Estimating and disentangling the contribution of different evolutionary processes such as genetic drift, mutation or gene flow is a longstanding and central issue in statistical population genetics. In many studies, the data come from a sample taken at one point in time and little is known about the demographic history of the population(s) of interest. However, the genetic configuration of a population is affected by past demographic events like population shrinkage or growth, fragmentation, admixture or founder events. This leads to the challenge that in order to get sound population genetic estimates, one needs to take history into account, but at the same time history is unknown. On of the few data sets for which population history is known comes from a structured population of Alpine ibex in the Swiss Alps. The species almost went extinct in the 17^th century, but was protected and reintroduced later on. The reintroduction into the Swiss Alps starting in 1906 was documented in great detail and population sizes have been monitored since then. This allows conditioning genetic inference on non-genetic information. Together with Nick Barton, Simon Aeschbacher works on obtaining estimates of migration rates, drift and ancestral diversity in this population. He applies a combination of computer simulations, Approximate Bayesian Computation and machine learning for inference. Simon collaborates with Iris Biebach and Lukas Keller (University of Zurich), who provided the ibex data, and with Mark A. Beaumont (University of Reading).