The dissertation focuses on ancestral inference in the field of population genetics: most of the emphasis is put on the reconstruction of past genealogies. Most of the inference is based on DNA polymorphism data but I also use the fossil record in the first and third chapter. I put the emphasis on statistical and methodological tools.

The first chapter presents statistical tools called Approximate Bayesian Computations (ABC) that are useful for ancestral inference. It provides an overview of Bayesian computation and discusses the motivations for using ABC. This chapter describes a new version of ABC that is useful when the likelihood of the data cannot be computed, a situation that occurs frequently in population genetics. This methodology is then applied to answer two questions. First, I infer the date of divergence of primates using information from the fossil record. Second, I use microsatellite data from 51 worldwide populations to infer information about human history: population sizes, migration rates and dates of divergence.

The second chapter analyzes the pattern of polymorphism, in particular the level of Linkage Disequilibrium (LD) in the plant Arabidopsis thaliana. Using a combination of sequencing data as well as re-sequencing tiling array data I analyze what factors drive the decay of LD: recombination, gene conversion and population structure in particular.

The third chapter discusses a longstanding issue in human genetics: the evolutionary relationships between modern humans and fossil hominine groups, such as Neanderthals. I present a new method for addressing whether archaic human groups contributed to the modern gene pool. Using DNA sequences from contemporary humans I provide suggestive evidence in favor of a rate of admixture at least equal to 5%, both in European and African populations. While Neanderthals form an obvious archaic source population candidate in Europe, there is not yet a clear source population candidate in West Africa.