The genome of bacterial species is much more flexible than that of
eukaryotes. Moreover, the distributed genome hypothesis for bacteria states
that the total number of genes present in a bacterial population is greater
than the genome of every single individual. The pangenome, i.e. the set of all
genes of a bacterial species (or a sample), comprises the core genes which are
present in all living individuals, and accessory genes, which are carried only
by some individuals. In order to use accessory genes for adaptation to
environmental forces, genes can be transferred horizontally between
individuals. Here, we extend the infinitely many genes model from Baumdicker,
Hess and Pfaffelhuber (2010) for horizontal gene transfer. We take a
genealogical view and give a construction -- called the Ancestral Gene Transfer
Graph -- of the joint genealogy of all genes in the pangenome. As application,
we compute moments of several statistics (e.g. the number of differences
between two individuals and the gene frequency spectrum) under the infinitely
many genes model with horizontal gene transfer.Comment: 31 pages, 3 figure
