Quantifying microbial fitness under conceptual uncertainty

Few concepts are as central to ecology and evolution as the notion of relative fitness, and yet the quantification of relative fitness in experiments is effectively a matter of choice. For the same data, alternative measures of relative fitness are available and continue to be used side-by-side. Are they all equivalent? What reasons can we give an experimentalist to choose one over the other? Here we develop such an argument, based on a single first principle: relative fitness measures must have the function to predict strain frequencies in the upcoming time window. From this axiom, we characterize the set of possible fitness metrics (it is large!) and settle two questions for high-throughput fitness measurements with barcoded mutant libraries: 1. In batch culture growth cycles, the relative fitness per-cycle provides the best all-around choice while the relative fitness per-generation is restricted to special-use cases and disagrees in the ranking of mutant genotypes. 2. In batch cultures with an entire mutant library, the mutant fitness is amplified compared to pairwise competitions due to higher-order interactions. We calculate this error for a typical trait distribution in Yeast knockouts and provide quantitative rules for the ideal inoculum frequency in barcoding experiments. Altogether, our axiomatic approach recovers all important fitness metrics used in the past and demonstrates that the same information content can be captured in almost arbitrary form, but some metrics are more practical than others.