Lecture 4 Covariation of parameter values

Scales of life 8a Life span 10 log a Volume 10 log m 3 earth whale bacterium water molecule life on earth whale bacterium ATP molecule

Bergmann 1847

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

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 : 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:

Primary parameters standard DEB model

Body weight Body weight has contributions from structure and reserve If reserve allocated to reproduction hardly contributes:

Scaling of metabolic rate intra-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)

Follows from: 1.maturity at birth equals a given value 2.reserve density at birth equals that of mother State variables: Parameters: Problem: Given parameter values, find Initial reserve of an egg Theory in Kooy2008

Effects of nutrition scaled res density at birth scaled length at birth scaled initial reserve scaled age at birth

Reduction of initial reserve scaled age scaled maturity scaled struct volume scaled reserve

Scaling relationships log zoom factor, z log scaled initial reserve log scaled age at birth log scaled length at birth approximate slope at large zoom factor

Incubation time: intra-species Eudyptes first lays a small egg, then a large one, which hatches earlier if fertile It can rise one chick only If all parameters are the same, maturity at birth is reached earlier with big initial reserve

Incubation time: inter-species 10 log egg weight, g 10 log incubation time, d l b equal ° tube noses slope = 0.25 Data from Harrison 1975 European birds tube noses

Gestation time 8.2.2l 10 log adult weight, g 10 log gestation time, d Data from Millar 1981 Mammals * Insectivora + Primates  Edentata  Lagomorpha  Rodentia  Carnivora  Proboscidea Hyracoidea  Perissodactyla  Artiodactyla slope = 0.33 Kooijman 1986 J Theor Biol 121:

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 

Feeding rate slope = 1 poikilothermic tetrapods Data: Farlow 1976 Mytilus edulis Data: Winter 1973 Length, cm Filtration rate, l/h

At 25 °C : maint rate coeff k M = 400 a -1 energy conductance v = 0.3 m a °C T A = 7 kK 10 log ultimate length, mm 10 log von Bert growth rate, a -1 ↑ 0 Von Bertalanffy growth rate

Reproduction rate

Costs for movement 8.2.2m slope = -1/3 Walking costs: 5.39 ml O 2 cm -2 km -1 Swimming costs: 0.65 ml O 2 cm -2 km -1 Movement costs per distance  V 2/3 Investment in movement  V included in somatic maintenance Home range  V 1/3 Data: Fedak & Seeherman, 1979 Data: Beamish, 1978

Ageing among species 8.2.2n Conclusion for life span hardly depends on max body size of ectotherms increases with length in endotherms slope 1/3, 1/5 Right whale Ricklefs & Finch 1995

Abundance feeding rate  V food production constant  Abundance  V -1 Data: Peters, 1983 Kooijman 1986 J Theor Biol 121:

DEB tele course Free of financial costs; Some 108 or 216 h effort investment Program for 2013: Feb/Mar general theory (5w) April symposium at NIOZ-Texel (NL) (8d +3 d) Target audience: PhD students We encourage participation in groups who organize local meetings weekly Software package DEBtool for Octave/ Matlab freely downloadable Slides of this presentation are downloadable from Cambridge Univ Press 2009 Audience : thank you for your attention