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

2. Simulation Code Construction Plant Quality Qi Energy Ei Probability of not moving Pi 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 Plant Quality Qi Energy Ei Probability of not moving Pi Pi=Ei/(Ei+Eh) Through parameter Eh, the movement behavior of the insects can be changed Eh=0.1 Eh=1 Eh=0.0001 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 Plant Quality Qi Energy Ei Probability of not moving Pi Eh~0 Insects don’t move except when plant quality is extremely low Eh>1 Insects move continuously regardless of plant quality Eh=0.1 Eh=1 Eh=0.0001

5. Simulation Case#1-FIXED QUALITY Plant Position 120 0 1 Plant Quality Eh=0.0001 Eh=0. 1 Eh=1 Insects are uniformly distributed among plants at t=0

6. Simulation Case#1-FIXED QUALITY Plant Position 120 0 1 Plant Quality Eh=0.0001 Eh=0. 1 Eh=1

7. Simulation Case#1-FIXED QUALITY Plant Position 120 0 1 Plant Quality Eh Average Energy Intake Optimal strategy is to NOT move unless plant the quality is very bad

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 Plant Position 120 0 1 Plant Quality Eh Average Energy Intake Optimal strategy is to NOT move unless plant the quality is very bad Model Prediction Simulation Prediction

10. Simulation Case#2-FIXED QUALITY Plant Position 120 0 1 Plant Quality Eh Average Energy Intake Optimal strategy is to NOT move unless plant the quality is very bad Model Prediction Simulation Prediction

11. Simulation Case#3-FIXED QUALITY Plant Position 120 0 1 Plant Quality Eh Average Energy Intake Optimal strategy is to NOT move unless plant the quality is very bad Model Predictions For 100 random quality distributions Quality Generated Randomly

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 1)Optimal strategy: DON’T MOVE unless plant the quality is very bad 2) ? 3) ?

13. Simulation Case#1-FIXED QUALITY Plant Position 120 0 1 Plant Quality Energy Intake rate is density dependent Ni Density Dependence

14. Simulation Case#1-FIXED QUALITY Plant Position 120 0 1 Plant Quality Eh Average Energy Intake Optimal strategy is to NOT move unless plant the quality is very bad r=0 r=0.01 r=0.02 Energy Intake rate is density dependent

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 1)Optimal strategy: DON’T MOVE unless plant the quality is very bad 2)Optimal strategy: DON’T MOVE unless plant the quality is very bad 3) ?

16. Simulation Case#1-DYNAMIC QUALITY Plant Position 120 0 1 Plant Quality 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. INITIAL QUALITY

17. Simulation Case#1-DYNAMIC QUALITY Plant Position 120 0 1 Plant Quality Eh=0.0001 Eh=0. 1 Eh=1 Insects are uniformly distributed among plants at t=0 INITIAL QUALITY

18. Simulation Case#1-DYNAMIC QUALITY Plant Position 120 0 1 Plant Quality Eh=0.0001 Eh=0. 1 Eh=1 Quality Plot INITIAL QUALITY Quality Plot

19. Simulation Case#1-DYNAMIC QUALITY Plant Position 120 0 1 Plant Quality Eh Average Energy Intake Simulation Results Optimal strategy is INTERMEDIATE between no movement and continuous movement

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 1)Optimal strategy: DON’T MOVE unless plant the quality is very bad 2)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…”