Representative plots of observed fitness (blue lines) and mutation rate (red lines) dynamics. (*A*) A numerical solution of Model 1 (infinite population) with parameters μ = 0.003, *f*_{B} = 10^{−6}, *f*_{D} = 0.1, *f*_{M} = 0.001, *f*_{A} = 0.0001, and *m*_{B} = *m*_{D} = *m*_{M} = *m*_{A} = 0.03, and initial condition *u*(*x*, *y*, 0) ≈ δ(*x* − *x**, *y* − *y**), where *x** and *y** were close to the minimum values allowed for *x* and *y*. (*B*) An individual-based simulation run (finite population) with population size *N* = 10,000 and parameters μ = 0.1, *f*_{B} = 3 × 10^{−4}, *f*_{D} = 0.5, *f*_{M} = 0.001, *f*_{A} = 0.0001, and *m*_{B} = *m*_{D} = *m*_{M} = *m*_{A} = 0.03. Initially, all individuals in the population had fitness zero and a relative mutation rate of one. The thin green line plots predicted fitness based on cumulative fitness variance and mutation rate: *x̄*(*t*) = ∫_{0}^{t} σ_{x}^{2}*d*τ − *f*_{D}m_{D}∫_{0}^{t} μ̄ *d*τ. The thin pink line plots predicted mutation rate: μ̄(*t*) = ∫_{0}^{t} cov(μ, *x*)*d*τ + *f*_{M}m_{M}∫_{0}^{t}μ^{2}*d*τ. Based on the number of fluctuations in cov(μ, *x*), we estimate that extinction was caused in this population by 27 associations between mutators and beneficial mutations.

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