Revealing the mechanism of stabilization in the predator-prey model (1)–(2).

<p>The trade-off function <i>a</i>(<i>R</i>) is given by (8) with <i>a₀</i> = 1; <i>Δα = </i>−2. (A) Evolution of the life history trait distribution for the prey population though a cycle. Curves 1 and 3 correspond to the minimal and the maximal predator density though a cycle; whereas curve 2 shows <i>ρ_Z</i> (<i>R</i>) for an intermediate density of predator. An increase of predator biomass results in a prevalence of prey cohorts with low vulnerability to predation. (B) The overall functional response of the predator as a function of the total biomass of prey <i>Z</i> constructed along system trajectories. The functional response <i>H₀</i> for the equilibrium life history trait distribution <i>z</i>(<i>R</i>) is shown by dashed line. The direction of motion is shown by arrows. The model parameters are <i>m = </i>0.1; <i>b</i> = 0.045; <i>θ</i> = 0.5.