bridging from individuals to...

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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


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.


Cornell Laboratory of OrnithologyAmerican Ornithologists Union

How much demographic data is available?

3


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


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


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


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

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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


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.

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Songbird nesting cycle

Failed

Nest-build/

Egg-laying

Incubation FledgeNestling

1 0

1 s s

=

− M

active

failed

faile

d

active


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

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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



�Must be compatible with ecological data (nest survival),

�Must be forward-compatible with anticipated data and changes to


competing risks),

• Must be compatible with current toxicological data (risk quotients),




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- 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.






competing risks),

�Must be compatible with current toxicological data (risk

quotients),




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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


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

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10 20 30 40 50 60 70 800

50

100

150

200


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


Pro

port

ion o

f F

em

ale

s

Bensulide-application on day 0

0.54 broods/female


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


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


Pro

port

ion o

f F

em

ale

s

1.06 broods/female

0.54 broods/female

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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?


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

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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.


Active

Nest

Fledged

Failed

sd

1-sd

qs

qf

1-qf

1-qs

Finished

Why do birds stop breeding?

(1)

(1)

Regular MCAbsorbing MC

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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


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

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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






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Active

Nest

Finished

Fledged

Failed

Is it really conservative to assume total failure?


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


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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



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

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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.

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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)


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.

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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

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