The proportion of mutants in a growing culture of organisms will depend upon (a) the rate at which the wild cells produce them (with or without growth), (b) the back mutation rate, and (c) the growth rates of the wild and mutant cells. If the mutation rate without growth and the back mutation rate are neglected, the growth of a mutant is expressed by

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and the ratio of the mutant to wild by

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in which λ = mutation frequency rate constant, "mutation rate," A = growth rate constant of wild cells W, B = growth rate constant of mutant cells M. If the term [B – (1 – 2λ)A] is positive, the proportion of mutants increases continuously. If it is negative, the proportion of mutants reaches a constant value

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If mutation is assumed to occur without growth at the rate C, then the corresponding equations are (11), (12), and (14).

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If (B + CA) is negative and t = ∞,

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If C << A,

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