Fig 3. When there are no group events, mutations cause community extinction, but group-level events prevent this fate, as exemplified by the three archetypal modes of fragmentation.

The figures show the time-dynamics of populations (initiated with 100 groups, each containing 100 cooperator cells). A: Example replicate with no group events (i.e., no group fission and extinction), showing fast initial rise in the number of mutants and the consequential decrease in the total cell number, resulting in extinction. B, C: Temporal dynamics of the number of groups (B) and total productivity (C) for different reproduction modes. Thin lines are moving averages of individual replicates; solid lines are averages across replicates. D: By simulating population dynamics for various values of the mutation rate (μ), we can identify the value at which the population undergoes mutational meltdown–driven extinction (i.e., the maximum mutation rate at which the population can persist). E: For every point in the strategy space, we calculated the maximum mutation rate (shown in panel D for the three archetypes). F: The percentage of wild-type cells at equilibrium decreases with mutation rate (μ); the plot depicts the fraction of wild-type cells relative to the equilibrium fraction when μ is very small (μ = 0.01). Parameters: for the lines with group events, B₀ = 0.01; all other parameters set to the default values (Table A in S1 Text).