Guillaume Charrier

Modelling frost acclimation in trees through the effect on climate on physiology

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Modeling frost acclimation in trees through the effect of climate on physiology.

INRA, UMR PIAF, F-63100 Clermont-Ferrand -Université Blaise Pascal, UMR PIAF, F-63177 Aubière 1,2 1,2

CHARRIER Guillaume , AMEGLIO Thierry

1 2
Frost hardiness and water content: Frost hardiness and soluble carbohydrates:

The relation between water content and frost hardiness is observed whatever the tissue and limited by two asymptotes representing:

-Nucleation temperature of a dilute solution (≈ -2°C), -Minimal water content in living wood (≈ 0.5)

Model architecture and outputs:

The relation between soluble carbohydrates content (Glucose + Fructose + Sucrose: GFS) and frost hardiness is not so clear. It seems to depend on the tissue. How this could be explained ?

Conclusion:

This model could be linked with "summer" models predicting impact of stresses on physiology (i.e. starch reserves at the begining of autumn, water deficit) in order to weight their potential effect on freezing resistance during the following winter. Moreover, as the simulated physiological parameters (water and osmolyte contents) are the main components of frost resistance (lowering the freezinng point of the intracellular sap vs extracellular sap) in all perennial species, its application could be wide.

Interaction between water and soluble carbohydrates:

How did we do ?

We worked on walnut trees (Juglans regia L.), in different environmental conditions (lowland and mountain), on several organs and tissues (fine roots, large roots, tap root, trunk, stems, bark, wood and buds) We measured: Frost hardiness by electrolyte leakage method Temperature requirements for dormancy release (chilling for endodormancy and heat for ecodormancy) Water and non structural carbohydrates (starch and soluble carbohydrates) contents.

Soluble carbohydrate are more efficient for increasing hardiness when water content is low. This could be modelled according to the following equation: Why should we take physiological modulations into account instead of classical direct relationship with temperature ?

Frost hardiness of stems of walnut trees cold exposed or cold deprived were different depending on treatment. Why studying frost hardiness while temperatures are predicted to rise within the next century ?

One of the main factors controling plant distribution is the frost. With climate change several risks could influence survival or reproduction of trees: -Insufficient hardening in autumn during transient heat wave, -Earlier budburst when probability of freezing events is still high, -Impact of cumulated stresses (i.e. drought or phytophagy) on hardening ability.

Early defoliation

Natural senescence

  Trees were either artificially defoliated in early October (left) or natural senescence occured in early November (right). Depending on date of defoliation, cold deprived trees were differently able to harden. In this case, temperature alone could not explain this difference but physiological modulations such as water and carbohydrate contents dynamics could (More explanations in Charrier & Améglio, 2011, Env. & Exp. Bot.).


domain: sdv shs

text:
The Spatial 2 Lag Model (S2LM) Monte Carlo Experiments Application example with Housing Price in Boston database Conclusion

Plan

Aim of the paper

We consider a regression model that includes a spatial lag of the endogenous variable and that allows the spatial parameter to vary among locations:

We propose for estimating this model to use a two steps estimator based on a linearized GMM and a mixed GWR. Geniaux The Spatial 2 Lag Model (S2LM) 1 True local variations of i's behavior 2 Bad specification of W 3 Bad model specification (SEM, SARAR, non linearities, ...) Geniaux The Spatial 2 Lag Model (S2LM) 1 True local variations of i's behavior 2 Bad specification of W 3 Bad model specification (SEM, SARAR, non linearities, ...) Geniaux The Spatial 2 Lag Model (S2LM) 1 True local variations of i's behavior 2 Bad specification of W 3 Bad model specification (SEM, SARAR, non linearities, ...) Geniaux The Spatial 2 Lag Model (S2LM) 1 True local variations of i's behavior 2 Bad specification of W 3 Bad model specification (SEM, SARAR, non linearities, ...) Geniaux The Spatial 2 Lag Model (S2LM) 1 True local variations of i's behavior 2 Bad specification of W 3 Bad model specification (SEM, SARAR, non linearities, ...) Geniaux The Spatial 2 Lag Model (S2LM)

Introduction

The Spatial 2 Lag Model (S2LM)

Monte Carlo Experiments

Application example with Housing Price in Boston database

Conclusion

Geniaux

The Spatial 2 Lag Model (S2LM)

Introduction

Several methodological contributions proposed estimators adapted to situations where some economic behaviors can change depending on their location.

Two main approaches in spatial regression: spatial regimes (-→ stratification / segmentation) spatially varying coefficients model.

Geniaux

The Spatial 2 Lag Model (S2LM)

Introduction

The first approaches in this field consisted in parametric models that incorporate the spatial coordinates of observations by different ways, such as the "Trend Surface Analysis" method [START_REF] Ripley | Spatial statistics[END_REF] and its generalization proposed by [START_REF] Casetti | The expansion method, mathematical modeling, and spatial econometrics[END_REF][START_REF] Casetti | Generating models by the expansion method: Applications to geographical research*[END_REF] under the name of "Variable Expansion" method.

Geniaux

The Spatial 2 Lag Model (S2LM)

Introduction

Since, the main contributions considered semi-parametric methods like the LWR [START_REF] Mcmillen | One hundred fifty years of land values in chicago: a nonparametric approach[END_REF] and GWR [START_REF] Brunsdon | Geographically weighted regression: a method for exploring spatial nonstationarity[END_REF] which provide a methodological framework to estimate local values of the parameters using local regressions.

Geniaux

The Spatial 2 Lag Model (S2LM)

Introduction

The

m i i = exp(-d 2 i i /h 2 ) Geniaux The Spatial 2 Lag Model (S2LM)

Introduction

By defining

M i a matrix n × n such that M i = diag [m i 1 , ..., m i n ] with
zero for all others elements, the vector of local coefficients (for a focal point) is as follows:

β(u i , v i ) = (X M i X ) -1 X M i Y (1)
A notable contribution to take into account spatial autocorrelation in a local regression framework has been made by [START_REF] Pace | Spatial autoregressive local estimation[END_REF].

They propose a Spatial Autoregressive Local Estimation (SALE) which is based on a recursive approach for maximum likelihood estimation of SLM, implying estimates on subsamples related to a neighboring of each observation.

Geniaux

The Spatial 2 Lag Model (S2LM)

Introduction

By defining

M i a matrix n × n such that M i = diag [m i 1 , ..., m i n ] with
zero for all others elements, the vector of local coefficients (for a focal point) is as follows:

β(u i , v i ) = (X M i X ) -1 X M i Y (1)
A notable contribution to take into account spatial autocorrelation in a local regression framework has been made by [START_REF] Pace | Spatial autoregressive local estimation[END_REF].

They propose a Spatial Autoregressive Local Estimation (SALE) which is based on a recursive approach for maximum likelihood estimation of SLM, implying estimates on subsamples related to a neighboring of each observation.

Geniaux

The Spatial 2 Lag Model (S2LM)

A MGWR [START_REF] Fotheringham | Some notes on parametric significance tests for geographically weigthed regression[END_REF] model can be expressed as:

y i = q j=1 β j x ij + p j=q+1 β j (u i , v i )x ij + i i , i = 1, 2, .., n (2)
Mei ( 2004) and [START_REF] Geniaux | A spatial hedonic approach on land use change anticipations[END_REF] propose the use of a two steps estimator for mixed GWR that is easy to implement.

S2LM Y i = λ(u i , v i ; M)WY i + X i β + i (3) with w ij = e (-d ij /h 1 ) 2 j e (-d ij /h 1 ) 2 resp. m ij = e (-d ij /h 2 ) 2 λ(u i , v i ) could
S2LM Y i = λ(u i , v i ; M)WY i + X i β + i (3) with w ij = e (-d ij /h 1 ) 2 j e (-d ij /h 1 ) 2 resp. m ij = e (-d ij /h 2 ) 2 λ(u i , v i ) could
S2LM Y i = λ(u i , v i ; M)WY i + X i β + i (3) with w ij = e (-d ij /h 1 ) 2 j e (-d ij /h 1 ) 2 resp. m ij = e (-d ij /h 2 ) 2 λ(u i , v i ) could
S2LM Y i = λ(u i , v i ; M)WY i + X i β + i (3) with w ij = e (-d ij /h 1 ) 2 j e (-d ij /h 1 ) 2 resp. m ij = e (-d ij /h 2 ) 2 λ(u i , v i ) could
S2LM Y i = λ(u i , v i ; M)WY i + X i β + i (3) with w ij = e (-d ij /h 1 ) 2 j e (-d ij /h 1 ) 2 resp. m ij = e (-d ij /h 2 ) 2 λ(u i , v i ) could

GMM estimator

First consider λ constant. Then a GMM estimator of θ = (λ, β) could be used with:

θ = argmin θ∈Θ Q(θ)
Where:

Q(θ) = S N (θ)Σ N S N (θ) S N (θ) = 1 N Z ũ(θ) Z ∈ X , WX , W 2 X , W 3 X ]
Σ N some positive definite matrix u(θ) the vector of residuals of the regression (3) considering λ constant

Geniaux

The Spatial 2 Lag Model (S2LM)

Linearized GMM estimator

With a convergent θ, we can use a LGMM estimator (KM2008):

u( θIV ) = P Z Y -λIV P Z WY -P Z X βIV (4)
The gradients of the GMM are quite simple:

G β i = P Z X (5)
G λ i = P Z WY (6)
To linearize the error term u i (β, λ), we use a taylor approximation.

ũi (β, λ) -ũi ( βIV , λIV ) = G (θ(u i , v i ) -θ 0 ) (7)
where G (.) is a gradient term:

ũi (β, λ) = G (θ(u i , v i ) -θ 0 ) + ũi ( βIV , λIV ) Geniaux The Spatial 2 Lag Model (S2LM)

MC Settings

We focus our experiments on the ability of the proposed estimator to identify the spatial pattern of λ(u i , v i , M) when W is known.

M is considered unkonwn.

MC Settings

An experiment is defined by a quadruplet (l , h, lambda c , lambda v )

Geniaux

The Spatial 2 Lag Model (S2LM)

MC Settings: locations l l ∈ (random, monocentric, polycentric).

MC Settings: Weighting scheme wt

The weighting scheme type for W is an exponential distance kernel

with w ij = e -(d ij /h 1 ) k j w ij
and we choose a set of bandwidth h equal to the distance of neighboring that contains 4, 10 or 20 mean number of neighbors (mnb), so we have h 1 ∈ (h 4 1 , h 10 1 , h 20 1 ).

Geniaux

The Spatial 2 Lag Model (S2LM)

MC Settings: spatial pattern of λ(u i , v i )

Three different spatial patterns for λ(u i , v i ):

λ c = i λ(u i , v i )/n ∈ (0, 0.2, 0.4, 0.6). Pattern 1: λ(u i , v i ) = λ c + f ( (u i -0.5) 2 + (v i -0.5) 2 ) Pattern 2: λ(u i , v i ) = λ c + f (u i + v i ) Pattern 3: λ(u i , v i ) = λ c + f u i +v i <1 (u i + v i ) Geniaux
The Spatial 2 Lag Model (S2LM)

MC settings

β = (1, 0.5) X 1 = 1, X 2 ∼ N(0, 3)
Coordinates of data (u i , v i ) and X are drawn once and only once for each type l . 1000 replications of using normal random ( ∼ N(0, 1)) to generate the vector of y

Geniaux

The Spatial 2 Lag Model (S2LM)

Random locations Case. Random locations Case.

n = 1000, r = 1000, β = (1, 0.5), l = random, W known Exp. parameters OLS IV S2LM λc mnb(h) pattern β 0 β 1 β 0 β 1 λ RMSE λ β 0 β 1 λ(u i , v i ) RMSE λ h 2 0 4 0.
n = 1000, r = 1000, β = (1, 0.5), l = random, W known Exp. parameters OLS IV S2LM λc mnb(h) pattern β 0 β 1 β 0 β 1 λ RMSE λ β 0 β 1 λ(u i , v i ) RMSE λ h 2 0.

Application example

Housing prices in Boston database [START_REF] Ii Harrison | Hedonic housing prices and the demand for clean air[END_REF] contains an aggregated house price index (median) for 506 census tracts and a set of 14 covariates, augmented with census coordinates projected to UTM Zone 19. [START_REF] Anselin | An introduction to spatial regression analysis in r[END_REF] proposes this SLM:

log (MEDV ) =λW log (MEDV ) + β 0 + β 1 CRIM + 2 + β 3 INDUS + β 4 CHAS + β 5 NOX 2 + β 6 RM 2 + β 7 AGE + β 8 log (DIS) + β 9 log (RAD) + β 10 TAX + β 11 PTRATIO + β 12 B + β 13 log (LSTAT ) + Geniaux The Spatial 2 Lag Model (S2LM) log (MEDV ) =β 0 (u i , v i ) + λ(u i , v i )W log (MEDV ) + β 1 CRIM + 2 + β 3 INDUS + β 4 CHAS + β 5 NOX 2 +

Conclusion

Our proposition has several advantages, compared to a simple extension of the GWR that takes into account spatial autocorrelation.

First, the mixed GWR framework with a limited number of spatial varying parameters allows to avoid numerous problems relative to the GWR framework.

Second, it is usable for large datasets Third, our estimator seems very promising by allowing a substantial gain in predictive accuracy on different datasets tested.

Conclusion

But it remains a lot of works to do:

To rerun the MC experiments with adaptive bandwidths.

To ameliorate the criteria to choose the bandwidth of M.

To test a wider range of spatial patterns of spatial lag parameter in order to draw conclusions on the accuracy of θ estimates.

To run Monte Carlo experiments with unobserved spatial heterogeneity Finding a way to deal with the presence of spatial discontinuities of λ(u i , v i )

Extension to Logit/Probit model.

  idea of LWR/GWR is to estimate as many regressions as focal points i (data coordinates or other sets of coordinates) by weighting the local regressions with respect to the observations' distance to these focal points. Let's note M the weight matrix with:

  vary du to :

	Introduction The Spatial 2 Lag Model (S2LM)
	Monte Carlo Experiments
	Application example with Housing Price in Boston database
	Conclusion

  vary du to :

	Introduction The Spatial 2 Lag Model (S2LM)
	Monte Carlo Experiments
	Application example with Housing Price in Boston database
	Conclusion

  vary du to :

	Introduction The Spatial 2 Lag Model (S2LM)
	Monte Carlo Experiments
	Application example with Housing Price in Boston database
	Conclusion

  vary du to :

	Introduction The Spatial 2 Lag Model (S2LM)
	Monte Carlo Experiments
	Application example with Housing Price in Boston database
	Conclusion

  vary du to :

	Introduction The Spatial 2 Lag Model (S2LM)
	Monte Carlo Experiments
	Application example with Housing Price in Boston database
	Conclusion

  β 6 RM 2 + β 7 AGE + β 8 log (DIS) + β 9 log (RAD) + β 10 TAX + β 11 PTRATIO + β 12 B + β 13 log (LSTAT ) +

		Introduction The Spatial 2 Lag Model (S2LM)
		Monte Carlo Experiments
	Application example with Housing Price in Boston database
			Conclusion
	Choosing (h 1 , k 1 ) and (h 2 ) OLS IV S2LM
	W M	DTRI coef (p-value) (p-value) (p-value) DTRI First h 1 /k EDK(4.34,2) coef coef	W TAX PTRATIO 0.225/1.1 EDK -0.00042 -0.000373 DTRI NA (0.000664) (0.000817) -0.0311 -0.014 (1.14e-09) (0.00357)	-0.00042 (0.0002) -0.01362 (0.0027)
	CRIM	step -0.0119 -0.00739 (< 2e-16) (1.39e-09) (7.50e-09) SSR IV -0.0058	B	14.418 0.000364 0.000287 13.276 (0.00046) (0.00221)	0.00032 (0.0003)
	ZN	Second 8.02e-05 0.000374 (0.874) (0.413)	h 2 0.00112 (0.03260)	3.13 log(LSTAT)	4.34 -0.236 (<2e-16) (<2e-16) -0.371	-0.21437 (<2e-16)
	(8) Min.: 0.7284 1st Qu.: 2.0446 Median: 2.3850 (6.24e-111) (2.61e-20) Mean: 2.5532 10.301 9.606 0.0265 0.0251 0.0289 0.0263 0.0321 0.0324 0.0349 4.56 2.38 3rd Qu.: 2.9209 Max.: 6.5365 Min.: -0.8631 1st Qu.: 0.2982 0.4643 Median: 0.4703 (4.33e-02) Mean: 0.4189 3rd Qu.: 0.5857 Max.: 1.0082 0.0343 0.0327 β0(u i , v i ) SMPA S2LM (n = 1) SSR S2LM SMPA IV (n = 1) SMPA S2LM (n = 10) SMPA IV (n = 10) 0.00024 0.00133 step Third step Third step 0.00181 (0.919) (0.535) (0.2360) 0.0914 0.0116 0.00432 (0.00613) (0.706) (0.8926) -0.638 -0.289 -0.33471 (2.88e-08) (0.00713) (0.0008) 0.00633 0.00675 0.00808 (1.89e-06) (2.04e-08) (5.02e-14) 9.07e-05 -0.000238 -0.00154 (0.863) (0.616) (0.00256) λ(u i , v i ) Third SMPA S2LM (n = 50) 0.0333 step SMPA IV (n = 50) 0.0352 0.0351 -0.191 -0.155 -0.19951 (1.78e-08) (4.45e-07) (5.66e-05) log(RAD) 0.0957 INDUS CHAS1 I(NOX 2 ) I(RM 2 ) AGE log(DIS) 0.0771 0.09359 (7.91e-07) (1.08e-05) (5.26e-06) n=506 DF=492 SSR 16.378 13.275 9.606 R2 0.9965 0.9972 0.9979 SMPA (m=1) 0.0351 0.0263 0.0251 SMPA (m=10) 0.0347 0.0343 0.0324 SMPA (m=50) 0.0348 0.0351 0.0333
			Geniaux Geniaux		The Spatial 2 Lag Model (S2LM) The Spatial 2 Lag Model (S2LM)

Geniaux

The Spatial 2 Lag Model (S2LM)

S2LM stimator

1 In the first step, estimate β OLS by OLS and keep the residuals vector u(β OLS , λ = 0). Estimate the gradient terms :


F Lefèvre
email: lefevre@avignon.inra.fr

Management of genetic diversity: protected areas and dynamic in situ conservation of genetic resource

Importance of the genetic diversity regarding climate change  Basic level of biodiversity determining the response of the ecosystem  The concept of genetic resources (GR) and their values 2) Conservation of GR in theory : necessary dynamic approach  Diversity means evolution  Dynamic approach of conservation 3) Conservation of GR in practice : the example of forest GR  Case studies at national (France) and continental (Europe) scale  Reconciliate GR conservation and protected areas systems 4) General recommendations

The genetic diversity within species is huge The genetic diversity within species is huge

© INRA M. Villar
The concept of genetic resources (GR) The concept of genetic resources (GR)



  Established in October 1994 to implement a resolution of the pan-European forest policy process (Ministerial Conference on the Protection of Forests in Europe) of the genetic diversity regarding climate change  Basic level of biodiversity determining the response of the ecosystem  The concept of genetic resources (GR) and their values 2) Conservation of GR in theory : necessary dynamic approach  Diversity means evolution  Dynamic approach of conservation 3) Conservation of GR in practice : the example of forest GR  Case studies at national (France) and continental (Europe) scale  Reconciliate GR conservation and protected areas systems 4) General recommendations

et al, 2007) (Pichot et al, 1998) frost drought

	Budburst Quercus petraea Survival in 1 test site, 22 provenances (2 species) 100%	Growth cessation Betula pendula
	80%				Diversity within species :
	60%
	40%			Latitude °N	Latitude	°N
	20%		Budset Pinus sylvestris	Growth cessation Picea abies
	0%	Pinus halepensis Pinus brutia
		1984 1986 1988 1990	1992	1994	1996
				Latitude °N	Latitude	°N

F. Lefèvre GoE Climate Change, Strasbourg 1-2 Oct 2012 © INRA, A. Ducousso (Savolainen -between populations within populations F. Lefèvre GoE Climate Change, Strasbourg 1-2 Oct 2012

(Lefèvre, 2004)

  Basic level of biodiversity determining the response of the ecosystem Basic level of biodiversity determining the response of the ecosystem

	domestic The concept of genetic resources (GR) wild 1) Importance of the genetic diversity regarding climate change A necessary dynamic approach of conservation 1) Importance of the genetic diversity regarding climate change European Forest Genetic Resources Conservation of forest genetic resources in France Programme Pinus radiata, the most planted tree : enlarging its realised climatic niche thanks to plasticity and/or genetic evolution  The concept of genetic resources (GR) and their values Jarkko Koskela
	wild Conservation of genetic resources : Annual Tmean (°C) Region rainfall (mm) coldest month EUFORGEN Coordinator warmest month dom. Tmean (°C) 2) Conservation of GR in theory : necessary dynamic approach Bioversity International, Regional Office for Europe, Rome management practices specific GR conservation protected areas California (5 pops) 420 -700 10 -11 16 -18 N-Z (Southland) 960 -1000 3 -5 13 -15 N-Z (Kaingaroa) 1300 -1500 7 -9 Chile (Valdivia) 2350 7.7 17 approach speciesoriented 11 -19 Complementary in situ and ex situ  A collaborative mechanism among countries to promote strategies conservation and sustainable use of FGR in Europe
	wild South Afr. (Cape) China (Sichuan) Aust. (Bathurst) Aust. (Tumut) beech sessile oak	wild 900 -1100 490 -590 650 -950 800 -1300 black poplar maritime pine wildcherry elm	dom 10 -13 -3.4 --0.7 0.4 -0.6 0.5 -0.8 silver fir ex situ	20 -24 25 -28 24 -28 25 -30 requirements for in situ conservation units
	F. Lefèvre	GoE Climate Change, Strasbourg 1-2 Oct 2012

  The concept of genetic resources (GR) and their values 2) Conservation of GR in theory : necessary dynamic approach  Diversity means evolution  Dynamic approach of conservation 3) Conservation of GR in practice : the example of forest GR  Case studies at national (France) and continental (Europe) scale  Reconciliate GR conservation and protected areas systems 4) General recommendations F. Lefèvre GoE Climate Change, Strasbourg 1-2 Oct 2012 Relatives are alike but not identical : sexual reproduction continuously generates new genetic combinations Genetic diversity is not fixed, genetic adaptation occurs if : (1) better performing genotypes emerge during reproduction (2) the best performing genotypes spread in the population before it goes extinct Dynamics F. Lefèvre GoE Climate Change, Strasbourg 1-2 Oct 2012 Diversity = evolution: the dynamics of adaptation As the community evolves during maturation of the forest, the genetic diversity evolves across generations F. Lefèvre GoE Climate Change, Strasbourg 1-2 Oct 2012 © INRA H. Davi © INRA F. Lefèvre Diversity = evolution: the dynamics of adaptation F. Lefèvre GoE Climate Change, Strasbourg 1-2 Oct 2012 Diversity = evolution: the dynamics of adaptation (Yan et al, 2006) Diversity = evolution: the dynamics of adaptation A matter of velocity : velocity of changes vs. velocity of adaptation (Lefèvre, 2006) F. Lefèvre GoE Climate Change, Strasbourg 1-2 Oct 2012  Facing multiple uncertainties, 2 principles: -preserve diversity -foster evolution  Think in trajectories rather than ideotype or steady state  Avoid hasty decisions that reduce future options F. Lefèvre GoE Climate Change, Strasbourg 1-2 Oct 2012   Diversity means evolution  Dynamic approach of conservation 3) Conservation of GR in practice : the example of forest GR  Case studies at national (France) and continental (Europe) scale  Reconciliate GR conservation and protected areas systems 4) General recommendations F. Lefèvre GoE Climate Change, Strasbourg 1-2 Oct 2012 F. Lefèvre GoE Climate Change, Strasbourg 1-2 Oct 2012

Conservation of forest genetic resources in Europe EUFGIS : information system on dynamic conservation of FGR at continental scale based on minimum requirements and standards Management objectives other than FGR conservation assigned to the conservation units: little connection between FGR conservation and protected areas