Is cooperation favored by horizontal gene transfer?

It has been hypothesized that horizontal gene transfer on plasmids can facilitate the evolution of cooperation, by allowing genes to jump between bacteria, and hence increase genetic relatedness at the cooperative loci. However, we show theoretically that horizontal gene transfer only appreciably increases relatedness when plasmids are rare, where there are many plasmid-free cells available to infect (many opportunities for horizontal gene transfer). In contrast, when plasmids are common, there are few opportunities for horizontal gene transfer, meaning relatedness is not appreciably increased, and so cooperation is not favored. Plasmids, therefore, evolve to be rare and cooperative, or common and noncooperative, meaning plasmid frequency and cooperativeness are never simultaneously high. The overall level of plasmid-mediated cooperation, given by the product of plasmid frequency and cooperativeness, is therefore consistently negligible or low.