A Comparison of Methods to Measure Fitness in Escherichia coli

Abstract

In order to characterize the dynamics of adaptation, it is important to be able to quantify how a population's mean fitness changes over time. Such measurements are especially important in experimental studies of evolution using microbes. The Long-Term Evolution Experiment (LTEE) with Escherichia coli provides one such system in which mean fitness has been measured by competing derived and ancestral populations. The traditional method used to measure fitness in the LTEE and many similar experiments, though, is subject to a potential limitation. As the relative fitness of the two competitors diverges, the measurement error increases because the less-fit population becomes increasingly small and cannot be enumerated as precisely. Here, we present and employ two alternatives to the traditional method. One is based on reducing the fitness differential between the competitors by using a common reference competitor from an intermediate generation that has intermediate fitness; the other alternative increases the initial population size of the less-fit, ancestral competitor. We performed a total of 480 competitions to compare the statistical properties of estimates obtained using these alternative methods with those obtained using the traditional method for samples taken over 50,000 generations from one of the LTEE populations. On balance, neither alternative method yielded measurements that were more precise than the traditional method.

Fig 1. Fitness trajectories over time.

Fitness trajectories for each method, shown separately, have the form w = (bT +1)^a, where w is fitness, T is time in generations, and a and b are model parameters. Black circles and curve show the Traditional method; blue squares and curve show the ASR method; red triangles and curve show the DCC method.

Fig 2. Coefficient of variation over time.

Lines are linear regressions on the relevant data. Black circles and line show the Traditional method; blue squares and line show the ASR method; red triangles and line show the DCC method. S1 Fig shows the confidence bands associated with each regression line.

Fig 3. Histogram of bootstrap analysis.

Histogram showing the distribution for the bootstrapped sums of squared differences in the coefficient of variation for 3 arbitrary groupings of the combined data. The dark arrow indicates the difference for the actual grouping of the 3 methods employed. The light arrow shows the most extreme 5% of the sums of the squared differences.