The scaling of metabolism in the perspective of DEB theory Bas Kooijman Dept theoretical biology VU University Amsterdam Bas.Kooijman@vu.nl http://www.bio.vu.nl/thb Krakow, 2015/08/27/11:45

Dynamic Energy Budget Start: Aug 1979 understanding effects of toxicants. Since then: 50 PhD’s Now: bibliography of 500 DEB papers: http://www.bio.vu.nl/thb/deb/ Dynamic: Full life cycle: embryo, juvenile, adult Energy: Feeding Digestion Storing Growth Maturation Maintenance Reproduction Product formation Aging Budget: Conservation: energy, mass, time, isotopes

Standard DEB scheme food faeces reserve structure  offspring 1 food type, 1 reserve, 1 structure, isomorph time: searching & handling feeding  surface area weak & strong homeostasis κ-rule for allocation to soma maintenance has priority somatic maint  structure maturity maint  maturity stage transition: maturation embryo: no feeding, reprod juvenile: no reproduction adult: no maturation maternal effect: reserve density at birth equals that of mother initially: zero structure, maturity egg = blob of reserve food faeces assimilation reserve feeding defecation structure somatic maintenance growth  1- maturity maintenance offspring maturation reproduction Assumptions of standard DEB model as member of DEB models One food type of constant composition and particle size that can be used to complete life cycle One reserve type One structure type Isomorphy only food is limiting, not e.g. dioxygen Extensions that are sometimes included in the standard DEB model foetal development (as alternative to egg development) ageing metabolic acceleration between birth and metamorphosis reproduction via reproduction buffer buffer handling rules

Add_my_pet www.bio.vu.nl/thb/deb/deblab/ started in Feb 2009 as exercise in DEB course (DEBtool application) referenced data, par-estimates, implied properties, Matlab code now 400 animal species most phyla, all chordate orders very good fits (typically: mean relative error < 0.2) Jan 2015 new set-up. Conversion completed by Dec 2015

Concepts  

Inter-species body size scaling parameter values tend to co-vary across species parameters are either intensive or extensive appropriate ratios of extensive parameters are intensive maximum structural length is allocation fraction to growth + maint. (intensive) volume-specific maintenance power (intensive) surface area-specific assimilation power (extensive) conclusion : (so are all extensive parameters) write physiological property as function of parameters (including maximum body weight) evaluate this property as function of max body weight Kooijman 1986 Energy budgets can explain body size scaling relations J. Theor. Biol. 121: 269-282

Scaling of respiration Respiration: contributions from growth and maintenance Weight: contributions from structure and reserve Kooijman 1986 J Theor Biol 121: 269-282

Metabolic rate 2 curves fitted: slope = 1 0.0226 L2 + 0.0185 L3 Log metabolic rate, w O2 consumption, l/h endotherms 0.0226 L2 + 0.0185 L3 0.0516 L2.44 slope = 2/3 ectotherms 20°C unicellulars Length, cm Log weight, g Intra-species Inter-species (Daphnia pulex) Data: Richman 1958; curve fitted from DEB theory Data: Hemmingson 1969; curve fitted from DEB theory

poikilothermic tetrapods Feeding rate slope = 1 Filtration rate, l/h Length, cm Intra-species: JXm  V2/3 Inter-species: JXm  V Mytilus edulis Data: Winter 1973 poikilothermic tetrapods Data: Farlow 1976

Specific O2 consumption slope = -1/4 20°C predicted max dry weight -- predicted specific O2 consumption

Thank you, organisors, for inviting me Thank you, audience, for your attention Any questions? DEB course 2015 had 124 participants → DEB course 2017 will be organized by Starrlight.Augustine@akvaplan.niva.no DEB newsletter: Laure.Pecquerie@ird.fr

Waste to hurry Exploiting blooming resources Kooijman 2013 Oikos 122: 348-357 Waste to hurry Exploiting blooming resources requires blooming yourself high numerical response short life cycle small body size fast reproduction fast growth high feeding rate resting stages between blooms -rule explains why [pM] needs to be high Ecosystem significance: flux through basis food pyramid Waste-to-hurry is the hypothesis that species increase somatic maintenance for the purpose of boosting growth and reproduction, such that max body size remains small. This strategy is possible because of the kappa-rule. Fast growth and reproduction is only possible if specific assimilation is large. If that would be the only difference a very large body size results, which comes with a long life cycle. Not fit for profiting from temporary resources.

No Effect Conc ↔ spec som maint Data sources NEC: EPA-data base survival data [pM]: add_my_pet energetics data Pesticides: NEC  [pM]-2 Baas & Kooijman 2015 Ecotoxicology, 24: 657-663 Metals: NEC  [pM]0 to be published

Supply-demand spectrum Lika et al 2014 J. Theor. Biol. 354:35-47 Supply-demand spectrum Species can be ranked in the gradient from supply to demand systems as stages in the evolution toward a high level of homeostasis. Extreme supply or demand systems don’t exist, all species represent a mixture of these extremes. Plants come close to the supply-end of the spectrum and can adapt their metabolism to the local environment relatively well. Demand systems adapt their metabolism much less and compensate that by a high level of behavioural flexibility. The characterizing property of demand systems is that the use of resources (growth, reproduction) is `pre-programmed’, which causes a particular need for food and growth curves that are given functions of age. metabolic control external metabolic control internal

Supply-demand spectrum 10.5.5 Lika et al 2014 J. Theor. Biol. 354:35-47 Supply-demand spectrum 10.5.5 The constraint R_m > 0 can be translated into the constraint kap^2 (1 – kap) < s_s, from which follows that s_s < 4/27. Moreover kap must be between the two positive roots of kap^2 (1 – kap) – s_s = 0. The metric s_d = 4/27 – s_s can be called “distance to puberty edge”, and has the interpretation of the distance to the demand-end of the supply-demand spectrum. Most species are supply species, only vertebrates classify as demand species. A more detailed study on the 5 fish classes shows that bony fish are supply species. The open symbols indicate acceleration.

Supply-demand spectrum Lika et al 2014 J. Theor. Biol. 354:35-47 Supply-demand spectrum The distance to the supply end of the supply-demand spectrum, s_s, is plotted against the minimum scaled functional response that is required to reach puberty, f_min. Contrary to s_s, f_min does depend on kappa. Only vertebrates populate the area under the curve s_s = f_min^3 4/27. Open symbols indicate acceleration. The value of kappa is indicated for birds (blue) and mammals (red) in the right picture. High kappa-values for birds are close the both axes (s_s = 0 and f_min – 1). High kappa-values for mammals are at low s_s and f_min. All evertebrates are in the lower-left corner of the picture.