Abstract: Statistical learning is a fairly new term referring to a set of supervised and unsupervised modelling and prediction techniques. It is based on traditional statistics but has been highly enhanced inspired by developments in machine learning and data mining. The main focus of statistical learning is to estimate the functions that quantify relations between several parameters and observed responses. These functions are further used for prediction, inference or a combination of both. For a particular case of quantitative responses, regularization techniques in regression are developed to overcome the weaknesses of ordinary least square (OLS) regression in prediction. These new shrinkage methods outperform OLS for prediction, especially in large datasets. In this study, a large dataset of field experiments on winter oilseed rape in Denmark for 22 years (1992 to 2013) was collected. Biweekly climatic data along with sowing date, harvest date, soil type and previous crop are considered as the explanatory variables. Yield of winter oilseed rape is considered as response variable. LASSO and Elastic Nets are the regularization techniques used to estimate the functions. Hold-one-out cross validation method for testing the prediction power reveals that these techniques are much useful in both prediction and inference. Since these techniques are included in recent versions of some software packages (e.g. R), they can be easily implemented by users at any level. The estimated function (model) is further used to predict the oilseed rape yield responses to climate change for several scenarios using representative weather data produced by a weather generator.

Abstract: • First model inter-comparison on crop rotations. • Continuous simulation of multi-year crop rotations yields outperformed single-year simulation. • Low accuracy of yield predictions in less commonly modelled crops such as potato, radish, grass vegetation. • Multi-model mean prediction was found to minimise the likely error arising from single-model predictions. • The representation of intermediate crops and carry-over effects in the models require further research efforts.
Diversification of crop rotations is considered an option to increase the resilience of European crop production under climate change. So far, however, many crop simulation studies have focused on predicting single crops in separate one-year simulations. Here, we compared the capability of fifteen crop growth simulation models to predict yields in crop rotations at five sites across Europe under minimal calibration. Crop rotations encompassed 301 seasons of ten crop types common to European agriculture and a diverse set of treatments (irrigation, fertilisation, CO2 concentration, soil types, tillage, residues, intermediate or catch crops). We found that the continuous simulation of multi-year crop rotations yielded results of slightly higher quality compared to the simulation of single years and single crops. Intermediate crops (oilseed radish and grass vegetation) were simulated less accurately than main crops (cereals). The majority of models performed better for the treatments of increased CO2 and nitrogen fertilisation than for irrigation and soil-related treatments. The yield simulation of the multi-model ensemble reduced the error compared to single-model simulations. The low degree of superiority of continuous simulations over single year simulation was caused by (a) insufficiently parameterised crops, which affect the performance of the following crop, and (b) the lack of growth-limiting water and/or nitrogen in the crop rotations under investigation. In order to achieve a sound representation of crop rotations, further research is required to synthesise existing knowledge of the physiology of intermediate crops and of carry-over effects from the preceding to the following crop, and to implement/improve the modelling of processes that condition these effects.

Abstract: Highlights • Regularization techniques for regression outperformed the classical regression techniques in predicting crop yields. • Different regression techniques with similar prediction accuracy showed different responses of major climatic variables to crop yield. • The regression models showed some responses of crop yield to climatic conditions that is mostly absent in process based crop models. Abstract Statistical regression models represent alternatives to process-based dynamic models for predicting the response of crop yields to variation in climatic conditions. Regression models can be used to quantify the effect of change in temperature and precipitation on yields. However, it is difficult to identify the most relevant input variables that should be included in regression models due to the high number of candidate variables and to their correlations. This paper compares several regression techniques for modeling response of winter oilseed rape yield to a high number of correlated input variables. Several statistical regression methods were fitted to a dataset including 689 observations of winter oilseed rape yield from replicated field experiments conducted in 239 sites in Denmark, covering nearly all regions of the country from 1992 to 2013. Regression methods were compared by cross-validation. The regression methods leading to the most accurate yield predictions were Lasso and Elastic Net, and the least accurate methods were ordinary least squares and stepwise regression. Partial least squares and ridge regression methods gave intermediate results. The estimated relative yield change for a +1°C temperature increase during flowering was estimated to range between 0 and +6 %, depending on choice of regression method. Precipitation was found to have an adverse effect on yield during autumn and winter. It was estimated that an increase in precipitation of +1 mm/day would result in a relative yield change ranging from 0 to −4 %. Soil type was also important for crop yields with lower yields on sandy soils compared to loamy soils. Later sowing was found to result in increased crop yield. The estimated effect of climate on yield was highly sensitive to the chosen regression method. Regression models showing similar performance led in some cases to different conclusions with respect to effect of temperature and precipitation. Hence, it is recommended to apply an ensemble of regression models, in order to account for the sensitivity of the data driven models for projecting crop yield under climate change.