Ree et al. 2005). However, this additional level of complexity brings some statistical limitations discussed below. Both models implement different sources of uncertainty (phylogenetic and reconstruction in BIB, and reconstruction in DEC).

      The DEC model is undoubtedly more realistic than BIB. In biogeography, widespread terminals and ancestors are biologically plausible: an extant or extinct taxon could have occupied more than one area, especially if these areas were connected and there was no dispersal barrier between them. However, such complexity comes with a cost: there are 2^N possible ancestral ranges for N areas, so the Q instantaneous rate matrix cannot be analytically calculated with more than 10 areas (1,024 states). This can be reduced by removing certain transitions from the Q matrix, for example, disallowing ancestral ranges that involve discrete areas that are non-adjacent in the physical space (Buerki et al. 2011), or using alternative estimation methods, such as data augmentation (Landis et al. 2013). Dispersal in DEC is equivalent to range expansion – the ancestor moves into a new area but keeps the original distribution for some time; in other words, moving between single areas requires going through a widespread state in which the ancestor is present in both areas (Figure 2.5(b)). This type of dispersal may be appropriate for continental settings in which areas are adjacent, that is, share a physical edge, and we expect gene flow to be maintained for some period of time between the allopatric populations (Ree and Sanmartín 2009). Yet, it comes with the necessity of modeling cladogenetic events or range inheritance scenarios (Figure 2.5(b)).

Figure 2.6. Parametric biogeographic reconstruction of the spatio-temporal evolution of genus Canarina. Canarina is a three-species genus in the angiosperm family Campanulaceae, with a disjunct distribution between the Canary Islands in the west and the Eastern African mountains and Horn of Africa plateaus in the east (Mairal et al. 2015). Both BIB and DEC explain this geographic disjunction as a sequence of migration events from Asia, where sister-genera occur, to Eastern Africa, and to Macaronesia; the latter along the 7 million-year branch separating C. eminii and C. canariensis. DEC infers a similar scenario, but vicariance in a widespread distribution is inferred at some nodes, mostly involving short internal branches and descendants with non-overlapping distributions. Pie charts represent the uncertainty in the estimation of ancestral ranges. For a color version of this figure, see www.iste.co.uk/guilbert/biogeography.zip

The original DEC model (Ree and Smith 2008) includes a “null” state in the Q matrix (∅), equivalent to global extinction. A species can become extinct across its entire range but only if this comprises a single area (A to ∅; Figure 2.5(b)); global extinction across a widespread range is assigned a zero rate in the DEC model (AB to ∅; Figure 2.5(b)). Also, global extinction behaves as an “absorbing state” in the Q matrix because the rate of abandoning this range is zero (e.g. ∅ to A; Figure 2.5(b)). One of the consequences of including a null range in the Q matrix is that extinction rates are typically underestimated in the DEC model, even several orders of magnitude compared with dispersal rates. Because global extinction can only occur within single-area ranges, it is often inferred at terminal branches, where dispersal cannot be countered off by a loss of areas via cladogenesis (vicariance or peripatry). Removing the null range from the Q matrix has the effect that extinction events are forced to occur within widespread ranges in order to counteract dispersal or range expansion along internal branches. In other words, loss of areas would be achieved via extinction in ancestral branches rather than via cladogenesis, and thus extinction rates are increased relative to dispersal if global extinction is disallowed (Massana et al. 2014). Bayesian extensions of DEC (Landis 2017) correct for this bias by conditioning the DEC inference to the survival of all lineages in the extant phylogeny, that is, never entering the null state.

The issues above do not affect the BIB model because it uses a simpler stochastic CTMC model similar to those employed in molecular character evolution. Widespread states (equivalent to “polymorphism” in nucleotide models) are not allowed in the CTMC matrix, and range evolution is limited to the anagenetic component. This is modeled as instantaneous transitions between single-area states, equivalent to “jump dispersal”, but which can vary across area pairs and may also be asymmetric, that is, the rate of moving from A to B, p, is not the same as from B to A, q (Figure 2.5(a)). Modeling dispersal as an instantaneous process, without going through a widespread state, may seem unrealistic but allows the BIB model to “borrow” the sophisticated machinery and statistical algorithms used in molecular models of nucleotide substitution; in fact, initial implementations of BIB used software routinely employed in molecular phylogenetics (Sanmartín et al. 2008; Lemey et al. 2009). In standard molecular models, nucleotide substitutions within a species DNA sequence are considered as instantaneous. In-between demographic-level processes, involving increased

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