Li YANG , Xiange XIA, Henghu DING, , Xianpeng FAN , Guiyun XIONG , Jiaqiong WU,

1. Institute of Plant Protection，Soil and Fertilizer, Hubei Academy of Agricultural Sciences, Wuhan 430064, China;

2. Qianjiang Scientific Observing and Experimental Station of Agro-environment and Arable Land Conservation, Ministry of Agriculture, Qianjiang 433166, China;

3. Hubei Academy of Agricultural Sciences, Wuhan 430064, China;

4. Soil and Fertilizer Workstation of Qianjiang City, Qianjiang 433199, China

In recent years,the wheat growing area in Hubei Province has reached approximately one million hm2, yielded 3.3 million tons every year, which are gradually increasing year by year[1-2]. Jianghan Plain is one of the important crop growing areas in Hubei, even in middle and lower Yangtze River. Here, wheat is planted mainly in two systems wheat-cotton intercropping and wheat-rice rotation.Scientific and rational fertilization and improved fertilizer use efficiency are important to develop wheat production, and improve wheat yield and quality. Field experiments about fertilizer effect are necessary to determine the optimal fertilizer amount, fertilizer proportion, fertilization time and methods for various corps, and they are also the basic steps to screen and verify soil nutrient testing methods, and establish fertilizer application indices.In addition, field experiments can determine soil fertility, crop nutrient demand and fertilizer use efficiency and other basic parameters,thus providing basis for the improvement rational fertilization and fertilizer formulations[3-7].Since 2002, “Questions and Answers about Soil Test-based Fertilization Recommendation” published by National Agricultural Technology Extension and Service Center has recommended farmers to adopt complete or incomplete 3414 design in field experiments about fertilizer effect. Generally,by 3414 design the functions about fertilizer effects of the main crops in a region can be established, according to which, the optimal crop yield, optimal fertilizer amount, corrected soil nutrient coefficients, soil fertility, fertilizer use efficiency and other basicparameters,as well as soil nutrient deficiency indies can be finally determined[8-11]. Therefore, 3414 is now the main design for developing soil testbased fertilization recommendation. It is an incomplete field test design including three nutrients (nitrogen,phosphorus and potassium) at four levels, and thus 14 treatments in total[13-14]. A field experiment was carried out based on 3414 design in this study, with an tempt to fertilization models for wheat production in Jianghan Plain. The optimal amount and proportion of nitrogen,phosphorus and potassium fertilizers we proposed provided scientific basis for the rational fertilization for wheat production,thereby increasing wheat yield and fertilizer use efficiency in Jianghan Plain.

Materials and Methods

Overview of study area

Field trials were carried out in the main towns for wheat production such as Jiyukou, Haokou and Yangshi in Qianjiang City of Jianghan Plain. Topsoil samples were collected before experiment to analyze their physical and chemical properties and contents of available nutrients(Table 1)[15].

Table 1 Soil properties in field

Table 2 N,P and K application in each treatment kg/hm2

Experimental design

The field experiment was designed to include three nutrients (nitrogen, phosphorus and potassium) at four levels, and thus 14 treatments in total, hereafter referred to as 3414 incomplete design. The subscripts 0, 1,2 and 3 of N,P and K stood for fertilizer levels. In detail, level 0 indicated no fertilizer; level 2 indicated the recommended fertilizer amount; level 1 was half of the amount in level 2; and level 3 was 1.5 folds of the amount in level 2. The fertilizer amount in each treatment was shown in Table 2.

The recommended amount for N,P and K fertilizers at each site(level 2)was determined according to soil nutrient state, crop nutrient demand, soil fertility in local wheat farmland, farmer investigation, fertilizer application in the past years and relevant literatures.The recommended amount for N, P and K fertilizers differed among these sites, which met the basic requirements for 3414 design of fertilization experiment.

The plots were 20 m2each, surrounded by guard rows, and arranged following a randomized block design.12% calcium superphosphate and 60%potassium chloride were selected as phosphorus and potassium fertilizers and applied totally as basal fertilizer.46%urea was selected as nitrogen fertilizer, of which 70% was applied as basal fertilizer and 30% was topdressed at tillering stage. The wheat cultivar Zhengmai 9023 was selected as the experimental plant,sown at 210 kg/hm2by drilling in early November,2008, and harvested in late May,2009. Except the different fertilizer amount and combination, the filed managements in these treatments like soil preparation, sowing, irrigation,pest control were performed the same as local practices. The wheat was attacked by Fusarium head blight in the rainy days in early May,2009,so pesticide was sprayed twice then. Wheat in each plot was harvested in late May,air-dried and weighed.

Results and Analysis

Prediction of N, P, K amount and wheat yield using unary quadratic functions

The dry weight of wheat grain in each treatment was listed in Table 3.The data about nitrogen amount and corresponding wheat yield were selected from treatment 2, 3, 6 and 11;the data about phosphorus amount and corresponding wheat yield were from treatment 4, 5, 6 and 7; the data about potassium amount and corresponding wheat yield were from treatment 6, 8, 9 and 10. Then, regression analysis on these data was performed using a unary quadratic model y=ax2+bx+c,wherein,y is wheat yield and x is the amount of each nutrient factor. As shown in Table 4, the wheat yield and the amount of each nutrient factor at each site fitted a unary quadratic function, and the quadratic coefficients in all the functions were less than zero,indicating that the curves were normal parabolas. Significance testing suggested that the correlation between fertilizer amount and wheat yield in these functions was not significant,but the multiple correlation coefficients R2 were all more than 0.8 except the N factor at site E2.

The partial derivative of each unary quadratic function was calculated according to the maximum marginal effect.The maximum amount of fertilizer was calculated by b+2ax=0 to predict the maximum wheat yield.The optimal fertilizer amount was calculated by b+2ax=Px/Py to predict the optimal wheat yield[6-8]. As shown in Table 5,the predicted values for wheat yield were consistent with the measured values.

It also could be seen from Table 5 that for nitrogen fertilizer the maximum amount was between 168.0 and 316.5 kg/hm2, and the optimal amount was between 127.5 and 145.5 kg/hm2; for phosphorus fertilizer the maximum amount was between 51.0 and 114.0 kg/hm2, and the optimal amount was between 45.0 and 99.0 kg/hm2; for potassium fertilizer the maximum amount was between 46.5 and 76.5 kg/hm2, and the optimal amount was between 40.5 and 49.5 kg/hm2. In view of local conditions of these study areas, it was suggested that the maximum amount for nitrogen, phosphorus and potassium fertilizers was 216.4, 69.0 and 60.4 kg/hm2, respectively. Based on this, the wheat yield was predicted to be 4 067.3 kg/hm2(3 802.5-4624.5 kg/hm2). The optimal amount for nitrogen, phosphorus and potassium fertilizers in the study areas we suggested was 134.6, 60.0 and 44.3 kg/hm2, respectively, and based on this, the wheat yield was predicted to be 4 005.4 kg/hm2(3 700.5-4 600.5 kg/hm2).

Table 3 Wheat yield in each treatment of 3414 design kg/hm2

Table 4 Unary quadratic function for every single nutrient factor and wheat yield at each site

Prediction of N, P, K amount and wheat yield using ternary quadratic functions

Regression analysis on the data in Table 3 was carried out using a ternary quadratic model y=b0+b1N+b2P+b3K+b4N2+b5P2+b6K2+b7NP+b8NK+b9PK,and four functions in wheat yield(y)and N(N),P(P2O5),K(K2O)amount at the four sites were obtained, as listed in Table 6. Significance testing showed that the correlation of fertilizer amount and wheat yield in the function at site E2 was not significant, but that of the functions at the other three sites was significant,indicating that the correlation of wheat yield with nitrogen,phosphorus and potassium amount reached significance level.

The partial derivative of each ternary quadratic function was calculated according to the maximum marginal effect[16-18].The maximum and optimal amounts of fertilizers were respectively calculated by two systemsof equations as follows:

System(1)

System

Finally, maximum and optimal wheat yields were predicted according to the maximum and optimal amounts of fertilizers calculated above.

It could be concluded from Table 7 that for nitrogen fertilizer the maximum amount was between 190.5 and 223.5 kg/hm2, and the optimal amount was between 21.0 and 133.5 kg/hm2;for phosphorus fertilizer the maximum amount was between 42.0 and 76.5 kg/hm2, and the optimal amount was between 18.0 and 46.5 kg/hm2; for potassium fertilizer the maximum amount was between 66.0 and 147 kg/hm2, and the optimal amount was between 27.0 and 46.5 kg/hm2.In view of other local conditions in the study area,the maximum amounts for nitrogen,phosphorus and potassium fertilizers we suggested were 207.5, 69 and 60.4 kg/hm2, respectively, and the optimal amounts for them were 78.8,36 and 39.8 kg/hm2.

Table 5 The maximum and optimal fertilizer amount and wheat yield predicted by unary quadratic functions

Table 6 Ternary quadratic function for N,P,K amount and wheat yield at each site

Corrected indices for soil nutrient demand and fertilizer application

The classification of soil nutrients have been reported in previous studies. As shown in Table 8 and Table 9,the existing indices for soil nutrient demand and fertilizer application in wheat production were modified in this study by referring to the studies of Zhang[19],Lu[20]and Bai et al.[21],the indies for soil nutrient demand in other counties and cities of Jianghan Plain, indices for fertilizer application of rice, as well as the soil fertility, crop yield and fertilizer application in the study areas[22].

Conclusions and Discussion

The wheat yield and fertilizer amount in each treatment of the fieldexperiments well fitted a unary quadratic function, by which we predicted that the maximum fertilizer amount was 216.4 kg/hm2N, 69.0 kg/hm2P2O5and 60.4 kg/hm2K2O in the study areas, while the optimum amount was 134.6 kg/hm2N, 60.0 kg/hm2P2O5and 44.3 kg/hm2K2O.Such results are basically consistent with the measured data in actual production. However, statistical analysis revealed that the correlation between wheat yield and fertilizer amount in these functions did not reach significance level. Whether such results were caused by limitations of the models,data deviation or the influence of other factors needs to be determined in future research.

Table 7 Table 5 The maximum and optimal fertilizer amount and wheat yield predicted by ternary quadratic functions

Table 8 Corrected indices for evaluating the abundance of main soil nutrient factors in Qianjiang mg/kg

By the ternary quadratic functions we predicted that application 207.5 kg/hm2N, 69.0 kg/hm2P2O5and 60.4 kg/hm2K2O could achieve the maximum wheat yield; and the optimal fertilizer amount was 78.8 kg/hm2N,36.0 kg/hm2P2O5and 39.8 kg/hm2K2O. In these functions, the correlations of wheat yield with nitrogen, phosphorus and potassium amount were significant, and the predicted wheat yield was close to the measured data in production.

The optimal amount for nitrogen,phosphorus and potassium fertilizers we predicted based on soil nutrient test, corrected soil nutrient deficiency indices and fertilizer application was very close to the data in actual production. However, the data were obtained from one-year experiment, and they should be corrected based on more tests in future.

Both the unary and ternary quadratic functions predict the maximum and optimal fertilizer amounts,which is consistent with the findings of Wang[23]and Liu et al.[23]. Although there still are some limitations, these models will be more effective in combination with soil nutrient deficiency indices,and can be widely promoted[25-26].So, it is important to determine these soil nutrient deficiency indices according to soil test, and other factors like water and climate, which still needs to be researched in future[27].

Based on the prediction of both unary and ternary quadratic functions,soil nutrient contents, crop yield and fertilizer application, 130-210 kg/hm2N, 40-70 kg/hm2P2O5and 40-60 kg/hm2K2O are optimal for wheat production in Jianghan Plain.

Table 9 Corrected indices for evaluating fertilizer application kg/hm2

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