Agron. Sustain. Dev. 27 (2007) 119-128
DOI: 10.1051/agro:2006029

A new method to analyse relationships between yield components with boundary lines

David Makowski^{a, b}, Thierry Doré^c and Hervé Monod<sup>b

a</sup>  INRA, UMR Agronomie INRA-INA P-G, BP 01, 78850 Thiverval-Grignon, France
^b  Unité Mathématiques et Informatique Appliquées INRA, domaine de Vilvert, 78352 Jouy-en-Josas Cedex, France
^c  INA-P-G, UMR Agronomie INRA-INA P-G, BP 01, 78850 Thiverval-Grignon, France

(Accepted 2 October 2006; published online 23 March 2007)

Abstract - Crop yield can be decreased by many limiting factors such as water stress, nitrogen stress and disease. The agronomic diagnosis method was developed by agronomists to understand the origin of crop yield variability, identify important limiting factors, and define new cropping systems. The rigorous implementation of this method requires the determination of boundary lines giving the maximum value of a yield component in relation to the value of another yield component; for example, grain weight versus grain number per square metre. Such boundary lines are used by agronomists to adjust cropping practices to environmental characteristics and, thus, to reduce the risk of pollution due to agricultural activities. We describe here a new method based on quantile regression to estimate boundary line parameters from experimental data. First, quantile values were computed from models describing the effect of limiting factors on yield components and accounting for measurement errors. Then, boundary line parameters were estimated by quantile regression, with observations weighted according to the quantile values. This approach was applied to two case studies. The quality of the parameter estimator derived by quantile regression was analysed in relation to the size of the dataset and the practical consequences of a misspecification of the quantile value was studied. Our findings show that quantile regression gives more accurate parameter estimators than the methods currently used by agronomists. Nonetheless, the bias and variances of these estimators highly depend on the chosen quantile value. The use of quantile regression should thus help agronomists to analyse crop yield variability from yield component measurements.

Key words: boundary line / model / parameter estimation / quantile regression / yield components / yield gap analysis

Corresponding author: david.makowski@jouy.inra.fr

© INRA, EDP Sciences 2007