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![Page 1: Connection My current lab group David Matlaga (PhD expected 2008)David Matlaga (PhD expected 2008) Demographic and experimental comparative ecology of.](https://reader036.fdocuments.us/reader036/viewer/2022062716/56649de55503460f94adcacb/html5/thumbnails/1.jpg)
connection
My current lab group
• David Matlaga (PhD expected 2008)David Matlaga (PhD expected 2008)Demographic and experimental comparative ecology Demographic and experimental comparative ecology
of clonal propagules vs. seedlings of a neotropical of clonal propagules vs. seedlings of a neotropical herbherb
• Carlos Garcia-Robledo (PhD expected 2009)Carlos Garcia-Robledo (PhD expected 2009)Demographic, ecological and evolutionary response of Demographic, ecological and evolutionary response of
specialist and generalist rolled-leaf herbivores to specialist and generalist rolled-leaf herbivores to novel exotic host plants in the Zingiberales: field novel exotic host plants in the Zingiberales: field and lab experimentsand lab experiments
• Lucero Sevillano (PhD expected 2009)Lucero Sevillano (PhD expected 2009)Demographic impact of two insects (biocontrol agents) Demographic impact of two insects (biocontrol agents)
on an invasive exotic tree in the Evergladeson an invasive exotic tree in the Everglades• John Cozza (PhD expected 2008)John Cozza (PhD expected 2008)
Gender plasticity and optimality in a neotroprical Gender plasticity and optimality in a neotroprical Begonia: effects of light, minerals and Begonia: effects of light, minerals and developmental constraintsdevelopmental constraints
• Robert McElderry (PhD expected 2013)Robert McElderry (PhD expected 2013)Not yet defined: something to do with demography, Not yet defined: something to do with demography,
herbivory and rarity in a tropical or subtropical plantherbivory and rarity in a tropical or subtropical plant
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Collaborative projects include
A time to grow and a time to die: size, light, age and death of tropical trees (J. Metcalf, CH, S. Tuljapurkar)
Context-dependent pollinator limitation: the future matters in a stochastically varying environment (CH and J. Ehrlen)
Rate of spread of an invasive, tropical shrub (Ardisia elliptica) depends upon proportion of seeds taken by mammalian vs avian dispersers (A. Koop and CH)
An integral projection model for a neotropical treelet: do pollinators matter and is there a pollinator-driven Allee effect? (S. Buzato and L. Lopes, J. Metcalf and CH)
Demographic dynamics of invasive strawberry guava in Hawaii before and after introduction of a biocontrol agent (J. Denslow and CH)
… and, among others, today’s talk:
![Page 3: Connection My current lab group David Matlaga (PhD expected 2008)David Matlaga (PhD expected 2008) Demographic and experimental comparative ecology of.](https://reader036.fdocuments.us/reader036/viewer/2022062716/56649de55503460f94adcacb/html5/thumbnails/3.jpg)
A new way to integrate selection when both
demography and selection gradients vary
over time
Carol Horvitz1, Tim Coulson2, Shripad Tuljapurkar3 , Douglas
Schemske4
1 University of Miami, Coral Gables, FL2Imperial College, Silwood Park, London,
UK3 Stanford University, Stanford, CA
4 Michigan State University, East Lansing, MI
![Page 4: Connection My current lab group David Matlaga (PhD expected 2008)David Matlaga (PhD expected 2008) Demographic and experimental comparative ecology of.](https://reader036.fdocuments.us/reader036/viewer/2022062716/56649de55503460f94adcacb/html5/thumbnails/4.jpg)
floral tube length and birth date
How can we integrate variable selection across years?
*for structured populations and overlapping generations
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Preview: Integrated selection
on Calathea floral tube length
El niño driven -0.071
Stasis -0.098
Tree-fall -0.156Dry season severity -0.103
Environmental driver Selection
_____________________________________________
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Preview: Integrated selection
on red deer birth date
NAO driven -0.247
26-yr cycle -0.289
IID and equal -0.287
Quality correlated -0.239
Environmental driver Selection
_____________________________________________
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Preview:
Integrated selection
•Environment-specific elasticity
X•Environment-specific selection gradient •summed across all relevant life history and
environmental paths
Horvitz, Coulson, Tuljapurkar, Schemske (in prep)
![Page 8: Connection My current lab group David Matlaga (PhD expected 2008)David Matlaga (PhD expected 2008) Demographic and experimental comparative ecology of.](https://reader036.fdocuments.us/reader036/viewer/2022062716/56649de55503460f94adcacb/html5/thumbnails/8.jpg)
a small tropical Mexican herb and a large Scottish mammal
• Fitness components and stochastic growth rate
• Selection gradients vary • Demographic transitions vary• Environmental states are
dynamic• Environmental driver matters
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a small tropical Mexican herb and a large Scottish mammal
Floral tube length
(pollinator related)3 yrs of selection
gradientsFruit productionDemographic
projection matrices for 4 yrs
Local, regional and global environmental dynamics
Birth date (seasonal
advantage)26 yrs of selection
gradients Recruitment and
survival for two classes
Demographic projection matrices for 26 yrs
Local, regional and global environmental dynamics
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Phenotypic selection theory
Relative fitness regressed against quantitative trait value
The slope of the regression = selection gradient for the trait
(Lande and Arnold 1983 Evolution)fitn
ess
something quantitative
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Candidate parameters for measuring fitness
• Fitness components• Reproduction (stage-
specific)• Survival (stage-specific)• Growth (stage-specific)
• Population growth rate
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Candidate parameters for measuring fitness
• Fitness components• Reproduction (stage-environment-
specific)• Survival (stage-environment-specific)• Growth (stage-environment-specific)
Stochastic growth rate
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Schemske and Horvitz 1989 Evolution
**83-84 84-85 85-86-8
-6
-4
-2
0
2
4
Habitat
Gra
die
nte
de
se
lecc
ion
Frutos maduros vs tamano de la flor (relativa, estandardizada por la media)
**
Fitness component vs floral tube length(relative, mean-standardized)
Sta
nd
ard
ized
sele
ctio
n
Years => Environments
mature fruits
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Years => Environments
Fitness component vs birth date(relative, mean-standardized)
Coulson et al. 2003 Evolution
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Demographic transitions and fitness in a constant world
• N(t+1) = A N(t) • A is a population projection matrix• Transitions and contributions
between stages, aij = fitness components
• λ = population growth rate
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• N(t+1) = X(t) N(t) • X(t) is a random variable A1, A2, A3…AK , K environments
• Transitions and contributions in each environment, aijβ
• λS = stochastic growth rate
Tuljapurkar 1982, 1990
Demographic transitions and fitness in a variable world
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In a variable world : sequences, frequencies and new sensitivities
• Environmental dynamics • sequences along sample paths• an expected long run stationary distribution
• λs is sensitive to perturbations of means,
variances, and transitions in particular environmental states
• Eδ, Eμ, Eβ and others…
Tuljapurkar et al. 2003 Am Nat
Horvitz et al. 2005 Ecology
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Environmental dynamics: Scaling up using climate data
• Calathea : “Dry season ” driver• Red Deer: “NAO” driver
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Sample years in context of historical record
Precipitacion por mes, epoca de sequia, novx - mayx+1
00030146 SAN ANDRES TUXTLA
020406080
100120
26-2
7
29-3
0
32-3
3
35-3
6
38-3
9
41-4
2
44-4
5
47-4
8
50-5
1
53-5
4
56-5
7
59-6
0
62-6
3
65-6
6
68-6
9
71-7
2
74-7
5
77-7
8
80-8
1
83-8
4
86-8
7
Monthly rainfall during the dry season only
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Sample years in context of historical record
Monthly rainfall during the dry season only
1860 1880 1900 1920 1940 1960 1980 2000 2020-6
-4
-2
0
2
4
6
Year, starting with 1864
Annual Deviations from Mean: NAO 1864-2006
Annual Deviations from Mean NAO 1864-2006
Year, starting with 1864
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1 2 3 4
1
2
3
4
Habitat en tiempo t
Transiciones del habitat
Ha
bita
t en
tie
mp
o t
+1
1 2 3 4
1
2
3
4
Habitat en tiempo t
Transiciones del habitat
Ha
bita
t en
tie
mp
o t
+1
1 2 3 4
1
2
3
4
Habitat en tiempo t
Transiciones del habitat
Ha
bita
t en
tie
mp
o t
+1
1 2 3 4
1
2
3
4
Habitat en tiempo t
Transiciones del habitat
Ha
bita
t en
tie
mp
o t
+1
Hypothetical environmental drivers markov chain models
El niño
Stasis
Dry season
Tree-falls
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Hypothetical environmental drivers markov chain models
Quality correlatedNAO
IID and equal
26-yr cycle
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Hypothetical environmental drivers markov chain models
Quality correlatedNAO
IID and equal
26-yr cycle
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• …2 3 4 3 3 2 2 2 4 4 3 1 3 2 2 3…El Niño
• …1 3 2 1 1 1 1 3 1 3 1 3 2 1 1 1…Dry season
• …3 3 3 3 3 3 3 1 4 4 2 2 3 3 3 3…Tree-falls
• …1 1 2 2 2 2 2 2 3 3 3 3 3 3 3 3…Stasis
Sequences for hypothetical environmental drivers
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Sequences for hypothetical environmental drivers
• …17 11 11 17 6 6 11 6 6 11 4 11 6 22 20…
NAO
• …7 15 22 10 22 3 13 3 22 21 13 2 20 …Quality correlated
• …2 18 19 6 2 4 1 25 3 17 4 20 10 9 4 …
IID and equal• …11 12 13 14 15 16 17 18 19 20 21 22 23 …
26-yr cycle
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3 4 5 6 7 80
1
2
3
4
5
6
7
8
9x 10
-3
Estadio de historia de vida
Ela
stic
ida
d p
or
ha
bita
t-e
sta
dio
Sensibilidad de s a reproduccion por distintos estadios
82-8383-8484-8585-86
3 4 5 6 7 80
1
2
3
4
5
6
7
8
9x 10
-3
Estadio de historia de vida
Ela
stic
ida
d p
or
ha
bita
t-e
sta
dio
Sensibilidad de s a reproduccion por distintos estadios
82-8383-8484-8585-86
3 4 5 6 7 80
0.5
1
1.5
2
2.5
3
3.5
4
4.5x 10
-3
Estadio de historia de vida
Ela
stic
ida
d p
or
ha
bita
t-e
sta
dio
Sensibilidad de s a reproduccion por distintos estadios
82-8383-8484-8585-86
3 4 5 6 7 80
0.5
1
1.5
2
2.5
3
3.5x 10
-3
Estadio de historia de vida
Ela
stic
ida
d p
or
ha
bita
t-e
sta
dio
Sensibilidad de s a reproduccion por distintos estadios
82-8383-8484-8585-86
Environment-specific elasticity of λs for each driver (to seed production)
El niño
Stasis
Dry season
Tree-falls
Years => Environments
En
vir
on
men
t-sp
eci
fic
Ela
stic
ity
Stage class
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Environment-specific elasticity of λs with NAO driver
0 2 4 6 8 10 120
0.5
1
1.5
2x 10
-3
age class
elas
ticity
habitat-stage elasticity of female recruitment, s=1.0275
0 2 4 6 8 10 120
2
4
6
8x 10
-3
age class
elas
ticity
habitat-stage elasticity of female survival, s=1.0275
1975
1976
1977
1978
1979
1980
1981
1982
1983
1984
1985
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
Survival
Recruitment
En
vir
on
men
t-sp
eci
fic
Ela
stic
ity
Age class
Years =
> E
nviro
nm
ents
NAO
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0 2 4 6 8 10 120
0.5
1
1.5
2x 10
-3
age class
elas
ticity
habitat-stage elasticity of female recruitment, s=1.0426
0 2 4 6 8 10 120
2
4
6
8x 10
-3
age class
elas
ticity
habitat-stage elasticity of female survival, s=1.0426
1975
1976
1977
1978
1979
1980
1981
1982
1983
1984
1985
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
Survival
Recruitment
En
vir
on
men
t-sp
eci
fic
Ela
stic
ity
Age class
Years =
>
En
viro
nm
en
tsQualitycorrelated
Environment-specific elasticity of λs for
different driver…
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Integrated elasticity
•stage-specific elasticity , eij = change in λ due to a change in one element of the matrix
X•selection gradient = change in one element
of the matrix due to a change in the trait value
(van Tienderen 2000 Ecology, Coulson et al. 2003 Evolution)
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Integrated stochastic elasticity Integrated selection
•Environment-specific elasticity, eijβ = change in λS due to a change in one matrix element in one state of the environment
X•selection gradient = change in one matrix
element in one state of the environment due to a change in the trait value
Horvitz, Coulson, Tuljapurkar, Schemske (in prep)
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Calathea
• Each matrix is 8x8• 4 environments (let’s look at 1) • Selection gradient
• only on top row• All reproductive stages have same
value
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1 2 3 4 5 6 7 8
1 2 3 4 5 6 7 8
0
0.05
0.1
Habitat-specific elasiticity, 83-84
1 2 3 4 5 6 7 8
1 2 3 4 5 6 7 8
0
2
4
Selection gradient, 83-84
1 2 3 4 5 6 7 8
1 2 3 4 5 6 7 8
0
0.005
0.01
0.015
Integrated selection, 83-84
1 example (there are 4 per driver) “dry season” driver, envt 83-84
×
=
(elementwise multiplication)
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Red deer
• Each matrix is 20 x 20• 26 environments• environment-specific elasticity
• males : zero• females : recruitment and survival each
age• females are in 11 x 11 matrix, top left
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12
34
56
78
910
11
12
34
56
78
910
11
-5
-4
-3
-2
-1
0
x 10-3
Integrated selection, envt 5
12
34
56
78
910
11
12
34
56
78
910
11
-2.5
-2
-1.5
-1
-0.5
0
Selection gradient, envt 5
12
34
56
78
910
11
12
34
56
78
910
11
0
2
4
6
8
x 10-3
Environment-specific elasticity, envt 5
1 example (there are 26 per driver) “NAO” driver, envt 5
×
=
(elementwise multiplication)
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Integrated selection by environmental state and TOTAL
82-83 83-84 84-85 85-86-0.14
-0.12
-0.1
-0.08
-0.06
-0.04
-0.02
0
0.02
0.04
E
last
icid
ad
X S
ele
ccio
n
Habitat
Seleccion integrada sobre el tamano de la flor, total = -0.070646
82-83 83-84 84-85 85-86-0.14
-0.12
-0.1
-0.08
-0.06
-0.04
-0.02
0
0.02
0.04
E
last
icid
ad
X S
ele
ccio
n
Habitat
Seleccion integrada sobre el tamano de la flor, total = -0.10324
82-83 83-84 84-85 85-86-0.14
-0.12
-0.1
-0.08
-0.06
-0.04
-0.02
0
0.02
0.04
E
last
icid
ad
X S
ele
ccio
n
Habitat
Seleccion integrada sobre el tamano de la flor, total = -0.15619
82-83 83-84 84-85 85-86-0.14
-0.12
-0.1
-0.08
-0.06
-0.04
-0.02
0
0.02
0.04
E
last
icid
ad
X S
ele
ccio
n
Habitat
Seleccion integrada sobre el tamano de la flor, total = -0.098643
El niñoTotal=-0.071
StasisTotal-0.098
Tree-fallsTotal=-0.156
Dry seasonTotal=-0.103
Years => Environments
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Integrated selection by environmental state and TOTAL
26-yr cycleTotal =-0.289
IID and equalTotal=-0.287
Quality correlatedTotal = -0.239
NAO Total = -0.247
Years => Environments
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yearling 2-yr old
3-yr old 4-yr old 5-yr old
6-yr old 7-yr old 8-yr old 9-yr old
10-yr old >10-yr old
yearling 2-yr old
3-yr old 4-yr old
5-yr old 6-yr old
7-yr old 8-yr old
9-yr old 10-yr old
>10-yr old
0
0.01
0.02
0.03
0.04
-Int
egra
ted
sele
ctio
n su
mm
ed b
y ij
Note:These are ALL negative
Integrated selection
by transition rate
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yearling 2-yr old 3-yr old 4-yr old 5-yr old 6-yr old 7-yr old 8-yr old 9-yr old 10-yr old >10-yr old-0.04
-0.035
-0.03
-0.025
-0.02
-0.015
-0.01
-0.005
0
Stage
Inte
grat
ed s
elec
tion
sum
med
for
each
sta
ge
reproduction
survival
Integrated selection by stage and type
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Conclusions
• New parameter • Integrates selection across the life cycle
and across changing environments• Uses λs and its sensitivities (by
environment)• The force of selection on a trait depends
upon environmental dynamics• Historical climate data combined with a few
years of demographic observations: plausible long run patterns
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Thanks
• 2006-08 NSF OPUS 1982-84, 1984-88 NSF • 1982National Geographic • NERC• Royal Society• Biotechnology and Biological Research
Council• Rum Red Deer Project• Field assistants, students and colleagues
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Extras for questions…
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Sample years in context of historical record
Precipitacion por mes, epoca de sequia, novx - mayx+1
00030146 SAN ANDRES TUXTLA
020406080
100120
26-2
7
29-3
0
32-3
3
35-3
6
38-3
9
41-4
2
44-4
5
47-4
8
50-5
1
53-5
4
56-5
7
59-6
0
62-6
3
65-6
6
68-6
9
71-7
2
74-7
5
77-7
8
80-8
1
83-8
4
86-8
7
Monthly rainfall during the dry season only
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Precipitacion por mes en epoca de sequia (nov-may)
-40
-20
0
20
40
60
82-83 83-84 84-85 85-86
Dif
eren
cia
de
la
med
ia l
arg
o
pla
zo,
mm
Monthly rainfall during the dry season only
Diff
ere
nce
fro
m
the lon
g-t
erm
mean
,
Years = Environments
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Sample years in context of historical record
Monthly rainfall during the dry season only
1860 1880 1900 1920 1940 1960 1980 2000 2020-6
-4
-2
0
2
4
6
Year, starting with 1864
Annual Deviations from Mean: NAO 1864-2006
Annual Deviations from Mean NAO 1864-2006
Year, starting with 1864
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-3 -2 -1 0 1 2 30
5
10
15
20
25
30
35Standardized deviations, (observed deviations)/std of NAO
Standardized annual deviations (observed/SD) of NAOHistorical data 1864-2006
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Flowers with trigger
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•Tongue length•Floral tube length
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Next slides exemplify differences due to sequence once frequency is accounted for…
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Elasticity of λs to stage-specific reproduction for each environmental state, normalized for frequency
3 4 5 6 7 80
0.002
0.004
0.006
0.008
0.01
0.012
0.014
Estadio de historia de vida
Ela
stic
ida
d p
or
ha
bita
t-e
sta
dio
, no
rma
liza
da
Sensibilidad de s a reproduccion por distintos estadios
82-8383-8484-8585-86
3 4 5 6 7 80
0.005
0.01
0.015
Estadio de historia de vida
Ela
stic
ida
d p
or
ha
bita
t-e
sta
dio
, no
rma
liza
da
Sensibilidad de s a reproduccion por distintos estadios
82-8383-8484-8585-86
3 4 5 6 7 80
0.005
0.01
0.015
Estadio de historia de vida
Ela
stic
ida
d p
or
ha
bita
t-e
sta
dio
, no
rma
liza
da
Sensibilidad de s a reproduccion por distintos estadios
82-8383-8484-8585-86
3 4 5 6 7 80
0.005
0.01
0.015
0.02
0.025
0.03
Estadio de historia de vida
Ela
stic
ida
d p
or
ha
bita
t-e
sta
dio
, no
rma
liza
da
Sensibilidad de s a reproduccion por distintos estadios
82-8383-8484-8585-86Stasis
Dry season
Tree-falls
Years => Environments
El niño
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1970 1975 1980 1985 1990 1995 2000 20050
0.05
0.1
0.15
0.2
survival of one-year olds
1970 1975 1980 1985 1990 1995 2000 20050
0.05
0.1
0.15
0.2
scal
ed h
abita
t-st
age
elas
ticity
survival of two-year olds
1970 1975 1980 1985 1990 1995 2000 20050
0.05
0.1
0.15
0.2
Habitat
survival of three-year olds
1970 1975 1980 1985 1990 1995 2000 20050
0.05
0.1
0.15
0.2
survival of one-year olds
1970 1975 1980 1985 1990 1995 2000 20050
0.05
0.1
0.15
0.2
scal
ed h
abita
t-st
age
elas
ticity
survival of two-year olds
1970 1975 1980 1985 1990 1995 2000 20050
0.05
0.1
0.15
0.2
Habitat
survival of three-year olds
1970 1975 1980 1985 1990 1995 2000 20050
0.05
0.1
0.15
0.2
survival of one-year olds
1970 1975 1980 1985 1990 1995 2000 20050
0.05
0.1
0.15
0.2
scal
ed h
abita
t-st
age
elas
ticity
survival of two-year olds
1970 1975 1980 1985 1990 1995 2000 20050
0.05
0.1
0.15
0.2
Habitat
survival of three-year olds
1970 1975 1980 1985 1990 1995 2000 20050
0.05
0.1
0.15
0.2
survival of one-year olds
1970 1975 1980 1985 1990 1995 2000 20050
0.05
0.1
0.15
0.2sc
aled
hab
itat-
stag
e el
astic
ity
survival of two-year olds
1970 1975 1980 1985 1990 1995 2000 20050
0.05
0.1
0.15
0.2
Habitat
survival of three-year olds
Elasticity of λs to the first 3 age-specific survivals for each environmental state, normalized for frequency
26 yr Cycle
Qualitycorrelated
Iid andequal
Years => Environments
NAO
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1 2 3 4 5 6 7 8
1 2 3 4 5 6 7 8
0
0.05
0.1
Habitat-specific elasiticity, 84-85
1 2 3 4 5 6 7 8
1 2 3 4 5 6 7 8
-10
-5
0
Selection gradient, 84-85
1 2 3 4 5 6 7 8
1 2 3 4 5 6 7 8
-0.03
-0.02
-0.01
0
Integrated selection, 84-85
×
=
Example: “dry season” driver, envt 84-85
(elementwise multiplication)
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Years => Environments
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1975 1977 1979 1981 1983 1985 1987 1989 1991 1993 1995 1997 1999-0.015
-0.01
-0.005
0
0.005
0.01
Environment
Inte
grat
ed s
elec
tion
sum
med
for
each
sta
ge
yearling
2-yr old
3-yr old
4-yr old
5-yr old
6-yr old
7-yr old
8-yr old
9-yr old
10-yr old
>10-yr old
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yearling 2-yr old 3-yr old 4-yr old 5-yr old 6-yr old 7-yr old 8-yr old 9-yr old 10-yr old >10-yr old-0.05
-0.045
-0.04
-0.035
-0.03
-0.025
-0.02
-0.015
-0.01
-0.005
0
Stage
Inte
grat
ed s
elec
tion
sum
med
for
each
sta
ge