Dynamic Energy Budget Theory - V

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

2. TheArrheniusrelationshiphasgoodempiricalsupport TheArrheniustemperatureisgivenbyminustheslope: thehighertheArrheniustemperaturethe more sensitiveorganisms are to changes in temperature Metabolic rates: the effect of temperature • Arrhenius relationship: ln rate reproduction young/d Daphnia magna ingestion 106 cells/h growth, d-1 aging, d-1 104 T-1, K-1

3. Metabolic rates: temperature range • TheArrheniusrelationshipisvalid in thetemperaturetolerance range • Attemperatures too hightheorganismusuallydies • Attemperatures too lowthe rates are usuallylowerthanpredictedbytheArrheniusrelationship, e.g., theblack bears spend the winter months in a state of hibernation. Their body temperatures drop, theirmetabolic rate is reduced, and they sleep for long periods. • Manyextinctions are tought to berelatedwith 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.

4. All parameters that have units time-1 depend on temperature Exercise: do allmetabolic rates dependontemperatureonthesameway? Yes, becauseotherwiseitwouldbedifficult for organisms to cope withchanges in temperature (evolutionaryprinciple) Metabolic rates: the effect of temperature

5. Metabolic rates: the effect of temperature • WhatistheeffectoftemperatureondL/dt? • How does thevonBertallanfygrowth rate dependsontemperature? • Does ultimatelengthdependsontemperature?

6. ThevonBertallanffygrowth rate increaseswithtemperature Theultimatelength does notchangewithtemperature Von Bertalanffy growth: the effect of temperature Length, mm Arrhenius Age, d

7. DEB prediction: ultimate size does not depend on temperature Lei de Bergmann: numaespéciequetenhaumadistribuiçãoque se extendaaolongo de diferentes latitudes as espécies com maiortamanho e maispesadasestãojunto dos polos How can weexplainthis rule using DEB theory? At a highertemperaturetheorganismhas a highermaximumingestion rate whichmeansthat to thesameabsoluteamountoffood in theenvironmentcorresponds a lower f(x) Ultimatesizeisproportional to mE (whichisequal to f(X)) implyingthat for thesameabsoluteamountsoffoodtheorganismreaches a smallerultimatelength in highertemperatures Ornitorrinco na Austrália Lei de Bergmann (1847)

8. Energetics: the importance of shape • Twoaspectsofshape are relevant for energetics: surfaceareas (acquisition processes) and volume (maintenance processes) • Shape defines howthesemeasures relate to eachother • An individual that does notchange in shapeduringgrowthis na isomorph, e.g., surfaceareais proportional tovolume2/3 • Prove that in an isomorph:

9. Change in body shape • Isomorph: surfaceareaproportional tovolume2 • V0-morph: surfaceareaproportional to volume0 • the dinoflagelateCeratium with a rigid cell wall • V1-morph: surfaceareaproportional to volume1 • The cyanobacterial colony Merismopedia Chorthippus biguttulus Psammechinus miliaris

10. Energetics: the importance of shape • 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:

11. Shape correction function • In the DEB modelequationthe surfaceV2/3(theisomorphicsurfacearea) shouldbereplacedbythe real surfacearea = • Whereistheshapecorrectionfunction volume • Prove that for: • Isomorph: • V0-morph: where vdisthe volume atwhichthesurfaceareaisequal to thesurfaceareaofanisomorph • V1-morph:

12. Measurements vs. DEB variables • Physical length • whereisthevolumetriclengthandtheshapecoefficient • What are theshapecoefficientsof a spherewith a diameterofand a cube withlength? • Physical volume • Wetweight

13. Scales of life: the importance of size Life span 10log a 30 Volume 10log m3 earth 20 10 life on earth whale whale 0 bacterium ATP molecule -10 bacterium -20 water molecule -30

14. Scales of life: the importance of size • Specificoxygenconsumptiondecreaseswith body weigth in mammals • Life-spanincreaseswithweigth in mammals

15. Differences between species are reduced to differences between parameters values Scaling relationships: the parameter values tend to co-vary across species Constant Primary Parameters: There are parameters that are similar across (related) species because they characterize biochemical processes that are similar across species: Cells of equal size have similar growth, maintenance and maturation costs, i.e., are similar Energy partioning of energy mobilized from reserves is done at the level of somatic and reproductive cells, i.e., is similar Two individuals of different but related species with the same size and reserve density have similar metabolic needs, i.e., is similar Empirical support: Cells are very similar independent of size of the organism Scaling Relations I

16. Differences between species are reduced to differences between parameters values Scaling relationships: the parameter values tend to co-vary across species Design Primary Parameters: There are parameters that are similar across (related) species because they characterize biochemical processes that are similar across species: Cells of equal size have similar specific maturation thresholds, i.e., and are proportional to Lm3. How do the following parameters vary across related species? mEm Scaling Relations II - maximum length - maximum reserve density

17. Inter vs. Intraspeciescomparisons • Interspecies comparisons are done for: • Fullygrownorganism • Abundantfood f(X)=1 • Nullheatinglength LT=0 • Therelationshipbetweenmaximumsizesisthe zoom factor: • Differencesbetweenintraandterspeciescomparisons:

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