# Norms of reaction for maritime pine

Victor Papin, Laurent Bouffier, Leopoldo Sanchez

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Victor Papin, Laurent Bouffier, Leopoldo Sanchez. Norms of reaction for maritime pine. Final B4EST Conference: Accelerating breeding to cope with new challenges and uncertain future, B4EST, Jun 2022, Lisbon, Portugal. [hal-04511414](https://hal.inrae.fr/hal-04511414)

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# Norms of reaction for maritime pine

**Session A : Accelerating breeding to cope with new challenges and uncertain future – 20th June 2022**

Victor Papin, INRAE (UMR BIOGECO Pierroton)

Laurent Bouffier, INRAE (UMR BIOGECO Pierroton)

Léopoldo Sanchez, INRAE (UMR BioForA Orléans)
# Norms of reaction for maritime pine

**Session A : Accelerating breeding to cope with new challenges and uncertain future – 20th June 2022**

Victor Papin, INRAE (UMR BIOGECO Pierroton)

Laurent Bouffier, INRAE (UMR BIOGECO Pierroton)

Léopoldo Sanchez, INRAE (UMR BioForA Orléans)
# Maritime pine (Pinus Pinaster) breeding in France

## « Landes de Gascogne » forest

* 0,8 million hectares (24% of French wood harvest)

* Main uses in carpentry, joinery, stationery

<figure><img src="image_1.png" /></figure>

* Plantations with improved seedlings

* Mainly based on the Landes provenance

## Recurrent selection scheme

* Started in the ~1960 → 3rd generation today

<figure><img src="image_2.png" /></figure>

* Targeted traits :

* Growth (height, circumference, straightness)

* Adaptation to the environment

* Wood quality

* Genetic values estimated with pedigree

## Dynamic phenotypes : NoR

* Classical selection focuses on final growth traits

* Integrative phenotypes with no consideration of the environment

NoR : pattern of phenotypic expression of a single genotype across a range of environments

<figure><img src="image_3.png" /></figure>

* Consideration of dynamic and explicative traits

* Evaluation and prediction of genetic values taking account of the environnement (even in unobserved environments)
# Maritime pine (Pinus Pinaster) breeding in France

## « Landes de Gascogne » forest

* 0,8 million hectares (24% of French wood harvest)

* Main uses in carpentry, joinery, stationery

<figure><img src="image_1.png" /></figure>

* Plantations with improved seedlings

* Mainly based on the Landes provenance

## Recurrent selection scheme

* Started in the ~1960 → 3rd generation today

<figure><img src="image_2.png" /></figure>

* Targeted traits :

* Growth (height, circumference, straightness)

* Adaptation to the environment

* Wood quality

* Genetic values estimated with pedigree

## Dynamic phenotypes : NoR

* Classical selection focuses on final growth traits

* Integrative phenotypes with no consideration of the environment

NoR : pattern of phenotypic expression of a single genotype across a range of environments

<figure><img src="image_3.png" /></figure>

* Consideration of dynamic and explicative traits

* Evaluation and prediction of genetic values taking account of the environnement (even in unobserved environments)
Construction of norms of reaction

<figure><img src="image_4.png" /></figure>

Modeling trajectories and
estimation of the genetic effect
Construction of norms of reaction

<figure><img src="image_4.png" /></figure>

Modeling trajectories and
estimation of the genetic effect
Construction of norms of reaction

<figure><img src="image_5.png" /></figure>

Modeling trajectories and
estimation of the genetic effect
Construction of norms of reaction

<figure><img src="image_5.png" /></figure>

Modeling trajectories and
estimation of the genetic effect
# Experimental design and measurements

## Experimental design for maritime pine (6300 trees)

<figure><img src="image_6.png" /></figure>

### Experimental design

* 2 locations : Cestas (humid) & Escource (dry)

* Installation in 1996 : 26 years old trees

* 150 half-sib families with 35 individuals/family → 6300 trees per site

* Complete block design (1 individual of each family per block)

### Phenotypic measurements :

* Classical growth measures at different ages (height, circumference, straightness)

* Core sampling of 325 trees per site :

150 half-sib families

25 families selected

13 individuals cored

<figure><img src="image_7.png" /></figure>

### Environmental measurements :

* Conventional annual climate measurements (temperature, rainfall...)
# Experimental design and measurements

## Experimental design for maritime pine (6300 trees)

<figure><img src="image_6.png" /></figure>

### Experimental design

* 2 locations : Cestas (humid) & Escource (dry)

* Installation in 1996 : 26 years old trees

* 150 half-sib families with 35 individuals/family → 6300 trees per site

* Complete block design (1 individual of each family per block)

### Phenotypic measurements :

* Classical growth measures at different ages (height, circumference, straightness)

* Core sampling of 325 trees per site :

150 half-sib families

25 families selected

13 individuals cored

<figure><img src="image_7.png" /></figure>

### Environmental measurements :

* Conventional annual climate measurements (temperature, rainfall...)
Experimental design and measurements

<figure><img src="image_8.png" /></figure>
Experimental design and measurements

<figure><img src="image_8.png" /></figure>
Construction of norms of reaction

<figure><img src="image_9.png" /></figure>

Modeling a trajectory and
estimation of the genetic effect
Construction of norms of reaction

<figure><img src="image_9.png" /></figure>

Modeling a trajectory and
estimation of the genetic effect
Construction of norms of reaction

<figure><img src="image_10.png" /></figure>

Modeling a trajectory and
estimation of the genetic effect
Construction of norms of reaction

<figure><img src="image_10.png" /></figure>

Modeling a trajectory and
estimation of the genetic effect
# Construction of norms of reaction

<figure><img src="image_11.png" /></figure>

Norm of reaction for Maritime pine - Papin, Bouffier, Sanchez-Rodriguez
# Construction of norms of reaction

<figure><img src="image_11.png" /></figure>

Norm of reaction for Maritime pine - Papin, Bouffier, Sanchez-Rodriguez
Construction of norms of reaction

<figure><img src="image_12.png" /></figure>

Modeling a trajectory and
estimation of the genetic effect
Construction of norms of reaction

<figure><img src="image_12.png" /></figure>

Modeling a trajectory and
estimation of the genetic effect
Construction of norms of reaction

<figure><img src="image_13.png" /></figure>

Modeling a trajectory and
estimation of the genetic effect
Construction of norms of reaction

<figure><img src="image_13.png" /></figure>

Modeling a trajectory and
estimation of the genetic effect
# Construction of norms of reaction

## A matrix

calculated with pedigree information

<figure><img src="image_14.png" /></figure>

## G matrix (VR1)

Calculated with 3000 SNPs information

<figure><img src="image_15.png" /></figure>

## Comparison of relatedness calculated with genomic data and relatedness calculated with pedigree data

<figure><img src="image_16.png" /></figure>
# Construction of norms of reaction

## A matrix

calculated with pedigree information

<figure><img src="image_14.png" /></figure>

## G matrix (VR1)

Calculated with 3000 SNPs information

<figure><img src="image_15.png" /></figure>

## Comparison of relatedness calculated with genomic data and relatedness calculated with pedigree data

<figure><img src="image_16.png" /></figure>
Construction of norms of reaction

<figure><img src="image_17.png" /></figure>

Modeling a trajectory and
estimation of the genetic effect
Construction of norms of reaction

<figure><img src="image_17.png" /></figure>

Modeling a trajectory and
estimation of the genetic effect
Construction of norms of reaction

<figure><img src="image_18.png" /></figure>

Modeling a trajectory and
estimation of the genetic effect
Construction of norms of reaction

<figure><img src="image_18.png" /></figure>

Modeling a trajectory and
estimation of the genetic effect
# Random regression model (RRM)

* We model individual trajectories according to the level of aridity of the environment (Martonne index)

<figure><img src="image_19.png" /></figure>

<figure><img src="image_20.png" /></figure>

* Mean trajectories, additive genetic effect and permanent environmental effects are modeled by 2-order Legendre polynomials
# Random regression model (RRM)

* We model individual trajectories according to the level of aridity of the environment (Martonne index)

<figure><img src="image_19.png" /></figure>

<figure><img src="image_20.png" /></figure>

* Mean trajectories, additive genetic effect and permanent environmental effects are modeled by 2-order Legendre polynomials
Construction of norms of reaction

<figure><img src="image_21.png" /></figure>

Modeling a trajectory and
estimation of the genetic effect
Construction of norms of reaction

<figure><img src="image_21.png" /></figure>

Modeling a trajectory and
estimation of the genetic effect
Construction of norms of reaction

<figure><img src="image_22.png" /></figure>
Construction of norms of reaction

<figure><img src="image_22.png" /></figure>
# Norms of reaction : heritability and genetic correlations

$$y_{ij} = \text{Mean trajectory}(t_j) + \text{Additive genetic effect}_i(t_j) + \text{Permanent environmental effect}_i(t_j) + \varepsilon_{ij}$$

<figure><img src="image_23.png" /><figcaption>Genetic correlations between environments (levels of aridity) estimated with RRM2</figcaption></figure>

<figure><img src="image_24.png" /></figure>
# Norms of reaction : heritability and genetic correlations

$$y_{ij} = \text{Mean trajectory}(t_j) + \text{Additive genetic effect}_i(t_j) + \text{Permanent environmental effect}_i(t_j) + \varepsilon_{ij}$$

<figure><img src="image_23.png" /><figcaption>Genetic correlations between environments (levels of aridity) estimated with RRM2</figcaption></figure>

<figure><img src="image_24.png" /></figure>
Norms of reaction : additive genetic trajectories

$$y_{ij} = \text{Mean trajectory}(t_j) + \text{Additive genetic effect}_i(t_j) + \text{Permanent environmental effect}_i(t_j) + \varepsilon_{ij}$$
Norms of reaction : additive genetic trajectories

$$y_{ij} = \text{Mean trajectory}(t_j) + \text{Additive genetic effect}_i(t_j) + \text{Permanent environmental effect}_i(t_j) + \varepsilon_{ij}$$
# Norms of reaction : additive genetic trajectories

$$y_{ij} = \text{Mean trajectory}(t_j) + \text{Additive genetic effect}_i(t_j) + \text{Permanent environmental effect}_i(t_j) + \varepsilon_{ij}$$

<figure><img src="image_25.png" /><figcaption>Evolution of individual genetic values across environments</figcaption></figure>
# Norms of reaction : additive genetic trajectories

$$y_{ij} = \text{Mean trajectory}(t_j) + \text{Additive genetic effect}_i(t_j) + \text{Permanent environmental effect}_i(t_j) + \varepsilon_{ij}$$

<figure><img src="image_25.png" /><figcaption>Evolution of individual genetic values across environments</figcaption></figure>
# Norms of reaction : additive genetic trajectories

$$y_{ij} = \text{Mean trajectory}(t_j) + \text{Additive genetic effect}_i(t_j) + \text{Permanent environmental effect}_i(t_j) + \varepsilon_{ij}$$

Evolution of individual genetic values across environments

<figure><img src="image_26.png" /></figure>

Clustering of trajectories (Genolini et al. 2015)

Clustering of individual genetic values trajectories

<figure><img src="image_27.png" /></figure>
# Norms of reaction : additive genetic trajectories

$$y_{ij} = \text{Mean trajectory}(t_j) + \text{Additive genetic effect}_i(t_j) + \text{Permanent environmental effect}_i(t_j) + \varepsilon_{ij}$$

<figure><img src="image_26.png" /></figure>

Evolution of individual genetic values across environments

<figure><img src="image_27.png" /></figure>

Clustering of individual genetic values trajectories

<figure><img src="image_28.png" /></figure>
# Norms of reaction : additive genetic trajectories

$$y_{ij} = \text{Mean trajectory}(t_j) + \text{Additive genetic effect}_i(t_j) + \text{Permanent environmental effect}_i(t_j) + \varepsilon_{ij}$$

<figure><img src="image_28.png" /></figure>

Evolution of individual genetic values across environments

<figure><img src="image_29.png" /></figure>

Genetic BLUP

Clustering of individual genetic values trajectories

<figure><img src="image_30.png" /></figure>

Genetic BLUP

Level of aridity (Martonne index)
# Norms of reaction : additive genetic trajectories

$$y_{ij} = \text{Mean trajectory}(t_j) + \text{Additive genetic effect}_i(t_j) + \text{Permanent environmental effect}_i(t_j) + \varepsilon_{ij}$$

Evolution of individual genetic values across environments

<figure><img src="image_29.png" /></figure>

Clustering of individual genetic values trajectories

<figure><img src="image_30.png" /></figure>
# Conclusion and prospects

* **With:**

* **Phenotypic measurements:** densitometric profiles

* **Simple climatic characterization:** Martonne's aridity index

* **Genetic data:** pedigree or molecular markers information

→ **Norms of reaction:** individual genetic values across a range of environments

* **Main prospects:**

* Improve **environmental characterization**:

* Consideration of previous years, better differentiation of experimental sites...

* Use of a **growth simulation model** (GO+ : based on environmental characteristics of each site (stand density, groundwater height)) to incorporate more explanatory parameters into the annual index (soil water reserve, evapotranspiration demand)

* Extend to other **inter-ring phenotypic traits** (ex: average ring density)

* Construct NoR for **intra-ring growth**

<figure><img src="image_31.png" /></figure>
# Conclusion and prospects

* **With:**

* **Phenotypic measurements:** densitometric profiles

* **Simple climatic characterization:** Martonne's aridity index

* **Genetic data:** pedigree or molecular markers information

→ **Norms of reaction:** individual genetic values across a range of environments

* **Main prospects:**

* Improve **environmental characterization:**

* Consideration of previous years, better differentiation of experimental sites...

* Use of a **growth simulation model** (GO+ : based on environmental characteristics of each site (stand density, groundwater height)) to incorporate more explanatory parameters into the annual index (soil water reserve, evapotranspiration demand)

* Extend to other **inter-ring phenotypic traits** (ex: average ring density)

* Construct NoR for **intra-ring growth**

<figure><img src="image_31.png" /></figure>
Thank you for your attention

<figure><img src="image_32.png" /></figure>
Thank you for your attention

<figure><img src="image_32.png" /></figure>