Extended Data Fig. 1: Simulations of chaotic dynamics in a simple two-genotype system.

(A) We model the dynamics of two genotypes, A and B, as coupled logistic maps (in discrete time). The model we analyse here is not intended to represent the underlying dynamics of the S/L system, but rather serves to demonstrate generic properties of chaotic dynamics. The parameters K_A and K_B are the carrying capacities of strains A and B, respectively. When the coupling parameter, c, goes to zero, we recover standard, independent logistic maps. Here, we consistently use r = 3.9, which puts the populations in the chaotic regime. (B-C) Examples of the abundance and genotype frequency dynamics. Here, we use c = 0.1. Even though the abundance dynamics are mildly coupled to each other, we still see fluctuations creeping into the genotype frequency dynamics. (D-E) Mean-variance scaling behaviors of the population abundance and genotype frequency. In both cases, we see power-law scaling with exponents of two, indicating the presence of effective offspring number correlations and decoupling noise. We varied the carrying capacities over several orders of magnitude to change the abundance and frequency. We computed the mean and variance of trajectories ran for 10⁵ iterations, and discarded the first 10⁴ iterations (to control for transient behaviors). We see that the degree of coupling does not affect the power-law exponent, but can change the intercept (as expected).