# Norm of reaction for maritime pine

Victor Papin, Laurent Bouffier, Léopoldo Sanchez

► To cite this version:

Victor Papin, Laurent Bouffier, Léopoldo Sanchez. Norm of reaction for maritime pine. B4EST Training course "Phenotypic plasticity and norms of reaction modelling", B4EST project, Oct 2021, On Line meeting, France. hal-04717539

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https://hal.inrae.fr/hal-04717539v1

Submitted on 1 Oct 2024

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Distributed under a Creative Commons Attribution 4.0 International License
Case study 3:
Norm of reaction for maritime pine

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Victor Papin, INRAE (UMR BIOGECO Pierroton)
Laurent Bouffier, INRAE (UMR BIOGECO Pierroton)
Léopoldo Sanchez, INRAE (UMR BioForA Orléans)
Outlines

* Maritime pine (Pinus pinaster)

* GxE in the French maritime pine breeding context

* Genetic component of individual norm of reaction (NoR)

* Concept of Random Regression (RR)

* Application on maritime pine based on wood longitudinal data
Maritime pine (*Pinus pinaster*)

* Natural distribution area (green) and field observations (frequency of occurrences)

<figure><img src="image_5.png" /><figcaption>Maritime pine clonal archive</figcaption></figure>

Abad Viñas, R., Caudullo, G., Oliveira, S., de Rigo, D., 2016. *Pinus pinaster* in Europe: distribution, habitat, usage and threats. In: San-Miguel-Ayanz, J., de Rigo, D., Caudullo, G., Houston Durrant, T., Mauri, A. (Eds.), *European Atlas of Forest Tree Species*. Publ. Off. EU, Luxembourg, pp. e012d59+

<figure><img src="image_6.png" /></figure>
# Maritime pine (Pinus pinaster)

* High genetic structuration:

6 main genepools identified from 36 natural populations

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

From Jaramillo-Correa *et al.* (2015)

* Phenotypic variability between provenances:

results from a progeny trial established in France

<figure><img src="image_8.png" /></figure>
# Maritime pine breeding in France

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

* "Landes de Gascogne" forest: 0.8 million hectares (7% of the French forest - 24% of French wood harvest): → high productivity in a limited area

* plantations with **improved seedlings** except in sand dunes (natural regeneration)

* **One breeding zone**

* Similar climatic conditions (dry summers and wet winters)

* Low variation in site types (poor soils with sandy podzol)

* Breeding population mainly based on the **local provenance** (Landes provenance)

* **Generalist varieties** produced in open seed orchards → additive effect
# In that breeding context: why studying GxE ?

* Even if environmental variation is limited in the current breeding zone, varieties could be designed per site type to increase genetic gains

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

Need to better understand GxE to design specialized varieties

* Anticipation for future environments: climate change and new pests (pine wood nematode)

- Current breeding population must be evaluated in drier environments ➔ establishment of progeny trials south of the current breeding zone

- Introduction of non-local provenances in the breeding population
  ➔ plus trees selected have to be characterized in the current
  breeding zone

<figure><img src="image_11.png" /><figcaption>Pine wood nematode</figcaption></figure>
* Opportunity to expand maritime pine plantations north of the current breeding zone (evaluation of the breeding population in new site types)

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

Climate Matching Tool (https://climatematch.org.uk/)

→ The breeding population (Landes provenances + other genepools) has to be characterized over a large range of environments to anticipate future changes

## Results Summary

Areas that will have a similar climate in 2021-2050 to the current (1981-2010) climate at the selected location (44.3199° N, 0.7306° W).

Note: Climate Difference scores closest to zero indicate the best match.

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

### Parameters

<table><tr><td>Study region</td><td>Europe</td></tr><tr><td>Climate difference variables</td><td>Precipitation, Temperature and Diurnal Range</td></tr><tr><td>Selected site</td><td>44.3199° N, 0.7306° W</td></tr><tr><td>Local climate</td><td>1981-2010</td></tr><tr><td>Search climate</td><td>2021-2050</td></tr><tr><td>Months matched</td><td>Jan, Feb, Mar, Apr, May, Jun, Jul, Aug, Sep, Oct, Nov, Dec</td></tr><tr><td>Number of matches requested</td><td>5,000</td></tr></table>
# Genetic component of individual norm of reaction

* **Phenotypic plasticity** = phenotypic trajectory over an heterogeneous environmental landscape

* Breeding is focused on the selection of superior genotypes to establish seed orchards → phenotypic plasticity must be studied at the **individual level** (≠ population level)

* Phenotypic plasticity implies multiple phenotypic states per genotype:

* **site-related plasticity:** measurements repeated over sites on the same genotype but different ramets (clonal trial)

* ✓ Independent measurements (simple statistical methodologies) but site selection can be tough (the environmental range covered by the sites is generally different from the range of interest for breeding)

* **time-related plasticity:** measurements repeated over time for the same individual

* ✓ Autocorrelation between measurements (specific statistical methodologies) but the environmental range explored is similar to the production conditions

* Phenotypic plasticity can be modelled statistically as a function of one or several explanatory environmental variables. The resulting function is then called **norm of reaction (NoR)**. The choice of environmental variables (climatic variables, soil variables, indexes...) is a key issue. Ecophysiology knowledge is required to select the relevant variables.

* Genotypes from a given population might show different NoRs over the same environmental cline, resulting for instance in intercrossing curves. This is typically a genotype by environment interaction → **Genotypic by environment interaction** measures variation in NoR.
# Maritime pine trials available to study GxE

* Clonal trials established from micro-cuttings: large genetic variability (natural populations from various genepools) established in several contrasted sites

* In the French breeding context:

* No clonal trials available

* Multisite progeny trials which explore the environmental variation of the current breeding zone (no site with extreme climates)

* Only since recently:

* exploration of new sites north or south of the breeding zone

* exploration of larger genetic variability (trials with various provenances)
# Genetic NoR based on familial data

* Estimation of site-related plasticity

* When no clonal data available, site-related plasticity can be estimated with familial data

Heritability

0.6

0.1

20 sibs

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

120 sibs

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

K

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L

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Family size

## Deciphering Hybrid Larch Reaction Norms Using Random Regression

Alexandre Marchal,* Carl D. Schlichting,† Rémy Gobin,* Philippe Balandier,‡ Frédéric Millier,* Facundo Muñoz,* Luc E. Pâques,* and Leopoldo Sánchez*

### Simulations (Metagene software):

* Full diallel design (10 parents) to generate full-sib families

* Only one sib per site (environmental gradient)

* 4 scenarios simulated which differ by the quantity (family size) and quality (h²) of information

* Accuracy = correlation between the parents' predicted additive performance and their true additive performance

### Simulation results:

High accuracy with either high number of sibs or high heritability
# Genetic NoR based on longitudinal data

* Estimation of time-related plasticity

* **Longitudinal data:** refers to repeated observations of the same variables on the same individuals over a given period of time

* Longitudinal data can be a way to explore a large range of environmental conditions

* **Limitations:** repeated measures are linked by autocorrelation and ontogeny can impact the phenotype studied

* **Example:** time series for growth

**Variance modelling of longitudinal height data from a *Pinus radiata* progeny test**

Luis A. Apiolaza, Arthur R. Gilmour, and Dorian J. Garrick

Can. J. For. Res. 30: 645-654 (2000)

<figure><img src="image_18.png" /></figure>
# Longitudinal data based on wood

* Wood = record of tree anatomical reaction to environmental changes

During wood formation, the cambium reacts to environmental changes by adjusting the anatomy of the newly formed xylem cells. This continuous modification leaves a permanent anatomical trace in the wood that follows seasonal changes and weather events (→ rings in a temperate climate)

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From Bouffier *et al.* 2008

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- In experimental trial (plantation): calendar year and tree age are confounding

- Indexing choice is important: cambial age indexing vs. calendar year indexing

- Analyses can focus on variability between rings or within rings
# Genetic parameters from NoR

* Same quantitative framework to estimate the genetic parameters (genetic variance, genetic correlation, $h^2$...):

* Pedigree / genomic data

* Estimation in several steps:

1. Fitting a NoR per genotype

2. Extraction of variables from each NoR (slope, inflexion point, max...)

3. Estimation of genetic parameters as for traditional traits

* Estimation in a single step:

mixed model (trajectory and genetic effect in the same model) → random regression

<figure><img src="image_23.png" /></figure>

**Biological interpretation**

* **Slope** = speed of wood density increase in response to drought constraint

* **Inflexion** = susceptibility of tree to drought constraint

* **Min** = wood density when there is no water limitation

* **Max** = wood density when water limitation is maximal

* **Diff** = plasticity level for wood density
# The concept of random regression
# The random regression as an extension of the classical linear mixed model

## Univariate model

Each level of the index variable = 1 trait

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$$y_i = \mu + \beta_i + \alpha_i + \varepsilon_i$$

* $\mu$ : mean

* $\beta_i$ : fixed effect

* $\alpha_j$ : random effects

## Multivariate model

Consideration of each level of the variable index as correlated traits

<figure><img src="image_25.png" /></figure>

$$y_{ij} = \mu_j + \beta_{ij} + \alpha_{ij} + \varepsilon_{ij}$$

* $\mu$ : mean

* $\beta_i$ : fixed effect

* $\alpha_j$ : random effects

## Random regression

Adjustment of a trajectory according to a meaningful index

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

$$y_{ij} = M(t_j) + F_{ij} + A_i(t_j) + P_i(t_j) + \varepsilon_{ij}$$

* $M(t_j)$ : mean trajectory

* $F_{ij}$ : fixed effects

* $A_i(t_j), P_i(t_j)$ : random effects
# Elements of random regression models

## Random regression

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$$ y_{ij} = M(t_j) + F_{ij} + A_i(t_j) + P_i(t_j) + \varepsilon_{ij} $$
Fixed part
Random part

* **M(t<sub>j</sub>)**: mean trajectory
  → of the whole population, of a subgroup...

* **F<sub>ij</sub>**: fixed effects
  → Site, Treatment...

**A<sub>i</sub>(t<sub>j</sub>)**: genetic additive effect
→ Part of the deviation from mean trajectory due to genetic additive effects
→ Variance constrained by relationship matrix

**P<sub>i</sub>(t<sub>j</sub>)**: Permanent environmental effect
→ Part of the deviation from mean trajectory due to permanent environmental effect

**ε<sub>ij</sub>**: residuals (variance can be homogeneous or heterogeneous)
# Elements of random regression models

Random regression

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

Phenotype

Genotype1

Deviation due to permanent env effect

Deviation due to additive genetic effect

Mean trajectory

Index variable

$$ y_{ij} = M(t_j) + F_{ij} + A_i(t_j) + P_i(t_j) + \varepsilon_{ij} $$
Fixed part
Random part

$M(t_j)$ : mean trajectory
→ of the whole population, of a subgroup...

$F_{ij}$ : fixed effects
→ Site, Treatment...

$A_i(t_j)$ : genetic additive effect
→ Part of the deviation from mean trajectory due to genetic additive effects
→ Variance constrained by relationship matrix

$P_i(t_j)$ : Permanent environmental effect
→ Part of the deviation from mean trajectory due to permanent environmental effect

$\varepsilon_{ij}$ : residuals (variance can be homogeneous or heterogeneous)
# Trajectory modeling in random regressions (1)

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

3 elements in each sum :

$\varphi_r(t_j), \varphi_r(t_j), \varphi_r(t_j)$

rth basis function evaluated for t_j

$k_m, k_\alpha, k_\gamma$

Polynomial order for modeling

$m_{ir}, \alpha_{ir}, \gamma_{ir}$

regression coefficients for mean trajectory, additive genetic, permanent environment effects
# Trajectory modeling in random regressions (2)

For additive genetic effect (α) with a 2-order plonymial modeling (k_α=3) :

$$ \sum_{r=1}^{k_{\alpha}} \alpha_{ir} \varphi_{r}(t_j) = \alpha_{i1} \varphi_{1}(t_j) + \alpha_{i2} \varphi_{2}(t_j) + \alpha_{i3} \varphi_{3}(t_j) $$

$\varphi_1(t_j)$

Basis function : Legendre polynomials

With k_α=3 and j ∈ [1:20]

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<table><thead><tr><th colspan="4">2-order Legendre polynomial coefficients</th></tr></thead><tbody><tr><td>j=1</td><td>0,71</td><td>-1,22</td><td>1,58</td></tr><tr><td>j=2</td><td>0,71</td><td>-1,10</td><td>1,11</td></tr><tr><td>j=3</td><td>0,71</td><td>-0,97</td><td>0,69</td></tr><tr><td>...</td><td>...</td><td>...</td><td>...</td></tr><tr><td>j=17</td><td>0,71</td><td>0,84</td><td>0,32</td></tr><tr><td>j=18</td><td>0,71</td><td>0,97</td><td>0,69</td></tr><tr><td>j=19</td><td>0,71</td><td>1,10</td><td>1,11</td></tr><tr><td>j=20</td><td>0,71</td><td>1,22</td><td>1,58</td></tr></tbody></table>

Results for each individual i

$$
\begin{bmatrix}
\alpha_{i1} \\
\alpha_{i2} \\
\alpha_{i3}
\end{bmatrix}
$$

3 regressions coefficients for the additive genetic effects
# Results of a random regression

For each individual *i*, for the additive genetic effect :

<figure><img src="image_31.png" /></figure>

Possible to extract one breeding value for each
individual at each value of the index variable

<table><thead><tr><th colspan="2">Breeding value</th></tr></thead><tbody><tr><td>j=1</td><td>a1</td></tr><tr><td>j=2</td><td>a2</td></tr><tr><td>j=3</td><td>a3</td></tr><tr><td>...</td><td>...</td></tr><tr><td>j=17</td><td>a17</td></tr><tr><td>j=18</td><td>a18</td></tr><tr><td>j=19</td><td>a19</td></tr><tr><td>j=20</td><td>a20</td></tr></tbody></table>

* Same procedure for mean trajectory, permanent environmental effects, genetic variance
Norm of reaction for Maritime pine
# Experimental design and measurements

<figure><img src="image_32.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_33.png" /></figure>

## Environmental measurements :

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

<figure><img src="image_34.png" /></figure>

<figure><img src="image_35.png" /></figure>
# Norm of reaction for maritime pine : trait/year

* We want to model **one trajectory** for each tree of each site : 650 trajectories

* First modelisation are done according to the **year** : index variable = year & j ∈ [1999:2019]

<figure><img src="image_36.png" /></figure>

* Mean trajectories, additive genetic effect and permanent environmental effects are modeled by 2-order Legendre polynomials
# Norm of reaction for maritime pine : trait/year

Fixed part of the model :

Mean trajectories according to each site

<figure><img src="image_37.png" /></figure>

Mean raw data

<figure><img src="image_38.png" /></figure>
# Norm of reaction for maritime pine : trait/year

Fixed part of the model :

Mean trajectories according to each group

<figure><img src="image_39.png" /></figure>

Random part of the model :

individual trajectories for additive genetic effect

<figure><img src="image_40.png" /></figure>

Random part of the model :

Family trajectories for additive genetic effect
# Norm of reaction for maritime pine : trait/year

## Evolution of heritability across the year

(estimated with RR model and independent univariate model)

<figure><img src="image_41.png" /></figure>

## Model quality : R² (coefficient of determination)

$$R2 = \frac{\text{Variance explained by the model}}{\text{Total variance}}$$

<figure><img src="image_42.png" /></figure>
# Norm of reaction for maritime pine : trait / env index

* In previous analysis, index variable = year

<figure><img src="image_43.png" /></figure>

* But in a context of breeding and rapid climatic change, our objective is **to predict the response of trees in a specific environment**: new index variable = environmental variable

<figure><img src="image_44.png" /></figure>

## Method :

Martonne aridity index, for a month :

$$I = \frac{12p}{t + 10}$$

<figure><img src="image_45.png" /></figure>

available through INRAE weather databases

For a year, mean of monthly Martonne index on growth season (April – September)

<figure><img src="image_46.png" /></figure>

Characterization of each year

<figure><img src="image_47.png" /></figure>
# Norm of reaction for maritime pine : trait / env index

<figure><img src="image_48.png" /><figcaption>re-organization</figcaption></figure>

<figure><img src="image_49.png" /><figcaption>Ring surface across aridity index</figcaption></figure>

<figure><img src="image_50.png" /><figcaption>Modeling</figcaption></figure>
# Norm of reaction for maritime pine : trait / env index

Ring surface across years

<figure><img src="image_51.png" /></figure>

Raw trajectories may contain hidden effects and not only responses to environmental conditions of the year

*For example the effect of age, of a disease attack...*

In our case, we have a constraint of **_the age effect_** (all trees were planted in the same year)

Possible improvements :

* Focus on 2005-2019

* 3-step approach :

* Perform a 1st RR on year to estimate the mean trajectory

* Correcting phenotypes with this mean effect

* Perform a 2nd RR env_index with corrected data
# Norm of reaction for maritime pine : prospects

<figure><img src="image_52.png" /></figure>

## Environmental index :

* Improve year characterization (soil humidity, water balance, impact of previous years, others indexes...)

* Compare the relevance of the different environmental variables in the RR models

## Genetic data :

* Replace pedigree information by genotypic data

## Phenotypic trait

* Model other inter-ring traits (mean density, percentage of final wood...)

* Consider intra-ring traits (conversion from a distance to time, model through a continuous environmental variable

## Main objectives :

* Identify environmentally sensitive traits & identify environmental variables that induce differential responses in trees

* Characterize the diversity of tree reactions & identify families of interest for selection