基于符号回归的谷物产量与化肥用量关系研究

Study on the Relationship between Grain Yield and Fertilizer Consumption Based on Symbolic Regression

随着化肥用量的增加,谷物产量逐年增加,但同时也出现了过量施肥导致的土壤退化等问题。传统的谷物产量及化肥用量研究一般采用假定模型结构的实证方法,但设定的模型不一定适用于各个国家,且可能遗漏更精准的模型。运用符号回归方法,对1961—2018年104个国家的谷物产量与化肥用量进行拟合,从时间和空间两个维度研究二者的演化模型。在时间维度中,分析得出二者关系随时间变动的模型;在空间维度中,对4个重要模型在不同时间段对不同国家的适用性进行分析。结果显示,时间变动影响二者之间的关系;单调递增模型在各国家不同时间区间适用度都较高;对于在不同时间段内二者关系波动较大的部分国家而言,存在适用度较低但拟合精度高的可较好描述二者关系的复杂模型。最后,对中国农业政策和谷物生产趋势进行了展望。

With the increase of chemical fertilizer, grain yields have increased year by year, but at the same time, there are some problems such as soil degradation caused by excessive fertilization. Traditional researches on grain yield and fertilizer usage generally adopt the empirical method of assuming the model structure, but the established model are not suitable for each country, and the more accurate model may be omitted. Using the symbolic regression method, the grain yield and fertilizer consumption of 104 countries from 1961 to 2018 were fitted, and the evolution models of the two were studied from two dimensions of time and space. In the time dimension, the model of the relationship between the two changes with time was analyzed and obtained;in the spatial dimension, the applicability of the four important models to different countries in different periods was analyzed. The results showed that time changes affect the relationship between them, the monotonically increasing model has a high applicability in different time intervals in each country, for some countries where the relationship fluctuates greatly in different time periods, and there are complex models with low applicability but high fitting accuracy, which can better describe the relationship between the two. Finally, the trends of agricultural policy and grain production in China were forecasted.