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