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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