Fig 1.
Schematic of the interaction between patch selection and the evolution of sensitivity threshold as a multilevel game.
On the lower level game, agents select between patches with differing total resources. Each agent seeks to select the patch with greater reward, but is limited by their individual sensitivity threshold. In the upper-level game agents reproduce according to a fitness function determined by their patch-selection rewards and the cost of their sensitivity threshold.
Fig 2.
Evolution of agents’ sensitivity threshold over 3000 generations, showing the proportion of agents across potential perceptual strategies (in 100 logistically-spaced intervals).
In panel A the population evolves from an initially homogeneous population with τ = 0, showing a bifurcation into two distinct sub-populations. Simulation parameters: 1000 agents, α = 0.5, r = 5, σ = 0.0025. The white line indicates the theoretical expected sensitivity for agents with finite sensitivity threshold. In panel B the population is initially homogeneous with τ = ∞, with the other simulation parameters unchanged. Here the population remains distributed close to the initially homogeneous starting distribution. In panel C the mutation rate is increased by a factor of three (σ = 0.0075). The population initially all remain close to τ = ∞, before a rapid bifurcation in part of the population moves to the more sensitive perceptual state.
Fig 3.
Stable distribution of sensitivity threshold (τ) in simulations of the agent-based model for different values of perceptual cost α, with r = 2 (A) and r = 5 (B).
In each case the white dashed line indicates the value of τ for informed agents predicted by the analytical mathematical model. (C) Proportion of uninformed individuals (τ > 2) in the agent-based model (solid lines) versus the analytical prediction (dashed lines) for r = 2 (black) and r = 5 (red).
Fig 4.
Evolution of agents’ sensitivity threshold over 3000 generations in the presence of variable patch ratio, showing the proportion of agents across potential perceptual strategies.
The population evolves from an initially homogeneous population with τ = 0, and develops into three distinct sub-populations. Simulation parameters: 1000 agents, α = 0.5, r = 2 and r = 10. The white line indicates the theoretical expected sensitivities for agents with finite sensitivity threshold.
Fig 5.
Stable distribution of sensitivity threshold (τ) in simulations of the agent-based model for different values of perceptual cost α and with variable patch ratios: (A) r = 2 and r = 5 and (B) r = 2 and r = 10.
In each case the white dashed line indicates the values of τ for informed agents predicted by the analytical mathematical model. (C) Proportion of uninformed individuals (τ > 2) in the agent-based model (points) versus the analytical prediction (dashed lines) for r = 2 and r = 5 (black) and r = 2 and r = 10 (red).
Fig 6.
Predicted and simulated stable distribution of sensitivity threshold (τ) for widely-varying patch ratios (r/(1 + r)∼U(0.5, 1)): (A) analytically-predicted distribution of stable sensitivity thresholds, colour-coded by expected occupancy; (B) steady-state distribution of sensitivities in agent-based simulations; and (C) proportion of uninformed individuals (τ > 2) in the agent-based model (points) versus the analytical prediction (dashed lines).