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Dynamische Energie Budget theorie Bas Kooijman Afd Theoretische Biologie Vrije Universiteit Amsterdam [email protected] http://www.bio.vu.nl/thb/ Amsterdam, 2009/12/13 My field trips (days till weeks per trip) Weight1/3, g1/3 diameter, m Isomorphic growth 4.2.3a Amoeba proteus Prescott 1957 Saccharomyces carlsbergensis Berg & Ljunggren 1922 time, h Weight1/3, g1/3 length, mm time, h Toxostoma recurvirostre Ricklefs 1968 Pleurobrachia pileus Greve 1971 time, d time, d volume, m3 4.2.3a Bacillus = 0.2 Collins & Richmond 1962 time, min Fusarium = 0 Trinci 1990 time, h volume, m3 volume, m3 hyphal length, mm Mixtures of V0 & V1 morphs Escherichia = 0.28 Kubitschek 1990 time, min Streptococcus = 0.6 Mitchison 1961 time, min Crocodylus johnstoni, Data from Whitehead 1987 weight, g embryo yolk O2 consumption, ml/h Embryonic development 2.6.2d time, d time, d -rule for allocation 2.4 vL2 kM L3 Length, mm • 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 Age, d in juveniles? vL2 kM L3 (1 g / f )kM L3p Length, mm Cum # of young Reproduction Ingestion rate, 105 cells/h O2 consumption, g/h Respiration Ingestion fL2 Length, mm Growth: d L rB ( L L) dt Von Bertalanffy Age, d Aging: endotherms & feeding embryo weight, g body weight, g 6.1l feeding level 1 0.75 0.44 survival probability time, d time, d 0.44 0.75 time, d 1 Van Leeuwen et al 2002 Biogerontology 3: 373-381 Life span • hardly depends on food in ecotherms • decreases for increasing food in endotherms Mus musculus data: Weindruch et al 1986, MacDowell et al 1927 Product Formation 4.9.1 pyruvate, mg/l According to Dynamic Energy Budget theory: Product formation rate = wA . Assimilation rate + wM . Maintenance rate + wG . Growth rate For pyruvate: wG<0 throughput rate, h-1 Glucose-limited growth of Saccharomyces Data from Schatzmann, 1975 Symbiosis 10.4m substrate product Symbiosis 10.4n substrate substrate Steps in symbiogenesis 10.4o Free-living, homogeneous Structures merge Free-living, clustering Internalization Reserves merge Evolution of DEB systems 10.3 1 strong homeostasis for structure 2 delay of use of internal substrates 3 internalisation of maintenance as demand process increase of maintenance costs 4 5 7 Kooijman & Troost 2007 Biol Rev, 82, 1-30 reproduction juvenile embryo + adult animals 8 strong homeostasis for reserve installation of maturation program prokaryotes variable structure composition 6 plants 9 specialization of structure 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 Space-time scales space Each process has its characteristic domain of space-time scales system earth ecosystem population individual cell molecule 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 time Empirical special cases of DEB year author model year author model 1780 Lavoisier multiple regression of heat against mineral fluxes 1950 Emerson cube root growth of bacterial colonies 1825 Gompertz 1891 Survival probability for aging DEB theory is axiomatic, 1951 Huggett & Widdas temperature dependence of Arrhenius 1951 Weibull based on mechanisms physiological rates allometric growth of body parts Huxleynot meant 1955 Best to glue empirical models 1902 Henri 1905 Blackman 1889 1910 1920 Michaelis--Menten kinetics 1957 foetal growth survival probability for aging diffusion limitation of uptake embryonic respiration Smith bilinear functional response 1959 Leudeking & Piret microbial product formation Since many empirical models Cooperative binding hyperbolic functional response Hill 1959 Holling turn out to be special cases of DEB theory von Bertalanffy growth of maintenance in yields of biomass Pütter 1962 Marr & Pirt individuals the data behind these models support DEB theory 1927 Pearl logistic population growth 1973 Droop reserve (cell quota) dynamics 1928 Fisher & Tippitt Weibull aging 1974 Rahn & Ar water loss in bird eggs 1932 Kleiber respiration scales with body weight3/ 4 1975 Hungate digestion 1932 Mayneord cube root growth of tumours 1977 Beer & Anderson development of salmonid embryos This makes DEB theory very well tested against data Kooijman 2010. Cambridge Univ Press