lecture 4 covariation of parameter values. scales of life 8a life span 10 log a volume 10 log m 3...
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![Page 1: 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](https://reader035.vdocument.in/reader035/viewer/2022070415/56649d485503460f94a2359d/html5/thumbnails/1.jpg)
Lecture 4
Covariation of parameter values
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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
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Bergmann 1847
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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
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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
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Primary parametersstandard DEB model
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Body weight
Body weight has contributions from structure and reserveIf reserve allocated to reproduction hardly contributes:
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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
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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)
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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
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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
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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
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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
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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
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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
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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
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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
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Feeding rateslope = 1
poikilothermic tetrapodsData: Farlow 1976
Mytilus edulisData: Winter 1973
Length, cm
Filt
ratio
n ra
te, l
/h
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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
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Reproduction rate
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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
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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
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Abundance 8.2.3
feeding rate Vfood production constant
Abundance V-1
Data: Peters, 1983
Kooijman 1986J Theor Biol
121: 269-282
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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