All individuals are NOT created equal
Feb 22, 2016
All individuals are NOT created equal
The homogeneous cohort
… is a myth
mean of responses response of average individual
How can we solve this?
Experimental Follow individuals over time …
Modelling Each individual with its own set of parameters …
Example Growth of the springtail Folsomia candida
– parthenogenetic animal (so clones)– data analysed in Jager et al 2004 (ES&T)
Simple growth model:
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)
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.
Adding cadmium
Exposed individuals grow to smaller size …– because they experience an effect on f ?– or, because they accidentally have a lower Lm?
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!
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 …
Effects of cadmium
First-order one-compartment toxicokinetics (scaled)
linear-with-threshold effect on f
Three parameters: ke, c0 and cT
Effects of cadmium
meta-optimisation, global parameters
individual 3individual 3individual 3individual 3individual 2
individual 1optimisationindividual(rB1, Lm1)
(ke, c0, cT)
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)
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)
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
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 …
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
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 …
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)
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
DEBkiss
b
maintenance
p
maturation
feeding
egg
k 1- k
structure buffer
egg