optimal foraging strategies trever, costas and bill “international team of mystery”
DESCRIPTION
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. - PowerPoint PPT PresentationTRANSCRIPT
Optimal Foraging StrategiesTrever, Costas and Bill“International team of mystery”
PlantsVirtuatum computata.
• Simulate the movement of insects on a ring of plants with varying quality• Investigate the movement rules that maximize energy intake
ZZZZZZ
Simulation Code Construction
Plant Quality Qi
Ener
gy E
i
Energy Ei
Prob
abili
ty o
f not
mov
ing
PiPi=Ei/(Ei+Eh)Through parameter Eh, the movement behavior of the insects can be changedThe probabilities of moving left or right are Pil and Pir
Simulation Code Construction
Plant Quality Qi
Ener
gy E
i
Energy Ei
Prob
abili
ty o
f not
mov
ing
PiPi=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 changedThe probabilities of moving left or right are Pil and Pir
Simulation Code Construction
Plant Quality Qi
Ener
gy E
i
Energy Ei
Prob
abili
ty o
f not
mov
ing
PiEh~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
Simulation Case#1-FIXED QUALITY
Plant Position1 200
1
Plan
t Qua
lity
Eh=0.0001 Eh=0. 1 Eh=1 Insects are uniformly distributed among plants at t=0
Simulation Case#1-FIXED QUALITY
Plant Position1 200
1
Plan
t Qua
lity
Eh=0.0001 Eh=0. 1 Eh=1
Simulation Case#1-FIXED QUALITY
Plant Position1 200
1
Plan
t Qua
lity
Eh
Ave
rage
Ene
rgy
Inta
ke
Optimal strategy is to NOT move unless plant the quality is very bad
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:
EhEEP
i
ii
iiii
iii NPNPNP
dtdN
1
21
21
11
11
where
Since we are interested in equilibrium solutions, we set the system of ODE’s to zero.
Simulation Case#1-FIXED QUALITY
Plant Position1 200
1
Plan
t Qua
lity
Eh
Ave
rage
Ene
rgy
Inta
ke
Optimal strategy is to NOT move unless plant the quality is very bad
Model Prediction
Simulation Prediction
Simulation Case#2-FIXED QUALITY
Plant Position1 200
1
Plan
t Qua
lity
Eh
Ave
rage
Ene
rgy
Inta
ke
Optimal strategy is to NOT move unless plant the quality is very bad
Model Prediction
Simulation Prediction
Simulation Case#3-FIXED QUALITY
Plant Position1 200
1
Plan
t Qua
lity
Eh
Ave
rage
Ene
rgy
Inta
ke
Optimal strategy is to NOT move unless plant the quality is very bad
Model PredictionsFor 100 random
quality distributions
Quality Generated Randomly
SUMMARY
SCENARIO
1) Plant quality is fixed; Energy intake is density
independent2) Plant quality is fixed; Energy intake is density
dependent3) 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) ?
Simulation Case#1-FIXED QUALITY
Plant Position1 200
1
Plan
t Qua
lity
Energy Intake rate is density dependent
irN
i
ii e
EhEEP
NiDen
sity
Dep
ende
nce
Density Dependence
Simulation Case#1-FIXED QUALITY
Plant Position1 200
1
Plan
t Qua
lity
Eh
Ave
rage
Ene
rgy
Inta
ke
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
SUMMARY
SCENARIO
1) Plant quality is fixed; Energy intake is density
independent2) Plant quality is fixed; Energy intake is density
dependent3) 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) ?
Simulation Case#1-DYNAMIC QUALITY
Plant Position1 200
1
Plan
t Qua
lity
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
Simulation Case#1-DYNAMIC QUALITY
Plant Position1 200
1
Plan
t Qua
lity
Eh=0.0001 Eh=0. 1 Eh=1 Insects are uniformly distributed among plants at t=0
INITIAL QUALITY
Simulation Case#1-DYNAMIC QUALITY
Plant Position1 200
1
Plan
t Qua
lity
Eh=0.0001 Eh=0. 1 Eh=1
Quality Plot
INITIAL QUALITY
Quality Plot Quality Plot
Simulation Case#1-DYNAMIC QUALITY
Plant Position1 200
1
Plan
t Qua
lity
Eh
Ave
rage
Ene
rgy
Inta
ke
Simulation Results
Optimal strategy is INTERMEDIATE between no movement and continuous movement
SUMMARY
SCENARIO
1) Plant quality is fixed; Energy intake is density
independent2) Plant quality is fixed; Energy intake is density
dependent3) 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
Optimal Foraging StrategiesTrever, Costas and Bill“International team of mystery”
“Oh, Behave…”