基于线性回归的玉米生物量预测模型及验证

玉米生物量是评估玉米长势的重要参数,为了实现玉米生物量的快速测量,该文拟以玉米株高H、茎粗长轴L、茎粗短轴S为输入,建立玉米生物量鲜质量FW和干质量DW的预测模型。采用多元回归和逐步回归方法对平展型和紧凑型玉米的小喇叭口期生物量数据进行线性回归分析。结果表明,玉米茎粗长轴和茎粗短轴与玉米鲜质量和干质量的相关性高于玉米株高,多元回归模型H+L+S、L×S和逐步回归模型具有较高的拟合精度,其对玉米鲜质量、干质量的决定系数高于0.874和0.877,均方根误差分别小于7.363和0.801 g,且单因素方差分析表明,3个模型之间没有明显差异,模型交叉验证结果表明,3个模型都具有较好的稳定性和预测能力。应用上述3个模型对玉米大喇叭口期的生物量进行预测,预测结果表明,模型对平展型玉米的预测精度优于紧凑型玉米。对平展型玉米生物量的预测中,逐步回归模型预测效果最优,其对玉米鲜质量、干质量的决定系数分别为0.866、0.875,均方根误差分别为30.790和2.752 g,相对均方根误差分别为13.53%、11.41%。该研究表明,利用玉米株高、茎粗长轴、茎粗短轴可实现对玉米生物量的估测,且对平展型玉米具有较好的预测效果。

Modeling and verification of maize biomass based on linear regression anaysis

Abstract: Maize biomass is an essential parameter for assessing plant vigor, which is also a vital parameter for estimating root growth. Traditionally, maize biomass is obtained by manual investigation, which is time consuming and laborious, and it is tough to acquire large samples. With the development of breeding, breeders are eager to rapidly measure or estimate maize biomass. In order to meet the requirement, many biomass models have been developed. Typically plant height is used to develop models to predict plant biomass; the research introduces stem diameter parameters into the models and develops linear models based on maize height, stem long diameter, and stem short diameter to estimate maize biomass. Spreading-leaf maize named Nongda 84 and upright-leaf maize named Jingnongke 728 were cultivated, and the samples at the small trumpet stage and the large trumpet stage were collected. Plant height was taken by measuring the difference between the soil surface and the top point of leaf. Stem diameters were measured using a digital caliper, and the long diameter and short diameter were taken by measuring the longest and shortest axes of the first stem internode. Maize samples were weighted to get their fresh weights on the same day. Maize dry weight was recorded when its weight was constant. Biomass data of Nongda 84 samples and Jingnongke 728 samples at the small trumpet stage were analyzed (40 groups respectively). With the use of multiple regression method and step regression method, linear regressions were conducted, and several biomass models were built. First, plant height(H), stem long diameter(L), and stem short diameter (S) were treated individually as input parameters of linear regression models, and the regression results indicated that the relationships between maize biomass and stem long diameter, short diameter are more significant than between maize biomass and maize height, and stem diameters are of great importance to estimate maize biomass. Then, plant height, stem long diameter, and stem short diameter were combined and integrated in the multiple regression models and step regression models, and the regression precisions of multiple regression models (H+L+S, L×S) and stepwise regression model are high; for maize fresh weight and dry weight, the coefficients of determination are both higher than 0.87, and the root mean square error (RMSE) values are smaller than 7.37 and 0.81 g, respectively. Although the structures of the multiple regression models are simpler than the step regression models, the one-way analysis of variance proved that there are no significant differences among the aforementioned 3 models. In addition, leave one out cross-validation was conducted to use the biomass samples more adequately and the aforementioned 3 models were tested. The coefficients of determination and RMSE values are similar to original models, which showed that the 3 models have a good performance in stability and prediction. After that, multiple regression models H+L+S and L×S, and stepwise regression model were used to estimate maize biomass at the large trumpet stage, and 40 groups of Nongda 84 samples and 37 groups of Jingnongke 728 samples were verified to test the model precisions. In terms of Nongda 84, the multiple regression model L×S and stepwise regression model are advisable to estimate biomass. For Jingnongke 728, the multiple regression model L×S is a prime candidate for estimating biomass. The results also showed that all the models perform better in estimating Nongda 84 than Jingnongke 728. Among all the models, the stepwise regression model has the best performance in estimating the biomass of Nongda 84, and for maize fresh weight and dry weight, the coefficients of determination are 0.866 and 0.875, the RMSE values are 30.790 and 2.752 g, and the relative root mean square errors are 13.53% and 11.41%, respectively. It indicates that maize height, stem long diameter and stem short diameter can be used to estimate maize biomass, and have good performance in estimating spreading-leaf maize biomass.