Mutualism equilibrium densities and traits.

<p>Equilibrium population densities (A, B) and trait values (C, D) under changing climatic conditions for conflicting, <i>d</i><0 (A, C), and nonconflicting mutualists, <i>d</i>>0 (B, D). The intrinsic rate of increase of species 1 (solid lines) increases linearly with the climate variable <i>E</i>, while the intrinsic rate of increase of species 2 (dashed lines) is unaffected. The <i>x</i>-axis represents the climatic effect on the intrinsic rate of increase of species 1, <i>b₁E</i>. Red lines give eco-evolutionary equilibriums assuming high genetic variation (<i>V</i>₁, <i>V</i>₂>>0), whereas for blue lines there is no evolution (<i>V</i>₁ = <i>V</i>₂ = 0). The trait value for species <i>i</i> (shown on the <i>y</i>-axis of C, D) dictates the benefits of mutualism accrued by species <i>i</i> per capita of species <i>j</i>. 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: <i>R</i>₁ = <i>R</i>₂ = 0.2, <i>d</i> = −0.9, <i>b</i>₁ = 0.025, <i>b</i>₂ = 0, and <i>f</i> = 0.16. For the nonconflicting case (B, D) parameter values used were as follows: <i>R</i>₁ = <i>R</i>₂ = 0.2, <i>d</i> = 0.4, <i>b</i>₁ = 0.01, <i>b</i>₂ = 0, and <i>f</i> = 0.16.