1.2 | Approximate Bayesian Computation demographic inference
Approximate Bayesian Computation (ABC) approaches (Beaumont, Zhang, & Balding, 2002; Tavaré, Balding, Griffiths, & Donnelly, 1997), represent a promising alternative to infer complex admixture histories from genetic data. Indeed, ABC has been successfully used previously to formally test alternative demographic scenarios hypothesized to be underlying observed genetic patterns, and to estimate, a posteriori , the parameters of the winning models, when ML methods could not operate (Boitard, Rodriguez, Jay, Mona, & Austerlitz, 2016; Fraimout et al., 2017; Verdu et al., 2009).
ABC model-choice and posterior-parameter estimation rely on comparing observed summary statistics to the same set of statistics calculated from simulations produced under competing demographic scenarios (Beaumont et al., 2002; Blum & François, 2010; Csilléry, François, & Blum, 2012; Pudlo et al., 2016; Sisson, Fan, & Beaumont, 2018; Wegmann, Leuenberger, & Excoffier, 2009). Each simulation, and corresponding vector of summary statistics, is produced using model-parameters drawn randomly from prior distributions explicitly specified by the user. This makes ABC a priori particularly well suited to investigate highly complex historical admixture scenarios for which likelihood functions are very often intractable, but for which genetic simulations are feasible (Gravel, 2012; Pritchard et al., 1999; Verdu & Rosenberg, 2011; Buzbas & Verdu, 2018).