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).
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