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?


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


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

ln r

ate

104 T-1, K-1

Daphnia magna

reproductionyoung/d


growth, d-1

aging, d-1


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

ctek T cte

T

ln r

ate

104 T-1, K-1

Daphnia magna

reproductionyoung/d


growth, d-1

aging, d-1


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


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


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?


How do feeding depends on temperature?

What is the implication for ?


11

( ) exp{ }A AT Tk T k

T T

=

All parameters that have units time-1 depend on 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


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?


𝑑𝐿𝑑𝑡

= 13

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


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


𝑑𝐿𝑑𝑡

= 13


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



How do growth and catabolic powers depend on temperature?


𝑑𝐿𝑑𝑡

= 13




How do growth and catabolic powers depend on temperature?


𝑑𝐿𝑑𝑡

= 13


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


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?


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


reserve density mE


Can you understand the meaning? Rewrite using mEm.

Exercises


EAmEE

V

f x Jdm vm

dt L v M


reserve density mE


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

Exercises


E EAm

T

Em Em

m JL L

m J

EAmEE

V

f x Jdm vm

dt L v M

EAm

Em

J

J


reserve density mE


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

Exercises


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

dynamic energy budget theory - i tânia sousa with contributions from :bas kooijman

Documents

temperature metabolic

effect of temperature

arrhenius temperature

temperature lei

temperature range slide

variable temperature

metabolic rates ln

temperature tolerance