تجزیه و تحلیل حساسیت جهانی برای محاسبه سهم پارامترهای ژنتیکی برای واریانس پیش بینی مدل محصول

Dynamic models are often used to predict the effects of farmers’ practices on crop yield, crop quality, and environment. These models usually include many parameters that must be estimated from experimental data before practical use. Parameter estimation is a difficult problem especially when some of the parameters vary across genotypes. These genetic parameters may be estimated from plant breeding experiments but this is very costly and requires a lot of experimental work. Moreover, some of the genetic parameters may account for only a very small part of the output variance and, so, do not deserve an accurate determination. This paper shows how methods of global sensitivity analysis can be used to evaluate the contributions of the genetic parameters to the variance of model prediction. Two methods are applied to a complex crop model for estimating the sensitivity indices associated to 13 genetic parameters. The results show that only five genetic parameters have a significant effect on crop yield and grain quality.

Crop models are complex nonlinear dynamic models simulating output variables related to crop yield, crop quality, farmer's income, and environment. These models are valuable tools for crop management because they can be used to predict the effects of farmers’ practices in function of soil type, climate, and crop characteristics [1]. Crop models can include up to 200 parameters whose values must be estimated from past experiments. The estimation of these parameters is an important step because crop model performances depend for a large part on the accuracy of the parameter estimates [2]. Predictions obtained with crop models are not reliable when inaccurate parameter values are used. A large amount of data is always required for estimating accurately crop model parameters, in particular when the model includes genetic parameters. As genetic parameters vary across genotypes, the estimation of these parameters must be based on specific measurements collected for each genotype. Such measurements can be performed in plant breeding experiments but this is very costly and requires a lot of experimental work. Moreover, recent studies have shown that crop model predictions are not systematically improved when genotypic parameters are estimated genotype per genotype [3]. This may be due to the small contribution of some of the genetic parameters to the total model output variance. In this study, we investigate how methods of sensitivity analysis can be used to reduce the quantity of field experiments performed for estimating genetic parameters. The basic principle consists in evaluating the contributions of the genetic parameters to the variance of the model prediction and, then, in estimating genotype per genotype only the key parameters whose uncertainty affects most the outputs. In this paper, two methods of global sensitivity analysis [4] are compared to evaluate the contribution of 13 genetic parameters to the variances of two output variables of a crop model.

Our study shows how global sensitivity analysis can be used to identify the genetic parameters that must be estimated from plant breeding experiments. The methods considered in this study allow agronomists to determine which subset of parameters accounts for most of the output variance. These methods are useful and easy to interpret. Those factors with a small contribution can be set equal to any value within their range. This contributes to a model simplification and a reduction of the number of experiments performed for estimating crop model parameters. Our application shows that only five parameters have a significant influence (total sensitivity index>0.1) on the yield and grain protein content values simulated by the AZODYN crop model. Among these parameters, some can be easily estimated from plant breeding experiments like, for instance, the parameter RDTMAXVAR. This parameter represents the maximal yield value of a wheat genotype and can be estimated from yield measurements. Other parameters, like the parameter R (ratio of total to above ground nitrogen), are more difficult to estimate. The comparison of the two methods of global sensitivity analysis shows that the extended FAST method seems to be more efficient. With the Winding stairs method, it is necessary to use at least 10,000 model evaluations per parameter for estimating accurately the first-order and total sensitivity indices. The sensitivity indices obtained by using extended FAST with only 5000 model evaluations per parameter are similar to those obtained by using the Winding stairs method with 10,000 model evaluations.