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Hairy versus naked caterpillars Ana Paula Assis Gabriel Moyano Kellen Siqueira Matheus Sousa Thomas Vilches Ubiratan Lima Monitor: Wendell Pereira Barreto

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Page 1: Hairy versus naked caterpillars - 200.145.112.249200.145.112.249/webcast/files/Group1_presentation.pdf · Hairy versus naked caterpillars Ana Paula Assis Gabriel Moyano Kellen Siqueira

Hairy versus naked caterpillarsAna Paula Assis Gabriel Moyano Kellen Siqueira Matheus Sousa Thomas Vilches Ubiratan Lima

Monitor: Wendell Pereira Barreto

Page 2: Hairy versus naked caterpillars - 200.145.112.249200.145.112.249/webcast/files/Group1_presentation.pdf · Hairy versus naked caterpillars Ana Paula Assis Gabriel Moyano Kellen Siqueira

Naked Hairy

Page 3: Hairy versus naked caterpillars - 200.145.112.249200.145.112.249/webcast/files/Group1_presentation.pdf · Hairy versus naked caterpillars Ana Paula Assis Gabriel Moyano Kellen Siqueira

caterpillars are voracious and compete for resources

Page 4: Hairy versus naked caterpillars - 200.145.112.249200.145.112.249/webcast/files/Group1_presentation.pdf · Hairy versus naked caterpillars Ana Paula Assis Gabriel Moyano Kellen Siqueira

competition

Page 5: Hairy versus naked caterpillars - 200.145.112.249200.145.112.249/webcast/files/Group1_presentation.pdf · Hairy versus naked caterpillars Ana Paula Assis Gabriel Moyano Kellen Siqueira

competition

Predation

Page 6: Hairy versus naked caterpillars - 200.145.112.249200.145.112.249/webcast/files/Group1_presentation.pdf · Hairy versus naked caterpillars Ana Paula Assis Gabriel Moyano Kellen Siqueira

competition

Parasitoidism

Page 7: Hairy versus naked caterpillars - 200.145.112.249200.145.112.249/webcast/files/Group1_presentation.pdf · Hairy versus naked caterpillars Ana Paula Assis Gabriel Moyano Kellen Siqueira
Page 8: Hairy versus naked caterpillars - 200.145.112.249200.145.112.249/webcast/files/Group1_presentation.pdf · Hairy versus naked caterpillars Ana Paula Assis Gabriel Moyano Kellen Siqueira

Transforming the drawing into math….

The model

Page 9: Hairy versus naked caterpillars - 200.145.112.249200.145.112.249/webcast/files/Group1_presentation.pdf · Hairy versus naked caterpillars Ana Paula Assis Gabriel Moyano Kellen Siqueira

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

Page 10: Hairy versus naked caterpillars - 200.145.112.249200.145.112.249/webcast/files/Group1_presentation.pdf · Hairy versus naked caterpillars Ana Paula Assis Gabriel Moyano Kellen Siqueira

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

Page 11: Hairy versus naked caterpillars - 200.145.112.249200.145.112.249/webcast/files/Group1_presentation.pdf · Hairy versus naked caterpillars Ana Paula Assis Gabriel Moyano Kellen Siqueira

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

Page 12: Hairy versus naked caterpillars - 200.145.112.249200.145.112.249/webcast/files/Group1_presentation.pdf · Hairy versus naked caterpillars Ana Paula Assis Gabriel Moyano Kellen Siqueira

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

Page 13: Hairy versus naked caterpillars - 200.145.112.249200.145.112.249/webcast/files/Group1_presentation.pdf · Hairy versus naked caterpillars Ana Paula Assis Gabriel Moyano Kellen Siqueira

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

Page 14: Hairy versus naked caterpillars - 200.145.112.249200.145.112.249/webcast/files/Group1_presentation.pdf · Hairy versus naked caterpillars Ana Paula Assis Gabriel Moyano Kellen Siqueira

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

Page 15: Hairy versus naked caterpillars - 200.145.112.249200.145.112.249/webcast/files/Group1_presentation.pdf · Hairy versus naked caterpillars Ana Paula Assis Gabriel Moyano Kellen Siqueira

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

Page 16: Hairy versus naked caterpillars - 200.145.112.249200.145.112.249/webcast/files/Group1_presentation.pdf · Hairy versus naked caterpillars Ana Paula Assis Gabriel Moyano Kellen Siqueira

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

Page 17: Hairy versus naked caterpillars - 200.145.112.249200.145.112.249/webcast/files/Group1_presentation.pdf · Hairy versus naked caterpillars Ana Paula Assis Gabriel Moyano Kellen Siqueira

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

Page 18: Hairy versus naked caterpillars - 200.145.112.249200.145.112.249/webcast/files/Group1_presentation.pdf · Hairy versus naked caterpillars Ana Paula Assis Gabriel Moyano Kellen Siqueira

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

Page 19: Hairy versus naked caterpillars - 200.145.112.249200.145.112.249/webcast/files/Group1_presentation.pdf · Hairy versus naked caterpillars Ana Paula Assis Gabriel Moyano Kellen Siqueira

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

Page 20: Hairy versus naked caterpillars - 200.145.112.249200.145.112.249/webcast/files/Group1_presentation.pdf · Hairy versus naked caterpillars Ana Paula Assis Gabriel Moyano Kellen Siqueira

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

Page 21: Hairy versus naked caterpillars - 200.145.112.249200.145.112.249/webcast/files/Group1_presentation.pdf · Hairy versus naked caterpillars Ana Paula Assis Gabriel Moyano Kellen Siqueira
Page 22: Hairy versus naked caterpillars - 200.145.112.249200.145.112.249/webcast/files/Group1_presentation.pdf · Hairy versus naked caterpillars Ana Paula Assis Gabriel Moyano Kellen Siqueira

Sugiura, Kamasaki. 2014

Page 23: Hairy versus naked caterpillars - 200.145.112.249200.145.112.249/webcast/files/Group1_presentation.pdf · Hairy versus naked caterpillars Ana Paula Assis Gabriel Moyano Kellen Siqueira
Page 24: Hairy versus naked caterpillars - 200.145.112.249200.145.112.249/webcast/files/Group1_presentation.pdf · Hairy versus naked caterpillars Ana Paula Assis Gabriel Moyano Kellen Siqueira

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

Page 25: Hairy versus naked caterpillars - 200.145.112.249200.145.112.249/webcast/files/Group1_presentation.pdf · Hairy versus naked caterpillars Ana Paula Assis Gabriel Moyano Kellen Siqueira

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

Page 26: Hairy versus naked caterpillars - 200.145.112.249200.145.112.249/webcast/files/Group1_presentation.pdf · Hairy versus naked caterpillars Ana Paula Assis Gabriel Moyano Kellen Siqueira
Page 27: Hairy versus naked caterpillars - 200.145.112.249200.145.112.249/webcast/files/Group1_presentation.pdf · Hairy versus naked caterpillars Ana Paula Assis Gabriel Moyano Kellen Siqueira

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

>

Page 28: Hairy versus naked caterpillars - 200.145.112.249200.145.112.249/webcast/files/Group1_presentation.pdf · Hairy versus naked caterpillars Ana Paula Assis Gabriel Moyano Kellen Siqueira

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

Page 29: Hairy versus naked caterpillars - 200.145.112.249200.145.112.249/webcast/files/Group1_presentation.pdf · Hairy versus naked caterpillars Ana Paula Assis Gabriel Moyano Kellen Siqueira

There is a non-trivial fixed point

Page 30: Hairy versus naked caterpillars - 200.145.112.249200.145.112.249/webcast/files/Group1_presentation.pdf · Hairy versus naked caterpillars Ana Paula Assis Gabriel Moyano Kellen Siqueira

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

Page 31: Hairy versus naked caterpillars - 200.145.112.249200.145.112.249/webcast/files/Group1_presentation.pdf · Hairy versus naked caterpillars Ana Paula Assis Gabriel Moyano Kellen Siqueira

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

Page 32: Hairy versus naked caterpillars - 200.145.112.249200.145.112.249/webcast/files/Group1_presentation.pdf · Hairy versus naked caterpillars Ana Paula Assis Gabriel Moyano Kellen Siqueira

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!

Page 33: Hairy versus naked caterpillars - 200.145.112.249200.145.112.249/webcast/files/Group1_presentation.pdf · Hairy versus naked caterpillars Ana Paula Assis Gabriel Moyano Kellen Siqueira

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

Page 34: Hairy versus naked caterpillars - 200.145.112.249200.145.112.249/webcast/files/Group1_presentation.pdf · Hairy versus naked caterpillars Ana Paula Assis Gabriel Moyano Kellen Siqueira

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

Page 35: Hairy versus naked caterpillars - 200.145.112.249200.145.112.249/webcast/files/Group1_presentation.pdf · Hairy versus naked caterpillars Ana Paula Assis Gabriel Moyano Kellen Siqueira

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

Page 36: Hairy versus naked caterpillars - 200.145.112.249200.145.112.249/webcast/files/Group1_presentation.pdf · Hairy versus naked caterpillars Ana Paula Assis Gabriel Moyano Kellen Siqueira

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

Page 37: Hairy versus naked caterpillars - 200.145.112.249200.145.112.249/webcast/files/Group1_presentation.pdf · Hairy versus naked caterpillars Ana Paula Assis Gabriel Moyano Kellen Siqueira

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

Page 38: Hairy versus naked caterpillars - 200.145.112.249200.145.112.249/webcast/files/Group1_presentation.pdf · Hairy versus naked caterpillars Ana Paula Assis Gabriel Moyano Kellen Siqueira

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

Page 39: Hairy versus naked caterpillars - 200.145.112.249200.145.112.249/webcast/files/Group1_presentation.pdf · Hairy versus naked caterpillars Ana Paula Assis Gabriel Moyano Kellen Siqueira

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

Page 40: Hairy versus naked caterpillars - 200.145.112.249200.145.112.249/webcast/files/Group1_presentation.pdf · Hairy versus naked caterpillars Ana Paula Assis Gabriel Moyano Kellen Siqueira

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

Page 41: Hairy versus naked caterpillars - 200.145.112.249200.145.112.249/webcast/files/Group1_presentation.pdf · Hairy versus naked caterpillars Ana Paula Assis Gabriel Moyano Kellen Siqueira

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

Page 42: Hairy versus naked caterpillars - 200.145.112.249200.145.112.249/webcast/files/Group1_presentation.pdf · Hairy versus naked caterpillars Ana Paula Assis Gabriel Moyano Kellen Siqueira

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

Page 43: Hairy versus naked caterpillars - 200.145.112.249200.145.112.249/webcast/files/Group1_presentation.pdf · Hairy versus naked caterpillars Ana Paula Assis Gabriel Moyano Kellen Siqueira

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

Page 44: Hairy versus naked caterpillars - 200.145.112.249200.145.112.249/webcast/files/Group1_presentation.pdf · Hairy versus naked caterpillars Ana Paula Assis Gabriel Moyano Kellen Siqueira

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

Page 45: Hairy versus naked caterpillars - 200.145.112.249200.145.112.249/webcast/files/Group1_presentation.pdf · Hairy versus naked caterpillars Ana Paula Assis Gabriel Moyano Kellen Siqueira
Page 46: Hairy versus naked caterpillars - 200.145.112.249200.145.112.249/webcast/files/Group1_presentation.pdf · Hairy versus naked caterpillars Ana Paula Assis Gabriel Moyano Kellen Siqueira

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

Page 47: Hairy versus naked caterpillars - 200.145.112.249200.145.112.249/webcast/files/Group1_presentation.pdf · Hairy versus naked caterpillars Ana Paula Assis Gabriel Moyano Kellen Siqueira

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

Page 48: Hairy versus naked caterpillars - 200.145.112.249200.145.112.249/webcast/files/Group1_presentation.pdf · Hairy versus naked caterpillars Ana Paula Assis Gabriel Moyano Kellen Siqueira

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

Page 49: Hairy versus naked caterpillars - 200.145.112.249200.145.112.249/webcast/files/Group1_presentation.pdf · Hairy versus naked caterpillars Ana Paula Assis Gabriel Moyano Kellen Siqueira

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

Page 50: Hairy versus naked caterpillars - 200.145.112.249200.145.112.249/webcast/files/Group1_presentation.pdf · Hairy versus naked caterpillars Ana Paula Assis Gabriel Moyano Kellen Siqueira

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

Page 51: Hairy versus naked caterpillars - 200.145.112.249200.145.112.249/webcast/files/Group1_presentation.pdf · Hairy versus naked caterpillars Ana Paula Assis Gabriel Moyano Kellen Siqueira

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

Page 52: Hairy versus naked caterpillars - 200.145.112.249200.145.112.249/webcast/files/Group1_presentation.pdf · Hairy versus naked caterpillars Ana Paula Assis Gabriel Moyano Kellen Siqueira

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

Page 53: Hairy versus naked caterpillars - 200.145.112.249200.145.112.249/webcast/files/Group1_presentation.pdf · Hairy versus naked caterpillars Ana Paula Assis Gabriel Moyano Kellen Siqueira

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

Page 54: Hairy versus naked caterpillars - 200.145.112.249200.145.112.249/webcast/files/Group1_presentation.pdf · Hairy versus naked caterpillars Ana Paula Assis Gabriel Moyano Kellen Siqueira
Page 55: Hairy versus naked caterpillars - 200.145.112.249200.145.112.249/webcast/files/Group1_presentation.pdf · Hairy versus naked caterpillars Ana Paula Assis Gabriel Moyano Kellen Siqueira

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

Page 56: Hairy versus naked caterpillars - 200.145.112.249200.145.112.249/webcast/files/Group1_presentation.pdf · Hairy versus naked caterpillars Ana Paula Assis Gabriel Moyano Kellen Siqueira

Conclusions

• Parasitoidism promotes coexistence in proportion to its influence

• But the coexistence it is still impossible in too intense or too asymmetrical competitions

Page 57: Hairy versus naked caterpillars - 200.145.112.249200.145.112.249/webcast/files/Group1_presentation.pdf · Hairy versus naked caterpillars Ana Paula Assis Gabriel Moyano Kellen Siqueira

Future directions

Page 58: Hairy versus naked caterpillars - 200.145.112.249200.145.112.249/webcast/files/Group1_presentation.pdf · Hairy versus naked caterpillars Ana Paula Assis Gabriel Moyano Kellen Siqueira

Our code will be uploaded at the wiki pagepython

ROctave

Thanks!!!!!! Questions????