Peptide cross-feeding between Prt+ and Prt- strains in a mixed culture of both variants. The extra cellular protease of Prt+ strains cleaves casein into peptides that diffuse away from the cell and can be utilized by invading Prt- cheating cells (Panel a). Modelling the dynamics between the two variant strains shows that at low cell densities and low Prt+ frequencies the fractional gain after one propagation step is high for Prt+ cells. If cultures are grown (inoculated) at high cell desities and high frequencies of Prt- cells the fractional gain of Prt+ cells is negative indicating that they are outcompeted by Prt- cells (Panel b). Reproduced from Bachmann et. al. 2010 with permission from the publisher.