The effects of genotype frequency and population density on fitness differentials in Escherichia coli

Two strains of Escherichia coli K-12, a lac+ wild type and a lac- auxotroph, were grown both as pure and mixed cultures, using a serial transfer procedure. Four different growth media were employed, consisting of the same minimal salts solution, but different total concentrations of the sugars lactose, arabinose, and glucose (in proportions 5:4:1). Population densities and genotypic frequencies were assayed every 48 hours, at the time of transfer. Population density of the pure lac+ culture was greater than that of the pure lac- culture for all media; this was expected, since the latter cannot utilize lactose. Mixed cultures quickly approached the same density as the corresponding lac+ controls, and the frequency of the lac+ genotype increased steadily for all media. Trajectories of lambda = log (P divided by Q) were strictly nonlinear, indicating a dependence of the selective differential on population density and genotypic frequency. The rate of substitution decreased slightly with increasing sugar concentration, contrary to theoretical expectation. It was speculated that either the generation interval was longer for denser cultures (higher substrate concentrations) of that buildup of organic by-products reduced the selective differential in denser cultures. For a single medium, however, the behavior of completing genotypic strains was reasonably well predicted by theoretical models of frequency and density-dependent selection, the parameters of which may be related to the experimental inputs.