1. Dynamic Energy Budget Theory - V Tânia Sousa with contributions from :Bas Kooijman with contributions from :Bas Kooijman

2.  ln rate 10 4 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 reproduction young/d ingestion 10 6 cells/h growth, d -1 aging, d -1  Arrhenius relationship:

3.   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., the black bears spend the winter months in a state of hibernation. Their body temperatures drop, theirmetabolic rate is reduced, and they sleep for long periods.  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

4.   All parameters that have units time -1 depend on temperature Metabolic rates: the effect of temperature  Exercise: do all metabolic rates depend on temperature on the same way?  Yes, because otherwise it would be difficult for organisms to cope with changes in temperature (evolutionary principle)

5.   What is the effect of temperature on dL/dt?  How does the von Bertallanfy growth rate depends on temperature?  Does ultimate length depends on temperature? Metabolic rates: the effect of temperature

6.  Von Bertalanffy growth: the effect of temperature  The von Bertallanffy growth rate increases with temperature  The ultimate length does not change with temperature Length, mm Age, d Arrhenius

7.   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 a higher temperature the organism has a higher maximum ingestion rate which means that to the same absolute amount of food in the environment corresponds a lower f(x)  Ultimate size is proportional to m E (which is equal to f(X)) implying that for the same absolute amounts of food the organism reaches a smaller ultimate length in higher temperatures  Ornitorrinco na Austrália

8.   Two aspects of shape are relevant for energetics: surface areas (acquisition processes) and volume (maintenance processes)  Shape defines how these measures relate to each other  An individual that does not change in shape during growth is na isomorph, e.g., surface area is proportional to volume 2/3  Prove that in an isomorph: Energetics: the importance of shape

9.   Isomorph: surface area proportional to volume 2  V0-morph: surface area proportional to volume 0  the dinoflagelate Ceratium with a rigid cell wall  V1-morph: surface area proportional to volume 1  The cyanobacterial colony Merismopedia Change in body shape Chorthippus biguttulus Psammechinus miliaris

10.   To judge weather or not an organism is isomorphic, we need to compare shapes at different sizes. All shapes can grow isomorphically  Are these organisms isomorphic?  Sphere with an increasing diameter:  Rectangle with constant width and high and an increasing length: Energetics: the importance of shape

11.  Shape correction function

12.  Measurements vs. DEB variables

13.  Scales of life: the importance of size Life span 10 log a Volume 10 log m 3 earth whale bacterium water molecule life on earth whale bacterium ATP molecule 30 20 10 0 -10 -20 -30

14.  Scales of life: the importance of size  Specific oxygen consumption decreases with body weigth in mammals  Life-span increases with weigth in mammals

15.  Scaling Relations I  Empirical support: Cells are very similar independent of size of the organism

16.  Scaling Relations II

17.  Inter vs. Intra species comparisons

18.  Primary parameters standard DEB model Kooijman 1986 J. Theor. Biol. 121: 269-282