Joint evolution of kin recognition and cooperation in spatially structured rhizobium populations

Abstract

In the face of costs, cooperative interactions maintained over evolutionary time present a central question in biology. What forces maintain this cooperation? Two potential ways to explain this problem are spatially structured environments (kin selection) and kin-recognition (directed benefits). In a two-locus population genetic model, we investigated the relative roles of spatial structure and kin recognition in the maintenance of cooperation among rhizobia within the rhizobia-legume mutualism. In the case where the cooperative and kin recognition loci are independently inherited, spatial structure alone maintains cooperation, while kin recognition decreases the equilibrium frequency of cooperators. In the case of co-inheritance, spatial structure remains a stronger force, but kin recognition can transiently increase the frequency of cooperators. Our results suggest that spatial structure can be a dominant force in maintaining cooperation in rhizobium populations, providing a mechanism for maintaining the mutualistic nodulation trait. Further, our model generates unique and testable predictions that could be evaluated empirically within the legume-rhizobium mutualism.

Figure 1. Root exudates and local resource environments.

(a) Schematic of root exudates in the model. Small open circles are general exudates that are usable by any free-living cells. Blue circles are nodulation induced exudates (b_N), also available to all free-living cells. Red triangles are rhizopines, which are only available to Rhiz+ cells. (b) Resources in local environments. Black portions of the bars represent the general exudates that are usable by all types. Red portions of bars show general use exudates induced by nodulation. Green portions of the bar represent the rhizopines. In the Nod+Rhiz+ bar, the two costs of Rhiz (c and d) can be seen to decrease the induced benefits of nodulation.

Figure 2. Dynamics and fitness of the unlinked model.

(a–c) Isoclines and dynamics. Zero growth net growth isoclines for the unlinked model for three different levels of spatial structure (φ = 0, 0.5, 1). The blue, curved isocline represents the equilibrium for the Rhiz locus and is unstable. The linear isocline is the equilibrium for the Nod locus and is stable. Vectors on the phase plane represent the evolutionary dynamics towards the equilibria. (d–f) Fitness of genotypes in each nodule environment. These panels of display the fitness of each cell type in each environment (i.e., nodule adjacency). Width of bars is proportional the probability of being found in that environment, as altered by degree of spatial structure (φ = 0, 0.5, 1). Black, red, green and blue bars (left to right within each cluster of bars) represent Nod+Rhiz+, Nod+Rhiz−, Nod−Rhiz+ and Nod−Rhiz−, respectively.

Figure 3. Invasibility at different levels of spatial structures.

(a–c) Increasing levels of spatial structure (φ = 0, 0.5, 1). Black filled circles represent stable equilibria, grey filled circles represent unstable internal equilibria, while open circles are unstable. Arrows represent the movement of the population along the edges of this genotype space.

Figure 4. Linked genotype frequency dynamics.

(a–c) Genotype frequency dynamics of the linked model for φ = {0, 0.5, 1}. Nod+Rhiz+, Nod+Rhiz−, Nod−Rhiz+ and Nod−Rhiz− are represented by red, blue, purple, and green lines, respectively. At low spatial structure, there is a transient increase in Nod+Rhiz+ frequency (red line). At higher spatial structures, this increase disappears, and Nod+Rhiz− goes to fixation. Genotype frequency is plotted on the y-axis, and time in generations is on the x-axis. (d–f) Evolutionary dynamics in the genotype space simplex. Blue arrows represents evolutionary trajectory, and black point represents the evolutionary endpoints. Open circles show initial condition.