Optimal Foraging Strategies Trever, Costas and Bill “International team of mystery”

1. Optimal Foraging Strategies Trever, Costas and Bill “International team of mystery” Plants Virtuatum computata. ZZZZZZ • Simulate the movement of insects on a ring of plants with varying quality • Investigate the movement rules that maximize energy intake

2. Simulation Code Construction Energy Ei Probability of not moving Pi Plant Quality Qi Energy Ei Pi=Ei/(Ei+Eh) Through parameter Eh, the movement behavior of the insects can be changed The probabilities of moving left or right are Pil and Pir

3. Simulation Code Construction Eh=0.0001 Eh=0.1 Energy Ei Probability of not moving Pi Eh=1 Plant Quality Qi Energy Ei Pi=Ei/(Ei+Eh) Through parameter Eh, the movement behavior of the insects can be changed Pi=Ei/(Ei+Eh) Through parameter Eh, the movement behavior of the insects can be changed The probabilities of moving left or right are Pil and Pir

4. Simulation Code Construction Eh=0.0001 Eh=0.1 Energy Ei Probability of not moving Pi Eh=1 Plant Quality Qi Energy Ei Eh~0 Insects don’t move except when plant quality is extremely low Eh>1 Insects move continuously regardless of plant quality

5. Simulation Case#1-FIXED QUALITY 1 Plant Quality 0 1 20 Plant Position Insects are uniformly distributed among plants at t=0 Eh=0.0001 Eh=0. 1 Eh=1

6. Simulation Case#1-FIXED QUALITY 1 Plant Quality 0 1 20 Plant Position Eh=0.0001 Eh=0. 1 Eh=1

7. Simulation Case#1-FIXED QUALITY 1 Plant Quality 0 1 20 Plant Position Optimal strategy is to NOT move unless plant the quality is very bad Average Energy Intake Eh

8. Models for FIXED QUALITY Plants If we consider space as discrete but time as continuous, then movement can be modeled as m coupled ODE’s, where m is number of plants Equation for a single plant: where Since we are interested in equilibrium solutions, we set the system of ODE’s to zero.

9. Simulation Case#1-FIXED QUALITY 1 Plant Quality 0 1 20 Plant Position Model Prediction Optimal strategy is to NOT move unless plant the quality is very bad Average Energy Intake Simulation Prediction Eh

10. Simulation Case#2-FIXED QUALITY 1 Plant Quality 0 1 20 Plant Position Model Prediction Optimal strategy is to NOT move unless plant the quality is very bad Average Energy Intake Simulation Prediction Eh

11. Simulation Case#3-FIXED QUALITY 1 Quality Generated Randomly Plant Quality 0 1 20 Plant Position Model Predictions For 100 random quality distributions Average Energy Intake Optimal strategy is to NOT move unless plant the quality is very bad Eh

12. SUMMARY SCENARIO 1)Plant quality is fixed; Energy intake is density independent 2)Plant quality is fixed; Energy intake is density dependent 3)Plant quality is dynamic; Energy intake is density independent • CONCLUSION • Optimal strategy: DON’T MOVE unless plant the quality is very bad • ? • 3)?

13. Simulation Case#1-FIXED QUALITY 1 Plant Quality 0 1 20 Plant Position Energy Intake rate is density dependent Density Dependence Density Dependence Ni

14. Simulation Case#1-FIXED QUALITY Energy Intake rate is density dependent 1 Plant Quality 0 1 20 Plant Position r=0 Optimal strategy is to NOT move unless plant the quality is very bad r=0.01 Average Energy Intake r=0.02 Eh

15. SUMMARY SCENARIO 1)Plant quality is fixed; Energy intake is density independent 2)Plant quality is fixed; Energy intake is density dependent 3)Plant quality is dynamic; Energy intake is density independent • CONCLUSION • Optimal strategy: DON’T MOVE unless plant the quality is very bad • Optimal strategy: DON’T MOVE unless plant the quality is very bad • 3)?

16. Simulation Case#1-DYNAMIC QUALITY 1 INITIAL QUALITY Plant Quality 0 1 20 Plant Position Insects are uniformly distributed among plants at t=0 Quality Update: At every iteration the simulation encounters standardized constant growth and consumption of the plant by the present insects.

17. Simulation Case#1-DYNAMIC QUALITY 1 INITIAL QUALITY Plant Quality 0 1 20 Plant Position Insects are uniformly distributed among plants at t=0 Eh=0.0001 Eh=0. 1 Eh=1

18. Simulation Case#1-DYNAMIC QUALITY 1 INITIAL QUALITY Plant Quality 0 1 20 Plant Position Eh=0.0001 Eh=0. 1 Eh=1 Quality Plot Quality Plot Quality Plot

19. Simulation Case#1-DYNAMIC QUALITY 1 Plant Quality 0 1 20 Plant Position Simulation Results Optimal strategy is INTERMEDIATE between no movement and continuous movement Average Energy Intake Eh

20. SUMMARY SCENARIO 1)Plant quality is fixed; Energy intake is density independent 2)Plant quality is fixed; Energy intake is density dependent 3)Plant quality is dynamic; Energy intake is density independent • CONCLUSION • Optimal strategy: DON’T MOVE unless plant the quality is very bad • Optimal strategy: DON’T MOVE unless plant the quality is very bad • 3)Optimal strategy: INTERMEDIATE between not moving and continuous movement

21. Optimal Foraging Strategies Trever, Costas and Bill “International team of mystery” “Oh, Behave…”