DEB-based body mass spectra Bas Kooijman Dept theoretical biology Vrije Universiteit Amsterdam Bas@bio.vu.nl http://www.bio.vu.nl/thb/ Marseille, 2007/01/17

Body mass spectrum Derive it from:

Primary scaling relationships assimilation {JEAm} max surface-specific assim rate  Lm feeding {b} surface- specific searching rate digestion yEX yield of reserve on food growth yVE yield of structure on reserve mobilization v energy conductance heating,osmosis {JET} surface-specific somatic maint. costs turnover,activity [JEM] volume-specific somatic maint. costs regulation,defence kJ maturity maintenance rate coefficient allocation  partitioning fraction egg formation R reproduction efficiency life cycle [MHb] volume-specific maturity at birth life cycle [MHp] volume-specific maturity at puberty aging ha aging acceleration Kooijman 1986 J. Theor. Biol. 121: 269-282 maximum length Lm =  {JEAm} / [JEM]

Metabolic rate 8.2.2 2 curves fitted: Intra-species Inter-species slope = 1 Log metabolic rate, w O2 consumption, l/h 2 curves fitted: endotherms 0.0226 L2 + 0.0185 L3 0.0516 L2.44 ectotherms slope = 2/3 unicellulars Log weight, g Length, cm Intra-species Inter-species (Daphnia pulex)

poikilothermic tetrapods Feeding rate 8.2.2 slope = 1 Filtration rate, l/h Mytilus edulis Data: Winter 1973 poikilothermic tetrapods Data: Farlow 1976 Length, cm Inter-species: JXm  V Intra-species: JXm  V2/3

Intra -  Inter-specific scaling feeding L2 L3 reproduction L2.5 L-1

Spectrum definition individuals follow standard DEB model in homogeneous environment kM = kJ; no reproduction buffer max lengths represent random trials from exponential distribution individuals eat other individuals in length-range linked to own length background mortality has constant hazard rate individuals with length below threshold feed on producers (constant) individuals with length below threshold feed on producers+consumers with a linear preference shift between the two thresholds

Spectrum determination

Parameters of spectrum {bP} spec searching for producers {bX} spec searching for consumers lb relative length at birth lp relative length at puberty [MV] mass-volume coupling MP mass of producer yEX yield of reserve on consumer yEP yield of reserve on producer yVE yield of structure on reserve  fraction to growth + som maint R fraction to embryo v energy conductance kM som maintenance rate coefficient P producer density Lma mean maximum length k number of species hb background mortality ll min relative prey length lu max relative prey length

Trials from exponential distribution Suppose that mean = 1, else multiply result by mean Expected value of the i-th ordered trial from a sample of size k

Canonical community 9.4 Short time scale: Long time scale: Mass recycling in a community closed for mass open for energy Long time scale: Nutrients leaks and influxes Memory is controlled by life span (links to body size) Spatial coherence is controlled by transport (links to body size)