A mixture of "cheats" and "co-operators" can enable maximal group benefit

Abstract

Is a group best off if everyone co-operates? Theory often considers this to be so (e.g. the "conspiracy of doves"), this understanding underpinning social and economic policy. We observe, however, that after competition between "cheat" and "co-operator" strains of yeast, population fitness is maximized under co-existence. To address whether this might just be a peculiarity of our experimental system or a result with broader applicability, we assemble, benchmark, dissect, and test a systems model. This reveals the conditions necessary to recover the unexpected result. These are 3-fold: (a) that resources are used inefficiently when they are abundant, (b) that the amount of co-operation needed cannot be accurately assessed, and (c) the population is structured, such that co-operators receive more of the resource than the cheats. Relaxing any of the assumptions can lead to population fitness being maximized when cheats are absent, which we experimentally demonstrate. These three conditions will often be relevant, and hence in order to understand the trajectory of social interactions, understanding the dynamics of the efficiency of resource utilization and accuracy of information will be necessary.

Figure 1. Final population size (Log(titre, normalized to maximum observed titre)) after exhaustion of resources as a function of initial invertase producer frequency, in theory (lines) and practice (points (*); mean ± s.e.m.; n = 9).

Observed data fit a quadratic function better than a linear function (F_2,3, = 41.3, p<0.01).

Figure 2. Relative producer fitness as a function of initial frequency in theory (lines) and practice (points (*); mean ± s.e.m.; n = 3).

Asterisks represent poorly mixed cultures (m low) while data points marked with an x represent better mixed cultures (m high).

Figure 3. The role of the rate-efficiency trade-off and the dynamics of sugar metabolism.

(a) Expected final population size (Log(titre)) after exhaustion of resources as a function of initial producer frequency in the absence of rate-efficiency trade-off. The temporal glucose spike, with glucose measured in mM/agar and time represented in hours, (b) when initially all the population are producers and (c) when 80% are producers with glucose measured in mM/agar and time is in hours. Note that the spike in (c) is lower and longer-lived, hence glucose is used more efficiently. (d) Efficiency of hexose usage by producers (g protein/mM hexose) when non-producers are present (80∶20 ratio: left hand panel) and when they are absent, i.e. 100% producers (right hand panel). Here we average across spatial structures.

Figure 4. The importance of costly invertase production and its coupling with sucrose levels.

(a) Sucrose and glucose levels (mM/agar) across the time course of the experiment (in the vicinity of region 3); (b) corresponding invertase production levels (mM glucose/g protein/hour); time of sucrose exhaustion is indicated by vertical black lines for m = 0.8 and m = 0.1. Note sucrose has disappeared relatively early but invertase is still produced thereafter; (c) expected final population size (Log(titre)) after exhaustion of resources as a function of initial co-operator frequency when cost of invertase production is reduced from 4% to 2% for invertase production of 86.7 mM glucose/g protein/hour that is 12% higher than the base-level invertase production.

Figure 5. Theoretical expectations for titre when invertase production matches sucrose levels (perfect information).