Lecture 4

Covariation of parameter values

Scales of life 8a

Life span

10log aVolume

10log m3earth

whale

bacterium

water molecule

life on earth

whale

bacteriumATP molecule

30

20

10

0

-10

-20

-30

Bergmann 1847

Dwarfing in Platyrrhini 8.1.2

Perelman et al 2011 Plos Genetics 7, 3, e1001342

24

.82

0.2

MYA

CallitrixCallitrix

CebuellaCebuella

MicoMicoLeontopithecusLeontopithecus

AotusAotus

SaimiriSaimiri

CebusCebus

780-1250 g

400-450 g480-700 g

400-535 g

3500 g

700-1000 g

200-400 g

130 g

180 g

CallimicoCallimico

SaguinusSaguinus

Ceb

idae

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

]/[}{ MAm ppL

}{ Ap

][ Mp

mA Lp }{

Kooijman 1986 Energy budgets can explain body size scaling relationsJ. Theor. Biol. 121: 269-282

Primary parametersstandard DEB model

Body weight

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

Scaling of metabolic rate

intra-species inter-species

maintenance

growth

weight

nrespiratio3

32

dl

llls

43

32

ldld

lll

EV

h

structure

reserve

32 vll

l0l

0

3lllh

Respiration: contributions from growth and maintenanceWeight: contributions from structure and reserveStructure ; = length; endotherms 3l l

3lllh

0hl

Metabolic rate

Log weight, g

Log metabolic rate,

w

endotherms

ectotherms

unicellulars

slope = 1

slope = 2/3

Length, cm

O2 consum

ption,

l/h

Inter-speciesIntra-species

0.0226 L2 + 0.0185 L3

0.0516 L2.44

2 curves fitted:

(Daphnia pulex)

Follows from:1. maturity at birth equals a given value2. 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 res density at birth

scaled res density at birth

scal

ed le

ngth

at b

irth

scal

ed in

itial

res

erve

scal

ed a

ge a

t birt

h

Reduction of initial reserve

1

0.8

0.5scaled age

scaled age

scaled age

scal

ed m

atur

itysc

aled

str

uct v

olum

e

scal

ed r

eser

ve

Scaling relationships

log zoom factor, z

log zoom factor, z

log zoom factor, z

log

scal

ed in

itial

res

erve

log

scal

ed a

ge a

t birt

h

log

scal

ed le

ngth

at b

irth 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

10log egg weight, g 10log egg weight, g

10lo

g in

cuba

tion

time,

d

10lo

g in

cuba

tion

time,

d

lb equal° tube noses

slope = 0.25

Data from Harrison 1975

European birdstube noses

Gestation time 8.2.2l

10log adult weight, g

10lo

g ge

stat

ion

time,

d

Data from Millar 1981

Mammals* Insectivora+ Primates Edentata Lagomorpha Rodentia Carnivora Proboscidea Hyracoidea Perissodactyla Artiodactyla

slope = 0.33

mL

396.0

weightbirth

weightadult timegestationactualtimegestation

3/1

Kooijman 1986J Theor Biol 121: 269-282

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 Lp ultimate length L

Feeding rateslope = 1

poikilothermic tetrapodsData: Farlow 1976

Mytilus edulisData: Winter 1973

Length, cm

Filt

ratio

n ra

te, l

/h

At 25 °C : maint rate coeff kM = 400 a-1

energy conductance v = 0.3 m a-1

25 °CTA = 7 kK

10log ultimate length, mm 10log ultimate length, mm

10lo

g vo

n B

ert

grow

th r

ate

, a-1

a↑0

Von Bertalanffy growth rate

Reproduction rate

Costs for movement 8.2.2m

slope = -1/3slope = -1/3

Walking costs:5.39 ml O2 cm-2 km-1

Swimming costs:0.65 ml O2 cm-2 km-1

Movement costs per distance V2/3

Investment in movement V included in somatic maintenanceHome range V1/3

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 8.2.3

feeding rate Vfood production constant

Abundance V-1

Data: Peters, 1983

Kooijman 1986J Theor Biol

121: 269-282

DEB tele course 2013http://www.bio.vu.nl/thb/deb/

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 http://www.bio.vu.nl/thb/users/bas/lectures/

Cambridge Univ Press 2009

Audience: thank you for your attention