case of migration, let the chosen neighbor of the focal point i be designated j. The state after migration (signified by t”) is given by (Eq. 6):
Removal occurs next. At point i, any player whose abundance is less than or equal to a critical value (acrit) is removed. Also, the sensitive player is removed if the producer is present. In the simulation, the dilution, migration, and removal are assumed to be instantaneous and followed by a new growth phase. Lastly, mutation can occur with probability π. In the case of a mutational event, a fraction γ of the total abundance of the resistant players (ancestral and mutant) of a point is converted to a random resistant type.
We initialize lattice point i with the starting abundances of each ancestral player [si (0),ri0 (0), and pi (0)], and [pi(0)] using the same method as in the bacterial experiment (SI Methods). After C growth cycles, we measured the expected fitness of a randomly chosen resistant cell relative to the resistant ancestor. This mean fitness is (Eq. 7):
In Table 6.1, we give values for all of the simulation parameters, which are tailored to our bacterial experiment or estimated from assays (SI Methods). For Figs. 6.4 and 6.5 and Fig. S3, we assume L = 100 and W = 100. For Figs. S4 and S5, we assume L = 16, W = 12, and C = 36, which are the values corresponding to our laboratory experiment.
We thank P. Aulakh, C. Eshelman, H. Lindsey, S. Smith, and J. West for help in the laboratory; B. Bohannan, S. Forde, and M. Riley for discussion surrounding the early conception of this work; and M. Clifford, J. Cooper, S. Drescher, J. Gallie, C. Glenney, S. Heilmann, H. Lindsey, B. Miner, and J. West for comments on a previous draft of this manuscript. B.K. thanks J. Avise, F. Ayala, D. Queller, and J. Strassmann for the invitation to participate in the Sackler colloquium “In the Light of Evolution V: Cooperation.” This material is based in part on work supported by National Institutes of Health Grant 07–004309 B-03 AM03, National Science Foundation under Cooperative Agreement Number DBI-0939454, a National Science Foundation Graduate Research Fellowship (to J.R.N.), and CAREER Award Grant DEB0952825 (to B.K.).