Figure 4. Mechanisms underlying the accelerated emergence of m-hit mutants in the cooperator/cheater scenario, using the model where wild-types do not benefit from shared goods.

(a) Quantification of replication events of intermediate mutants. The number of replication events of intermediate mutants was counted both for the sequential evolution scenario (dashed line) and for the cooperator/cheater scenario (solid line). Significantly more replication events are seen for the cooperator/cheater scenario once the complex phenotype arises as an emerging property. (b) Evolutionary dynamics in space and time. Each image is a snapshot of the grid status at 10 successive time points. Red indicates wild-type individuals with fitness R; blue indicates mutants with at least one cooperating site, with base fitness R⁺ minus the appropriate cost for cooperation; yellow indicates partial mutant individuals containing only cheating sites with fitness R⁺; cyan indicates any individual with fitness R⁻; green indicates m-hit cheating mutants, with fitness R⁺; grey indicates an empty spot. Initially, the population is dominated by wild-type individuals (red) and partial mutants have low fitness R⁻ due to absence of cooperation (cyan). Over time, all public goods become available within the required radius due to cooperation, and individuals with enhanced fitness R⁺ emerge. This includes both individuals that contain cooperating sites (blue) and those that only contain cheating sites (yellow). This population grows to dominate the grid. Due to cheating, relatively large areas containing individuals with reduced fitness, R⁻, appear. Within these areas, the m-hit cheater mutants (green) can thrive if they are generated, because in this environment, the m-hit cheater mutants enjoy a fitness advantage relative to the cooperator/cheater cloud. This occurs in snapshot 7. The areas of reduced fitness in which the m-hit cheater mutants grow are indicated by circles. In the remaining areas, where the fitness of the individuals is higher, the m-hit cheaters do not initially grow because they are not advantageous compared to the existing cooperator/cheater cloud. Over time, the m-hit cheaters take over the grid. Parameters were chosen as follows. Grid size = 100×100; m = 5; R = 0.15; R⁺ = 0.5; R⁻ = 0.135; D = 0.1; f = 1/70; u = 3.17×10⁻³; cooperation and replication radii = 10.