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Des modèles de capture-recapture
pour l’écologie évolutive
Olivier Gimenez
Centre d’Ecologie Fonctionnelle et Evolutive
What I will not address today
Church of the Flying Spaghetti Monster
Investigating evolution in the wild
Investigating evolution in the natural
populations (Grant, Reznick, ...)
Long-term individual monitoring datasetsLong-term individual monitoring datasets
Methodological issues when moving from lab
to natural conditions
Investigating evolution in the wild
Investigating evolution in the natural
populations (Grant, Reznick, ...)
Long-term individual monitoring datasetsLong-term individual monitoring datasets
Methodological issues when moving from lab
to natural conditions
Issue 1: detectability < 1
Issue 2: individual heterogeneity (IH)
Issue 1: detectability < 1
Individuals may be seen or not
How to reliably estimate fitness in the wild?
If they’re not... Are they breeding? Are theyIf they’re not... Are they breeding? Are they
on the study site? Are they dead?
Individually mark and monitor individuals:
capture-recapture (CR) data
Capture-
recapture
Why bother with p < 1?
recapture
approach
Naïve
approach
with p = 1
Why bother with p < 1?
0.60.81.0
Capture-
recapture
Survival
Bias in survival and rate of senescence
(Gimenez et al. 2008 Am. Nat.)
2 4 6 8 10 12 14
0.20.4
recapture
approach
Naïve
approach
with p = 1Age
Why bother with p < 1?
0.40.60.81.0
Survival
Capture-
recapture
approach
-4 -2 0 2 4
0.00.20.4
Body mass
Survival
approach
Naïve
approach
with p = 1
Bias in shape of selection
(Gimenez et al. 2008 Am. Nat.)
Issue 2: individual heterogeneity
Simple CR models assume homogeneity
From a statistical point of view, IH can cause
bias in parameter estimatesbias in parameter estimates
150
200
250
300
H+P+QI
CJS
Homogeneity
N
Impact of IH on abundance estimation
Heterogeneity
0
50
100
64 [29 ; 111]
33 [17 ; 54]
Bias in abundance estimation
(Cubaynes et al. 2010 Cons. Biol.; L. Marescot’s PhD)
time
Issue of individual heterogeneity
Standard CR models assume homogeneity
From a statistical point of view, IH can cause
bias in parameter estimatesbias in parameter estimates
From a biological point of view, IH is of
interest – individual quality
What is individual quality?
Quality varies among individuals within a
population
High quality individuals have greater fitness
than low quality ones
⇒ Among-individual heterogeneity that⇒ Among-individual heterogeneity that
is positively correlated to fitness (Wilson &
Nussey in press)
Quality varies among individuals within a population
High quality individuals have greater fitness than low
quality ones
⇒ Among-individual heterogeneity that is
positively correlated to fitness (Wilson & Nussey 2009)
Why is it so important?
What is individual quality?
Why is it so important?
Natural selection can occur if individuals
vary in phenotype and fitness
A response to selection depends on this
variation having a genetic basis
IH may lead to flawed inference
Accounting for individual heterogeneity
CR models do not cope that well with quality
Accumulation of long-term individual data
If you’re a biologist, rely on empirical
measures (mass, gender, age, experience, etc.)
How to account for individual heterogeneity?
measures (mass, gender, age, experience, etc.)
How to incorporate this information?
If you’re a statistician, intrinsic property of
individuals
How to filter out the signal from noisy obs.?
Survival kit in CR
How to account for variation in individual
quality when assessing senescence and
trade-offs
Case study 1: describing senescence
Outline of the talk
Case study 1: describing senescence
Case study 2: detecting trade-offs
Can quality have a genetic basis or is it a
consequence of environmental effects?
Case study 3: quantifying heritability
Perspectives
Survival kit in CR
How to account for variation in individual
quality when assessing senescence and
trade-offs
Case study 1: describing senescence
Outline of the talk
Case study 1: describing senescence
Case study 2: detecting trade-offs
Can quality have a genetic basis or is it a
consequence of environmental effects?
Case study 3: quantifying heritability
Perspectives
Common marking methods
• Ear tags for mammals / leg bands for birds.
• Passive integrated transponder (PIT) tags.
tigers
Marking by camera-trap / photo-identification
whales
• Individuals are uniquely identified using
microsatellite profiling on hair, dung, … samples
wolf (dung)
Marking by noninvasive genetic sampling
bear (hair) bat (droppings)
elephant (dung)orang-utan (hair)
Capture-recapture data
An encounter history: hi = (1 0 1)
An encounter history: hi = (1 0 1)
1 0 1
φ
Modelling CR data
Survival probability φ
1 0 1
An encounter history: hi = (1 0 1)
1 0 1
φ
Modelling CR data
Detection probability p
1 0 1
p−1
An encounter history: hi = (1 0 1)
1 0 1
φ φ
Modelling CR data
1 0 1
p−1
An encounter history: hi = (1 0 1)
1 0 1
φ φ
Modelling CR data
1 0 1
p−1 p
An encounter history: hi = (1 0 1)
1 0 1
φ φ
( ) ( ) pph 1Pr φφ −=
Modelling CR data
Survival probability φ
Detection probability p
1 0 1
p−1 p
( ) ( ) pphi 1Pr φφ −=
A probabilistic framework
( ) ( ) pphi 1Pr φφ −=
Modelling CR data
A probabilistic framework
Central role of likelihood (frequentist / bayesian)
( ) ( ) pphi 1Pr φφ −=
Modelling CR data
Central role of likelihood (frequentist / bayesian)
( )∏=
i
ihL Pr
A probabilistic framework
Central role of likelihood (frequentist / bayesian)
( ) ( ) pphi 1Pr φφ −=
Modelling CR data
Central role of likelihood (frequentist / bayesian)
How to account for IH in
iφ
( )∏=
i
ihL Pr
Introduction: survival kit in CR
How to account for variation in individual
quality when assessing senescence and
trade-offs
Case study 1: describing senescence
Outline
Case study 1: describing senescence
Case study 2: detecting trade-offs
Can quality have a genetic basis or is it a
consequence of environmental effects?
Case study 3: quantifying heritability
Perspectives
« Over time, the observed hazard rate will
approach the hazard rate of the more robust
subcohort » Vaupel and Yashin 1985 Am. Stat.
Suggest that analyses conducted at the
population vs. individual level should differ (Cam
Impact of IH on age-varying survival
population vs. individual level should differ (Cam
et al. 2002)
What if detection p < 1 ?
Scenario 1: finite mixture of individuals
Use mixture models (Pledger et al. 2003)
Latent variable for the class to which an
individual belongs (Pradel 2009)individual belongs (Pradel 2009)
2 classes of individuals (low vs. high quality)
Probabilities in a mixture model
Under heterogeneity:
π is the probability that the individual belongs
to state L
φL is survival for low quality individuals
φH is survival for high quality individuals
Probabilities in a mixture model
Under heterogeneity:
( ) ( ) ( ) ( ) pppp HHLL
⋅⋅−⋅⋅−+⋅⋅−⋅⋅= φφπφφπ 111101Pr
π is the probability that the individual belongs
to state L
φL is survival for low quality individuals
φH is survival for high quality individuals
Scenario 1: finite mixture of individuals
2 classes of individuals (fragile vs. robust)
Use mixture models (Pledger et al. 2003)
A model with a hidden structure, with aA model with a hidden structure, with a
latent variable for the class to which an
individual belong to (HMM; Pradel 2009)
Mimic examples in Vaupel and Yashin (1985)
with p < 1 using simulated data
0.6
0.7
0.8
0.9
1
Sub-cohort 2
100 individuals
(the most robust)
Survival
0 2 4 6 8 10 12 14
0.2
0.3
0.4
0.5
Sub-cohort 1
400 individuals
(the most fragile)
Age
0.6
0.7
0.8
0.9
1
Fit at the population level
Sub-cohort 2
100 individuals
(the most robust)
Survival
0 2 4 6 8 10 12 14
0.2
0.3
0.4
0.5
Sub-cohort 1
400 individuals
(the most fragile)
Age
0.5
0.6
0.7
0.8
0.9
1
Fit at the population level
Sub-cohort 2
100 individuals
(the most robust)
Survival
0 2 4 6 8 10 12 14
0
0.1
0.2
0.3
0.4
Fit at the individual level
using a 2-class mixture
Sub-cohort 1
400 individuals
(the most fragile)
Age
Real case study on Black-headed Gulls
Not so simple in real life
Guillaume Péron’s PhD on Black-
headed gulls (R. Pradel & P.-A. Crochet)headed gulls (R. Pradel & P.-A. Crochet)
Several potential sources of IH
Detection heterogeneity (1)
zone 1: nests inside
the vegetation
La Ronze pond
Detection heterogeneity (1)
zone 1: nests inside the
vegetation
zone 2: nests on the
edge of vegetation
clusters
La Ronze pond
Even more heterogeneity
Emigration
heterogeneity (2) ♀
♂
Immigrant
Locally born Emigration –
Emigration +
Survival
heterogeneity (3) ♀
♂
Poor quality
Good quality Survival +
Survival –
Modelling multiple sources of heterogeneity
But,
Little sexual dimorphism
Sometimes no knowledge of birth site,
No measure of individual quality
Consider mixture of individuals: low / highConsider mixture of individuals: low / high
Survival senescence with / without IH
Results - Péron et al. (in press) Oïkos
• Absence of survival
heterogeneity
Results - Péron et al. (in press) Oïkos
• Absence of survival
heterogeneity
• Presence of detection and
emigration heterogeneity
Results - Péron et al. (in press) Oïkos
• Absence of survival
heterogeneity
• Presence of detection and
emigration heterogeneity
• If ignored, heterogeneity
in emigration masks
senescence in survival
Results - Péron et al. (in press) Oïkos
0.60.81
Survivalprobabilities
Estimation of survival senescence
00.20.40.6
0 10 20
Age
Survivalprobabilities
• Absence of survival
heterogeneity
• Presence of detection and
emigration heterogeneity
• If ignored, heterogeneity
in emigration masks
senescence in survival
Case study 2: continuous mixture of individuals
What if I have a continuous mixture of
individuals?
Use individual random-effect modelsUse individual random-effect models
CR mixed models (Gimenez & Choquet 2010)
Explain individual variation in survival
No variation – homogeneity
Individual random-effect models
φ
Random effect – in-between
Saturated – full heterogeneity
iφ
( )2
,~ σφφ Ni
Explain individual variation in survival
No variation – homogeneity
Individual random-effect models
φ
Random effect – in-between
Saturated – full heterogeneity
iφ
( )2
,~ σφφ Ni
Explain individual variation in survival
No variation – homogeneity
Individual random-effect models
φ
Individual random effect – in-between
Saturated – full heterogeneity
iφ
( )2
,~ σµφ Ni
Case study 2: continuous mixture of individuals
What if I have a continuous mixture of
individuals?
Use individual random-effect models (Royle
2008, Gimenez & Choquet 2010)2008, Gimenez & Choquet 2010)
Mimic examples in Vaupel and Yashin (1985)
with p < 1 using simulated data
0.7
0.8
0.9
1 300 individuals
logit(φφφφi(a)) = 1.5 - 0.05 a + ui
ui ~ N(0,σσσσ=0.5)
Survival
0 2 4 6 8 10 12 14
0.4
0.5
0.6
Age
0.7
0.8
0.9
1 Expected pattern
E(logit(φφφφi(a))) = 1.5 - 0.05 aSurvival
0 2 4 6 8 10 12 14
0.4
0.5
0.6
Age
0.7
0.8
0.9
1 Fit at the population level
Survival
0 2 4 6 8 10 12 14
0.4
0.5
0.6
Age
0.7
0.8
0.9
1 Fit at the individual level
with an individual random effectSurvival
0 2 4 6 8 10 12 14
0.4
0.5
0.6
Age
Senescence in European dippers
Senescence in European dippers
with IH: onset = 1.94
Marzolin et al. (in revision) Ecology
Senescence in European dippers
without IH: onset = 2.28
with IH: onset = 1.94
Marzolin et al. (in revision) Ecology
Introduction: survival kit in CR
How to account for variation in individual
quality when assessing senescence and
trade-offs
Case study 1: describing senescence
Outline
Case study 1: describing senescence
Case study 2: detecting trade-offs
Can quality have a genetic basis or is it a
consequence of environmental effects?
Case study 3: quantifying heritability
Perspectives
M. Buoro (co-dir. E. Prévost1)
Photo: Paul Nicklen (National Geographic)
1 UMR INRA/UPPA Ecobiop, Saint Pée s/ Nivelle, France
Natural selection favors individuals that
maximize their fitness
Limited energy budget: strategy of
resource allocation
Assessing trade-offs in the wild
resource allocation
Trade-off between traits related to
fitness
Issue of detectability, again
Atlantic salmon life cycle
Freshwater
Reproduction Development of
juveniles
Sea
Migration to sea
Growth at sea
Migration to stream
Freshwater
Development of
juveniles
Atlantic salmon life cycle
Sea
Freshwater
Juveniles
1st year
of life
Autumn
Spring
Sea
Freshwater
Juveniles
Migrants
1st year
of life
Autumn
Spring
Sea
Freshwater
Residents
Juveniles
Migrants
Autumn
Spring
1st year
of life
Sea
Freshwater
Sexual
maturation2nd year
Residents
Juveniles
Migrants
Autumn
Spring
Autumn
1st year
of life
Migrants
maturation
Sea
2nd year
of life
Spring
Freshwater
Sexual
maturation
Residents
Juveniles
Migrants
2nd year
1st year
of life
Autumn
Spring
Autumn
Migrants
maturation
Sea
Adults
2nd year
of life
Spring
Juveniles
Migrants
Autumn
Spring
Juveniles
Migrants
Winter survival
Autumn
Spring
Juveniles
Migrants
Is there a tradeoff between
Winter survival
Autumn
Spring
Is there a tradeoff between
migration and winter survival?
State-space model (Gimenez et al. 2007)
Dynamic process model Observation
State-space model
Dynamic process model Observation
Juveniles
marked in
autumn
Migrants
recaptured in
spring
State-space model
Observation
Migration
choice
Juveniles
marked in
autumn
Dynamic process model
iM
Migrants
recaptured in
spring
State-space model
Observation
Migration
probability
Migration
choice
Juveniles
marked in
autumn
Dynamic process model
iκ iM
Migrants
recaptured in
spring
Dynamic process model
State-space model
Observation
Probabilistic reaction norm
Size
Migration
probability
Migration
choice
Juveniles
marked in
autumn
iκ iMisize
Migrants
recaptured in
spring
( ) ii size×+= 21logit ββκ
State-space model
Observation
Size
Migration
probability
Migration
choice
Juveniles
marked in
autumn
Dynamic process model
Migrants
recaptured in
spring
Migrants
Surviving
Survival
probability
iφ
State-space model
Observation
Size
Migration
probability
Juveniles
marked in
autumn
Migration
choice
Selective mortality
iM
Migrants
recaptured in
spring
Migrants
Survivor
Survival
probability
iφ
State-space model
Observation
Size
Migration
probability
Juveniles
marked in
autumn
Migration
choice
Selective mortality
iM
Migrants
recaptured in
spring
Migrants
Survivor
Survival
probability
Random
effect
( ) iii M εααφ +×+= 21logit
iφiε
State-space model
Observation
Size
Migration
probability
Juveniles
marked in
autumn
Migration
choice
Dynamic process model
Migrants
recaptured in
spring
Migrants
Survivor
Survival
probability
Random
effect
Detection
probability
State-space model
Observation
Size
Migration
probability
Juveniles
marked in
autumn
Migration
choice
Dynamic process model
( ) size×+=logit ββκ
iκ iMisize
Migrants
recaptured in
spring
Migrants
Survivor
Survival
probability
Random
effect
Detection
probability
( ) iii M εααφ +×+= 21logit
( ) ii size×+= 21logit ββκ
iφiε
HDR Olivier Gimenez
50 55 60 65 70 75 80 85 90 95 100 105 110 115 120 125 130
0.00.20.40.60.81.0
MigrationProbability
Probabilistic reaction norm
Size-dependent
probabilistic reaction
norm for age at
migration
Results (1) – Buoro et al. (in press) Evolution
Size (mm)
50 55 60 65 70 75 80 85 90 95 100 105 110 115 120 125 130
0.00.20.40.60.81.0
MigrationProbability
Probabilistic reaction norm
Size-dependent
probabilistic reaction
norm for age at
migration
Results (1) – Buoro et al. (in press) Evolution
Size (mm)
Juveniles longer than 100 mm in autumn has a probability to migrate close to 1.
50 55 60 65 70 75 80 85 90 95 100 105 110 115 120 125 130
0.00.20.40.60.81.0
MigrationProbability
Probabilistic reaction norm
Size-dependent
probabilistic reaction
norm for age at
migration
Results (1) – Buoro et al. (in press) Evolution
Size (mm)
Juveniles longer than 100 mm in autumn has a probability to migrate close to 1.
A juvenile of 90 mm has 50% of chance of migrating to the sea at 1year of age.
50 55 60 65 70 75 80 85 90 95 100 105 110 115 120 125 130
0.00.20.40.60.81.0
MigrationProbability
Probabilistic reaction norm
Size-dependent
probabilistic reaction
norm for age at
migration
Results (1) – Buoro et al. (in press) Evolution
Size (mm)
Juveniles longer than 100 mm in autumn has a probability to migrate close to 1.
Juveniles shorter than 60 mm in autumn has a probability to migrate almost null.
A juvenile of 90 mm has 50% of chance of migrating to the sea at 1year of age.
50 55 60 65 70 75 80 85 90 95 100 105 110 115 120 125 130
0.00.20.40.60.81.0
MigrationProbability
Probabilistic reaction norm
Size-dependent
probabilistic reaction
norm for age at
migration
Results (2) – Buoro et al. (in press) Evolution
Size (mm)
Migrants
Residents
0.00.20.40.60.81.0
Survival cost in
deciding to stay an
extra year in
freshwater
Selective mortality
SurvivalProbability
Introduction: survival kit in CR
How to account for variation in individual
quality when assessing senescence and
trade-offs
Case study 1: describing senescence
Outline
Case study 1: describing senescence
Case study 2: detecting trade-offs
Can quality have a genetic basis or is it a
consequence of environmental effects?
Case study 3: quantifying heritability
Perspectives
Heritability in the wild
Quantitative genetics: assess the ability of
a trait to respond to natural selection
Increasing used in animal and plant pops
Heritability: proportion of the phenotypicHeritability: proportion of the phenotypic
var. attributed to additive genetic var.
For (demographic) parameters strongly
related to fitness, we expect low heritability
Predictions not so clear in wild populations
Heritability in the wild
Animal models: mixed models incorporating
genetic, environmental and other factors.
Capture-recapture models: assess
demographic parameters with p < 1 anddemographic parameters with p < 1 and
individual variability.
The idea of combining Animal and Capture-
recapture models is in the air (O’Hara et al.
2008; Cam 2009).
The idea is in the air (O’Hara et al. 2008)
The idea is in the air (Cam 2009)
" [The animal model has] been applied to
estimation of heritability in life history traits,
either in the rare study populations where
detection probability is close to 1, or withoutdetection probability is close to 1, or without
considering the probability of detecting
animals (...) "
Introducing the threshold model
Main issue: survival is a discrete
process, but animal models use continuous
distributions
Introducing the threshold model
Main issue: survival is a discrete
process, but animal models use continuous
distributions
Survival is related to a continuousSurvival is related to a continuous
underlying latent
Liability
ind. i dies on (t,t+1)
li,t ∼ N( i,t ,σ2)
ind. i survives on (t,t+1)
It can be shown that survival and mean
liability are linked
For some function G, we have:
Plug in the animal model
( ) iittii,t aebG +++== ηµφ ,
It can be shown that survival and mean
liability are linked
For some function G, we have:
Plug in the animal model
( ) iittii,t aebG +++== ηµφ ,
mean survival
It can be shown that survival and mean
liability are linked
For some function G, we have:
Plug in the animal model
( ) iittii,t aebG +++== ηµφ ,
yearly effect
mean survival
( )2
,0~ tt Nb σ
It can be shown that survival and mean
liability are linked
For some function G, we have:
Plug in the animal model
( ) iittii,t aebG +++== ηµφ ,
yearly effect
mean survival
non-genetic effect
( )2
,0~ tt Nb σ
( )2
,0~ ei Ne σ
It can be shown that survival and mean
liability are linked
For some function G, we have:
Plug in the animal model
( ) iittii,t aebG +++== ηµφ ,
additive genetic effect
yearly effect
mean survival
non-genetic effect
( )2
,0~ tt Nb σ
( )2
,0~ ei Ne σ
( ) ( )AMNaa aN
2
1 ,0~,, σK
Case study on blue tits in Corsica
Mark-recapture data Social pedigree
• Blue tits – Study site in
Corsica.
• 1979 – 2007 ⇒ 29 years of
monitoring)!
654 individuals,
218 fathers (sires),
215 mothers (dams),
12 generations.
Additive genetic variance
Papaïx et al. (to be resubmitted) Evolution
Posterior median = 0.110,
95% credible interval = [0.006; 0.308]
Introduction: survival kit in CR
How to account for variation in individual
quality when assessing senescence and
trade-offs
Case study 1: describing senescence
Outline
Case study 1: describing senescence
Case study 2: detecting trade-offs
Can quality have a genetic basis or is it a
consequence of environmental effects?
Case study 3: quantifying heritability
Conclusions & perspectives
Conclusions
IH needs to be accounted for, otherwise
Mask senescence (PhD G. Péron)
Obscur life-history tradeoffs (PhD M. Buoro)
Influence decision-making in management (PhD L. Marescot)
CR methodology is catching up with ‘p=1’
world
CR methodology is catching up with ‘p=1’
world
Recent statistical methods can help in coping
with IH when p < 1
Whenever possible, adopt a biological view
and measure quality in the field
Perspectives - methods
Continue efforts in developing methods to
properly account for individual heterogeneity
Fit and compare models (PhD S. Cubaynes)
Is heritability important in blue tits (model
selection)?selection)?
Speed up estimation?
Perspectives - Methods
Continue efforts in developing methods
Individual heterogeneity: fit and compare models
(PhD S. Cubaynes)
Speed up estimation?
Is heritability important in blue tits (model selection)?
Shall we go for discrete or continuous heterogeneity?Shall we go for discrete or continuous heterogeneity?
Transfer of knowledge - teaching
Perspectives - Methods
Continue efforts in developing methods
Individual heterogeneity: fit and compare models
(PhD S. Cubaynes)
Speed up estimation?
Is heritability important in blue tits (model selection)?
Shall we go for discrete or continuous heterogeneity?Shall we go for discrete or continuous heterogeneity?
Transfer of knowledge - workshops
Workshops
Bayesian ecology – StAndrews 2009 Occupancy – Montpellier 2008Bayesian ecology – StAndrews 2009
Capture-recapture – Montpellier 2002
Occupancy – Montpellier 2008
Population dynamics – Mytilini 2007
Perspectives - Methods
Continue efforts in developing methods
Individual heterogeneity: fit and compare models
(PhD S. Cubaynes)
Speed up estimation?
Is heritability important in blue tits (model selection)?
Shall we go for discrete or continuous heterogeneity?Shall we go for discrete or continuous heterogeneity?
Transfer of knowledge
Software implementation
Implementation issues: software
Program E-SURGE
Individual covariates, mixtures and
individual random effects
R. Choquet & E. Nogué
Perspectives - Biology
Consider other demographic parameters
(dispersal and breeding probabilities e.g.);
→ A. Charmantier & B. Doligez
From individuals to species
→ E. Papadatou’s post-doc & S. Cubaynes’s PhD→ E. Papadatou’s post-doc & S. Cubaynes’s PhD
→ Museum for community ecology aspects
Combine evolutionary and demography
→ S. Servanty’s post-doc & M. Gamelon’s Master
Biologists
Biological
question
Quant. methods
needed
Quant. methods
employed
Knowing what methods
are available
Addressing
assumptions in
study design
Enriches the
biologist
Enriches the
quant. types
Methodologists
needed
Methods
developed
employed
Understanding biology
Communication
Making methods
available
biologist quant. types
Courtesy of P. Doherty
ACKNOWLEDGMENTS
Mentoring
G. Ducharme
J.-D. Lebreton
R. Pradel
S.T. Buckland
B.J.T. Morgan
Inspiring
T. Lenormand
A. Charmantier
J.-M. Gaillard
E. Cam
M. Schaub
M. Ancrenaz
A. Besnard
C. Barbraud
V. Grosbois
P.-A. Crochet
Stimulating
M. Buoro F. Guilhaumon L. Marescot
S. Cubaynes
G. PéronS. Véran E. Papadatou
S. Servanty
M. Desprez M. Gamelon B. Testi

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HDR Olivier Gimenez

  • 1. Des modèles de capture-recapture pour l’écologie évolutive Olivier Gimenez Centre d’Ecologie Fonctionnelle et Evolutive
  • 2. What I will not address today Church of the Flying Spaghetti Monster
  • 3. Investigating evolution in the wild Investigating evolution in the natural populations (Grant, Reznick, ...) Long-term individual monitoring datasetsLong-term individual monitoring datasets Methodological issues when moving from lab to natural conditions
  • 4. Investigating evolution in the wild Investigating evolution in the natural populations (Grant, Reznick, ...) Long-term individual monitoring datasetsLong-term individual monitoring datasets Methodological issues when moving from lab to natural conditions Issue 1: detectability < 1 Issue 2: individual heterogeneity (IH)
  • 5. Issue 1: detectability < 1 Individuals may be seen or not How to reliably estimate fitness in the wild? If they’re not... Are they breeding? Are theyIf they’re not... Are they breeding? Are they on the study site? Are they dead? Individually mark and monitor individuals: capture-recapture (CR) data
  • 6. Capture- recapture Why bother with p < 1? recapture approach Naïve approach with p = 1
  • 7. Why bother with p < 1? 0.60.81.0 Capture- recapture Survival Bias in survival and rate of senescence (Gimenez et al. 2008 Am. Nat.) 2 4 6 8 10 12 14 0.20.4 recapture approach Naïve approach with p = 1Age
  • 8. Why bother with p < 1? 0.40.60.81.0 Survival Capture- recapture approach -4 -2 0 2 4 0.00.20.4 Body mass Survival approach Naïve approach with p = 1 Bias in shape of selection (Gimenez et al. 2008 Am. Nat.)
  • 9. Issue 2: individual heterogeneity Simple CR models assume homogeneity From a statistical point of view, IH can cause bias in parameter estimatesbias in parameter estimates
  • 10. 150 200 250 300 H+P+QI CJS Homogeneity N Impact of IH on abundance estimation Heterogeneity 0 50 100 64 [29 ; 111] 33 [17 ; 54] Bias in abundance estimation (Cubaynes et al. 2010 Cons. Biol.; L. Marescot’s PhD) time
  • 11. Issue of individual heterogeneity Standard CR models assume homogeneity From a statistical point of view, IH can cause bias in parameter estimatesbias in parameter estimates From a biological point of view, IH is of interest – individual quality
  • 12. What is individual quality? Quality varies among individuals within a population High quality individuals have greater fitness than low quality ones ⇒ Among-individual heterogeneity that⇒ Among-individual heterogeneity that is positively correlated to fitness (Wilson & Nussey in press)
  • 13. Quality varies among individuals within a population High quality individuals have greater fitness than low quality ones ⇒ Among-individual heterogeneity that is positively correlated to fitness (Wilson & Nussey 2009) Why is it so important? What is individual quality? Why is it so important? Natural selection can occur if individuals vary in phenotype and fitness A response to selection depends on this variation having a genetic basis IH may lead to flawed inference
  • 14. Accounting for individual heterogeneity CR models do not cope that well with quality Accumulation of long-term individual data If you’re a biologist, rely on empirical measures (mass, gender, age, experience, etc.) How to account for individual heterogeneity? measures (mass, gender, age, experience, etc.) How to incorporate this information? If you’re a statistician, intrinsic property of individuals How to filter out the signal from noisy obs.?
  • 15. Survival kit in CR How to account for variation in individual quality when assessing senescence and trade-offs Case study 1: describing senescence Outline of the talk Case study 1: describing senescence Case study 2: detecting trade-offs Can quality have a genetic basis or is it a consequence of environmental effects? Case study 3: quantifying heritability Perspectives
  • 16. Survival kit in CR How to account for variation in individual quality when assessing senescence and trade-offs Case study 1: describing senescence Outline of the talk Case study 1: describing senescence Case study 2: detecting trade-offs Can quality have a genetic basis or is it a consequence of environmental effects? Case study 3: quantifying heritability Perspectives
  • 17. Common marking methods • Ear tags for mammals / leg bands for birds. • Passive integrated transponder (PIT) tags.
  • 18. tigers Marking by camera-trap / photo-identification whales
  • 19. • Individuals are uniquely identified using microsatellite profiling on hair, dung, … samples wolf (dung) Marking by noninvasive genetic sampling bear (hair) bat (droppings) elephant (dung)orang-utan (hair)
  • 20. Capture-recapture data An encounter history: hi = (1 0 1)
  • 21. An encounter history: hi = (1 0 1) 1 0 1 φ Modelling CR data Survival probability φ 1 0 1
  • 22. An encounter history: hi = (1 0 1) 1 0 1 φ Modelling CR data Detection probability p 1 0 1 p−1
  • 23. An encounter history: hi = (1 0 1) 1 0 1 φ φ Modelling CR data 1 0 1 p−1
  • 24. An encounter history: hi = (1 0 1) 1 0 1 φ φ Modelling CR data 1 0 1 p−1 p
  • 25. An encounter history: hi = (1 0 1) 1 0 1 φ φ ( ) ( ) pph 1Pr φφ −= Modelling CR data Survival probability φ Detection probability p 1 0 1 p−1 p ( ) ( ) pphi 1Pr φφ −=
  • 26. A probabilistic framework ( ) ( ) pphi 1Pr φφ −= Modelling CR data
  • 27. A probabilistic framework Central role of likelihood (frequentist / bayesian) ( ) ( ) pphi 1Pr φφ −= Modelling CR data Central role of likelihood (frequentist / bayesian) ( )∏= i ihL Pr
  • 28. A probabilistic framework Central role of likelihood (frequentist / bayesian) ( ) ( ) pphi 1Pr φφ −= Modelling CR data Central role of likelihood (frequentist / bayesian) How to account for IH in iφ ( )∏= i ihL Pr
  • 29. Introduction: survival kit in CR How to account for variation in individual quality when assessing senescence and trade-offs Case study 1: describing senescence Outline Case study 1: describing senescence Case study 2: detecting trade-offs Can quality have a genetic basis or is it a consequence of environmental effects? Case study 3: quantifying heritability Perspectives
  • 30. « Over time, the observed hazard rate will approach the hazard rate of the more robust subcohort » Vaupel and Yashin 1985 Am. Stat. Suggest that analyses conducted at the population vs. individual level should differ (Cam Impact of IH on age-varying survival population vs. individual level should differ (Cam et al. 2002) What if detection p < 1 ?
  • 31. Scenario 1: finite mixture of individuals Use mixture models (Pledger et al. 2003) Latent variable for the class to which an individual belongs (Pradel 2009)individual belongs (Pradel 2009) 2 classes of individuals (low vs. high quality)
  • 32. Probabilities in a mixture model Under heterogeneity: π is the probability that the individual belongs to state L φL is survival for low quality individuals φH is survival for high quality individuals
  • 33. Probabilities in a mixture model Under heterogeneity: ( ) ( ) ( ) ( ) pppp HHLL ⋅⋅−⋅⋅−+⋅⋅−⋅⋅= φφπφφπ 111101Pr π is the probability that the individual belongs to state L φL is survival for low quality individuals φH is survival for high quality individuals
  • 34. Scenario 1: finite mixture of individuals 2 classes of individuals (fragile vs. robust) Use mixture models (Pledger et al. 2003) A model with a hidden structure, with aA model with a hidden structure, with a latent variable for the class to which an individual belong to (HMM; Pradel 2009) Mimic examples in Vaupel and Yashin (1985) with p < 1 using simulated data
  • 35. 0.6 0.7 0.8 0.9 1 Sub-cohort 2 100 individuals (the most robust) Survival 0 2 4 6 8 10 12 14 0.2 0.3 0.4 0.5 Sub-cohort 1 400 individuals (the most fragile) Age
  • 36. 0.6 0.7 0.8 0.9 1 Fit at the population level Sub-cohort 2 100 individuals (the most robust) Survival 0 2 4 6 8 10 12 14 0.2 0.3 0.4 0.5 Sub-cohort 1 400 individuals (the most fragile) Age
  • 37. 0.5 0.6 0.7 0.8 0.9 1 Fit at the population level Sub-cohort 2 100 individuals (the most robust) Survival 0 2 4 6 8 10 12 14 0 0.1 0.2 0.3 0.4 Fit at the individual level using a 2-class mixture Sub-cohort 1 400 individuals (the most fragile) Age
  • 38. Real case study on Black-headed Gulls Not so simple in real life Guillaume Péron’s PhD on Black- headed gulls (R. Pradel & P.-A. Crochet)headed gulls (R. Pradel & P.-A. Crochet) Several potential sources of IH
  • 39. Detection heterogeneity (1) zone 1: nests inside the vegetation La Ronze pond
  • 40. Detection heterogeneity (1) zone 1: nests inside the vegetation zone 2: nests on the edge of vegetation clusters La Ronze pond
  • 41. Even more heterogeneity Emigration heterogeneity (2) ♀ ♂ Immigrant Locally born Emigration – Emigration + Survival heterogeneity (3) ♀ ♂ Poor quality Good quality Survival + Survival –
  • 42. Modelling multiple sources of heterogeneity But, Little sexual dimorphism Sometimes no knowledge of birth site, No measure of individual quality Consider mixture of individuals: low / highConsider mixture of individuals: low / high Survival senescence with / without IH
  • 43. Results - Péron et al. (in press) Oïkos • Absence of survival heterogeneity
  • 44. Results - Péron et al. (in press) Oïkos • Absence of survival heterogeneity • Presence of detection and emigration heterogeneity
  • 45. Results - Péron et al. (in press) Oïkos • Absence of survival heterogeneity • Presence of detection and emigration heterogeneity • If ignored, heterogeneity in emigration masks senescence in survival
  • 46. Results - Péron et al. (in press) Oïkos 0.60.81 Survivalprobabilities Estimation of survival senescence 00.20.40.6 0 10 20 Age Survivalprobabilities • Absence of survival heterogeneity • Presence of detection and emigration heterogeneity • If ignored, heterogeneity in emigration masks senescence in survival
  • 47. Case study 2: continuous mixture of individuals What if I have a continuous mixture of individuals? Use individual random-effect modelsUse individual random-effect models CR mixed models (Gimenez & Choquet 2010)
  • 48. Explain individual variation in survival No variation – homogeneity Individual random-effect models φ Random effect – in-between Saturated – full heterogeneity iφ ( )2 ,~ σφφ Ni
  • 49. Explain individual variation in survival No variation – homogeneity Individual random-effect models φ Random effect – in-between Saturated – full heterogeneity iφ ( )2 ,~ σφφ Ni
  • 50. Explain individual variation in survival No variation – homogeneity Individual random-effect models φ Individual random effect – in-between Saturated – full heterogeneity iφ ( )2 ,~ σµφ Ni
  • 51. Case study 2: continuous mixture of individuals What if I have a continuous mixture of individuals? Use individual random-effect models (Royle 2008, Gimenez & Choquet 2010)2008, Gimenez & Choquet 2010) Mimic examples in Vaupel and Yashin (1985) with p < 1 using simulated data
  • 52. 0.7 0.8 0.9 1 300 individuals logit(φφφφi(a)) = 1.5 - 0.05 a + ui ui ~ N(0,σσσσ=0.5) Survival 0 2 4 6 8 10 12 14 0.4 0.5 0.6 Age
  • 53. 0.7 0.8 0.9 1 Expected pattern E(logit(φφφφi(a))) = 1.5 - 0.05 aSurvival 0 2 4 6 8 10 12 14 0.4 0.5 0.6 Age
  • 54. 0.7 0.8 0.9 1 Fit at the population level Survival 0 2 4 6 8 10 12 14 0.4 0.5 0.6 Age
  • 55. 0.7 0.8 0.9 1 Fit at the individual level with an individual random effectSurvival 0 2 4 6 8 10 12 14 0.4 0.5 0.6 Age
  • 57. Senescence in European dippers with IH: onset = 1.94 Marzolin et al. (in revision) Ecology
  • 58. Senescence in European dippers without IH: onset = 2.28 with IH: onset = 1.94 Marzolin et al. (in revision) Ecology
  • 59. Introduction: survival kit in CR How to account for variation in individual quality when assessing senescence and trade-offs Case study 1: describing senescence Outline Case study 1: describing senescence Case study 2: detecting trade-offs Can quality have a genetic basis or is it a consequence of environmental effects? Case study 3: quantifying heritability Perspectives
  • 60. M. Buoro (co-dir. E. Prévost1) Photo: Paul Nicklen (National Geographic) 1 UMR INRA/UPPA Ecobiop, Saint Pée s/ Nivelle, France
  • 61. Natural selection favors individuals that maximize their fitness Limited energy budget: strategy of resource allocation Assessing trade-offs in the wild resource allocation Trade-off between traits related to fitness Issue of detectability, again
  • 62. Atlantic salmon life cycle Freshwater Reproduction Development of juveniles Sea Migration to sea Growth at sea Migration to stream
  • 68. Freshwater Sexual maturation Residents Juveniles Migrants 2nd year 1st year of life Autumn Spring Autumn Migrants maturation Sea Adults 2nd year of life Spring
  • 71. Juveniles Migrants Is there a tradeoff between Winter survival Autumn Spring Is there a tradeoff between migration and winter survival?
  • 72. State-space model (Gimenez et al. 2007) Dynamic process model Observation
  • 73. State-space model Dynamic process model Observation Juveniles marked in autumn Migrants recaptured in spring
  • 76. Dynamic process model State-space model Observation Probabilistic reaction norm Size Migration probability Migration choice Juveniles marked in autumn iκ iMisize Migrants recaptured in spring ( ) ii size×+= 21logit ββκ
  • 77. State-space model Observation Size Migration probability Migration choice Juveniles marked in autumn Dynamic process model Migrants recaptured in spring Migrants Surviving Survival probability iφ
  • 78. State-space model Observation Size Migration probability Juveniles marked in autumn Migration choice Selective mortality iM Migrants recaptured in spring Migrants Survivor Survival probability iφ
  • 79. State-space model Observation Size Migration probability Juveniles marked in autumn Migration choice Selective mortality iM Migrants recaptured in spring Migrants Survivor Survival probability Random effect ( ) iii M εααφ +×+= 21logit iφiε
  • 80. State-space model Observation Size Migration probability Juveniles marked in autumn Migration choice Dynamic process model Migrants recaptured in spring Migrants Survivor Survival probability Random effect Detection probability
  • 81. State-space model Observation Size Migration probability Juveniles marked in autumn Migration choice Dynamic process model ( ) size×+=logit ββκ iκ iMisize Migrants recaptured in spring Migrants Survivor Survival probability Random effect Detection probability ( ) iii M εααφ +×+= 21logit ( ) ii size×+= 21logit ββκ iφiε
  • 83. 50 55 60 65 70 75 80 85 90 95 100 105 110 115 120 125 130 0.00.20.40.60.81.0 MigrationProbability Probabilistic reaction norm Size-dependent probabilistic reaction norm for age at migration Results (1) – Buoro et al. (in press) Evolution Size (mm)
  • 84. 50 55 60 65 70 75 80 85 90 95 100 105 110 115 120 125 130 0.00.20.40.60.81.0 MigrationProbability Probabilistic reaction norm Size-dependent probabilistic reaction norm for age at migration Results (1) – Buoro et al. (in press) Evolution Size (mm) Juveniles longer than 100 mm in autumn has a probability to migrate close to 1.
  • 85. 50 55 60 65 70 75 80 85 90 95 100 105 110 115 120 125 130 0.00.20.40.60.81.0 MigrationProbability Probabilistic reaction norm Size-dependent probabilistic reaction norm for age at migration Results (1) – Buoro et al. (in press) Evolution Size (mm) Juveniles longer than 100 mm in autumn has a probability to migrate close to 1. A juvenile of 90 mm has 50% of chance of migrating to the sea at 1year of age.
  • 86. 50 55 60 65 70 75 80 85 90 95 100 105 110 115 120 125 130 0.00.20.40.60.81.0 MigrationProbability Probabilistic reaction norm Size-dependent probabilistic reaction norm for age at migration Results (1) – Buoro et al. (in press) Evolution Size (mm) Juveniles longer than 100 mm in autumn has a probability to migrate close to 1. Juveniles shorter than 60 mm in autumn has a probability to migrate almost null. A juvenile of 90 mm has 50% of chance of migrating to the sea at 1year of age.
  • 87. 50 55 60 65 70 75 80 85 90 95 100 105 110 115 120 125 130 0.00.20.40.60.81.0 MigrationProbability Probabilistic reaction norm Size-dependent probabilistic reaction norm for age at migration Results (2) – Buoro et al. (in press) Evolution Size (mm) Migrants Residents 0.00.20.40.60.81.0 Survival cost in deciding to stay an extra year in freshwater Selective mortality SurvivalProbability
  • 88. Introduction: survival kit in CR How to account for variation in individual quality when assessing senescence and trade-offs Case study 1: describing senescence Outline Case study 1: describing senescence Case study 2: detecting trade-offs Can quality have a genetic basis or is it a consequence of environmental effects? Case study 3: quantifying heritability Perspectives
  • 89. Heritability in the wild Quantitative genetics: assess the ability of a trait to respond to natural selection Increasing used in animal and plant pops Heritability: proportion of the phenotypicHeritability: proportion of the phenotypic var. attributed to additive genetic var. For (demographic) parameters strongly related to fitness, we expect low heritability Predictions not so clear in wild populations
  • 90. Heritability in the wild Animal models: mixed models incorporating genetic, environmental and other factors. Capture-recapture models: assess demographic parameters with p < 1 anddemographic parameters with p < 1 and individual variability. The idea of combining Animal and Capture- recapture models is in the air (O’Hara et al. 2008; Cam 2009).
  • 91. The idea is in the air (O’Hara et al. 2008)
  • 92. The idea is in the air (Cam 2009) " [The animal model has] been applied to estimation of heritability in life history traits, either in the rare study populations where detection probability is close to 1, or withoutdetection probability is close to 1, or without considering the probability of detecting animals (...) "
  • 93. Introducing the threshold model Main issue: survival is a discrete process, but animal models use continuous distributions
  • 94. Introducing the threshold model Main issue: survival is a discrete process, but animal models use continuous distributions Survival is related to a continuousSurvival is related to a continuous underlying latent
  • 95. Liability ind. i dies on (t,t+1) li,t ∼ N( i,t ,σ2) ind. i survives on (t,t+1)
  • 96. It can be shown that survival and mean liability are linked For some function G, we have: Plug in the animal model ( ) iittii,t aebG +++== ηµφ ,
  • 97. It can be shown that survival and mean liability are linked For some function G, we have: Plug in the animal model ( ) iittii,t aebG +++== ηµφ , mean survival
  • 98. It can be shown that survival and mean liability are linked For some function G, we have: Plug in the animal model ( ) iittii,t aebG +++== ηµφ , yearly effect mean survival ( )2 ,0~ tt Nb σ
  • 99. It can be shown that survival and mean liability are linked For some function G, we have: Plug in the animal model ( ) iittii,t aebG +++== ηµφ , yearly effect mean survival non-genetic effect ( )2 ,0~ tt Nb σ ( )2 ,0~ ei Ne σ
  • 100. It can be shown that survival and mean liability are linked For some function G, we have: Plug in the animal model ( ) iittii,t aebG +++== ηµφ , additive genetic effect yearly effect mean survival non-genetic effect ( )2 ,0~ tt Nb σ ( )2 ,0~ ei Ne σ ( ) ( )AMNaa aN 2 1 ,0~,, σK
  • 101. Case study on blue tits in Corsica Mark-recapture data Social pedigree • Blue tits – Study site in Corsica. • 1979 – 2007 ⇒ 29 years of monitoring)! 654 individuals, 218 fathers (sires), 215 mothers (dams), 12 generations.
  • 102. Additive genetic variance Papaïx et al. (to be resubmitted) Evolution Posterior median = 0.110, 95% credible interval = [0.006; 0.308]
  • 103. Introduction: survival kit in CR How to account for variation in individual quality when assessing senescence and trade-offs Case study 1: describing senescence Outline Case study 1: describing senescence Case study 2: detecting trade-offs Can quality have a genetic basis or is it a consequence of environmental effects? Case study 3: quantifying heritability Conclusions & perspectives
  • 104. Conclusions IH needs to be accounted for, otherwise Mask senescence (PhD G. Péron) Obscur life-history tradeoffs (PhD M. Buoro) Influence decision-making in management (PhD L. Marescot) CR methodology is catching up with ‘p=1’ world CR methodology is catching up with ‘p=1’ world Recent statistical methods can help in coping with IH when p < 1 Whenever possible, adopt a biological view and measure quality in the field
  • 105. Perspectives - methods Continue efforts in developing methods to properly account for individual heterogeneity Fit and compare models (PhD S. Cubaynes) Is heritability important in blue tits (model selection)?selection)? Speed up estimation?
  • 106. Perspectives - Methods Continue efforts in developing methods Individual heterogeneity: fit and compare models (PhD S. Cubaynes) Speed up estimation? Is heritability important in blue tits (model selection)? Shall we go for discrete or continuous heterogeneity?Shall we go for discrete or continuous heterogeneity? Transfer of knowledge - teaching
  • 107. Perspectives - Methods Continue efforts in developing methods Individual heterogeneity: fit and compare models (PhD S. Cubaynes) Speed up estimation? Is heritability important in blue tits (model selection)? Shall we go for discrete or continuous heterogeneity?Shall we go for discrete or continuous heterogeneity? Transfer of knowledge - workshops
  • 108. Workshops Bayesian ecology – StAndrews 2009 Occupancy – Montpellier 2008Bayesian ecology – StAndrews 2009 Capture-recapture – Montpellier 2002 Occupancy – Montpellier 2008 Population dynamics – Mytilini 2007
  • 109. Perspectives - Methods Continue efforts in developing methods Individual heterogeneity: fit and compare models (PhD S. Cubaynes) Speed up estimation? Is heritability important in blue tits (model selection)? Shall we go for discrete or continuous heterogeneity?Shall we go for discrete or continuous heterogeneity? Transfer of knowledge Software implementation
  • 110. Implementation issues: software Program E-SURGE Individual covariates, mixtures and individual random effects R. Choquet & E. Nogué
  • 111. Perspectives - Biology Consider other demographic parameters (dispersal and breeding probabilities e.g.); → A. Charmantier & B. Doligez From individuals to species → E. Papadatou’s post-doc & S. Cubaynes’s PhD→ E. Papadatou’s post-doc & S. Cubaynes’s PhD → Museum for community ecology aspects Combine evolutionary and demography → S. Servanty’s post-doc & M. Gamelon’s Master
  • 112. Biologists Biological question Quant. methods needed Quant. methods employed Knowing what methods are available Addressing assumptions in study design Enriches the biologist Enriches the quant. types Methodologists needed Methods developed employed Understanding biology Communication Making methods available biologist quant. types Courtesy of P. Doherty
  • 114. Mentoring G. Ducharme J.-D. Lebreton R. Pradel S.T. Buckland B.J.T. Morgan
  • 115. Inspiring T. Lenormand A. Charmantier J.-M. Gaillard E. Cam M. Schaub M. Ancrenaz A. Besnard C. Barbraud V. Grosbois P.-A. Crochet
  • 116. Stimulating M. Buoro F. Guilhaumon L. Marescot S. Cubaynes G. PéronS. Véran E. Papadatou S. Servanty M. Desprez M. Gamelon B. Testi