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

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:

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

floral tube length and birth date

How can we integrate variable selection across years?

*for structured populations and overlapping generations

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

_____________________________________________

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

_____________________________________________

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)

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

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

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

Candidate parameters for measuring fitness

• Fitness components• Reproduction (stage-

specific)• Survival (stage-specific)• Growth (stage-specific)

• Population growth rate

Candidate parameters for measuring fitness

• Fitness components• Reproduction (stage-environment-

specific)• Survival (stage-environment-specific)• Growth (stage-environment-specific)

Stochastic growth rate

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

Years => Environments

Fitness component vs birth date(relative, mean-standardized)

Coulson et al. 2003 Evolution

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

• 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

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

Environmental dynamics: Scaling up using climate data

• Calathea : “Dry season ” driver• Red Deer: “NAO” driver

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

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

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

Hypothetical environmental drivers markov chain models

Quality correlatedNAO

IID and equal

26-yr cycle

Hypothetical environmental drivers markov chain models

Quality correlatedNAO

IID and equal

26-yr cycle

• …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

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

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

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

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…

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)

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)

Calathea

• Each matrix is 8x8• 4 environments (let’s look at 1) • Selection gradient

• only on top row• All reproductive stages have same

value

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)

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

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)

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

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

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

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

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

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

Extras for questions…

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

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

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

-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

Flowers with trigger

•Tongue length•Floral tube length

Next slides exemplify differences due to sequence once frequency is accounted for…

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

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

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)

Years => Environments

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

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