PT - JOURNAL ARTICLE AU - Noah Ribeck AU - Richard E. Lenski TI - Modeling and quantifying frequency-dependent fitness in microbial populations with cross-feeding interactions AID - 10.1101/012807 DP - 2014 Jan 01 TA - bioRxiv PG - 012807 4099 - http://biorxiv.org/content/early/2014/12/16/012807.short 4100 - http://biorxiv.org/content/early/2014/12/16/012807.full AB - Coexistence of multiple 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.