Dina Lika Dept of Biology TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAA Covariation of parameter values UNIVERSITY OF CRETE Texel, 15/4/2013

Contents Scales of life in space & time Primary vs compound parameters Covariation of parameter values –Intensive & extensive parameters –Primary and secondary scaling relationships What parameters can be estimated from what data?

Scales of life Life span 10 log a Volume 10 log m 3 earth whale bacterium water molecule life on earth whale bacterium ATP molecule

Dwarfing in Platyrrhini Perelman et al 2011 Plos Genetics 7, 3, e MYA Callitrix Cebuella Mico Leontopithecus Aotus Saimiri Cebus g g g g 3500 g g g 130 g 180 g Callimico Saguinus Cebidae

Primary vs Compound parameters Primary parameters –Connected to a single underlying process Compound parameters –Depend on several underlying processes

Primary DEB parameters time-length-energy time-length-mass The two frames are related to each other via Chemical potential of reserves: Conversion coefficient: Temperature: T= K Arrhenius temperature: T A =8 kK Max length:

Compound parameters

Covariation of parameter values Primary scaling relationships –Covariation of primary parameters Secondary scaling relationships –Covariation of compound parameters Tertiary scaling relationships –Deal with phenomena at larger scales in time and space

Covariation of primary parameter Intensive parameters –Depend on local (bio)chemical environment –Relate to molecular processes –Size independent –Density-based Extensive parameters –Relate to the physical design –Size dependent

Primary scaling relationships assimilation {p Am } max surface-specific assim rate  L m feeding {F m } surface- specific searching rate digestion κ X digestion efficiency mobilisation venergy conductance allocation  allocation fraction to soma reproduction  R reproduction efficiency turnover,activity [p M ] volume-specific somatic maint. costs heating,osmosis {p T } surface-specific somatic maint. costs development k J maturity maintenance rate coefficient Growth[E G ] specific growth for structure life cycleE H b maturity at birth  L m 3 life cycle E H p maturity at puberty  L m 3 aging h a Weibul aging acceleration  L m agings G Gompertz stress coefficient maximum length L m =  {p Am } / [p M ] Kooijman 1986 J. Theor. Biol. 121:

Inter-species zoom factor

Secondary scaling relationships The reserve capacity The energy investment ratio Somatic maintenance rate coefficient

25 °C T A = 7 kK 10 log ultimate length, mm 10 log von Bert growth rate, a -1 ↑ ↑ 0 Von Bertalanffy growth rate

Feeding rate slope = 1 poikilothermic tetrapods Data: Farlow 1976 Inter-species: J Xm  L 3 Intra-species: J Xm  L 2 Mytilus edulis Data: Winter 1973 Length, cm Filtration rate, l/h

Body weight Body weight has contribution from structure and reserve if reproduction buffer is excluded

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

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) Data: Hemmingson 1969; curve fitted from DEB theoryData: Richman 1958; curve fitted from DEB theory

One-sample case

Two-sample case: D. magna 20°C

measured quantities  primary pars Standard DEB model (isomorph, 1 reserve, 1 structure) reserve & maturity: hidden variables measured for 2 food levels primary parameters

DEBtool/animal/get_pars Functions get_pars_* obtain compound DEB parameters from easy-to-observe quantities get_pars_* Functions iget_pars_* do the reverse, which can be used for checking. iget_pars_* The routines are organized as follows: get_pars iget_pars food level one several one several Constraint kJ = kM kJ != kM kJ = kM kJ = kM kJ != kM kJ = kM growth get_pars_g get_pars_h get_pars_i iget_pars_g iget_pars_h iget_pars_iget_pars_gget_pars_hget_pars_iiget_pars_giget_pars_higet_pars_i growth & reprod get_pars_r get_pars_s get_pars_t iget_pars_r iget_pars_s iget_pars_tget_pars_rget_pars_sget_pars_tiget_pars_riget_pars_siget_pars_t Functions for several food levels do not use age at birth data. If one food level is available, we have to make use of the assumption of stage transitions at fixed amounts of structure ( kM = kJ ). If several food levels are available, we no longer need to make this assumption, but it does simplify matters considerably. Functions elas_pars_g and elas_pars_r give elasticity coefficients. elas_pars_g elas_pars_r Function get_pars_u converts compound parameters get_pars_u into unscaled primary parameters at abundant food. Kooijman at al 2008 Biol Rev 83:

DEBtool/animal/get_pars g get_pars_  iget_pars_  r s h u s h r g red quantities depend on food level, green do not Kooijman at al 2008 Biol Rev 83:

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