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Office of Research and DevelopmentNational Health and Environmental Effects Research Laboratory, Mid Continent Ecology Division, Duluth, MN 12/1/2007
Bridging from Individuals to Populations
Matthew Etterson & Richard BennettUSEPA/ORD/NHEERL
Mid Continent Ecology DivisionDuluth, MN
Office of Research and DevelopmentNational Health and Environmental Effects Research Laboratory, Mid Continent Ecology Division, Duluth, MN 1
2
Office of Research and DevelopmentNational Health and Environmental Effects Research Laboratory, Mid Continent Ecology Division, Duluth, MN 2
What data do we need to predict population-level effects?
• Estimated vital rates (survival, fecundity) in the absence of the
stressor, and
• Estimated effects of the chemical stressor on vital rates.
Office of Research and DevelopmentNational Health and Environmental Effects Research Laboratory, Mid Continent Ecology Division, Duluth, MN 3
Cornell Laboratory of OrnithologyAmerican Ornithologists Union
How much demographic data is available?
3
Office of Research and DevelopmentNational Health and Environmental Effects Research Laboratory, Mid Continent Ecology Division, Duluth, MN 4
Annual Reproductive Success
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
None 1 2 3 4 ≥5
Data for approx 300 songbirds
Fre
qu
en
cy
Office of Research and DevelopmentNational Health and Environmental Effects Research Laboratory, Mid Continent Ecology Division, Duluth, MN 5
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Annual Survival
None 1 2 3 4 ≥5
Data for approx 300 songbirds
Fre
qu
en
cy
4
Office of Research and DevelopmentNational Health and Environmental Effects Research Laboratory, Mid Continent Ecology Division, Duluth, MN 6
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
AnnualReproductiveSuccess
AnnualSurvival
BothMissing
EitherMissing
Frequency of Missing Data
Fre
qu
en
cy
Therefore, accounting for paucity of demographic data must
be part of our modeling strategy
Office of Research and DevelopmentNational Health and Environmental Effects Research Laboratory, Mid Continent Ecology Division, Duluth, MN 7
Avian reproduction test (ART)• Designed experiment using Mallards or Bobwhite
• 3 dietary concentrations of pesticide versus control (no pesticide).
• Analysis of Variance used to determine highest dietary concentration at which no adverse effects are observed (NOAEC).
• Specific endpoints include:
– adult body weight
– egg production and fertility
– eggshell thickness
– embryonic development and hatchability
– survival and weight of young to 14 days.
• NOAECs compared to estimated exposure (risk quotients)
• Core requirement for pesticide registration nationally and internationally
For more background on the avian reproduction test see Bennett & Etterson 2006 Human and
Ecological Risk Assessment 12:762-781, and citations therein
5
Office of Research and DevelopmentNational Health and Environmental Effects Research Laboratory, Mid Continent Ecology Division, Duluth, MN 8
Problems with risk quotients (RQ)
• Not obvious how experimental endpoints relate to population effects.
– adult body weight
– egg production and fertility
– eggshell thickness
– embryonic development and hatchability
– survival and weight of young to 14 days.
• does not provide dose-response information.
• does not account for renesting after failure or success.
• The estimated RQs pertain to only two species (a quail & a duck).
For more background on the avian reproduction test see Bennett & Etterson 2006 Human and
Ecological Risk Assessment 12:762-781, and citations therein
Office of Research and DevelopmentNational Health and Environmental Effects Research Laboratory, Mid Continent Ecology Division, Duluth, MN 9
We need a better model than risk quotients:
• Must be compatible with ecological data (nest survival),
• Must be forward-compatible with anticipated data and changes to
testing protocols (dose-response relationships, indirect effects,
competing risks),
• Must be compatible with current toxicological data (risk quotients),
• Must be a realistic representation of avian productivity,
• Must be able to accommodate severe data limitation, and
• Must be defensible against inevitable challenges.
6
Office of Research and DevelopmentNational Health and Environmental Effects Research Laboratory, Mid Continent Ecology Division, Duluth, MN 10
Songbird nesting cycle
Failed
Nest-build/
Egg-laying
Incubation FledgeNestling
1 0
1 s s
=
− M
active
failed
faile
d
active
Office of Research and DevelopmentNational Health and Environmental Effects Research Laboratory, Mid Continent Ecology Division, Duluth, MN 11
Some pesticides may slow development rate
Failed
FledgeNest-build/
Egg-laying
Incubation Nestling
Indirect effects
( ) ( )( )
1 0 0
( ) 0 1 0
1 1
a
s F a s F a s
= − −
M
Etterson & Bennett 2005 Ecology
Etterson & Bennett 2006 Ecological Modelling
7
Office of Research and DevelopmentNational Health and Environmental Effects Research Laboratory, Mid Continent Ecology Division, Duluth, MN 12
Competing Risks
• Some nest attempts that fail due to pesticide exposure would ultimately
fail anyway due to other (ecological) causes.
• The total probability of failure with two (or more) causes is less than the
sum of the probabilities of failure due to each cause in isolation.
• Routine concept in human epidemiology and in reliability theory, not so
common in ecology.
• Math gets a bit tricky…
4 1 2 3
1 0 0 0 0
0 1 0 0 0
0 0 1 0 0
0 0 0 1 0
m m m m s
1
1,,,,0
4321
4321
=++++
≤≤
mmmms
mmmms
Etterson et al. 2007 Auk
Etterson et al. 2007 Studies in Avian Biology
Etterson et al. In Review. Auk
Office of Research and DevelopmentNational Health and Environmental Effects Research Laboratory, Mid Continent Ecology Division, Duluth, MN 13
We need a better model than risk quotients:
�Must be compatible with ecological data (nest survival),
�Must be forward-compatible with anticipated data and changes to
testing protocols (dose-response relationships, indirect effects,
competing risks),
• Must be compatible with current toxicological data (risk quotients),
• Must be a realistic representation of avian productivity,
• Must be able to accommodate severe data limitation, and
• Must be defensible against inevitable challenges.
8
Office of Research and DevelopmentNational Health and Environmental Effects Research Laboratory, Mid Continent Ecology Division, Duluth, MN 14
- adult body weight- egg production and fertility- eggshell thickness- embryonic development and hatchability- survival and weight of young to 14 days.
Start
Breeding
Failed
Nest-build/
Egg-laying
Incubation FledgeNestling Stop
Breeding
Evolving from risk quotients to annual reproductive success: our hopeful monster.
We’ve got the best nest-survival model, but we need more…
Bennett et al. 2005. Ecotoxicology
Bennett & Etterson, In Press, Integ. Env. Assess. Manag.
Office of Research and DevelopmentNational Health and Environmental Effects Research Laboratory, Mid Continent Ecology Division, Duluth, MN 15
We need a better model than risk quotients:
�Must be compatible with ecological data (nest survival),
�Must be forward-compatible with anticipated data and changes to
testing protocols (dose-response relationships, indirect effects,
competing risks),
�Must be compatible with current toxicological data (risk
quotients),
• Must be a realistic representation of avian productivity,
• Must be able to accommodate severe data limitation, and
• Must be defensible against inevitable challenges.
9
Office of Research and DevelopmentNational Health and Environmental Effects Research Laboratory, Mid Continent Ecology Division, Duluth, MN 12/1/2007
Pair Formation
Copulation
Laying
Incubation
Nestling
Abandoned due to Pesticide
Failed due to Background Causes
Successful
10 20 30 40 50 60 70 800
0.2
0.4
0.6
0.8
1
Days Since Onset of Breeding Season
Pro
port
ion o
f F
em
ale
s
Must be a realistic representation of avian productivity
1.06 broods/female
Office of Research and DevelopmentNational Health and Environmental Effects Research Laboratory, Mid Continent Ecology Division, Duluth, MN 17
Pesticide Examples
Endpoint NOAECs
Bensulide
(mg/kg/d)
Dicrotophos
(µg/kg/d)
Adult Body Weight 167 128
Eggs Laid 167 46
Eggshell Thickness 167 330
% Fertile Eggs 167 128
% Hatch (in ovo) 29 128
% Chick Survival (in ovo) 74 330
5-day Dietary Test 1574 1792
10
Office of Research and DevelopmentNational Health and Environmental Effects Research Laboratory, Mid Continent Ecology Division, Duluth, MN 12/1/2007
10 20 30 40 50 60 70 800
50
100
150
200
Days Since Onset of Breeding Season
Estim
ate
d D
ieta
ry E
xposure Adult Dietary Exposure
Nestling Dietary Exposure
Minimum NOEC
1
PF C L I N A F S
10 20 30 40 50 60 70 800
0.2
0.4
0.6
0.8
1
Days Since Onset of Breeding Season
Pro
port
ion o
f F
em
ale
s
Bensulide-application on day 0
0.54 broods/female
Office of Research and DevelopmentNational Health and Environmental Effects Research Laboratory, Mid Continent Ecology Division, Duluth, MN 19
Comparative Profiles: Bensulide
1
PF C L I N A F S
10 20 30 40 50 60 70 800
0.2
0.4
0.6
0.8
1
Days Since Onset of Breeding Season
Pro
port
ion o
f F
em
ale
s
10 20 30 40 50 60 70 800
0.2
0.4
0.6
0.8
1
Days Since Onset of Breeding Season
Pro
port
ion o
f F
em
ale
s
1.06 broods/female
0.54 broods/female
11
Office of Research and DevelopmentNational Health and Environmental Effects Research Laboratory, Mid Continent Ecology Division, Duluth, MN 20
Some validation issues
Start
Breeding
Failed
Nest-build/
Egg-laying
Incubation FledgeNestling Stop
Breeding
I. Why do birds stop breeding?
II. Is it really conservative to assume that an exceeded NOAEC results in total nest loss?
III. When estimating effects on reproductive success can we ignore potential effects on survival?
Office of Research and DevelopmentNational Health and Environmental Effects Research Laboratory, Mid Continent Ecology Division, Duluth, MN 21
Does it really matter what the stopping rules are?
0 20 40 60 80 100 1200
0.5
1
1.5
2
2.5
A B
CD
Day of Season (t ≤ T)
Su
cce
ssfu
l B
rood
s p
er
Fe
ma
le
12
Office of Research and DevelopmentNational Health and Environmental Effects Research Laboratory, Mid Continent Ecology Division, Duluth, MN 22
A field guide to Markov chains
• Good for modeling iterative (esp. cyclic) stochastic processes
• Two species
– absorbing (process with an internal stopping mechanism)
– regular (time-limited process – traditional view)
• Can be very simple
– relatively few parameters
– easy to understand
• Very powerful methods of analysis
– mean & variance of state transitions
– mean time to arrive at a given state
– conditional probabilities of arriving at a given state given passage
through some other state of interest.
Office of Research and DevelopmentNational Health and Environmental Effects Research Laboratory, Mid Continent Ecology Division, Duluth, MN 23
Active
Nest
Fledged
Failed
sd
1-sd
qs
qf
1-qf
1-qs
Finished
Why do birds stop breeding?
(1)
(1)
Regular MCAbsorbing MC
13
Office of Research and DevelopmentNational Health and Environmental Effects Research Laboratory, Mid Continent Ecology Division, Duluth, MN 24
Can we find enough data to parameterize both an absorbing and regular Markov chain for some species and see how they perform?
Jim Rathert,
Eastern Meadowlark
Sturnella magna
Dickcissel
Spiza americana
Office of Research and DevelopmentNational Health and Environmental Effects Research Laboratory, Mid Continent Ecology Division, Duluth, MN 25
Observed 0.73 0.39 --- ---
Absorbing 0.72 0.54 -0.01 0.54
Regular 1.00 0.35 0.27 0.42
Regular MC is best
( )b̂ � ( )ˆvar b ( )ˆbias b ( )ˆMSE b
Eastern Meadowlark
14
Office of Research and DevelopmentNational Health and Environmental Effects Research Laboratory, Mid Continent Ecology Division, Duluth, MN 26
Observed 0.49 0.31 --- ---
Absorbing 0.38 0.25 -0.11 0.26
Regular 0.73 0.26 0.24 0.32
Absorbing MC is best
( )b̂ � ( )ˆvar b ( )ˆbias b ( )ˆMSE b
DickcisselJim Rathert,
Etterson & Bennett, in review, Journal of Avian Biology
Office of Research and DevelopmentNational Health and Environmental Effects Research Laboratory, Mid Continent Ecology Division, Duluth, MN 27
Some validation issues
I. Why do birds stop breeding?
II. Is it really conservative to assume that an exceeded NOAEC results in total nest loss?
III. When estimating effects on reproductive success can we ignore potential effects on survival?
15
Office of Research and DevelopmentNational Health and Environmental Effects Research Laboratory, Mid Continent Ecology Division, Duluth, MN 28
Active
Nest
Finished
Fledged
Failed
Is it really conservative to assume total failure?
Office of Research and DevelopmentNational Health and Environmental Effects Research Laboratory, Mid Continent Ecology Division, Duluth, MN 29
Active
Nest
NOAEC
Exceeded
NOAEC not
Exceeded
Finished
Fledged
Failed
( ) ( )
1 0 0 0
0 1 0
0 1 0 1 1
0 1 0
s s
d d
f f
q q
e s e s
q q
− = − − −
−
M
e
sd
qs
qf
1-qf
1-qs
Is it really conservative to assume total failure?
16
Office of Research and DevelopmentNational Health and Environmental Effects Research Laboratory, Mid Continent Ecology Division, Duluth, MN 30
Active
NestFledged
p (red. cl.)
Fledged
(full cl.)
Failed
NOAEC
Exceeded
NOAEC not
Exceeded
Finished
( )
1 0 0 0 0
0 0 1 0
0 0 1 0
0 1 0 1
0 0 1 0
s s
s s
d d
f f
q q
q q
eS e s s
q q
− −
− − −
e
sd
qs
qf
sd
1 - qs qs
1-qf
1-qs
Is it really conservative to assume total failure?
Office of Research and DevelopmentNational Health and Environmental Effects Research Laboratory, Mid Continent Ecology Division, Duluth, MN 31
The total failure model is protective when:( ) ( ) ( )
1
1 1
fd
s f
qps
p e q q>
− − −
What we can learn from this inequality?
1. We are more likely to be protective when:
• proportional brood reduction (1 − p) is large,
• exposure exceeding the NOAEC is less likely,
• qf is small,
• the difference between qs and qf is large and positive.
2. We can use it to classify life histories:
• qs >≈ qf → assuming total failure is never protective
• qs < qf → assuming total failure is always protective
• qs > qf → assuming total failure might be protective
• qs >> qf → assuming total failure is probably protective
17
Office of Research and DevelopmentNational Health and Environmental Effects Research Laboratory, Mid Continent Ecology Division, Duluth, MN 32
Some validation issues
I. Why do birds stop breeding?
II. Is it really conservative to assume that an exceeded NOAEC results in total nest loss?
III. When estimating effects on reproductive success can we ignore potential effects on survival?
Office of Research and DevelopmentNational Health and Environmental Effects Research Laboratory, Mid Continent Ecology Division, Duluth, MN 33
We need a better model than risk quotients:
�Must be compatible with ecological data (nest survival),
�Must be forward-compatible with anticipated data and changes to
testing protocols (dose-response relationships, indirect effects,
competing risks),
�Must be compatible with current toxicological data (risk
quotients),
�Must be a realistic representation of avian productivity,
�Must be able to accommodate severe data limitation, and
?Must be defensible against inevitable challenges.
18
Office of Research and DevelopmentNational Health and Environmental Effects Research Laboratory, Mid Continent Ecology Division, Duluth, MN 34
General Conclusions
• Crossing from in silico, in vitro, or even in vivo to in populo is a
challenge that we’ve only just begun to grapple with.
• Success will require creative (ad hoc) modeling solutions,
• We need quantitative probabilistic estimates of effects, not just on
individuals, but also on their vital rates (survival, fecundity)
Office of Research and DevelopmentNational Health and Environmental Effects Research Laboratory, Mid Continent Ecology Division, Duluth, MN 35
Future directions
• Develop a user-friendly version of the model,
• Integrate with EPA OPP exposure model,
• Incorporate adult morality,
• Explore similar methods for taxa other than birds.
19
Office of Research and DevelopmentNational Health and Environmental Effects Research Laboratory, Mid Continent Ecology Division, Duluth, MN 36
Collaborators
• R. Greenberg, Smithsonian Institution
• L. Nagy, USEPA
• B. Olsen, Penn State Univ.
• T. Rodden Robinson, Oregon State Univ.
• T. Stanley, USGS
Reviewers• M. Conroy, Univ. Georgia
• D. Green, Univ. MN Duluth
• J. Grzybowski, Oklahoma State Univ.
• D. Heisey, USFWS
• J. Nichols, Patuxent Nat. Wild. Res. Ctr.
• J. Pastor, NRRI & Univ. MN Duluth
• J. Sauer, Patuxent Nat. Wild. Res. Ctr.
• T. Stanley, USGS