The approach presented here is under development in the framework of my thesis and will soon be published in a scientific article. It is presented here as an example but should be discussed and validated with us before being reused and reproduced.

Introduction : Norms of reaction : definition and modeling

What is a norm of reaction ?

For a genotype, the norm of reaction describes all phenotypes that it can produce within a range of environments.

We refere here to the phenotypic plasticity

NoR-def


What is the point of norms of reaction ?

Conventional and genomic selection focuses mainly on final growth traits (height, circumference, straightness). These phenotypic parameters are very integrative: they do not take into account the evolutions during the long trees growth, in connection with the various environments encountered.

The modeling of individual norms of reaction allows to describe phenotypic evolution of trees across a range of environments. Genetic parameters can be then declined for each environment considered.

Therefore, breeders can apply a selection strategy that explicitly takes into account the environmental effect (ex: Specialized varieties for a single type of environment, or generalist varieties with high genetic values in all environments)

How to construct norms of reaction in a forest tree context ?

To construct norms of reaction, repeated phenotypic measurments across environmentsfor each individual are needed. But in some contexts, such as for maritime pine, it is very difficult to evaluate the same individual in different environments. Clonal experimental design are rather rare.

Fortunately, we can use longitudinal data based on wood. Wood is a 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)

Wood-longitudinal-data

Densitometric profiles continuously describe the trees growth over the years. Environmental conditions being variable within and between years, we have repeated phenotypic measurements of the same individuals in different environments.

Several approches are possible to construct norms of reaction from densitometric profils. Here we describe probably the simpliest one : norms of reaction based on annual growth. In this approach we will consider each ring as a unit of measurement. For a given ring, the growth of the tree can be summarized by a general phenotypic variable (ring width, ring surface, ring mean density). At the same time, this same ring corresponding to one year can also be associated with the global climate fo the year. From then on, we can model the evolution of the ring phenotypic variable as a function of the annual climate index.

Wood-growth



The statistical tool : the random regression model

Here, we want to model individual norms of reaction for maritime pines, using the phenotypic trajectories previously described. The statistical tool we’ll use is the random regression model.


models


Random regression models integrate three types of data :

  1. Phenotypic data : phenotypic trajectories we want to model

  2. Environmental/Climatic data : envrionmental parameters characterizing each environments (each year in this case)

  3. Genetic data : to describre relationships between indviduals (using pedigree or genomic information)


1. Phenotypic data : exprimental design and measurments

a. Experimental design

In this design, we have two sites (Cestas & Escource) located the Landes forest in the south west of France. Experimental devices were installed in 1996.

Each site includes 150 half-sib families with 35 individual per family.

We have a complete block plan, with one indiviudal of each family in each block.