Statistical Methods for Predicting Responses to Applied Nitrogen and Calculating Optimal Nitrogen Rates

Abstract

plied to a set of winter wheat experiments in the Paris Basin of France. The proposed methods are quite gen-Models of response to applied N can be useful for deriving imeral and can be used with different response functions. proved N dose recommendations. Here we show how response model parameters can be estimated and how model predictions and modelParameter estimation in N response models is gener-N dose recommendations can be evaluated. For parameter estimation, ally based on ordinary least squares (e.g., Mombiela et we use a statistical approach based on random parameter models. al., 1981; Sain and Jauregui, 1993). This method is easily Two methods for evaluating models are applied. The first method implemented. However, the underlying assumption that is to calculate mean squared error of prediction (MSEP) by cross model errors are independent is unrealistic for data like validation, and the second is to perform nonparametric regressions to N response data where several measurements (correevaluate the profitability of calculated optimal N rates. The proposed sponding to different N doses) are made for the same methods are used with a data set consisting of 37 winter wheat (Tritisite-year. In this paper, we propose an alternative cum aestivum L.) experiments. Different functions taking into account method for parameter estimation. Our approach conend-of-winter mineral soil N are evaluated. The results show that the sists of using a statistical model called a random paramedifferent functions all have similar MSEP values for predictions of yield and grain protein content and lead to N recommendations of ter model, which is a specific type of mixed-effects similar profitability. However, there are substantial differences in model. A random parameter model assumes that the MSEP for residual mineral N at harvest. One of these models is form of the modeled response is common to all sitethen compared with a model that does not include any site-year years but that parameter values vary between site-years. characteristic and with a model that does not have random parameters.The parameters are thus treated as having some random We find that using the model without a site-year characteristic leads variation around their mean values. This approach is to predictions that are less accurate and optimal N rates that are less consistent with the data that are usually observed, and profitable by F 17 to F 105 ha Ϫ1 . Another result is that the gross it automatically introduces correlations among errors margin obtained with the optimal N rates calculated using the model for the same site-year. This method was applied by Walwithout random parameters is lower by F 438 to F 550 ha Ϫ1 . lach (1995a, 1995b) to a simple quadratic (Q) model for yield as a function of applied fertilizer.We show in this paper how random parameter models D. Makowski and D. Wallach, unité d'agronomie, INRA, B.P. 27, however, the goal of developing the models is either to 31326 Castanet-Tolosan Cedex, France; and J.-M. Meynard, Laboratoire d'agronomie, INRA...

Estimation of economically optimum seed rates for winter wheat from series of trials

“…Approximate non-Bayesian methods for fitting such models are available (e.g. Davidian & Giltinan 1995) Makowski et al (2001) use this approach for modelling the response of winter wheat to applied nitrogen across trials. The adoption in the present paper of a Bayesian approach permits expert knowledge of the crop to be incorporated into the analysis of the data.…”

Rationality in the Use of Non Renewable Natural Resources in Agriculture

“…It has being utilized a variety of empirical models to predict the responses to nutrients and to calculate the optimum levels of nutrients. Among then, it is included the model of Mitscherlich, square root (Mombiela et al, 1981;Sain & Jauregui, 1993), exponential, linearplus-plateau, linear-plus-hyperbola, quadratic and quadratic-plus-plateau (Cerrato & Blackmer, 1990;Bullock & Bullock, 1994;Makowski et al, 1999Makowski et al, , 2001). The use of saturation kinetics to explain the nutritional responses to nutrients by superior life beings are rarely employed (Morgan et al, 1975).…”

Which decision support tools for the environmental management of nitrogen?

“…These models can therefore be used to optimise nitrogen fertilisation, establishing compromises between the various conflicting objectives. For example, the model of Makowski et al [47,48] was used to calculate, for different crops, optimal nitrogen fertiliser rates for maximising farmers' income, and to analyse the consequences of applying the calculated fertiliser rates on crop production and residual mineral nitrogen in the soil at harvest. Table I gives examples of results obtained with this model for winter wheat.…”

“…It can also be used by the authorities to compare the economic and environmental consequences of various possible regulations: they can then choose those which most effectively attain the desired objectives. These models provide the stakeholders with an objective basis for analysing the consequences of compromises considered during negotiations (see [5] and [48] for details).…”