hairy versus naked caterpillars -...
TRANSCRIPT
Hairy versus naked caterpillarsAna Paula Assis Gabriel Moyano Kellen Siqueira Matheus Sousa Thomas Vilches Ubiratan Lima
Monitor: Wendell Pereira Barreto
Naked Hairy
caterpillars are voracious and compete for resources
competition
competition
Predation
competition
Parasitoidism
Transforming the drawing into math….
The model
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
= naked caterpillar population= intrinsic growth rate
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
= carrying capacity
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
with competition between caterpillars
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
= competition coefficientdN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
= hairy caterpillar population
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
Generalist (eats a variety of food itens) has low dependence on the caterpillars as
resources
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
= predation rate
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
= parasitoids population
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
= parasitoidism rate
Specialist in caterpillars
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �HH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �HH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �HH)
� µPaType II saturation
Specialist in caterpillars
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �HH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �HH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �HH)
� µPa
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
= competition coefficient
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �HH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �HH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �HH)
� µPa
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �HH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �HH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �HH)
� µPa
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �HH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �HH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �HH)
� µPa
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �HH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �HH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �HH)
� µPa
Sugiura, Kamasaki. 2014
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
>dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
= parasitoidism rates
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
,
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
= predation rates
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
,dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
= competition coefficients
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
,
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa= handling time
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �HH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �HH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �HH)
� µPa
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �HH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �HH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �HH)
� µPa
Model
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
>
How do competition, predation and parasitoidism contribute to the coexistence of both caterpillar species?
Question
Hypothesis
Higher parasitoidism on hairy caterpillars counterbalances the higher predation rate on naked caterpillars, being thus
essential to coexistence in the presence of competition
There is a non-trivial fixed point
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
= 0.44
= 0.15
= 0.15= 0.30
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
= =1.01dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
= =200
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa=0.005
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa=10
ParasitoidHairyNaked
Fixed Point Stability
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
= =1.01dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
= =200
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa=0.005
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa=10
0.0 0.5 1.0 1.5 2.0
0.0
0.5
1.0
1.5
2.0
0
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
= 0.44
= 0.15
= 0.15= 0.30
Competition
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
= =1.01dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
= =200
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa=0.005
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa=10
0.0 0.5 1.0 1.5 2.0
0.0
0.5
1.0
1.5
2.0
0
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
= 0.44
= 0.15
= 0.15= 0.30
Competition
Coexistence evenwith high competition!
0.0 0.5 1.0 1.5 2.0
0.0
0.5
1.0
1.5
2.0
0
Competition
0.0 0.5 1.0 1.5 2.0
0.0
0.5
1.0
1.5
2.0
0
100
Pa > 0 Pa = 0
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
= =1.01dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
= =200
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa=0.005
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa=10
0 0.2 0.4 0.6 0.8 10
0.2
0.4
0.6
0.8
1
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
= 0.15= 0.10
Predation
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
= =1.01dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
= =200
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa=0.005
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa=10
0 0.2 0.4 0.6 0.8 10
0.2
0.4
0.6
0.8
1
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
= 0.15
PredationdN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
= 0.20
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
= =1.01dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
= =200
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa=0.005
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa=10
0 0.2 0.4 0.6 0.8 10
0.2
0.4
0.6
0.8
1
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
= 0.15
PredationdN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
= 0.30
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
= =1.01dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
= =200
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa=0.005
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa=10
0 0.2 0.4 0.6 0.8 10
0.2
0.4
0.6
0.8
1
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
= 0.15
PredationdN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
= 0.40
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
= =1.01dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
= =200
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa=0.005
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa=10
0 0.2 0.4 0.6 0.8 10
0.2
0.4
0.6
0.8
1
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
= 0.15
PredationdN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
= 0.50
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
= =1.01dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
= =200
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa=0.005
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa=10
0 0.2 0.4 0.6 0.8 10
0.2
0.4
0.6
0.8
1
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
= 0.15
PredationdN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
= 0.60
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
= =1.01dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
= =200
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa=0.005
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa=10
0 0.2 0.4 0.6 0.8 10
0.2
0.4
0.6
0.8
1
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
= 0.15
PredationdN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
= 0.70
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
= =1.01dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
= =200
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa=0.005
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa=10
0 0.2 0.4 0.6 0.8 10
0.2
0.4
0.6
0.8
1
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
= 0.15
PredationdN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
= 0.80
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
= =1.01dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
= =200
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa=0.005
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa=10
0 0.2 0.4 0.6 0.8 10
0.2
0.4
0.6
0.8
1
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
= 0.15
PredationdN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
= 0.90
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
= =1.01dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
= =200
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa=0.005
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa=10
0 0.2 0.4 0.6 0.8 10
0.2
0.4
0.6
0.8
1
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
= 0.15
PredationdN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
= 1.00
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
= =1.01dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
= =200
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa=0.005
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa=10
0 0.2 0.4 0.6 0.8 10
0.2
0.4
0.6
0.8
1
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
= 0.15
PredationdN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
= 1.10
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
>dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
0 0.2 0.4 0.6 0.8 10
0.2
0.4
0.6
0.8
1
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
= =1.01dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
= =200
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa=0.005
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa=10
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
= 0.20
= 0.15
Parasitoidism
0 0.2 0.4 0.6 0.8 10
0.2
0.4
0.6
0.8
1
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
= =1.01dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
= =200
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa=0.005
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa=10
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
= 0.30
= 0.15
Parasitoidism
0 0.2 0.4 0.6 0.8 10
0.2
0.4
0.6
0.8
1
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
= =1.01dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
= =200
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa=0.005
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa=10
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
= 0.40
= 0.15
Parasitoidism
0 0.2 0.4 0.6 0.8 10
0.2
0.4
0.6
0.8
1
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
= =1.01dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
= =200
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa=0.005
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa=10
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
= 0.50
= 0.15
Parasitoidism
0 0.2 0.4 0.6 0.8 10
0.2
0.4
0.6
0.8
1
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
= =1.01dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
= =200
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa=0.005
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa=10
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
= 0.60
= 0.15
Parasitoidism
0 0.2 0.4 0.6 0.8 10
0.2
0.4
0.6
0.8
1
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
= =1.01dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
= =200
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa=0.005
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa=10
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
= 0.70
= 0.15
Parasitoidism
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
= =1.01dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
= =200
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa=0.005
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa=10
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
dN
dt= rNN(1� N + ↵H
KN)� �NN � �NPaN
1 + h(�NN + �NH)
dH
dt= rHH(1� H + �N
KH)� �HH � �HPaH
1 + h(�NN + �NH)
dPa
dt= Pa
(�HH + �NN)
1 + h(�NN + �NH)
� µPa
= 0.0= 0.0
N + H + Pa H + Pa N + HHN
Predation x Parasitoidism
How do competition, predation and parasitoidism contribute to the coexistence of both caterpillar species?
Question
Hypothesis
Higher parasitoidism on hairy caterpillars counterbalances the higher predation rate on naked caterpillars, being thus
essential to coexistence in the presence of competition
Conclusions
• Parasitoidism promotes coexistence in proportion to its influence
• But the coexistence it is still impossible in too intense or too asymmetrical competitions
Future directions
Our code will be uploaded at the wiki pagepython
ROctave
Thanks!!!!!! Questions????