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

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

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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

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

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

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

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

Simulation Case#1-FIXED QUALITY

1

Plant Quality

0

1

20

Plant Position

Eh=0.0001 Eh=0. 1 Eh=1

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

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.

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

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

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

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)?

Simulation Case#1-FIXED QUALITY

1

Plant Quality

0

1

20

Plant Position

Energy Intake rate is density dependent

Density Dependence

Density Dependence

Ni

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

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)?

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.

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

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

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

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

Optimal Foraging Strategies

Trever, Costas and Bill

“International team of mystery”

“Oh, Behave…”