Dynamische Energie Budget theorie Bas Kooijman Afd Theoretische Biologie Vrije Universiteit Amsterdam Amsterdam, 2009/12/13

My field trips (days till weeks per trip)

Isomorphic growth 4.2.3a diameter,  m Weight 1/3, g 1/3 length, mm time, h time, d Amoeba proteus Prescott 1957 Saccharomyces carlsbergensis Berg & Ljunggren 1922 Pleurobrachia pileus Greve 1971 Toxostoma recurvirostre Ricklefs 1968 Weight 1/3, g 1/3

Mixtures of V0 & V1 morphs 4.2.3a volume,  m 3 hyphal length, mm time, h time, min Fusarium  = 0 Trinci 1990 Bacillus  = 0.2 Collins & Richmond 1962 Escherichia  = 0.28 Kubitschek 1990 Streptococcus  = 0.6 Mitchison 1961

Embryonic development 2.6.2d time, d weight, g O 2 consumption, ml/h Crocodylus johnstoni, Data from Whitehead 1987 yolk embryo

 -rule for allocation 2.4 Age, d Length, mm Cum # of young Length, mm Ingestion rate, 10 5 cells/h O 2 consumption,  g/h large part of adult budget is allocated to reproduction in Daphnia magna puberty at 2.5 mm no change in ingest., resp., or growth where do resources for reprod. come from? Or: what is fate of resources in juveniles? Respiration  Ingestion  Reproduction  Growth: Von Bertalanffy

Aging: endotherms & feeding 6.1l time, d survival probability embryo weight, g body weight, g Mus musculus data: Weindruch et al 1986, MacDowell et al 1927 feeding level Life span hardly depends on food in ecotherms decreases for increasing food in endotherms Van Leeuwen et al 2002 Biogerontology 3:

Product Formation throughput rate, h -1 glycerol, ethanol, g/l pyruvate, mg/l glycerol ethanol pyruvate Glucose-limited growth of Saccharomyces Data from Schatzmann, 1975 According to Dynamic Energy Budget theory: Product formation rate = w A. Assimilation rate + w M. Maintenance rate + w G. Growth rate For pyruvate: w G <0

Symbiosis 10.4m product substrate

Symbiosis 10.4n substrate

Internalization Structures merge Reserves merge Free-living, clustering Free-living, homogeneous Steps in symbiogenesis 10.4o

Evolution of DEB systems 10.3 variable structure composition strong homeostasis for structure delay of use of internal substrates increase of maintenance costs internalisation of maintenance as demand process installation of maturation program strong homeostasis for reserve reproduction juvenile  embryo + adult Kooijman & Troost 2007 Biol Rev, 82, specialization of structure 7 8 animals 6 prokaryotes 9 plants

Some DEB pillars life cycle perspective of individual as primary target embryo, juvenile, adult (levels in metabolic organization) life as coupled chemical transformations (reserve & structure) time, energy, entropy, mass & isotope balances surface area/ volume relationships (spatial structure & transport) homeostasis (stoichiometric constraints via Synthesizing Units) syntrophy (basis for symbioses, evolutionary perspective) intensive/extensive parameters: body size scaling

molecule cell individual population ecosystem system earth time space Space-time scales When changing the space-time scale, new processes will become important other will become less important This can be used to simplify models, by coupling space-time scales Complex models are required for small time and big space scales and vv Models with many variables & parameters hardly contribute to insight Each process has its characteristic domain of space-time scales

Empirical special cases of DEB yearauthormodelyearauthormodel 1780Lavoisier multiple regression of heat against mineral fluxes 1950Emerson cube root growth of bacterial colonies 1825Gompertz Survival probability for aging 1951Huggett & Widdas foetal growth 1889Arrhenius temperature dependence of physiological rates 1951Weibull survival probability for aging 1891Huxley allometric growth of body parts 1955Best diffusion limitation of uptake 1902Henri Michaelis--Menten kinetics 1957Smith embryonic respiration 1905Blackman bilinear functional response 1959Leudeking & Piret microbial product formation 1910Hill Cooperative binding 1959Holling hyperbolic functional response 1920Pütter von Bertalanffy growth of individuals 1962Marr & Pirt maintenance in yields of biomass 1927Pearl logistic population growth 1973Droop reserve (cell quota) dynamics 1928Fisher & Tippitt Weibull aging 1974Rahn & Ar water loss in bird eggs 1932Kleiber respiration scales with body weight 3/ Hungate digestion 1932Mayneord cube root growth of tumours 1977Beer & Anderson development of salmonid embryos DEB theory is axiomatic, based on mechanisms not meant to glue empirical models Since many empirical models turn out to be special cases of DEB theory the data behind these models support DEB theory This makes DEB theory very well tested against data Kooijman Cambridge Univ Press