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We study the effect of biological confounders on the model selection problembetween Kingman coalescents with population growth, and Xi-coalescentsinvolving simultaneous multiple mergers. We use a low dimensional,computationally tractable summary statistic, dubbed the singleton-tailstatistic, to carry out approximate likelihood ratio tests between these modelclasses. The singleton-tail statistic has been shown to distinguish betweenthem with high power in the simple setting of neutrally evolving, panmicticpopulations without recombination. We extend this work by showing that crypticrecombination and selection do not diminish the power of the test, but thatmisspecifying population structure does. Furthermore, we demonstrate that thesingleton-tail statistic can also solve the more challenging model selectionproblem between multiple mergers due to selective sweeps, and multiple mergersdue to high fecundity with moderate power of up to 30%.

Robust model selection between population growth and multiple merger coalescents