Figure 4.

Plots of trait mean for optimal temperature, z₁ (panel 1), investment in predator defense, z₂ (panel 2), variance in z₁ (panel 3) and z₂ (panel 4), and covariance between z₁ and z₂ (panel 5) versus time for growth functions modeling tradeoffs in predator-prey dynamics, optimal temperature, and the combined effects of predator prey and optimal temperature. These are results from the same simulations as in Fig. (3). The simulations all use Eq. (32). For optimal temperature alone, the parameter values are p = 5, σ² = 2, K = 20, d = 0.1, $E_1=15+10sin\left(\frac{2\pi t}{100}\right)$, r = 0, g = 0, and E₂ = 0. For predator-prey dynamics alone, the parameter values are p = 5, K = 20, r = 0.1, g = 1, d = 0.1, $E_2=2sin(\frac{2\pi t}{100}+25)$, E₁ = 0, and z₂ = 0. For combined effects of predator-prey dynamics and optimal temperature tradeoffs, the parameter values are p = 5, σ² = 2, K = 20, d = 0.1, $E_1=15+10sin\left(\frac{2\pi t}{100}\right)$, r = 0.1, g = 1, and $E_2=2sin\left(\frac{2\pi t}{100}+25\right)$. Total immigration per time step is 0.1 for the single trait simulations and 1 for the two-trait simulations. More immigration is necessary for the two-trait case because there are many more functional groups (species), and immigration occurs for each one.