Figure 1.
Competition density and trait trajectories.
For competition, trajectories of species 1 (solid lines) and species 2 (dashed lines) densities (A) and trait values (B) as the climate variable E increases from 0 to 5 over the course of 100 time steps. The model describes conflicting competition (d<0), and additive genetic variances range from 0 (light blue) to 0.75 (red). Trajectories began at an eco-evolutionary equilibrium, and densities are scaled relative to this equilibrium. The trait value for species i dictates the strength of competition felt by species i per capita of species j. The top x-axis represents the climatic effect on the intrinsic rate of increase of species 1, b1E. Parameter values used were: R1 = R2 = 0.1, d = −0.9, bn1 = 0. 001, bn2 = 0, and f = 0.045.
Figure 2.
Competition equilibrium densities and traits.
Equilibrium population densities (A, B) and trait values (C, D) for two competing species at different climatic conditions. The intrinsic rate of increase of species 1 (solid lines) increases linearly with climate E, while the intrinsic rate of increase of species 2 (dashed lines) is unaffected. Results are for conflicting competition, d<0 (A, C), and nonconflicting competition, d>0 (B, D). Red lines give eco-evolutionary equilibriums assuming high genetic variation (V1, V2>>0), whereas for blue lines there is no evolution (V1 = V2 = 0). The trait value (shown on the y-axis of C, D) for species i dictates the strength of competition felt by species i per capita of species j. The x-axis represents the climatic effect on the intrinsic rate of increase of species 1, b1E. For the conflicting case (A, C) parameter values used were: R1 = R2 = 0.1, d = −0.9, b1 = 0.001, b2 = 0, and f = 0.45. For the nonconflicting case (B, D) parameter values used were as follows: R1 = R2 = 0.1, d = 0.5, b1 = 0.01, b2 = 0, and f = 0.02.
Figure 3.
Mutualism equilibrium densities and traits.
Equilibrium population densities (A, B) and trait values (C, D) under changing climatic conditions for conflicting, d<0 (A, C), and nonconflicting mutualists, d>0 (B, D). The intrinsic rate of increase of species 1 (solid lines) increases linearly with the climate variable E, while the intrinsic rate of increase of species 2 (dashed lines) is unaffected. The x-axis represents the climatic effect on the intrinsic rate of increase of species 1, b1E. Red lines give eco-evolutionary equilibriums assuming high genetic variation (V1, V2>>0), whereas for blue lines there is no evolution (V1 = V2 = 0). The trait value for species i (shown on the y-axis of C, D) dictates the benefits of mutualism accrued by species i per capita of species j. When the intrinsic rate of increase of species 1 is high enough and species are allowed to coevolve, there is no equilibrium in the nonconflicting mutualism model (B, D), as the growth of each species is unbounded. For the conflicting case (A, C) parameter values used were: R1 = R2 = 0.2, d = −0.9, b1 = 0.025, b2 = 0, and f = 0.16. For the nonconflicting case (B, D) parameter values used were as follows: R1 = R2 = 0.2, d = 0.4, b1 = 0.01, b2 = 0, and f = 0.16.
Figure 4.
Predation equilibrium densities and traits.
Equilibrium prey (solid lines) and predator (dashed lines) densities (A, B) and trait values (C, D) for different climatic conditions. Densities are scaled to equilibrium at E = 0. (A, C) The prey intrinsic rate of increase increases linearly with climate E, while the predation rate is unaffected. (B, D) The predation rate increases linearly with E, while the prey intrinsic rate of increase is unaffected. The x-axis for panels A and C represents the climatic effect on the intrinsic rate of increase of prey, bnE, and the x-axis for panels B and D represents the climatic effect on the predation rate, bpE. Red lines give eco-evolutionary equilibrium assuming high genetic variation (V1, V2>>0), and blue lines give the case of no coevolution (V1 = V2 = 0). Increases in either prey or predator trait values reduce per capita predation rate. Parameter values used were: R = 0.5, Q0 = 2, c = 0.25, f = 0.04, g = 0.04, and m0 = 0.005. Climate change effect parameters were either bp = 0.2 and bn = 0 (A, C) or bp = 0 and bn = 0.02 (B, D).