Download - All individuals are NOT created equal
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All individuals are NOT created equal
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The homogeneous cohort
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… is a myth
mean of responses response of average individual
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How can we solve this?
Experimental Follow individuals over time …
Modelling Each individual with its own set of parameters …
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Example Growth of the springtail Folsomia candida
– parthenogenetic animal (so clones)– data analysed in Jager et al 2004 (ES&T)
Simple growth model:
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Control growth
Fixed: f = 1 and L0 = 0.12 mm Fitted: rB and Lm for each animal
0 20 40 60 80 100 1200
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
time (days)
volu
met
ric b
ody l
engt
h (m
m)
0.03 0.04 0.05 0.06 0.07 0.080.55
0.6
0.65
0.7
0.75
0.8
rB (d-1)
L m(m
m)
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Control growth
Fixed: f = 1 and L0 = 0.12 mm Fitted: rB and Lm for each animal
0.04
0.045
0.05
0.055
0.06
0.065
0.07
0.6
0.61
0.62
0.63
0.64
0.65
0.66
0.67
0.68
0.69
0.7
rB Lm
mean indiv. mean indiv.
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Adding cadmium
Exposed individuals grow to smaller size …– because they experience an effect on f ?– or, because they accidentally have a lower Lm?
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Adding cadmium
Exposed individuals grow to smaller size …– because they experience an effect on f ?– or, because they accidentally have a lower Lm?
0 20 40 60 80 100 1200
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
time (days)
volu
met
ric b
ody l
engt
h (m
m)
0.03 0.04 0.05 0.06 0.07 0.080.55
0.6
0.65
0.7
0.75
0.8
rB (d-1)
L m(m
m)
For an individual in a treatment, we cannot know its control response!
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0 20 40 60 80 100 1200
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
time (days)
volu
met
ric b
ody l
engt
h (m
m)
0.03 0.04 0.05 0.06 0.07 0.080.55
0.6
0.65
0.7
0.75
0.8
rB (d-1)
L m(m
m)
Adding cadmium
Exposed individuals grow to smaller size …– because they experience an effect on f ?– or, because they accidentally have a lower Lm?
Practical approach:– fit rB and Lm for each individual … but
– control distribution of rB and Lm as multivariate prior– force same treatment effect on all individuals …
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Effects of cadmium
First-order one-compartment toxicokinetics (scaled)
linear-with-threshold effect on f
Three parameters: ke, c0 and cT
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Effects of cadmium
meta-optimisation, global parameters
individual 3individual 3individual 3individual 3individual 2
individual 1optimisationindividual(rB1, Lm1)
(ke, c0, cT)
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Effects of cadmium
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8 Conc. 64 mg/kg food
volu
met
ric b
ody
leng
th (m
m)
Conc. 139 mg/kg food Conc. 300 mg/kg food
0 20 40 60 80 100 1200
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8 Conc. 646 mg/kg food
time (days)
volu
met
ric b
ody
leng
th (m
m)
0 20 40 60 80 100 120
Conc. 1392 mg/kg food
time (days)0 20 40 60 80 100 120
Conc. 3000 mg/kg food
time (days)
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Effects of cadmium
0.55
0.6
0.65
0.7
0.75
0.8 Conc. 64 mg/kg food
Lm (m
m)
Conc. 139 mg/kg food Conc. 300 mg/kg food
0.03 0.04 0.05 0.06 0.07 0.080.55
0.6
0.65
0.7
0.75
0.8 Conc. 646 mg/kg food
rB (d-1)
Lm (m
m)
0.03 0.04 0.05 0.06 0.07 0.08
Conc. 1392 mg/kg food
rB (d-1)0.03 0.04 0.05 0.06 0.07 0.08
Conc. 3000 mg/kg food
rB (d-1)
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Effects of cadmium
Parameter fit on indiv.
ke (d-1) 0.139 (0.100-0.235)
c0 (mg/kg) 1.83 (0-46.4)
cT (mg/kg) 8.99 (8.41-9.69) 103
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
mean indiv.
ke
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Concluding remarks I
What have I learned? Even with clones, individuals differ
– causes bias in parameter estimates– bias increases with increasing variation …
Inter-individual differences can be included … but:– extremely calculation-intensive– requires good quality data for each individual– statistical method can/should be refined …
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Concluding remarks II
This is “proof of concept”, next: more endpoints simultaneously
– more complete DEB models … primary parameters– but not too complex … “DEBkiss”:
• no reserve, no maturity, simple embryonic rules
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Concluding remarks II
This is “proof of concept”, next: more endpoints simultaneously
– more complete DEB models … primary parameters– but not too complex … “DEBkiss”:
• no reserve, no maturity, simple embryonic rules
more extreme variation between individuals– Alpar Barsi on the pond snail …
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See my poster DEBkiss: The quest for the simplest energy-budget model
More informationon DEBtox/GUTS: http://www.debtox.infoon DEB: http://www.bio.vu.nl/thb
CoursesSummercourse TKTD modelling Denmark 2013 (survival)
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Results
Parameter fit on means fit on indiv.
ke (d-1) 1.62 (>0.310) 0.139 (0.100-0.235)
c0 (mg/kg) 0 (0-84.5) 1.83 (0-46.4)
cT (mg/kg) 10.8 (10.0-11.5) 103 8.99 (8.41-9.69) 103
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DEBkiss
b
maintenance
p
maturation
feeding
egg
k 1- k
structure buffer
egg