Bacteriophage Density Influences the Rate of Resistance Evolution

The antagonistic relationship between bacteria and bacteriophages (phages) drives genetic changes that result in phage resistance, making it important to understand the dynamics of resistance acquisition in both natural microbial communities and therapeutic contexts. We developed a generalized Lotka-Volterra model describing the interaction among phage-susceptible bacteria, phage-resistant bacteria, and a lytic phage, incorporating asymmetric interspecific competition and partial phage resistance. The model was fitted to growth data from four bacterial strains-Pseudomonas aeruginosa PA103 and PAK challenged with a phage cocktail, and Paenibacillus larvae Y-3650 and 25747 challenged with phage Fern IDv1-across four levels of multiplicity of infection (MOI). We compared two parameterization schemes: M1, in which the interspecific competition coefficients $a_{\mathrm{rs}}$ and $a_{\mathrm{sr}}$ are shared across MOI treatments, and M2, in which these coefficients are allowed to vary by treatment. For the two P. aeruginosa strains, M1 produced adequate fits (mean $R^2=0.91$ and 0.89). For the two P. larvae strains, M1 failed catastrophically at specific treatments ( $R^2$ as low as $-19.7$ ), while M2 achieved mean $R^2$ of 0.90 and 0.95 for Y-3650 and 25747, respectively. Information-theoretic model comparison ( $\Delta \text{AIC}=-753$ and $-458$ ) and profile likelihood analysis confirmed that the competition coefficients are fundamentally MOI-dependent, with per-treatment optima diverging by up to three orders of magnitude. These findings indicate an effect that extends beyond phage-mediated apparent competition-which assumes zero direct competition between the susceptible and resistant subpopulations-because the fitted interspecific competition coefficients are nonzero and MOI-dependent. We observed three distinct growth patterns-delayed growth, two-phase growth, and complete suppression-with non-monotonic dose-response relationships in which intermediate phage doses produced stronger suppression than higher doses. This non-monotonicity demonstrates that the boundaries between growth regimes are governed by competitive dynamics rather than phage dose alone. Our results establish that phage resistance evolution is fundamentally an ecological process: the competitive context, shaped by phage pressure, determines population-level outcomes independently of intrinsic mutation capacity. These findings have implications for phage therapy, suggesting that optimal dosing strategies must account for the competitive environment created by treatment, not solely the direct bactericidal effect.