Data from: 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.基于频率依赖选择（frequency-dependent selection）的两个或多个种群共存现象在自然界中极为常见，即便在微生物的充分混合实验中也时常出现。若要将生态学理论纳入种群遗传学模型，精准刻画频率依赖相互作用（frequency-dependent interaction）的函数形式便至关重要。然而，传统适合度测定（fitness assay）方法存在固有局限：这类方法假设在整个测定过程中，竞争双方的适合度差异始终保持恒定。为此，我们提出一套理论框架，可通过考量竞争测定过程中种群丰度与相对适合度的动态变化，实现对频率依赖适合度函数形式的测定。我们借助一项大肠杆菌（Escherichia coli）长期进化实验中发现的两类生态共存案例，展示了如何对频率依赖相对适合度的函数形式进行精准量化。通过采用生长动力学的莫诺德模型（Monod-type model），我们证实：在典型的交叉营养相互作用——即一个细菌种群利用另一种群产生的代谢副产物——中，两种生态型的相对适合度与相对频率呈线性相关关系。