Maximum likelihood estimation of spontaneous mutation rates from large initial populations

Abstract

When estimating a spontaneous mutation rate from either a single culture ( C = 1) or from the C parallel cultures ( C > 1) of a fluctuation experiment, the use of a large initial population size N 0 to seed each culture will permit a gaussian approximation for the probability distribution of the number M of mutants at the time when the culture(s) has(have) grown to size N = N 02 g , i.e., experienced g doublings. Using this gaussian approximation we find that the maximum likelihood estimate μ̂ of the expected number μ of mutants present in a culture in generation g is (exactly) μ ̂ = 1 2 ( r 2+4 M 2 −r) where r = 2 g / g and M 2 is the average of the squares of the C mutant counts. The maximum likelihood estimate p ̂ of the unknown mutation rate p is p ̂ = 2 μ ̂ gN assuming an ‘ideal’ experiment and that there were no mutants in the initial population. A well-behaved maximum likelihood estimate is known to be efficient in large samples and we illustrate by Monte Carlo simulation that indeed p ̂ is better (has smaller mean squared error) than our previous (Rossman et al., 1995) estimator p ̌ = 2 M gN ( M is the average mutant count) provided N 0 is of the order of 1 p or larger. This advantage exists even without a fluctuation experiment, i.e., for C = 1.