Abstract
The Legofit statistical package uses genetic data to estimate parameters describing population history. Previous versions used computer simulations to estimate probabilities, an approach that limited both speed and accuracy. This article describes a new deterministic algorithm, which makes Legofit faster and more accurate. The speed of this algorithm declines as model complexity increases. With very complex models, the deterministic algorithm is slower than the stochastic one. In an application to simulated data sets, the estimates produced by the deterministic and stochastic algorithms were essentially identical. Reanalysis of a human data set replicated the findings of a previous study and provided increased support for the hypotheses that (a) early modern humans contributed genes to Neanderthals, and (b) a "superarchaic" population (which separated from all other humans early in the Pleistocene) was either large or deeply subdivided.