Hidden Markov Models in Population Genomics.

With the advent of sequencing techniques population genomics took a major shift. The structure of data sets has evolved from a sample of a few loci in the genome, sequenced in dozens of individuals, to collections of complete genomes, virtually comprising all available loci. Initially sequenced in a few individuals, such genomic data sets are now reaching and even exceeding the size of traditional data sets in the number of haplotypes sequenced. Because all loci in a genome are not independent, this evolution of data sets is mirrored by a methodological change. The evolutionary processes that generate the observed sequences are now modeled spatially along genomes whereas it was previously described temporally (either in a forward or backward manner). Although the spatial process of sequence evolution is complex, approximations to the model feature Markovian properties, permitting efficient inference. In this chapter, we introduce these recent developments that enable the modeling of the evolutionary history of a sample of several individual genomes. Such models assume the occurrence of meiotic recombination, and therefore, to date, they are dedicated to the analysis of eukaryotic species.