Fig. 5. Trapping and segregation by coherent structures gives cooperators a boost.
In a two-species Replicase R2, one species (the replicase) plays the role of a cooperator (at no cost, provides a catalytic benefit of size β to all non-self organisms within a radius Rint), while the other species plays the role of a parasite. a Chaotic flows generate LCSs with finite lifetimes, which act as traps for particles. Here a six-vortex (teal dots) example is shown with the finite-time Lyapunov exponent (FTLE) at left and trapping regions (negative FTLE) at right. b In a well-mixed population obeying a Wright–Fisher update rule on constant population size, each species would be equally likely to fix (reflected by Pcoop, the fixation probability of cooperators shown on the y-axis, equaling 1/2) if they began at equal fractions. To test whether flow-segregation helped replicases, we performed Wright–Fisher simulations on a population of size N = 200 at different Rint and Da. Intermediate values of Da show a boost for cooperation at specific values of Rint. c Returning to a birth–death process, where the population either goes extinct or grows to infinite size, we tracked the average replicase fraction of the population over 1000 simulations from t = 0 to t = 10, with roughly 50 members of each species at t = 0. We never saw either population go extinct when starting from even such a small size; rather, the population tends to sustain both parasites and replicases, with on average slightly more replicases than parasites.