Simulation of Selected Genealogies

Algorithms for generating genealogies with selection conditional on the sample configuration of n genes in one-locus, two-allele haploid and diploid models are presented. Enhanced integro-recursions using the ancestral selection graph, introduced by S. M. Krone and C. Neuhauser (1997, Theor. Popul. Biol. 51, 210–237), which is the non-neutral analogue of the coalescent, enables accessible simulation of the embedded genealogy. A Monte Carlo simulation scheme based on that of R. C. Griffiths and S. Tavaré (1996, Math. Comput. Modelling 23, 141–158), is adopted to consider the estimation of ancestral times under selection. Simulations show that selection alters the expected depth of the conditional ancestral trees, depending on a mutation–selection balance. As a consequence, branch lengths are shown to be an ineffective criterion for detecting the presence of selection. Several examples are given which quantify the effects of selection on the conditional expected time to the most recent common ancestor.