Ecological factors shaping the genetic quality of seeds and seedlings in forest trees. A simulation study coupled with sensitivity analyses Project BRG-Regeneration

Reproduction cycle in trees ADULT TREES SEEDLINGS dispersal then germination SAPLINGS SEEDS dispersal growth / mortality PollenOvules fecundation Sexual allocation Pseudo -cycle : Evolution in space And in demographic and genetic composition growth / mortality

Experimental « calibration » of input factors: project BRG-Reneration, 6 species Demographic et genetic evolutions in natural regeneration From 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]

Simulation model (TranspopRege, under Capsis4)

Input and output variables ADULT TREES SAPLINGS Growth / mortality SEEDS Pollen dispersal fecundation PollenOvules Male versus female fertility Density, spatial distribution Phenotypic diversity Genetic diversity and structure Seed dispersal then germination SEEDLINGS Genetic quality: ― Level of diversity (drift) ― Spatial structure

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 ?

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

Method presentation k input factors  X Each factor X i takes p values Variation space = grid k  p Elementary effect of factor X i : =incremented ratio defined in a point x of the variation space Property : the transformed point x+eiΔ also belongs to the variation space

Distribution of elementary effects associated to factor Xi = Fi # of elementary effects = G i = distribution of absolute values of elementary effects (Campogolo et al. 2003) k = 2 p = 5 Δ = 1/4 X1X1 X2X2

How to measure the sensitivity of Y to factor Xi (Fi, Gi) μ = mean of distribution F i μ* = mean of distribution G i σ = standard deviation of distribution F i 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)

An exemple of graphical representation of Morris sensitivity measures σ μ*

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 F i, 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)]

Morris sampling method Randomly select an input parameter set x*; each xi drawn randomly in {0,1/p-1, 2/p-1,…, 1} 1 rst sampling point x (1) : obtained by incrementing one or more elements in x* by Δ 2 d sampling point x (2) : obtained < x (1) so that x (2) ≠ x (1) only at its i th component (+/- Δ), i Є {1,2,..,k} 3 rd sampling point x (3): so that x (3) ≠ x (2) only at its j th 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

Visualisation Orientation matrix B* Example of trajectory for k = 3

Estimation For a given trajectory, k+1 evaluation of the model, and each elementary effect associated with each factor ican be computed as : : ou With r trajectories, one can estimate :

Implementation Triangular matrix, (k+1)  k, with two consecutive rows differing only for one column But the elementary effects produced would not be random X* J k+1,1 1. Which orientation matrix B* ??

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. X* J k+1,1 1. Which orientation matrix B* ?? Diaginal D matrix with either 1 or -1 randomly

2. Choice of p = number and value of the levels of the input factors If X i 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

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.

Simulation model (TranspopRege, under Capsis4)

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

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

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

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)

Input parameters in TranspopRege 3. Panmixy/ isolation by distance Random pollen dispersal Adult under consideration Maternal progeny Paternal progeny Selfed progeny Dispersal folowing a gaussian law

b = 2  Normale b = 1  Exponentielle Autres b : Exponentielle puissance b > 1  « light-tailed » b < 1  «fat-tailed» Input parameters in TranspopRege 4. Pollen/seed dispersal function

Input parameters in TranspopRege 5. Fecundity = f(diameter)

Depends on tree growth model Model with year effect : cones ~ A * (cir - 100)^ (2.8 * A ) + stochastic variability

Ne=31 Ne=92 Ne=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)

Input parameters in TranspopRege 7. Male fecundity vs female fecundity

Adult stand Mating system Growth, mortality Input parameters in TranspopRege Mortality = f(genotype, survival rate on plot) (2P)

Adult stand Mating system Growth, mortality Input parameters in TranspopRege 4P 9P 2P 15 parameters r = 100 > 20 trajectories 1600 runs > 320 runs

Problems…solutions ? Script mode OK, but within simulation, out of memory errors Necessity to include routine for population genetics computation