Evolutionary parameters that permit cooperative regulation. Evolutionary parameters that permit the evolution of gene regulation by cooperative transcription factors. Threshold number of shared targets for gain (black) and loss (red) of cooperative binding to be advantageous in a population at equilibrium under stabilising selection. The black line shows the value of βabove which a new mutation that results in cooperative binding will invade in a population that lacks cooperative binding. The red line shows the value of βbelow which a mutation resulting in loss of cooperative binding will invade, in a population that has cooperative binding. For values of βthat lie in the gray region, the dynamics are bistable: a population with cooperative binding will preserve it, and one without binding will not gain binding. The threshold fraction of shared targets varies with (top left) strength of selection, s, (top right) strength of cooperativity in reducing the effects of deleterious mutations 1/h, (bottom left) the cost of pleiotropy t and (bottom right) the population size, N. Lines show our analytic equations (Equations 2 and 3), and points show the results of 105replicate Monte-Carlo simulations. Parameter values (unless stated otherwise) are ul=2×10−7, ug=10−7, K1 + K2=100, s=10−3, h=10−1, t=10−4and N=104.
Stewart et al. BMC Evolutionary Biology 2012 12:173 doi:10.1186/1471-2148-12-173