Dynamic Energy Budget Theory - I Tânia Sousa with contributions from :Bas Kooijman

Dynamic Energy Budget Theory - I

Tânia Sousa with contributions from : Bas Kooijman

Metabolic rates: the effect of temperature

Why do metabolic rates depend on temperature?

Metabolic rates: the effect of temperature

Low metabolism (body temperature between 27ºC – 33ºC)

ln r

ate

104 T-1, K-1

Daphnia magna

reproductionyoung/d

ingestion106 cells/h

growth, d-1

aging, d-1

Metabolic rates: the effect of temperature

How do metabolic rates ln k(T) depend on temperature?

ln r

ate

104 T-1, K-1

Daphnia magna

reproductionyoung/d

ingestion106 cells/h

growth, d-1

aging, d-1

Metabolic rates: the effect of temperature

How do metabolic rates depend on temperature?ln ( ) '

ctek T cte

T

ln r

ate

104 T-1, K-1

Daphnia magna

reproductionyoung/d

ingestion106 cells/h

growth, d-1

aging, d-1

Metabolic rates: the effect of temperature

How do metabolic rates depend on temperature? What is the meaning of the slope cte=TA?

Write the constant as a function of T1

Write na expression for k(T)

K 293K; 6400

}exp{)(

1

11

TTT

T

T

TkTk

A

AA ln r

ate

104 T-1, K-1

Daphnia magna

Metabolic rates: the effect of temperature

The Arrhenius relationship has good empirical support The Arrhenius temperature is given by minus the slope:

the higher the Arrhenius temperature the more sensitive organisms are to changes in temperature

reproductionyoung/d

ingestion106 cells/h

growth, d-1

aging, d-1

Arrhenius relationship:

The Arrhenius relationship is valid in the

temperature tolerance range At temperatures too high the organism usually dies At temperatures too low the rates are usually

lower than predicted by the Arrhenius relationship, e.g., at cold temperatures the sloths become letargic

Many extinctions are tought to be related with to changes in temperature late Pleistocene, 40,000 to 10,000 years

ago, North America lost over 50 percent of its large mammal species. These species include mammoths, mastodons, giant ground sloths, among many others.

Metabolic rates: temperature range

How do feeding power depends on

temperature?

Metabolic rates: the effect of temperature

How do feeding depends on temperature?

What is the implication for ?

Metabolic rates: the effect of temperature

11

( ) exp{ }A AT Tk T k

T T

=

All parameters that have units time-1 depend on temperature

Metabolic rates: the effect of temperature

Xm Xm 11exp A Ap p T T T T

Am Am 11exp A Ap p T T T T

11expT T A Ap p T T T T

11expM M A Ap p T T T T

1 1expJ J A Ak k T T T T

1 1exp A Av v T T T T

All parameters that have units time-1 depend

on temperature

Metabolic rates: the effect of temperature

Xm Xm 11exp A Ap p T T T T

Am Am 11exp A Ap p T T T T

11expT T A Ap p T T T T

11expM M A Ap p T T T T

1 1expJ J A Ak k T T T T

1 1exp A Av v T T T T

�̇�𝑋= �̇� 𝑋 𝐴𝜇𝑋= 𝑓 (𝑋 ) {�̇�𝑋𝑚 }𝑉 2/ 3

�̇�𝐴= �̇� 𝐸𝐴𝜇𝐸= 𝑓 (𝑋 ) {�̇�𝐴𝑚 }𝑉 2 / 3

�̇�𝑆= �̇� 𝐸𝑆𝜇𝐸=[�̇�𝑀 ]𝑉 + {�̇�𝑇 }𝑉 2 /3

=

What is the effect of temperature on dL/dt?

Metabolic rates: the effect of temperature

𝑑𝐿𝑑𝑡

= 13

𝑘𝑚𝐸 �̇� [𝑀𝑉 ]− [ �̇� 𝐸𝑀 ]𝐿− { �̇�𝐸𝑇 }𝑘𝑚𝐸 [𝑀𝑉 ]+[𝑀𝑉 ] 𝑦𝐸𝑉

What is the effect of temperature on dL/dt?

How do the von Bertallanfy growth rate and ultimate length depend on temperature?

Metabolic rates: the effect of temperature

𝑑𝐿𝑑𝑡

= 13

𝑘𝑚𝐸 �̇� [𝑀𝑉 ]− [ �̇� 𝐸𝑀 ]𝐿− { �̇�𝐸𝑇 }𝑘𝑚𝐸 [𝑀𝑉 ]+[𝑀𝑉 ] 𝑦𝐸𝑉

DEB prediction: ultimate

size does not depend on temperature

Lei de Bergmann: numa espécie que tenha uma distribuição que se extenda ao longo de diferentes latitudes as espécies com maior tamanho e mais pesadas estão junto dos polos

Lei de Bergmann (1847)

How can we explain this rule using DEB theory?

Ornitorrinco na Austrália

DEB prediction: ultimate

size does not depend on temperature

Lei de Bergmann: numa espécie que tenha uma distribuição que se extenda ao longo de diferentes latitudes as espécies com maior tamanho e mais pesadas estão junto dos polos

Lei de Bergmann (1847)

How can we explain this rule using DEB theory? At lower temperatures they have a higher ultimate size because

they have more food (higher reserve density) Closer to the poles you have stronger seasons. The bleak season

thins populations, so reduces intra-specific competition, so more food per individual. More food means higher m_E.

Ornitorrinco na Austrália

What is the effect of temperature on dL/dt?

How do the von Bertallanfy growth rate and ultimate length depend on temperature?

How do growth and catabolic powers depend on temperature?

Metabolic rates: the effect of temperature

𝑑𝐿𝑑𝑡

= 13

𝑘𝑚𝐸 �̇� [𝑀𝑉 ]− [ �̇� 𝐸𝑀 ]𝐿− { �̇�𝐸𝑇 }𝑘𝑚𝐸 [𝑀𝑉 ]+[𝑀𝑉 ] 𝑦𝐸𝑉

What is the effect of temperature on dL/dt?

How do the von Bertallanfy growth rate and ultimate length depend on temperature?

How do growth and catabolic powers depend on temperature?

Metabolic rates: the effect of temperature

𝑑𝐿𝑑𝑡

= 13

𝑘𝑚𝐸 �̇� [𝑀𝑉 ]− [ �̇� 𝐸𝑀 ]𝐿− { �̇�𝐸𝑇 }𝑘𝑚𝐸 [𝑀𝑉 ]+[𝑀𝑉 ] 𝑦𝐸𝑉

�̇�𝐶= �̇�𝐸𝐶𝜇𝐸=𝐸( �̇�𝐿 − �̇�)�̇�𝐺= �̇� 𝐸𝐺𝜇𝐸=[𝐸𝐺 ] 𝑑𝑉𝑑𝑡

Metabolic rates: the effect of temperature

All metabolic rates depend on temperature on the same way because otherwise it would be difficult for organisms to cope with changes in temperature (evolutionary principle)

Endotherms: mantain their body temperature

Most mammals mantain their body mperature at 36ºC - 40ºC

Most birds mantain their body temperature at 40-43ºC

How?

Ectotherms: have a variable temperature mostly dictated by environmental conditions Any regulation?

Expected differences in metabolism?

Metabolic rates: the effect of temperature

Obtain an expression for the dynamics of the

reserve density mE

Set dmE/dt=0 (weak homeostasis). What is the maximum value of mE?

Can you understand the meaning? What is the value for mE in weak homeostasis?

Exercises

- maximum reserve density

EAmEE

V

f x Jdm vm

dt L v M

E Emm f x m

Obtain an expression for the dynamics of the

reserve density mE

Set dmE/dt=0 (weak homeostasis). What is the maximum value of mE?

Can you understand the meaning? Rewrite using mEm.

Exercises

- maximum reserve density

EAmEE

V

f x Jdm vm

dt L v M

Obtain an expression for the dynamics of the

reserve density mE

Set dmE/dt=0 (weak homeostasis). What is the maximum value of mE?

Can you understand the meaning? Rewrite using mEm. What is the meaning of ?

Exercises

- maximum reserve density

E EAm

T

Em Em

m JL L

m J

EAmEE

V

f x Jdm vm

dt L v M

EAm

Em

J

J

Obtain an expression for the dynamics of the

reserve density mE

Set dmE/dt=0 (weak homeostasis). What is the maximum value of mE?

Can you understand the meaning? Rewrite using mEm. What is the meaning of ?

Exercises

- maximum reserve density

E EAm

T

Em Em

m JL L

m J

EAmEE

V

f x Jdm vm

dt L v M

- maximum length- maximum reserve density

Metabolic rates: the effect of temperature

Metabolic rates: the effect of temperature