The application of DEB theory to fish energetics Bas Kooijman Dept theoretical biology Vrije Universiteit Amsterdam Sète, 2005/01/12

Contents DEB theory introduction Allocation & growth Body parts Scaling Schooling Sète, 2005/01/12

Dynamic Energy Budget theory for metabolic organisation Uptake of substrates (nutrients, light, food) by organisms and their use (maintenance, growth, development, reproduction) First principles, quantitative, axiomatic set up Aim: Biological equivalent of Theoretical Physics Primary target: the individual with consequences for sub-organismal organization supra-organismal organization Relationships between levels of organisation Many popular empirical models are special cases of DEB

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 Individuals are special because of straightforward energy/mass balances 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

These gouramis are from the same nest, they have the same age and lived in the same tank Social interaction during feeding caused the huge size difference Age-based models for growth are bound to fail; growth depends on food intake : These gouramis are from the same nest, they have the same age and lived in the same tank Social interaction during feeding caused the huge size difference Age-based models for growth are bound to fail; growth depends on food intake Not age, but size: Trichopsis vittatus

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 & mass 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

Biomass: reserve(s) + structure(s) Reserve(s), structure(s): generalized compounds, mixtures of proteins, lipids, carbohydrates: fixed composition Compounds in reserve(s): equal turnover times, no maintenance costs structure: unequal turnover times, maintenance costs Reasons to delineate reserve, distinct from structure metabolic memory explanation of respiration patterns (freshly laid eggs don’t respire) biomass composition depends on growth rate fluxes are linear sums of assimilation, dissipation and growth basis of method of indirect calorimetry explanation of inter-species body size scaling relationships

1-  maturity maintenance maturity offspring maturation reproduction Basic DEB scheme foodfaeces assimilation reserve feeding defecation structure somatic maintenance growth 

 -rule for allocation Age, d Length, mm Cum # of young Length, mm Ingestion rate, 10 5 cells/h O 2 consumption,  g/h 80% of adult budget to reproduction in daphnids 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

Embryonic development time, d weight, g O 2 consumption, ml/h ;  : scaled time l : scaled length e: scaled reserve density g: energy investment ratio Carettochelys insculpta Data from Web et al 1986 yolk embryo

Embryonic development time, d weight, g Salmo trutta Data from Gray 1926 yolk embryo

Growth at constant food time, dultimate length, mm length, mm time Length L. at birth ultimate L. von Bert growth rate energy conductance maint. rate coefficient shape coefficient Von Bert growth rate -1, d Von Bertalanffy growth curve:

Von Bertalanffy growth Length, mm Age, d Arrhenius Data from Greve, 1972

1-  1-  u Competitive tumour growth foodfaeces assimilation reserve feeding defecation structure somatic maintenance growth maturity maintenance maturity offspring maturation reproduction tumour  uu Allocation to tumour  relative maint workload Isomorphy: is constant Tumour tissue: low spec growth costs low spec maint costs Van Leeuwen et al., 2003 The embedded tumour: host physiology is important for the evaluation of tumour growth. British J Cancer 89, maint

Competitive organ growth Allocation to velum vs gut  relative workload Macoma high food Macoma low food Collaboration: Katja Philipart (NIOZ) fraction of catabolic flux

Change in body shape Isomorph: surface area  volume 2/3 volumetric length = volume 1/3 V0-morph: surface area  volume 0 V1-morph: surface area  volume 1 Ceratium Mucor Merismopedia

Mixtures of V0 & V1 morphs 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

Reproduction Definition: Conversion of adult reserve(s) into embryonic reserve(s) Energy to fuel conversion is extracted from reserve(s) Implies: products associated with reproduction (e.g. CO 2, NH 3 ) Allocation to reproduction in adults: Allocation per time increment is infinitesimally small We therefore need a buffer with buffer-handling rules for egg prod (no buffer required in case of placental mode) Strong homeostasis: Fixed conversion efficiency Weak homeostasis: Reserve density at birth equals that of mother Reproduction rate: follows from maintenance + growth costs, given amounts of structure and reserve at birth

Reproduction at constant food length, mm 10 3 eggs Gobius paganellus Data Miller, 1961 Rana esculenta Data Günther, 1990

Application to flatfish name (english)plaiceflounderdabsole name (latin)Pleuronectes platessa Platichthys flesusLimanda limandaSolea solea habitatcoldwarm, euryhalinecoldwarm max life span (a) max length (cm) max weight (kg) reprod/ body wght length at pub m,f (cm) 15,2211,1310, Arrhenius temp (K) 5878, , , , 9708 partitioning fraction  {p Xm } (W m -2, 283 K) E 0 (J/egg) {p Am }/{p Xm } = 0.2 [p M ] = 225 W m -3 [E G ] = 7 kJ cm -3 [Em]  2.5 kJ cm -3

Inter-species body size scaling parameter values tend to co-vary across species parameters are either intensive or extensive ratios of extensive parameters are intensive maximum body 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:

Body weight Body weight has contribution from structure and reserve If reserves allocated to reproduction hardly contribute: intra-spec body weight inter-spec body weight intra-spec structural volume Inter-spec structural volume reserve energy compound length-parameter specific density for structure molecular weight for reserve chemical potential of reserve maximum reserve energy density

Usually quantified in three different ways consumption of dioxygen production of carbon dioxide dissipation of heat DEB theory: These fluxes are weighted sums of assimilation maintenance growth Weight coefficients might differ Not constant, depends on size & feeding conditions Metabolic rate

Scaling of metabolic rate comparisonintra-speciesinter-species maintenance growth Respiration: contributions from growth and maintenance Weight: contributions from structure and reserve Structure ; = length; endotherms

Metabolic rate Log weight, g Log metabolic rate, w endotherms ectotherms unicellulars slope = 1 slope = 2/3 Length, cm O 2 consumption,  l/h Inter-species Intra-species L L L curves fitted: (Daphnia pulex)

Von Bertalanffy growth rate

Length at puberty L , cm L p, cm  Clupea Brevoortia ° Sprattus  Sardinops Sardina  Sardinella + Engraulis * Centengraulis  Stolephorus Data from Blaxter & Hunter 1982 Clupoid fishes Length at first reproduction L p  ultimate length L 

Spatial structure: schooling Isomorphic schools: Number of feeding individuals  N 2/3 Feeding rate per individual  N -1/3 Population models require rules for birth and death of schools; shools are just “super individuals” Scomber scombrus

DEB tele-course 2005 Feb – April 2005, 10 weeks, 200 h no financial costs Download slides of Sète lecture by Bas Kooijman Vacancies at Dept Theor Biol VUA EU-projects Modelkey (1PhD+1PD), Nomiracle (1PhD) see