Borrowing both from population genetics and phylogenetics, the field of population genomics emerged as full genomes of several closely related species were available. Providing we can properly model sequence evolution within populations undergoing speciation events, this resource enables us to estimate key population genetics parameters such as ancestral population sizes and split times. Furthermore we can enhance our understanding of the recombination process and investigate various selective forces. With the advent of resequencing technologies, genome-wide patterns of diversity in extant populations have now come to complement this picture, offering an increasing power to study more recent genetic history.We discuss the basic models of genomes in populations, including speciation models for closely related species. A major point in our discussion is that only a few complete genomes contain much information about the whole population. The reason being that recombination unlinks genomic regions, and therefore a few genomes contain many segments with distinct histories. The challenge of population genomics is to decode this mosaic of histories in order to infer scenarios of demography and selection. We survey modeling strategies for understanding genetic variation in ancestral populations and species. The underlying models build on the coalescent with recombination process and introduce further assumptions to scale the analyses to genomic data sets.
Keywords: Ancestral population; Coalescence; Demography; Divergence; Markov model; Migration; Recombination; Selection; Speciation.