ecological factors shaping the genetic quality of seeds and seedlings in forest trees
DESCRIPTION
Ecological factors shaping the genetic quality of seeds and seedlings in forest trees. A simulation study coupled with sensitivity analyses Project BRG-Regeneration 2003-2005. Reproduction cycle in trees. Pseudo -cycle : Evolution in space And in demographic and genetic composition. - PowerPoint PPT PresentationTRANSCRIPT
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Ecological factors shaping the genetic quality of seeds and
seedlings in forest trees.
A simulation study coupled with sensitivity analyses
Project BRG-Regeneration 2003-2005
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Reproduction cycle in trees
ADULT TREES
SEEDLINGSdispersal then germination
SAPLINGS
SEEDS
dispersal
growth / mortality
Pollen Ovules
fecundation
Sexual allocation
Pseudo -cycle :
Evolution in space
And in demographic and genetic composition
growth / mortality
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Experimental « calibration » of input factors: project BRG-Reneration, 6 species
Demographic et genetic evolutions in natural regenerationFrom seed… …..to sapling
Impact of : sur :
A) Stand structure (seed trees density) -> mating system, seed genetic quality (in situ) [1]
B) Temporal variation in fertility, phenology -> mating system, seed genetic quality (in situ + simulation)[5]
C) Seed G.Q. in controlled conditions -> phenotypic value of des saplings (ex situ : germination test in lab, nursery) [2]
D) Seed G.Q. in natural conditions -> demography (survival, growth) : installing sapling plots in forest (in situ) [3]E) Q. G. of natural regeneration -> demography (survival, growth) : monitoring natural regeneration in forest . (in situ) [4]
[1]
[5]
[2]ex situ
[3] in situ [4]
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Simulation model (TranspopRege, under Capsis4)
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Input and output variables
ADULT TREES
SAPLINGS
Growth / mortality
SEEDS
Pollen dispersal
fecundation
Pollen Ovules
Male versus female fertility
Density, spatial distributionPhenotypic diversityGenetic diversity and structure
Seed dispersal then germinationSEEDLINGS
Genetic quality:― Level of diversity (drift)― Spatial structure
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OBJECTIVES
•How these different processes (adult stand characteristics), mating system, survival rate) respectively affect saplings genetic quality (factor screening)•How the way each process is modeled affects the output variable
• “The study of how the variation in the output of a model (numerical or otherwise) can be apportioned (qualitatively or quantitatively) to different sources of uncertainty in the model input” Andrea Saltelli, Sensitivity Analysis
• Originally, SA focuses on uncertainty in model inputs, then by extension to the very structure of the model (hypothesis, specification)
What is sensitivity analyses ?
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Sensitivity analyses : Morris method
Screening the factors that mostly affect the variance of output variable (Y)
Economic method in terms of computation/simulation (# evaluations = a# parameters)
Identifying factor(s) that can be fixed without significant reduction in Y variance
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Method presentation
• k input factors X
• Each factor Xi takes p values
• Variation space = grid kp
• Elementary effect of factor Xi :
)(,...,,,,...,
)( 111 xyxxxxxyxd kiii
i
=incremented ratio defined in a point x of the variation space
Property : the transformed point x+eiΔ also belongs to the variation space
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Distribution of elementary effects associated to factor Xi = Fi
• # of elementary effects = )1(1 pppk
• Gi = distribution of absolute values of elementary effects (Campogolo et al. 2003)
k = 2p = 5Δ = 1/4
X1
X2
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How to measure the sensitivity of Y to factor Xi (Fi, Gi)
• μ = mean of distribution Fi • μ* = mean of distribution Gi
• σ = standard deviation of distribution Fi
• High μ* value & low μ value large effect of factor Xi + effects of different signs according to the point in space where it is computed
• High σ value the values of elementary effect are greatly affected by the point in space where they are computed (strong interaction with other factors)
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An exemple of graphical representation of Morris sensitivity measures
σ
μ*
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Estimation of the distribution statistics (μ*, μ and σ )
• Problem = sampling r elementary effects associated to factor Xi
• # runs needed to obtain r values of each Fi, 1≤i ≤k : n=2rk ↔ économy = rk/2rk=1/2
Morris sampling method• B* = matrix k k+1, each row = input parameter set
so that k+1 runs allow estimating k elementary effects ↔ economy = k/k+1– Choice of p and Δ:
• p uniforme entre 0 et 1• Δ = p/[2(p-1)]
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Morris sampling method
• Randomly select an input parameter set x*; each xi drawn randomly in {0,1/p-1, 2/p-1,…, 1}
• 1rst sampling point x(1) : obtained by incrementing one or more elements in x* by Δ
• 2d sampling point x(2) : obtained < x(1) so that x(2) ≠ x(1) only at its ith component (+/- Δ), i Є {1,2,..,k}
• 3rd sampling point x(3): so that x(3) ≠ x(2) only at its jth component (+/- Δ), j Є {1,2,..,k}
• … Two consecutive points differ only for one
component, and each component iof the base vector x* is selected at least once to be increased by Δ
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Visualisation
)1(
)2(
)1(
...kx
x
x
Orientation matrix B*Example of trajectory for
k = 3
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Estimation
• For a given trajectory, k+1 evaluation of the model, and each elementary effect associated with each factor ican be computed as : :
)()1(
)(ll
li
xyxyxd
)1()(
)(ll
li
xyxyxd
ou
• With r trajectories, one can estimate :
r
ji rd
1
/
r
ji rd
1
2 /
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Implementation
11
01
00
B
Triangular matrix, (k+1)k, with two consecutive rows
differing only for one column But the elementary effects produced would not
be random
13/2
3/13/2
3/10
3/10
1
1
1
' BB
X*
Jk+1,1
1. Which orientation matrix B* ??
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Consider a model with 2 input factors taking their values in {0, 1/3, 2/3, 1}; we have a k=2; p=4; Δ=2/3.
**22/3/10
1
1
1
* ,1,1 PJDJBB kkkk
X*
Jk+1,1
11
11
11
22
02
00
02
22
20
11
11
11
11
11
11
1. Which orientation matrix B* ??
11
11
11
10
01
Diaginal D matrix with either 1 or -1 randomly
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2. Choice of p = number and value of the levels of the input factors
• If Xi follows a uniform law divide the interval of variation in equalsegments
• For any other distribution, select the levels in the quantiles of the distributions
• # of p-values ?– Linked to r : if r small, p high is of no use
– Simulation study show that p=4 and r=10 not bad
Implementation
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Conclusion on Morris method
• Elementary effect are basically local sensitivity measures
• But through μ* & μ, Morris method can be seen as global
• Do not allow to separate the effects of interaction between factors from that of non linearity of the model.
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Simulation model (TranspopRege, under Capsis4)
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Adult stand
Input parameters in TranspopRege
Density (1P)
Spatial distribution : Neyman Scott (1P)
Mean and sd diameter (2P)
# locus, # allèles (1P)
Spatial genetic structure (1P)
Mating system
Growth, mortality
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Input parameters in TranspopRege
1. Density/distribution of adult trees
Poisson, 100 trees, DBH = 50 cm, σ = 7 cm Neyman Scott, 100 arbres, 10 agrégats (~ 50 m) DBH = 50 cm, σ = 7 cm
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Poisson, 100 trees, DBH = 50 cm, σ = 7 cm Poisson, 100 trees, DBH = 50 cm, σ = 14 cm
Input parameters in TranspopRege 2. Phenotype/Genotype of adult trees
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Adult stand
Mating system
Growth, mortality
Input parameters in TranspopRege
Pollen dispersal type (panmixy/ibd = 1TP)
Mean distance and form of pollen dispersal function (2P)
Mean distance and form of seeds dispersal function(2P)
Male fecundity = f (diameter) (1P)
Female fecundity = f(diameter, year, individual) (3P)
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Input parameters in TranspopRege 3. Panmixy/ isolation by distance
Random pollen dispersal
Adult under considerationMaternal progenyPaternal progenySelfed progeny
Dispersal folowing a gaussian law
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b
a
yx
ba
byxba
22
exp )/2(Γ π2
),;,(2
b = 2 Normale b = 1 ExponentielleAutres b : Exponentielle puissance
b > 1 « light-tailed »b < 1 «fat-tailed»
Input parameters in TranspopRege 4. Pollen/seed dispersal function
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Input parameters in TranspopRege 5. Fecundity = f(diameter)
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Input parameters in TranspopRege 5. Fecundity = f(diameter)
Depends on tree growth model
Model with year effect : cones ~ A * (cir - 100)^0.25 - (2.8 * A + 25.7)+ stochastic variability
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700
4571977873982210
58478227743
Ne=31
Ne=92Ne=76Ne=36Ne=57
Ne=59Ne=85Ne=83
Ne ~ (4N-2) / (V+2)
(Krouchi et al, 2004)
Input parameters in TranspopRege 6. Stochastic variations in female fecundity
(example : cedrus atlantica)
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Input parameters in TranspopRege 7. Male fecundity vs female fecundity
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Adult stand
Mating system
Growth, mortality
Input parameters in TranspopRege
Mortality = f(genotype, survival rate on plot) (2P)
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Adult stand
Mating system
Growth, mortality
Input parameters in TranspopRege
4P
9P
2P
15 parametersr = 100 > 20 trajectories
1600 runs > 320 runs
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Problems…solutions ?
• Script mode OK, but within simulation, out of memory errors
• Necessity to include routine for population genetics computation