The role of recognition error in the stability of green-beard genes

Abstract

The empirical examples of the green-beard genes, once a conundrum of evolutionary biology, are accumulating, while theoretical analyses of this topic are occasional compared to those concerning (narrow-sense) kin selection. In particular, the recognition error of the green-beard effect that the cooperator fails to accurately recognize the other cooperators or defectors is readily found in numerous green-beard genes. To our knowledge, however, no model up to date has taken that effect into account. In this article, we investigated the effect of recognition error on the fitness of the green-beard gene. By employing theories of evolutionary games, our mathematical model predicts that the fitness of the green-beard gene is frequency dependent (frequency of the green-beard gene), which was corroborated by experiments performed with yeast FLO1. The experiment also shows that the cells with the green-beard gene (FLO1) are sturdier under severe stress. We conclude that the low recognition error among the cooperators, the higher reward of cooperation, and the higher cost of defection confer an advantage to the green-beard gene under certain conditions, confirmed by numerical simulation as well. Interestingly, we expect that the recognition error to the defectors may promote the cooperator fitness if the cooperator frequency is low and mutual defection is detrimental. Our ternary approach of mathematical analysis, experiments, and simulation lays the groundwork of the standard model for the green-beard gene that can be generalized to other species.

Keywords: evolution of cooperation; experimental evolution; green-beard gene; recognition error; sociality.

Figure 1.

The general schematics of the game-theoretical interpretation of yeast green-beard effect. (A) The payoff table of interactions between the actor and the recipient. C refers to cooperation, and D refers to defection. R, T, S, P are the expected payoff of the actor determined by the actions of the actor and the recipient. (B) In an experimental sense, C corresponds to the provision of adhesion (mediated by secretion of flocculin illustrated by the spikes on the cell surface), while D corresponds to the nonprovision of adhesion. If there is no recognition error, cooperators (FLO1⁺ cells) exclusively cooperate with the conspecific. Depending on which strategy the cell follows and the recognition errors, cells receive different payoffs (R, T, S, P), which later transform to fitness and the resultant allele frequency. (C) When exposed to chemical stress, the cells forming the floc (mostly FLO1⁺ cells) are protected from the stress, while planktonic cells (mostly flo1⁻ cells) are fully exposed to stress. However, secretion of the flocculin requires cost. These effects can be reflected in the payoff table and the baseline cost (Δ), making R, T, S, P the function against external stress and frequency of FLO1⁺ cells. (D) The description of graphical components in (A–C).

Figure 2.

The process of stress exposure and spreading under 10%-ethanol stress. (A) The tubes containing yeast cells with different initial proportions in 10% (v/v) ethanol dissolved in YPGal after 2-hr stress exposure. Higher amounts of flocculating cells induced flocs in the suspension, by which the suspension became more transparent due to the lack of planktonic cells. Five rectified pictures were merged into one picture without any change in brightness or contrast. (B) After 2-hr stress exposure, cells were deflocculated by EDTA and equal amounts of diluted suspension were spread on SC and SC–His plates. Flocculating cells (FLO1⁺ cells) cannot grow on SC–His plates. The number of colony-forming units (CFUs) was used to estimate the proportion of both types of cells after the stress exposure. The CFU counts of all plates used for analysis are shown in Supplementary Tables S2–S4. (C) The estimated numbers of CFU after 2-hr stress on SC plates with the initial ratio of 5:5 were used as the index of the stress in statistical analysis. Plates from the same culture were used for the analysis (the dots linked with light gray lines) to eliminate the effect of the viability of each cell culture. Red dots are averages, and error bars show 95% confidence intervals. CFUs under ethanol concentration of 0% or 10% do not differ much.

Figure 3.

Schematics of the simulation steps for 3 × 3 exemplar lattice. (A) As the first step of a generation, each agent (A₁–A₉) plays games with all of its neighbors. The number of such pairs is 12 shown by red bidirectional arrows. Agents gain payoff values as a result of the iterated games. (B) Regardless of the accumulated payoff, the randomly selected agent is eliminated (A₄ in this case). (C) The grid of the eliminated agent becomes vacant, which later will be occupied by a replicated agent. (D) The accumulated payoff is transformed into fitness that stochastically determines which agent becomes the replicator (A₂ in this case). The higher the fitness of the agent is, the more likely the agent replicates. (E) The positions of the agents are shuffled, which is the last step of a single generation. Agents play games as in (A), initiating the subsequent generation.

Figure 4.

The design of the simulation and the results. (A) An individual in each grid sequentially plays the two-person game with other individuals in the neighborhood (left, right, top, bottom). (B) The fitness surface of the cooperators against toxicity and initial cooperator proportion when both accuracy rates are 0.9. The cost of cooperation (Δ) is 0.6. The transparent gray flat surface illustrates the relative fitness of 1. The black, blue, and red lines along the surface indicate the fitness against the initial proportion given that toxicity (χ) values are 0, 0.3, and 0.6, respectively. These lines are shown in (C). (C) The fitness of the cooperator given that toxicity values are 0 (black), 0.3 (blue), and 0.6 (red).

Figure 5.

The relative fitness of FLO1⁺ (flocculating) cells compared with flo1⁻ (nonflocculating) cells. (A–C) The estimates of FLO1 relative fitness with different initial proportions and stress intensity. The data from the same set were linked with gray lines. The same set here refers to the cells from the same culture, which are expected to share similar viability. Three conditions of chemical stress were tested: 0% (A), 10% (B), and 20% EtOH (C). The inset of (B) represents the histogram of residuals obtained from the generalized linear mixed-effects model used in the statistical analysis. The contour of the histogram is similar to the normal distribution. (D) The average relative fitness in different stress conditions. Three lines are average (colored) lines from (A–C).

Figure 6.

Cooperation with defectors by adopting recognition error to the defectors could be evolutionarily advantageous if the cooperator frequency is low and the cost of mutual defection is severe. (A) If the flocculating cells are scarce, forming adhesion with nonflocculative cells (cooperation) can induce larger flocs where most nonflocculative cells are located at the periphery of the floc. Forming adhesion with nonflocculative cells may preclude the inclusion of several flocculative cells into the floc. However, as the peripheral region of the floc is damaged from external stress, the total survival of the flocculative cells could be higher if they bind with the nonflocculative cells. The susceptible part in the floc is illustrated with the dark transparent circular ring. (B) If the flocculating cells form a floc purely with its infrequent conspecifics, the floc size would be small, and most part of the floc will be susceptible to external stress. This strategy is less advantageous than cooperating with nonflocculative cells. (C) Using our simulation model, we measured the relative fitness of the cooperators with different cooperator proportions and the accuracy of distinction to the defectors $({\beta }_D)$. The colored dots in the upper left region shows the cooperator proportion from 0.1 to 0.9. As expected by Proposition 6.2, low ${\beta }_D$ is advantageous for the cooperator fitness when the cooperator frequency is low. If the cooperator proportion is 0.1, 0.2, or 0.3, then the slopes of the lines are negative, indicating that increasing ${\beta }_D$ is disadvantageous (marked with a “−” sign). For other proportion values, the slope is positive (marked with a “+” sign). Toxin intensity (χ) and accuracy of distinction to the cooperators $({\beta }_C)$ were both fixed as 0.9. The general fitness surface is presented in Supplementary Animation S3.