Lecture 4 Covariation of parameter values. Scales of life 8a Life span 10 log a Volume 10 log m 3...
-
date post
20-Jan-2016 -
Category
Documents
-
view
213 -
download
0
Transcript of Lecture 4 Covariation of parameter values. Scales of life 8a Life span 10 log a Volume 10 log m 3...
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