Modeling and quantifying frequency‐dependent fitness in microbial populations with cross‐feeding interactions

Coexistence of two or more populations by frequency‐dependent selection is common in nature, and it often arises even in well‐mixed experiments with microbes. If ecology is to be incorporated into models of population genetics, then it is important to represent accurately the functional form of frequency‐dependent interactions. However, measuring this functional form is problematic for traditional fitness assays, which assume a constant fitness difference between competitors over the course of an assay. Here, we present a theoretical framework for measuring the functional form of frequency‐dependent fitness by accounting for changes in abundance and relative fitness during a competition assay. Using two examples of ecological coexistence that arose in a long‐term evolution experiment with Escherichia coli, we illustrate accurate quantification of the functional form of frequency‐dependent relative fitness. Using a Monod‐type model of growth dynamics, we show that two ecotypes in a typical cross‐feeding interaction—such as when one bacterial population uses a byproduct generated by another—yields relative fitness that is linear with relative frequency.