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Acta Agronomica Sinica ›› 2019, Vol. 45 ›› Issue (8): 1221-1229.doi: 10.3724/SP.J.1006.2019.83082

• TILLAGE & CULTIVATION·PHYSIOLOGY & BIOCHEMISTRY • Previous Articles     Next Articles

Establishment and application of spring maize leaf longevity model based on Gaussian function

LI Yao-Yao,FAN Pan-Pan,MING Bo,WANG Chun-Xia,WANG Ke-Ru,HOU Peng,XIE Rui-Zhi(),LI Shao-Kun()   

  1. Institute of Crop Sciences, Chinese Academy of Agricultural Sciences/Key Laboratory of Crop Physiology and Ecology, Beijing 100081, China
  • Received:2018-12-11 Accepted:2019-04-15 Online:2019-08-12 Published:2019-07-16
  • Contact: Rui-Zhi XIE,Shao-Kun LI E-mail:xieruizhi@caas.cn;lishaokun@caas.cn
  • Supported by:
    This study was supported by the National Key Research and Development Program of China(2017YFD0300302);China Agriculture Research System(CARS-02-20);the Science and Technology Innovation Program of Chinese Academy of Agricultural Sciences

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Abstract:

Leaf longevity is a key factor affecting photosynthetic productivity. The quantitative evaluation of canopy leaf longevity is of significance for maize plant growth and yield formation. The experiments were conducted in the experiment station of Institute of Crop Sciences, the Chinese Academy of Agricultural Sciences, Gongzhuling, Jilin province in 2015-2017. The dates of leaf expanded and senesced at each leaf position were recorded from fixed plants of Xianyu 335 and Zhengdan 958. The maize leaf longevity model was established based on Gaussian function ($y=a+b\times {{\text{e}}^{\frac{-{{\left( x-c \right)}^{2}}}{2{{d}^{2}}}}}$) with 2015 and 2016 test data, and validated with 2017 data. The physiological significance of model parameters was specified and the method developing leaf longevity model was simplified. The maize leaf longevity model constructed under the research conditions had good inter-annual stability and large differentiation ability across cultivars. By further analyzing, five turning points were definitely well fitted to establish this model, which greatly simplified the data requirements for developing this model and the possibility of using this model to group the maize leaves was discussed. The five turning points were these calculated by the first derivative (the point for maximum longevity), the second derivative (the point for the highest rate of longevity), and the third derivative (the point for longevity beginning to increase rapidly) equal to zero, also the topmost leaf position (n) and the bottom leaf position. This study provides ideas and methods for analyzing the maize leaf productive ability quantitatively, and the reference for improving various maize growth models and other related researches.

Key words: maize, leaf longevity, Gaussian function, growth model

Fig. 1

Maximum, minimum, and average temperature from April to September in 2015-2017 The gray area represents the temperature range, and the black line represents the average temperature."

Table 1

Development progress from 2015 to 2017 (month/day) "

年份
Year		 播种日期
Sowing date		 出苗日期
Emergence date		 收获日期
Harvest date		 初霜日期
First frost date
2015 05/01 05/22 09/26 10/16
2016 04/29 05/20 09/23 09/28
2017 04/27 05/21 09/30 09/30

Fig. 2

Leaf expanded and senescence time at different leaf positions Fig. A shows the leaf expanded and senescence time of Xianyu 335, and Fig. B shows the leaf expanded and senescence time of Zhengdan 958. The solid circle represents the days from sowing to leaf expanded, the hollow circle represents the days from sowing to leaf senescence, and the dashed line represents the position of ear leaf."

Fig. 3

Fitting of leaf longevity in 2015 and 2016 The dashed line represents the position of ear leaf. XY335: Xianyu 335; ZD958: Zhengdan 958."

Fig. 4

Comparison between simulated and measured values XY335表示先玉335, ZD958表示郑单958。XY335: Xianyu 335; ZD958: Zhengdan 958."

Table 2

Model parameters of the leaf longevity"

品种
Cultivar		 模型参数 Model parameter
a b a+b c d
先玉335 Xianyu 335 214.30 636.47 850.76 15.92 6.71
郑单958 Zhengdan 958 195.48 683.29 878.77 16.00 6.89

Table 3

Feature analysis of Gaussian model"

求导公式
Derivation formula		 转折点
Turning point		 转折叶位 Turning leaf position
先玉335 Xianyu 335 郑单958 Zhengdan 958
— 1 1 1
$f{{\left( x \right)}^{\prime }}{{^{\prime }}^{\prime }}=\frac{b}{{{d}^{2}}}\times {{\text{e}}^{-\frac{{{\left( x-c \right)}^{2}}}{2{{d}^{2}}}}}\times \frac{\left( x-c \right)}{{{d}^{2}}}\times \left[ 3-\frac{{{\left( x-c \right)}^{2}}}{{{d}^{2}}} \right] $ $f{{\left( x \right)}^{\prime }}{{^{\prime }}^{\prime }}=0,\ \ \ \ \ \ x=c,c\pm \sqrt{3}d$ 4 4
$f{{\left( x \right)}^{\prime }}^{\prime }=\frac{b}{{{d}^{2}}}\times {{\text{e}}^{-\frac{{{\left( x-c \right)}^{2}}}{2{{d}^{2}}}}}\times \left[ \frac{{{\left( x-c \right)}^{2}}}{{{d}^{2}}}-1 \right] $ $f{{\left( x \right)}^{\prime }}^{\prime }=0,\ \ \ \ \ \ x=c\pm d$ 9 9
$f{{\left( x \right)}^{\prime }}=\frac{b}{{{d}^{2}}}\times {{\text{e}}^{-\frac{{{\left( x-c \right)}^{2}}}{2{{d}^{2}}}}}\times \left( x-c \right) $ $f{{\left( x \right)}^{\prime }}=0,\ \ \ \ \ \ x=c$ 16 16
— n 20 22

Fig. 5

Fitting diagram of five leaf positions during the leaf longevity from 2015 to 2017 The dashed line represents the position of ear leaf. XY335: Xianyu 335; ZD958: Zhengdan 958."

Fig. 6

Comparison between simulated and measured values XY335: Xianyu 335; ZD958: Zhengdan 958."

Fig. 7

Schematic diagram of leaf grouping S1: a slow-growing leaf group; S2: a fast-growing leaf group; S3: a slow-declining leaf group."

Table 4

Leaf grouping interval"

分组区间
Grouping interval		 区间 Interval length
起始点
Initial point		 终止点
Termination point		 先玉335
Xianyu 335		 郑单958
Zhengdan 958
S1 1 $c-\sqrt{3}d$ (1, 4) (1, 4)
S2 $c-\sqrt{3}d$ c (5, 16) (5, 16)
S3 c n (17, 21) (17, 22)
95% $c-d\times \sqrt{-2\times \ln \left( 0.95-\frac{0.05a}{b} \right)}$ $c+d\times \sqrt{-2\times \ln \left( 0.95-\frac{0.05a}{b} \right)}$ (14, 18) (14, 18)
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