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      2.6. Population-level and individual-based models

All models described above were designed to deal with phylogenies in which the terminal tips represent individual species (though BIB-DTA has been used in a phylogeographic context). CTMC processes are less appropriate to model the geographic evolution of individuals within a population, or between closely related populations, because they require the a priori definition of discrete geographic ranges and assume that movement between states is rare, that is, the chain remains in the same state and rarely jumps among states. When dealing with within-species biogeography or phylogeography, it is often difficult to define geographic ranges because boundaries are blurred by the frequent movement of individuals within populations and by gene flow. A Brownian Motion (BM) process, also termed “random walk” or diffusion model, is typically used for modeling the geographic evolution of populations and individuals (Lemey et al. 2011). This is a stochastic process with one parameter governing range evolution: there is a central value from where individuals move away with speed equal to this parameter. Unlike in biogeographic Markov models, tips in the phylogeny are individuals with associated geographical coordinates. Finally, models based on electric circuit-resistance theory (McRae et al. 2008) have been used in phylogeography to model the rate and path of movement or gene flow on heterogeneous landscapes. A special attraction of this model is the possibility to define connectivity maps based on 2D landscapes with barriers: low resistances are assigned to landscape feature types that are most permeable to movement or best promote gene flow, and high resistances assigned to movement barriers. The field of parametric phylogeography is in rapid expansion (Bloomquist et al. 2010), especially coalescent-based methods using approximate Bayesian computation, a likelihood-free Bayesian approach in which parameters in the model are estimated via simulation, and models are compared via summary statistics (Hickerson et al. 2007).

      One class of expanding simulation models is forward-time, individual-based models, also termed in silico or automat models (Gotelli et al. 2009; Overcast et al. 2019). These models set up a series of rules by which speciation, extinction and dispersal of lineages can occur within an environmentally heterogeneous, two-dimensional gridded landscape; they are therefore spatially explicit models (Gotelli et al. 2009). These models have been used for testing macroecological hypotheses on species richness and distribution patterns, but some incorporate evolutionary predictions (Rangel et al. 2018). Recently, simulation modeling has experienced a spur forward, especially within the realm of phylogeography (Overcast et al. 2019), with the introduction of machine learning approaches and the integration of genetic data. Both in silico and machine learning approaches use simulations under pre-specified scenarios, as well as statistical comparison of observations against the distribution of simulated values to discriminate among alternative biogeographic scenarios. These models are less efficient for parameter inference than parametric approaches such as DEC or BIB, because a large range of values needs to be explored via simulation. Conversely, simulation models are more powerful in modeling complex phylogeographic scenarios involving multiple interacting parameters, since there is no need to derive the likelihood function and parameter dependencies. In particular, machine-learning methods are extremely flexible, with no cap on the number of parameters, and have been used for merging ecological and evolutionary processes (Overcast et al. 2019), trait-based biogeography (Sukumaran et al. 2016) or the integration of the spatial landscape (Tagliocollo et al. 2015). Some ML approaches do not rely on summary statistics and can be more efficient than ABC methods for phylogeographic inference (Fonseca et al. 2020).