Fig. 5

Invasion rates and spatial dynamics of competition for cooperative and selfish individuals. a Cooperators’ invasion rate increases with larger public good production and lower costs; selfish invasion rate increases with increasing costs and it is insensitive to the production rates of the cooperators that support them. The invasion rates for cooperators invading empty space (red circles) and selfish individuals invading a population of cooperators (blue circles) was measured for each combination of cost and public good production rate (benefit is constant, and set to b=10) in 10. b A population with lower public good production rate out-competes one with larger production in the back of a wave. Parameters: cooperators (yellow wave-front) p _yellow=6.0, selfish individuals (magenta and blue wave-back) p _blue=0.2 and p _magenta=1.0. c The population with a larger production rate out-competes the one with lower production at the front of a wave. Parameters: p _purple=5.0, p _green=6.0. For both a and b, μ=0, b=10, c=4.0, background in white. Other parameters as in Fig. 2