  The complex pattern of presence and absence of many genes across different
species provides tantalising clues as to how genes evolved through the
processes of gene genesis, gene loss and lateral gene transfer (LGT). The
extent of LGT, particularly in prokaryotes, and its implications for creating a
`network of life' rather than a `tree of life' is controversial. In this paper,
we formally model the problem of quantifying LGT, and provide exact
mathematical bounds, and new computational results. In particular, we
investigate the computational complexity of quantifying the extent of LGT under
the simple models of gene genesis, loss and transfer on which a recent
heuristic analysis of biological data relied. Our approach takes advantage of a
relationship between LGT optimization and graph-theoretical concepts such as
tree width and network flow.
