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作物学报 ›› 2019, Vol. 45 ›› Issue (8): 1221-1229.doi: 10.3724/SP.J.1006.2019.83082

• 耕作栽培·生理生化 • 上一篇    下一篇

基于高斯函数的春玉米叶片功能期模型构建与应用

李姚姚,范盼盼,明博,王春霞,王克如,侯鹏,谢瑞芝(),李少昆()   

  1. 中国农业科学院作物科学研究所/农业部作物生理生态重点实验室, 北京100081
  • 收稿日期:2018-12-11 接受日期:2019-04-15 出版日期:2019-08-12 网络出版日期:2019-07-16
  • 通讯作者: 谢瑞芝,李少昆
  • 作者简介:E-mail: 981457781@qq.com, Tel: 010-82105791
  • 基金资助:
    本研究由国家重点研发计划项目(2017YFD0300302);国家现代农业产业技术体系建设专项(CARS-02-20);中国农业科学院科技创新工程项目资助

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 Published:2019-08-12 Published online:2019-07-16
  • Contact: Rui-Zhi XIE,Shao-Kun LI
  • 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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摘要：

叶片功能期是影响光合生产能力的关键因素, 冠层叶片功能期的量化评估对玉米植株生长和产量形成具有重要意义。本研究于2015—2017年在中国农业科学院作物科学研究所吉林公主岭试验站进行, 定株观测先玉335和郑单958 两个品种各个叶位叶片展开时间和衰老时间, 基于2015年和2016年试验数据, 以高斯函数($y=a+b\times {{\text{e}}^{\frac{-{{\left( x-c \right)}^{2}}}{2{{d}^{2}}}}}$)模拟玉米各叶位叶片功能期的动态变化, 并用2017年数据验证, 在此基础上进一步明确了模型特征参数的生理学意义, 简化了叶片功能期模型构建的方法。研究条件下利用高斯函数构建的玉米叶片功能期模型年际间稳定性好、品种间区分度大。进一步解析利用一阶导(功能期最大值)、二阶导(功能期变化速率最大的点)、三阶导(功能期开始快速增大的点)等于零取整后的叶位并配合最顶部叶位(n)和基部第1叶这5个转折叶位叶片功能期构建的模型拟合度良好, 极大地简化了该模型参数拟合的数据需求, 并探讨了利用该模型函数对玉米叶片功能分组的可能性。本研究为玉米生产能力的量化分析提供了思路和方法, 对各类玉米生长模型的完善和其他相关研究也有借鉴意义。

关键词: 玉米, 叶片功能期, 高斯函数, 生长模型

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

图1

2015-2017年4月至9月最高、最低、平均气温图 灰色区域表示气温变化范围, 黑色线表示平均气温。"

表1

2015-2017年生育进程"

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

图2

不同叶位叶片展开与衰老时间 图A为先玉335叶片展开时间与衰老时间, 图B为郑单958叶片展开时间与衰老时间。实心圆表示出苗到叶片展开的天数, 空心三角表示出苗到叶片衰老的天数, 虚线表示穗位叶所在。"

图3

2015年和2016年叶片功能期拟合图 虚线表示穗位叶所在, XY335表示先玉335, ZD958表示郑单958。"

图4

模型拟合值与实测值比较"

表2

叶片功能期模型参数表"

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

表3

高斯模型特征分析"

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

图5

2015-2017年5个叶位叶片功能期拟合图 虚线表示穗位叶所在, XY335表示先玉335, ZD958表示郑单958。"

图6

模型拟合值与实测值比较 XY335表示先玉335, ZD958表示郑单958。"

图7

叶片分组示意图 S1表示缓慢增长叶组, S2表示快速增长叶组, S3表示缓慢下降叶组。"

表4

叶片分组区间"

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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