Fig. 3: Population cycles exist in the absence of external forcing.

a Schematic representation of the in silico chemostat experiment. The chemostat facilitates continuous growth of the ΔtyrA, ΔpheA community through constant inflow of glucose, tyrosine, and phenylalanine. Perfusion is governed by the dilution rate \(D\), which acts on the inflow of external resource, and the outflow of chemostat resource and excess cells. b Two-dimensional bifurcation diagram of the ΔtyrA, ΔpheA community dynamics in a virtual chemostat. As the amino acid supply concentrations vary along each axis, the steady state community composition is indicated according to the color bar. A gray hashed region indicates the amino acid supply concentrations that do not produce stable equilibria but instead display limit cycle oscillations. Transcritical bifurcations beyond which the community collapses into a monoculture are indicated with solid black lines. Two inset plots demonstrate simulations of stable equilibrium and cycling dynamics. c Steady state stability for randomly sampled values of \({q}_{{ij}}\). Stability analysis by analyzing the Jacobian matrix was used to determine the steady state stability for a range of \({q}_{11}{q}_{22}\) and \({q}_{12}{q}_{21}\) from 250 to 4750. Each point in the scatter plot represents the stability of a steady state for a given parameter sample. Filled in blue points represent stable steady states, while empty orange circles represent unstable steady states. A black line separates the region where \({q}_{11}{q}_{22} > {q}_{12}{q}_{21}\).