developmentofademo-geneticmodelforsfeand...

Context Model Parameter estimation Ongoing work

Development of a demo-genetic model for SFE andparameter estimation using Approximate Bayesian

Computing methods

Dominique Lamonica, Jörn Pagel, Frank Schurr

Applibugs - 21/06/2018

1/20


Study sites and species

Bordeaux Mont Ventoux

Barcelona

2/20


Collected data

• 15 "isolated" patches of spontaneous forests

• Exhaustive tree mapping (location and size)• Dendrochronological data• Genetic data

3/20


Collected data

• 15 "isolated" patches of spontaneous forests• Exhaustive tree mapping (location and size)• Dendrochronological data• Genetic data

3/20


Model overview

• Individual based model of tree population• Spatialized on a grid of 1m2 cell• One year time step

• Included processes : growth, mortality, fecundity, pollen and seeddispersal, tree establishment, parenthood relationship betweentrees

4/20


Model overview

• Individual based model of tree population• Spatialized on a grid of 1m2 cell• One year time step• Included processes : growth, mortality, fecundity, pollen and seeddispersal, tree establishment, parenthood relationship betweentrees

4/20


Model overview

5/20


Model overview

Growthdbh and neighbours

5/20


Model overview


Pollen fecundity dbhDispersal

5/20


Model overview



Seed fecundity dbhDispersal

5/20


Model overview



Seed fecundity dbhDispersal

Seed and pollenimmigration5/20


Model overview



Seed fecundity dbhDispersalYoung tree establishment

neighbours Seed and pollenimmigration5/20


Model overview




neighbours Seed and pollenimmigration

Parenthood assignation

5/20


Model overview






Mortalitydbh and growth rate

5/20


Model overview






Mortalitydbh and growth rate

22 parameters

5/20


Simulated forest development0 10 20 30 40 50 60 70

0

20

40

60

80

Population size

Years

Num

ber

of in

divi

dual

s0 10 20 30 40 50 60 70

0

2

4

6

8

Surface occupied by trees

Years

Sur

face

occ

upie

d by

tree

s (m

2)

−20 0 20 40 60

010

3050

Individual location on the grid and size

01320

60

100

0 10 20 30 40 50 60 700

102030405060

Size distribution

Years

Indi

vidu

al s

ize

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102030405060

Size trajectories of individuals alive after 70 years

Years

Indi

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al s

ize

0 10 20 30 40 50 60 700

1

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3

4

Growth rate trajectories of individuals alive after 70 years

Years

Indi

vidu

al g

row

th r

ate

6/20



0

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80

Population size

Years

Num

ber

of in

divi

dual

s0 10 20 30 40 50 60 70

0

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4

6

8


Years

Sur

face

occ

upie

d by

tree

s (m

2)

−20 0 20 40 60

010

3050


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100

0 10 20 30 40 50 60 700

102030405060

Size distribution

Years

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al s

ize

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102030405060


Years

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al g

row

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ate

General dataeg final size distribution

6/20



0

20

40

60

80

Population size

Years

Num

ber

of in

divi

dual

s0 10 20 30 40 50 60 70

0

2

4

6

8


Years

Sur

face

occ

upie

d by

tree

s (m

2)

−20 0 20 40 60

010

3050


01320

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100

0 10 20 30 40 50 60 700

102030405060

Size distribution

Years

Indi

vidu

al s

ize

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102030405060


Years

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al s

ize

0 10 20 30 40 50 60 700

1

2

3

4


Years

Indi

vidu

al g

row

th r

ate

General dataeg final size distributionSpatial data

eg clumping index

6/20



0

20

40

60

80

Population size

Years

Num

ber

of in

divi

dual

s0 10 20 30 40 50 60 70

0

2

4

6

8


Years

Sur

face

occ

upie

d by

tree

s (m

2)

−20 0 20 40 60

010

3050


01320

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100

0 10 20 30 40 50 60 700

102030405060

Size distribution

Years

Indi

vidu

al s

ize

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102030405060


Years

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al s

ize

0 10 20 30 40 50 60 700

1

2

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4


Years

Indi

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al g

row

th r

ate

General dataeg final size distributionSpatial data

eg clumping index Genetic dataeg number of relatives

?

6/20


Simulated forest developmentD

bh

7/20


Simulated forest developmentD

bh

Dynamics dataeg size according to age

7/20


Summary statistics

• Summary of model outputs to compare simulated and observeddata

• Around 20 different sumstats for now (tree density, mean size,clumping indexes, fit of size according to neigbourhood index, fitof age according to size, etc.)

8/20


Summary statistics

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1

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0 3 6 9 12

Mean weighted distance to neighboors

Log(

dbh)

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0

1

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4

Coefficient Intercept

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0

20

40

60

80

0 20 40 60

Age

Dbh

2

4

6

8

Intercept Coefficient

9/20


Summary statistics

• Summary of model outputs to compare simulated and observeddata

• Around 20 different sumstats for now (tree density, mean size,clumping indexes, fit of size according to neigbourhood index, fitof age according to size, etc.)

• Genetic sumstats ? Example: distribution of number of relativesaccording to size ?

• Choice of the summary statistics ?

10/20


Number of simulations to run

0.00

0.25

0.50

0.75

1.00

0 2 4 6 8gm

n=5000

0.0

0.3

0.6

0.9

0 2 4 6 8gm

n=1000

0.0

0.5

1.0

1.5

2.0

0 2 4 6 8gm

p

0.01

0.05

0.1

1

type

Posterior

Prior

n=500

11/20


Number of simulations to run

●●

●

●●●●●●●●0.00

0.25

0.50

0.75

Ref 500 1000 5000Number of ABC simulations

Per

cent

age

of s

urfa

ce o

ccup

ied

by tr

ees

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20

40

60


Mea

n db

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40

60


Med

ian

dbh

●

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0

10

20

30


Sta

ndar

d de

viat

ion

of d

bh

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20

40

60


9th

deci

le o

f dbh

●●●

●

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●

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●

●

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●●●●●●●●

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●

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0.00

0.01

0.02

0.03


Tree

den

sity

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100

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Clu

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500

1000


Clu

mpi

ng in

dex

− s

mal

l grid

post sample size = 100

12/20


Quantification of data information


13/20



Parenthood assignationGeneral data

13/20




Spatial data

13/20




Dynamics data

General dataSpatial data

13/20




Dynamics data


Genetic data

13/20




Dynamics data


Genetic data

Recruitment and fecundity data13/20


Exemple with growth rate parameters


14/20




Spatial data

14/20




Dynamics data


14/20


Prior densities

0 2 4 6 8

0.00

0.02

0.04

0.06

0.08

0.10

0.12

gm

Den

sity

0 10 20 30 40 50

0.00

00.

005

0.01

00.

015

0.02

0

x0

Den

sity

0.0 0.5 1.0 1.5

0.0

0.2

0.4

0.6

log10(xb)

Den

sity

15/20


Prior densities

0 2 4 6 8

0.00

0.02

0.04

0.06

0.08

0.10

0.12

gm

Den

sity

0 10 20 30 40 50

0.00

00.

005

0.01

00.

015

0.02

0

x0

Den

sity

0.0 0.5 1.0 1.5

0.0

0.2

0.4

0.6

log10(xb)

Den

sity

0 5 10 15

0.0

0.1

0.2

0.3

0.4

gm

Den

sity

0 10 20 30 40 50 60

0.00

0.02

0.04

0.06

0.08

0.10

x0

Den

sity

−0.5 0.0 0.5 1.0

0.0

0.5

1.0

1.5

2.0

log10(xb)

Den

sity

0 5 10 15

0.0

0.1

0.2

0.3

0.4

gm

Den

sity

0 10 20 30 40 50 60

0.00

0.02

0.04

0.06

0.08

0.10

x0

Den

sity

−0.5 0.0 0.5 1.0

0.0

0.5

1.0

1.5

2.0

log10(xb)

Den

sity

ABC withoutdynamics data

ABC with dynamics data

15/20


Prior densities

0 2 4 6 8

0.00

0.02

0.04

0.06

0.08

0.10

0.12

gm

Den

sity

0 10 20 30 40 50

0.00

00.

005

0.01

00.

015

0.02

0

x0

Den

sity

0.0 0.5 1.0 1.5

0.0

0.2

0.4

0.6

log10(xb)

Den

sity

0 5 10 15

0.0

0.1

0.2

0.3

0.4

gm

Den

sity

0 10 20 30 40 50 60

0.00

0.02

0.04

0.06

0.08

0.10

x0

Den

sity

−0.5 0.0 0.5 1.0

0.0

0.5

1.0

1.5

2.0

log10(xb)

Den

sity

0 5 10 15

0.0

0.1

0.2

0.3

0.4

gm

Den

sity

0 10 20 30 40 50 60

0.00

0.02

0.04

0.06

0.08

0.10

x0

Den

sity

−0.5 0.0 0.5 1.0

0.0

0.5

1.0

1.5

2.0

log10(xb)

Den

sity


ABC with dynamics data

MCMC onlydynamics data


15/20


Results without dynamics data

0.0

0.2

0.4

0.6

0.8

0 2 4 6 8gm

0.00

0.01

0.02

0.03

0 10 20 30 40 50x0

0.00

0.25

0.50

0.75

0.0 0.5 1.0

log10(xb)

type

Posterior

Prior

16/20


Results with dynamics data method 1

0.0

0.1

0.2

0.3

0.4

0 2 4 6 8gm

0.00

0.01

0.02

0.03

0.04

0 10 20 30 40 50x0

0.0

0.5

1.0

1.5

2.0

0.0 0.5 1.0

log10(xb)

type

Posterior

Prior

17/20


Results with dynamics data method 2

0.0

0.1

0.2

0.3

0.4

0 5 10 15gm

0.000

0.025

0.050

0.075

0.100

0.125

0 20 40 60x0

0

2

4

−0.5 0.0 0.5

log10(xb)

type

Posterior

Prior

18/20


Future work

• Parameter estimation• All parameters• Quantification of information for all types of data• Prior information• Effect of patch size

• Model changes

• Two size class• Processes (mortality, masting, etc.)• Hierarchy on patches ?• Demo-genetic model ?

19/20


Future work

• Parameter estimation• All parameters• Quantification of information for all types of data• Prior information• Effect of patch size

• Model changes• Two size class• Processes (mortality, masting, etc.)• Hierarchy on patches ?• Demo-genetic model ?

19/20


Thank you for your attention.

20/20

developmentofademo-geneticmodelforsfeand...

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