Know more

Our use of cookies

Cookies are a set of data stored on a user’s device when the user browses a web site. The data is in a file containing an ID number, the name of the server which deposited it and, in some cases, an expiry date. We use cookies to record information about your visit, language of preference, and other parameters on the site in order to optimise your next visit and make the site even more useful to you.

To improve your experience, we use cookies to store certain browsing information and provide secure navigation, and to collect statistics with a view to improve the site’s features. For a complete list of the cookies we use, download “Ghostery”, a free plug-in for browsers which can detect, and, in some cases, block cookies.

Ghostery is available here for free:

You can also visit the CNIL web site for instructions on how to configure your browser to manage cookie storage on your device.

In the case of third-party advertising cookies, you can also visit the following site:, offered by digital advertising professionals within the European Digital Advertising Alliance (EDAA). From the site, you can deny or accept the cookies used by advertising professionals who are members.

It is also possible to block certain third-party cookies directly via publishers:

Cookie type

Means of blocking

Analytical and performance cookies

Google Analytics

Targeted advertising cookies


The following types of cookies may be used on our websites:

Mandatory cookies

Functional cookies

Social media and advertising cookies

These cookies are needed to ensure the proper functioning of the site and cannot be disabled. They help ensure a secure connection and the basic availability of our website.

These cookies allow us to analyse site use in order to measure and optimise performance. They allow us to store your sign-in information and display the different components of our website in a more coherent way.

These cookies are used by advertising agencies such as Google and by social media sites such as LinkedIn and Facebook. Among other things, they allow pages to be shared on social media, the posting of comments, and the publication (on our site or elsewhere) of ads that reflect your centres of interest.

Our EZPublish content management system (CMS) uses CAS and PHP session cookies and the New Relic cookie for monitoring purposes (IP, response times).

These cookies are deleted at the end of the browsing session (when you log off or close your browser window)

Our EZPublish content management system (CMS) uses the XiTi cookie to measure traffic. Our service provider is AT Internet. This company stores data (IPs, date and time of access, length of the visit and pages viewed) for six months.

Our EZPublish content management system (CMS) does not use this type of cookie.

For more information about the cookies we use, contact INRA’s Data Protection Officer by email at or by post at:

24, chemin de Borde Rouge –Auzeville – CS52627
31326 Castanet Tolosan CEDEX - France

Dernière mise à jour : Mai 2018

Menu Logo Principal

Home page

A novel individual-tree mixed model to account for competition and environmental heterogeneity: a Bayesian approach

Munoz, F. ; Cappa, E. ; Sanchez, L. ; Cantet, R. J. C.
Tree Genetics and Genomes, 2015, 11 (6) : 15 p.
Pièces jointes : 2015_Munoz_TGG_postprint.pdf
Negative correlation caused by competition among individuals and positive spatial correlation due to environmental heterogeneity may lead to biases in estimating genetic parameters and predicting breeding values (BVs) from forest genetic trials. Former models dealing with competition and environmental heterogeneity did not account for the additive relationships among trees or for the full spatial covariance. This paper extends an individual-tree mixed model with direct additive genetic, genetic, and environmental competition effects, by incorporating a two-dimensional smoothing surface to account for complex patterns of environmental heterogeneity (competition + spatial model (CSM)). We illustrate the proposed model using simulated and real data from a loblolly pine progeny trial. The CSM was compared with three reduced individual-tree mixed models using a real dataset, while simulations comprised only CSM versus true-parameters comparisons. Dispersion parameters were estimated using Bayesian techniques via Gibbs sampling. Simulation results showed that the CSM yielded posterior mean estimates of variance components with slight or negligible biases in the studied scenarios, except for the permanent environment variance. The worst performance of the simulated CSM was under a scenario with weak competition effects and small-scale environmental heterogeneity. When analyzing real data, the CSM yielded a lower value of the deviance information criterion than the reduced models. Moreover, although correlations between predicted BVs calculated from CSM and from a standard model with block effects and direct genetic effects only were high, the ranking among the top 5 % ranked individuals showed differences which indicated that the two models will have quite different genotype selections for the next cycle of breeding.