玉米/大豆套作体系中大豆茎秆生长过程模拟

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杜勇利, 周涛, 杨欢, 刘婷, 官思成, 邓瑜川, 刘卫国, 杨文钰. 玉米/大豆套作体系中大豆茎秆生长过程模拟. 草业科学, 2018,35(3): 624-634
Du Yong-li, Zhou Tao, Yang Huan, Liu Ting, Guan Si-cheng, Deng Yu-chuan, Liu Wei-guo, Yang Wen-yu. Dynamic simulation of the dry weight of soybean stems in intercropping systems. Pratacultural Science, 2018,35(3): 624-634. 复制到剪切板

Doi: 10.11829/j.issn.1001-0629.2017-0310
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《草业科学》编辑部

玉米/大豆套作体系中大豆茎秆生长过程模拟

杜勇利¹, 周涛¹, 杨欢¹, 刘婷¹, 官思成¹, 邓瑜川², 刘卫国¹, 杨文钰¹

1.四川农业大学农学院/农业部西南作物生理生态与耕作重点实验室/四川省作物带状复合种植工程技术研究中心, 四川成都 611130

2.南充市农业科学院,四川南充 637000

共同通信作者:刘卫国(1979-),男,四川中江人,副教授,硕导,博士,主要从事作物逆境生理及调控研究。E-mail:[email protected]

第一作者:杜勇利(1991-),男,四川宜宾人,在读硕士生,主要从事作物高产稳产优质高效栽培研究。E-mail:[email protected]

收稿日期: 2017-06-06 接受日期: 2017-12-21

资助项目: 国家自然科学基金(31671626); 国家重点研发计划重点专项(2016YFD0300200); 四川省育种攻关项目(2016NYZ0031); 四川农业大学科研兴趣计划资助

摘要

为建立套作系统中大豆( Glycine max)茎秆生长过程的模拟方程,本研究以玉米( Zea mays)/大豆套作为对象,单作大豆为对照,3种不同株型大豆(南豆032-4、南豆12、九月黄)为材料,对两种种植模式下大豆茎秆生长进行定量化模拟。运用Richards方程[ y=α/(1+βe^- ^γx)^1/δ],构建大豆茎长、茎粗生长变化的动态模型,方程参数α值(终极生长量参数)为各品种遗传参数,β值(初值生长量参数)、γ值(生长速率参数)和δ值(形状参数)在不同栽培模式、品种间变异较大, 可见主要通过调节参数β、γ、δ值来实现对整个方程的调控。采用Logistic方程[ y=α/(1+βe^- ^γx )],构建大豆茎秆干重动态模型,β、γ值在不同栽培模式、品种间变异较大,主要通过调节参数β、γ值来实现对整个方程的调控。因此分别建立套作和单作栽培模式下的大豆模拟方程,构建大豆茎秆长、茎秆粗的生长动态模型,以及构建大豆茎秆干重积累的动态模型,所建立套作和单作生长模型方程精确度( R²)均在0.99以上。检验结果表明,模型对不同类型大豆材料在单套作体系下茎秆节间长度、粗度、干重都能很好的预测,能较好地拟合茎秆生长动态。本研究结果对探究玉米/大豆套作体系下大豆茎秆生长规律研究,具有一定的生物学意义。

关键词: 大豆; 玉米; 套作; 茎秆; 栽培模式; 模拟模型

中图分类号:S344.3;S513;S52 文献标志码:A 文章编号:1001-0629(2018)03-0624-11

Dynamic simulation of the dry weight of soybean stems in intercropping systems

Du Yong-li¹, Zhou Tao¹, Yang Huan¹, Liu Ting¹, Guan Si-cheng¹, Deng Yu-chuan², Liu Wei-guo¹, Yang Wen-yu¹

1.College of Agronomy, Sichuan Agricultural University/Key Laboratory of Crop Physiology, Ecology and Cultivation in Southwest, Ministry of Agriculture, Chengdu 611130, Sichuan, China

2.Nanchong Academy of Agricultural Sciences, Nanchong 637000, Sichuan, China

Corresponding author: Yang Wen-yu E-mail:[email protected]

Abstract

The intercropping of maize and soybean is practiced in several parts of the world. Using models for forecasting soybean growth is a good cropping technique; however, few research models are available that predict soybean growth in monocropping and intercropping practices. This study was based on the systematic observations of Nandou 032-4, Jiuyuehuang, and Nandou 12. The growth of soybean stems can be quantitatively simulated by the patterns of growth in monocropping and intercropping cultivation modes. A dynamic model was established using Richards equation for model building, where the time step was represented by the physiological development time (PDT), describing the elongation of soybean stem internodes and the enlargement of the dynamic processes at the internodes, in monocropping and intercropping practices. In the dynamic model, the time step was estimated by the growth and development taking place on the actual number of days by logistic equations, for predicting the dry weight of the soybean stem in monocropping and intercropping cultivation practices. From the model, the potential length and thickness of the internodes gradually increased as the number of soybean internodes increased and reached a maximum at the ninth and seventh internodes, respectively, and then gradually decreased. Therefore, the potential length of the ninth internode and the potential thickness of the seventh internode were identified as the potential genetic parameters that can be used to calculate the potential length and thickness of other internodes. At the same time, the potential dry weight of the stem was used to determine the potential dry weight of other stems. The inspection results showed that different varieties of soybean have different cultivation patterns. The model reflected a satisfactory prediction rate. This model, developed using soybean varieties having different modes of cultivation, internode lengths, internode thicknesses, physiological development times, and dry weights of the stem, has good predictability and reliability, and the stem growth dynamics predicted by the model conformed well to the biological rules of stem growth, highlighting the biological significance of the model.

Key words: soybean; stem; cultivation mode; simulation model

文章图片

大豆(Glycine max)起源于中国, 种植历史可以追溯到3 000年以前, 除了作为重要的粮油作物外, 其生物固氮、土壤磷活化、碳截获等生态意义越来越受到重视。以我国西南地区为例, 土壤发育程度浅, 有机质、速效氮、磷的含量低。但是受制于人口和粮食生产压力, 该地区复种指数高, 在旱地生态系统中, 间/套作占据主导地位^[1]。套作豆科植物相比单作能显著提高产量, 主要体现在豆科植物活化土壤中难溶态磷、生物固氮供自身和共生作物吸收利用^{[2, 3, 4]}。玉米(Zea mays)-大豆带状复合种植体系以其高产、生态等特点在我国西南地区得到大面积推广^[5]。玉米/大豆套作模式不仅能使土壤水分、养分和光资源的供给得到改善, 还可以增加这些资源的可利用性, 产生互利, 从而提高复种系数^[6]。间、套作种植模式不仅遵循了时间镶嵌原则、空间扩展原则、种间搭配原则和物能流畅原则, 而且还能解决用地和养地的矛盾、复种和季节不够用的矛盾, 同时, 作物茎秆还可解决发展畜牧业饲料不足的矛盾。

作物形态建成模拟是作物生长模拟中重要的一部分。明确作物外部形态变化规律, 定量化研究作物形态建成过程, 对指导作物生产具有重要的理论意义和实际应用价值。同时, 也是虚拟作物和作物可视化的研究基础^[7]。我国西南地区属于寡日照区域, 在玉米和大豆共生期, 受高位作物玉米遮阴导致苗期大豆受到一定程度的阴蔽胁迫, 大豆植株茎长增加, 茎粗、光合速率和地上部生物量显著下降, 导致大豆易发生倒伏, 从而影响大豆产量^{[8, 9]}。但是不同耐阴性大豆品种在套作环境中的茎秆生长特性呈现较大差异, 强耐阴大豆品种茎秆抗倒伏能力明显强于一般或不耐阴品种^[10]。因此, 研究套作大豆的茎秆生长特性及不同品种茎秆在特殊光环境中的变化对于保障套作大豆产量和整个套作体系的稳产具有重要意义。

已有研究报道表明, 以生理发育时间(physiological development time, PDT)为步长, 可以对许多作物的形态生长动态进行模拟^{[11, 12, 13]}。如, 不同施氮水平和水分条件下水稻(Oryza sativa)的地上部器官形态特征建成^{[14, 15]}; 不同播期条件下大麦(Hordeum vulgare)茎秆、穗的生长动态^[16]; 不同大豆品种茎、叶、荚的形态建成^[17]。以生长日(growing degree days, GDD)为步长, Logistic方程可以很好的描述小麦叶片、穗、叶鞘和节间的动态生长变化^{[18, 19]}。同样, 以扩充的Logistic模型可以对小麦(Triticum aestivum)株高和叶面积变化动态进行模拟^[20]。此外, 利用系统分析方法和动态建模技术, 成功构建小麦叶片茎鞘夹角的动态模拟模型^[21]。已有研究从不同角度对不同作物的生长发育规律进行了研究和模拟, 通过模型模拟植物的生长动态技术得到广泛应用。虽然对单作大豆的形态建成动态模拟已有研究, 但是套作大豆的生长环境与单作有较大差异, 所以已有模型不能完全适用于描述套作大豆茎秆的生长动态。

因此, 本研究以玉米/大豆带状套作复合种植模式中大豆为研究对象, 通过对大豆茎秆生长过程的系统观测与分析, 在定量研究的基础上, 分别构建套作和单作条件下大豆节间伸长和增粗生长的动态模型, 以及大豆茎秆干重变化动态模拟模型, 旨为构建大豆在不同种植模式下生长决策支持系统奠定基础, 也为实现大豆植株形态的虚拟显示、可视化研究提供关键技术。

1 材料与方法

1.1 供试材料

3个供试大豆品种株型间差异较大, 分别为“ 南豆032-4” (无限型, 弱耐阴性, 四川省南充市农业科学院育种材料), 株高120 cm左右, 茎秆较细; “ 九月黄” (有限型, 中度耐阴性, 四川省阆中市地方品种), 株高75 cm左右, 茎秆粗细中等; “ 南豆12” (亚有限型, 强耐阴性, 四川省南充市农业科学院选育, 西南地区套作大豆主推品种), 株高90 cm左右, 茎秆较粗。玉米选用半紧凑型品种“ 川单418” (四川农业大学玉米所选育)。

1.2 试验设计

试验于2012年和2013年在四川农业大学雅安校区教学科研园区(29° 98' N, 103° 00' E)进行, 属亚热带湿润季风气候区。年均温16.2 ℃, 年日照时数1 005~1 200 h, 年降水量1 250~1 750 mm; 土壤类型为紫色土, 质地为重壤土。pH 7.4, 有机质含量为27.86 g· kg^-1, 全氮含量为1.79 g· kg^-1, 全磷含量为0.89 g· kg^-1, 全钾含量为29.76 g· kg^-1, 速效氮含量为115 mg· kg^-1, 速效磷含量为37 mg· kg^-1, 速效钾含量为136 mg· kg^-1。田间采用随机区组排列, 每个区组内包含3个玉米/大豆套作处理(3个大豆品种)和3个大豆单作处理, 小区面积24 m², 重复3次。套作模式采用宽窄行种植, 玉米窄行行距40 cm, 宽行行距160 cm, 穴距35 cm, 每穴2株, 分别于当年4月初播种玉米。大豆于玉米宽行间播种两行, 窄行行距为50 cm, 穴距10 cm, 穴留2株, 玉米/大豆间距55 cm, 分别于2012年6月22日和2013年6月23日播种。单作模式中, 大豆行距50 cm, 穴距10 cm, 每穴定苗1株。氮(N)、磷(P₂O₅)、钾(K₂O)用量分别为195、75和105 kg· hm^-2; 玉米于每年4月初挖窝点播, 窝深7 cm左右, 宽15 cm左右, 将30%的氮和全部的磷、钾肥施于窝的一侧, 另一侧放种子避免种子与肥料接触, 而后覆土, 种子覆土深度不超过5 cm; 再于玉米拔节期和大喇叭口期分别追施30%、40%的氮, 均采用兑清水冲施于株旁的方式。大豆不施肥, 田间杂草病虫害管理方式同当地农户高产田。

1.3 观测项目及建模方法

由于大豆第1节和第2节的叶片分别为子叶、真叶, 从第3节间才开始长出复叶。因前两个节均不会开花结荚, 且节间长度较短, 同时品种间差异不大, 所以本研究中所有指标的模拟值和观测值均从第3节间开始。从大豆第3节始, 每小区选长势一致的大豆植株挂牌标记, 测定以下指标。

1.3.1 茎秆生长的观测每隔3 d定点定株测量已标记大豆茎秆第3节及其以上各节的节间长度和粗度。节间长度使用米尺测量, 粗度使用游标卡尺测量, 其测量部位为节间中部。

1.3.2 茎干重测定自播种大豆后7 d (即套作和单作大豆生育期都为VE)开始调查取样。每小区选取生长一致的300株挂牌标记。每隔7 d取样, 直至大豆收获。每次选取10株从茎秆第1节剪断, 单株按叶片、茎分解植株, 然后分别装入牛皮纸袋中, 置于烘箱中105 ℃杀青30 min, 再于75 ℃下烘干至恒重, 最后称重, 计算干重。

1.3.3 数据处理及建模本研究以生理发育日(PDT)为步长, 运用Richards方程构建大豆茎长、茎粗生长的动态模型, 获取方程特征参数α 、β 、γ 、δ , 参数α 为增长量的极限值、β 为初始值参数、γ 为增长速率参数、δ 为曲线形状参数。方程模拟图形是以α 为渐近线的S形曲线。以作物生长发育实际天数为步长, 运用Logistic方程构建大豆茎干重积累的动态模型, 获取方程特征参数α 、β 、γ , 参数α 为增长量的极限值, β 、γ 均为方程特征参数。利用 Curve Expert 1.3 软件对单作和套作大豆的生长动态进行拟合, 探明生理发育时间与大豆茎秆生长的关系, 建立大豆生长动态模型所需的量化关系。大豆各发育阶段的生理发育时间的计算参照陈传梅等使用的方法^[22]。并利用SPSS 17.0 软件分析这些特征参数。2012年试验数据用于模型构建和参数调试, 2013年数据用于模型检验。采用根均方差RMSE来对模型进行检验, 统计分析模拟值与观测值之间的符合情况。RMSE值越小, 说明模拟值与观测值的一致性越好, 模型的模拟结果越精确、可靠。RMSE的计算公式如下:

RMSE= $\begin{matrix} \sqrt[]{\frac{\overset{n}{\sum_{i = 1}} (OB S_{i} - SI M_{i})^{2}}{n}} \end{matrix}$ 。

式中:OBS_i为观测值, SIM_i为模拟值, n为样本容量。优化不同大豆品种在不同栽培模式下, 建立具有生物学意义的动态共性模拟方程, 同时使用Excel分析软件进行回归分析。

2 结果与分析

2.1 品种遗传参数的确定

3个供试大豆品种的茎秆节间潜在长度、茎秆潜在粗度和茎秆潜在干重如表1所列。3个供试大豆品种的遗传参数, 品种间和不同种植模式下都表现出了差异。且在套作种植模式下品种间的节间潜在长度、潜在粗度和茎的潜在干重均表现出显著差异性; 单作种植模式下, 品种间的遗传参数也表现出差异, 说明不同种植模式会改变品种的遗传参数。

表1 单作、套作下的大豆节间潜在长度、潜在粗度和茎的潜在干重 Table 1 Genetic coefficients of the three varieties of soybean

2.2 模型构建

2.2.1 大豆茎秆节间伸长的动态模型试验结果表明, 在套作模式下大豆各节间从开始伸长到定长需要16.53个生理日, 各节间开始伸长的时间间隔为2.8个生理日。大豆第3节间开始伸长的生理发育时间为11.21个生理日。在单作模式下大豆各节间从开始伸长到定长需要14.88个生理日, 各节间开始伸长的时间间隔为1.9个生理日。大豆第3节间开始伸长的生理发育时间为8.95个生理日。各节间伸长的动态方程分别如下: 个大豆品种在套作和单作栽培模式下的方程, 其相关系数均在0.99以上。α 为每个品种潜在极限值, β 值和γ 值在栽培模式和不同大豆品种间变异均较大。δ 值在单作栽培模式下变异较小, 套作模式下变异较大。因此, 需要通过对套作和单作栽培模式下的大豆分别建立共性模拟方程。

套作:L_n(PDT)= $\begin{matrix} \{\begin{matrix} 0, & PDT < 11.21 + 2.8 (n - 3), & n \geq 3 。 \\ \frac{Lma x_{n}}{(1 + e^{β - γ [PDT - 11.21 + 2.8 (n - 3)])^{1 / δ}}}, & 11.21 + 2.8 (n - 3) \leq PDT \leq 27.24 + 2.8 (n - 3), & n \geq 3 。 \\ Lma x_{n}, & PDT > 27.24 + 2.8 (n - 3), & n \geq 3 。 \end{matrix} \end{matrix}$

单作:L_n(PDT)= $\begin{matrix} \{\begin{matrix} 0, & PDT < 8.95 + 1.9 (n - 3), & n \geq 3 。 \\ \frac{Lma x_{n}}{(1 + e^{β - γ [PDT - 8.95 + 1.9 (n - 3)])^{1 / δ}}}, & 8.95 + 1.9 (n - 3) \leq PDT \leq 23.83 + 1.9 (n - 3), & n \geq 3 。 \\ Lma x_{n}, & PDT > 23.83 + 1.9 (n - 3), & n \geq 3 。 \end{matrix} \end{matrix}$

式中:L_n(PDT)为大豆在某一生理发育时刻的第n节的节间长度(cm); Lmax_n为大豆第n节节间潜在长度(cm)。α 、β 、γ 、δ 均为模型参数(表2)。可以看出, 套作和单作栽培模式下, α 、β 、γ 、δ 值变异均大。但是, 3

表2 单作、套作下不同大豆品种相对节间长度的方程系数 Table 2 Coefficients of normalized internode lengths calculated using the dynamic equations in three varieties of soybean in intercropping and monocropping practices

套作模式下, 随着大豆节间数的增加, 其各节节间潜在长度Lmax_n逐渐增长, 均在第7节间达到最大值, 然后又逐渐下降(图1)。因此, 在套作栽培模式下对南豆032-4、南豆12和九月黄的前7节茎秆节间长与PDT进行共性化处理, 得到如下方程:

Lmax_n= $\begin{matrix} \{\begin{matrix} \frac{Lma x_{7}}{(1 + 149.75 e^{- 0.939 589 n})^{0.177 302}}, & 3 \leq n \leq 7 。 \\ 2.451 9 Lma {x_{7}}^{e^{- 0.15 n}}, & n > 7 。 \end{matrix} \end{matrix}$

单作模式下, 随着大豆节间数的增加, 其各节节间潜在长度(Lmax_n)逐渐增长, 不同品种大豆均在第12节间达到最大值, 然后又逐渐下降(图1)。因此, 在单作栽培模式下对南豆032-4、南豆12和九月黄的前12节茎秆节间长与PDT进行共性化处理, 得到如下方程:

Lmax_n= $\begin{matrix} \{\begin{matrix} \frac{Lma x_{12}}{(1 + 39.225 e^{- 0.637 577 n})^{0.495 77}}, & 3 \leq n \leq 12 。 \\ 2.203 4 Lma {x_{12}}^{e - 0.08 n}, & n > 12 。 \end{matrix} \end{matrix}$

2.2.2 节间增粗的动态模型大豆节间增粗是从慢到快再到慢的过程。在套作模式下, 大豆各节间从开始增粗到粗度固定需要14.88个生理日, 各节间开始增粗的时间间隔为1.9个生理日。在单作模式下, 大豆各节间从开始增粗到粗度固定需要16.53个生理日, 各节间开始增粗的时间间隔为2.8个生理日。各节间增粗的动态方程如下:

套作:L_n(PDT)= $\begin{matrix} \{\begin{matrix} 0, & PDT < 8.95 + 1.9 (n - 3), & n \geq 3 。 \\ \frac{Lma x_{n}}{(1 + e^{β - γ [PDT - 8.95 + 1.9 (n - 3)]})^{1 / δ}}, & 11.21 + 2.8 (n - 3) \leq PDT \leq 27.24 + 2.8 (n - 3), & n \geq 3 。 \\ Lma x_{n}, & PDT > 23.83 + 1.9 (n - 3), & n \geq 3 \end{matrix} \end{matrix}$

单作:L_n(PDT)= $\begin{matrix} \{\begin{matrix} 0, & PDT < 11.21 + 2.8 (n - 3), & n \geq 3 。 \\ \frac{Lma x_{n}}{((1 + e^{β - γ (PDT - 11.21 + 2.8 (n - 3)]})^{1 / δ}}, & 8.95 + 1.9 (n - 3) \leq PDT \leq 23.83 + 1.9 (n - 3), & n \geq 3 。 \\ Lma x_{n}, & PDT > 27.24 + 2.8 (n - 3), & n \geq 3 \end{matrix} \end{matrix}$

方程式中:L_n(PDT)为大豆在某一生理发育时刻的第n节的节间粗度(cm); PDT为生理发育时间, 8.95为在套作中大豆第3节间开始增粗的生理发育时间, 11.21为在单作中大豆第3节间开始增粗的生理发育时间。Lmax_n为大豆第n节节间的潜在粗度, 是品种遗传参数。

可以看出(表3), 3个大豆品种在不同栽培模式下的方程, 其相关系数均在0.94以上, α 为潜在极限值; β 值和γ 值在栽培模式和不同大豆品种间变异均较大。δ 值在单作和套作栽培模式下变异均较大。

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	图1 单作、套作下各节间潜在长度随节间数的动态变化Fig. 1 Changes in internode length with respect to the number of internodes

表3 单作、套作下不同大豆品种相对节间粗度的方程系数 Table 3 Coefficients of normalized internode thickness calculated using the dynamic equations in three varieties of soybean in intercropping and monocropping cultivation practices

套作模式下, 随着大豆节间数的增加, 其各节节间潜在粗度Lmax_n逐渐增加, 在第5节间达到最大值, 然后又逐渐下降(图2)。因此, 在套作栽培模式下对南豆032-4、南豆12和九月黄的前5节茎秆节间长与PDT进行共性化处理, 得到如下方程:

Lmax_n= $\begin{matrix} \{\begin{matrix} \frac{Lma x_{5}}{(1 + 72 355.92 e^{- 3.455 n})^{0.003 923}}, & 3 \leq n \leq 5 。 \\ 1.221 Lma x^{5 e^{- 0.067 n}}, & n > 5 。 \end{matrix} \end{matrix}$

单作模式, 随着大豆节间数的增加, 其各节节间潜在粗度INL_maxn逐渐增加, 在第7节间达到最大值, 然后又逐渐下降(图2)。因此, 在单作栽培模式下对南豆032-4、南豆12和九月黄的前7节茎秆节间长与PDT进行共性化处理, 得到如下方程:

Lmax_n= $\begin{matrix} \{\begin{matrix} \frac{Lma x_{7}}{(1 + 9 524.3 e^{- 1.833 079 n})^{0.006 862 3}}, & 3 \leq n \leq 7 。 \\ 1.248 Lma {x_{7}}^{e^{- 0.057 n}}, & n > 7 。 \end{matrix} \end{matrix}$

2.2.3 大豆干物质量动态变化模型大豆地上生物量干质量呈“ 缓慢生长-快速生长-缓慢生长” 的生长过程。开始生长时较为缓慢, 随着时间的推移(或温度的升高), 在某一段时间内增长速度很快, 当达到某一值后, 增长速度又趋于缓慢, 直至最后停止生长。这一特点符合 Logistic生长曲线。利用 Curve Expert 1.3软件对单作和套作大豆茎干重和生长发育实际天数之间的关系进行拟合, 得到最优化的Logistic方程y=α /(1+β e^-γ^x)], 其中, y为干重, x为实际生长天数, 获得方程特征参数α 、β 、γ (表4)。

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	图2 单作、套作下各节间潜在粗度随节间数的动态变化Fig. 2 Changes in internode thickness with respect to the number of internodes

表4 单作、套作下不同大豆品种相对茎秆干重的方程系数 Table 4 Coefficients of normalized dry weights of the stems calculated by dynamic equations in three soybean varieties in intercropping and monocropping cultivation practices

在不同栽培模式下对南豆032-4、南豆12和九月黄的茎秆干重与实际生长天数进行共性化处理。

套作种植模式下的方程:

W_n(PDT)= $\begin{matrix} \begin{matrix} \frac{W {(\max)}_{77}}{1 + 79.53 e^{- 0.103 8 n}}, & 7 \leq n \leq 77 。 \end{matrix} \end{matrix}$

式中:W_n(PDT)为套作大豆在某一实际生长时刻的茎干重(g); n为生长实际时间(d); 通过动态观测套作大豆结果得出, Wmax₇₇为大豆在第77天的时候大豆茎潜在干重达到最大(图3)。

单作种植模式下的方程:

W_n(PDT)= $\begin{matrix} \begin{matrix} \frac{Wma x_{75}}{1 + 139.61 e^{- 0.115 14 n}}, & 7 \leq n < 80 。 \end{matrix} \end{matrix}$

式中:W_n(PDT)为单作大豆在某一实际生长时刻的茎干重(g); n为生长实际时间(d); 通过动态观测单作大豆得出, Wmax₇₅为大豆在第75天的时候大豆茎潜在干重达到最大(图3)。

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	图3 大豆茎潜在干重随生长时间的动态变化Fig. 3 Dynamic changes of potential stem dry weight of intercropping and monocropping soybean

2.3 模型的检验

通过2012-2013年的试验数据对套作和单作大豆茎秆动态模型进行检验。不同栽培模式下不同品种的大豆茎秆模拟值的RMSE结果(表5)表明, 套作大豆节间长度、粗度、干重的模拟误差分别为0.24~0.33 cm、0.007~0.030 cm、0.21~0.37 g。单作大豆节间长度、粗度、干重的的模拟误差分别为0.11~0.17 cm、0.021~0.027 cm、0.46~0.54 g。说明套作模式下的模型和单作模式下的模型模拟值与观测值都表现出很好的一致性, 模型的模拟结果精确、可靠。

采用RMSE分别对不同栽培模式下不同大豆节间长度、节间粗度、茎干重模型进行检验, 对其模拟值与观测值分别做1∶ 1关系图(图4、5、6)。可以看出, 不同栽培模式下不同大豆品种模拟值与实测值较接近, 在套作模式下节间长度、节间粗度、茎干重模拟的准确度R²均在0.93以上, 在单作模式下节间长度、节间粗度、茎干重模拟的准确度R²均在0.98以上。

表5 模型检验RMSE值 Table 5 The root mean square errors of the validated model

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	图4 大豆不同节间长度的预测误差Fig. 4 Prediction errors for internode length in the different varieties of soybean

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	图5 大豆不同节间粗度的预测误差Fig. 5 Prediction errors for internode thickness in different varieties of soybean

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	图6 大豆不同生理发育时期茎干重的预测误差Fig. 6 Prediction errors of the dry weight of soybean stems over the physiological growth time

3 讨论

3.1 不同大豆品种茎秆生长动态模型的建立

作物生长模型可以很好地描述作物生长发育的特征, 如在水稻^[23]、玉米^[24]、大豆^[25]等作物上均有相关研究报道。但是, 对大豆生长模型的描述多侧重于单作大豆的全生育期, 而对套作大豆模型的研究鲜有报道。单作模式下, 大豆节间较短、较粗, 保持较好的形态特征; 与单作相比, 套作大豆受高秆作物玉米遮阴的影响, 光照不足, 呈避阴反应, 茎秆伸长变细; 同一品种大豆在不同栽培模式下形态有差异明显。因此本研究分别对不同栽培模式大豆茎秆生长的动态模拟, 通过量化各节间同步生长以及与生理发育时间的关系, 以固定的节间潜在长度和潜在粗度来推算模型参数, 以确定模型参数。以生理发育时间(PDT)为步长, 建立了符合大豆茎秆和生理发育时间关系的Richards方程y=α /(1+β e^-γ^x)^1/δ, 该方程能很好地模拟大豆茎秆随生理发育时间变化的动态特征, 其方程参数有很好的生物学意义。当生理发育时间趋于无穷大时, 不同栽培模式、品种的相对最大茎长、茎粗均趋于α , α 值即为各品种的遗传参数, 由品种自身决定; β 值(初值参数)在栽培模式间变化幅度较大, 在品种间变化幅度较小; γ 值(生长速率参数)在栽培模式和品种间变化幅度均较大; δ 值(形状参数)在不同栽培模式下变异很大。通常某一大豆品种对生理发育时间的需求是一定的, 同一品种在单作和套作环境下表现出不同的形态特征。因此通过调试方程中的β 、γ 、δ 值, 对Richards方程模型进行拟合, 检验结果表明, 在单作栽培模式下, 节间长度、节间粗度观测值和模拟值的拟合较好(R²均大于0.983)。同样, 在套作栽培模式下, 节间长度、节间粗度观测值和模拟值的拟合较好(R²均大于0.934)。说明分别在不同品种及在单作、套作栽培模式下所建立的模型方程都表现出很好的拟合性, 符合茎秆生长的生物学规律, 具有一定的生物学意义。

3.2 不同大豆品种茎秆干重动态模型的建立

大豆茎秆干重积累速率随着生长而变化, 呈先上升后下降趋势, 可分为渐增期、快增期和缓增期。前人的研究主要集中在大豆单作栽培模式下进行的模拟, 根据Logistic方程分析不同耕作方式对夏大豆干物质积累与分配规律的影响^[26]; 根据Logistic方程建立大豆干物质累积曲线, 从而预报大豆产量^[27]。然而, 在带状套作复合种植模式下对大豆茎秆干重的模拟鲜见报道。本研究结果表明, 不同的栽培模式, 3个大豆品种的全生育期的茎秆干物质积累不同, 套作大豆茎秆干重显著(P< 0.05)低于单作大豆, 由于光照不足亦导致大豆光合作用减弱, 最终使大豆茎秆干物质积累降低^[9]。因此分别对单作和套作栽培模式下进行模拟, 以生长发育的实际天数为时间步长, 通过Logistic方程的拟合, 其在单作、套作栽培模式下的拟合效果较好(R²均大于0.979)。说明在单作、套作栽培模式下所建立的模型方程能很好的预测不同大豆品种生长发育实际天数与茎干重, 能较好地拟合茎秆生长动态, 符合茎秆生长的生物学规律, 具有一定的生物学意义, 将经验性和机理性有机地结合起来, 具有较好的描述性和预测性。

4 结论

本研究采用单作、套作栽培模式, 3种大豆在不同栽培模式下茎秆形态建成具有较大差异的材料, 使模拟研究的可靠性更高。在系统观察的基础上, 通过对这3种不同生长习性的大豆生长进行动态模拟, 量化了各节间同步生长以及与生理发育时间的关系, 根据观测结果, 以固定的潜在节间长度和直径来推算其他模型参数。但本研究中由于仅考虑了栽培模式和品种对大豆茎秆生长的影响, 并未深入研究养分、水分等外界因子的影响, 所以需要进一步考虑温度、光照时间、养分等条件对大豆器官形态建成影响。今后将继续调试和优化模型, 考虑水肥热等因素对大豆生育进程影响, 使其在更多品种和更大地域范围内接受检验。

The authors have declared that no competing interests exist.

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[20]	王声锋, 段爱旺, 徐建新. 冬小麦株高和叶面积指数变化动态分析及模拟模型. 灌溉排水学报, 2010, 29(4): 97-100. Wang S F, Duan A W, Xu J X. Dynamic changes and simulation model of plant height and leaf area index of winter wheat. Journal of Irrigation and Drainage, 2010, 29(4): 97-100. (in Chinese) [本文引用:1]
[21]	张文宇, 汤亮, 朱相成, 杨月, 曹卫星, 朱艳. 基于过程的小麦茎鞘夹角动态模拟. 应用生态学报, 2011, 22(7): 1765-1770. Zhang W Y, Tang L, Zhu X C, Yang Y, Cao W X, Zhu Y. Dynamic simulation of wheat stem sheath angle based on process. Chinese Journal of Applied Ecology, 201l, 22(7): 1765-1770. (in Chinese) [本文引用:1]
[22]	陈传梅, 赵达, 李志刚, 徐寿军, 杨恒山, 郭艳锋. 大豆花芽分化和物候期的机理模型. 中国油料作物学报, 2012, 34(5): 502-507. Chen C M, Zhao D, Li Z G, Xu S J, Yang H S, Guo Y F. Mechanism model for flower bud differentiation and phenophase of soybean. Chinese Journal of Oil Crop Sciences, 2012, 34(5): 502-507. (in Chinese) [本文引用:1]
[23]	韦还和, 孟天瑶, 李超, 张洪程, 史天宇, 马荣荣, 王晓燕, 杨筠文, 戴其根, 霍中洋, 许轲, 魏海燕, 郭保卫. 甬优籼粳杂交稻花后干物质积累模型与特征分析. 作物学报, 2016, 42(2): 265-277. Wei H H, Meng T Y, Li C, Zhang H C, Shi T Y, Ma R R, Wang X Y, Yang J W, Dai Q G, Huo Z Y, Xu K, Wei H Y, Guo B W. Dynamic model and its characteristics analysis for dry matter production after heading of Indica/Japonica hybrid rice of yongyou series. Acta Agronomica Sinica, 2016, 42(2): 265-277. (in Chinese) [本文引用:1]
[24]	李向岭, 赵明, 李从锋, 葛均筑, 侯海鹏, 李琦, 侯立白. 播期和密度对玉米干物质积累动态的影响及其模型的建立. 作物学报, 2010, 36(12): 2143-2153. Li X L, Zhao M, Li C F, Ge J Z, Hou H P, Li Q, Hou L B. Effect of sowing-date and planting density on dry matter accumulation dynamic and establishment of its simulated model in maize. Acta Agronomica Sinica, 2010, 36(12): 2143-2153. (in Chinese) [本文引用:1]
[25]	杨萍, 李杰, 剡斌, 牛俊义. 胡麻/大豆间作体系下施氮对胡麻干物质积累和产量的影响. 中国油料作物学报, 2015(4): 489-497. Yang P, Li J, Yan B, Liu J Y. Effects of applied nitrogen on dry matter accumulation and oil flax yield in flax/soybean intercropping system. Chinese Journal of Oil Crop Sciences, 2015(4): 489-497. (in Chinese) [本文引用:1]
[26]	唐江华, 苏丽丽, 罗家祥, 李亚杰, 徐文修, 彭姜龙. 不同耕作方式对夏大豆干物质积累及转运特性的影响. 核农学报, 2015(10): 2026-2032. Tang J H, Su L L, Luo J X, Li Y J, Xu W X, Peng J L. Effects of different tillage methods on dry matter accumulation and transfer characteristics of summer soybean. Acta Agriculturae Nucleatae Sinica, 2015(10): 2026-2032. (in Chinese) [本文引用:1]
[27]	姜丽霞, 那济海, 朱海霞, 韩俊杰, 纪仰慧, 闫平, 王萍, 王晨轶, 李秀芬. 基于Logistic方程的大豆产量预报方法. 大豆科学, 2008(3): 414-419. Jiang L X, Na J H, Zhu H X, Han J J, Ji Y H, Yai P, Wang P, Wang C Y, Li X F. A method to forecast yield of soybena which based on Logistic equation. Soybean of Science and Technology, 2008(3): 414-419. (in Chinese) [本文引用:1]

2011

0.0

杨文钰, 杨峰, 雍太文. 我国间套作大豆研究方向和发展对策研讨会纪要. 大豆科技, 2011, 27(1): 35-36.

Yang W

, Yang

, Yong T

. Symposium of research and development countermeasure of interplanting soybean in China. Soybean of Science and Technology, 2011, 27(1): 35-36. (in Chinese)

... 但是受制于人口和粮食生产压力,该地区复种指数高,在旱地生态系统中,间/套作占据主导地位^[1] ...

2014

0.0

雍太文, 刘小明, 刘文钰, 苏本营, 宋春, 杨峰, 王小春, 杨文钰. 减量施氮对玉米-大豆套作体系中作物产量及养分吸收利用的影响. 应用生态学报, 2014, 25(2): 474-482.

Yong T

, Liu X

, Liu W

, Su B

, Song

, Yang

, Wang X

, Yang W

. Effects of reduced N application rate on yield and nutrient uptake and utilization in maize-soybean relay strip intercropping system. Chinese Journal of Applied Ecology, 2014, 25(2): 474-482. (in Chinese)

A field experiment with three N application rates (0, 180, 240 N kg·hm -2 , representing zero, reduced and conventional N application, respectively) and three planting patterns (maize monoculture, soybean monoculture and maizesoybean relay strip intercropping) was conducted to reveal the effects of cropping patterns and N application rates on yield, nutrient uptake and nitrogen use efficiency of maize and soybean. The results showed that the grain yield, N, P and K uptake and harvest index of the intercropped maize reduced slightly compared with the monoculture maize, however these indices of the intercropped soybean increased significantly compared with the monoculture. With the increase in nitrogen fertilizer application, the excellence of relay strip intercropping was weakened in the maize-soybean intercropping system. The grain yield, economic coefficient, N, P and K uptake, harvest index, N agronomy efficiency and N uptake efficiency of maize and soybean increased significantly at the reduced nitrogen rate (180 N kg·hm -2 ), but the rate of soil N contribution declined, compared with the conventional rate of N application by local farmers (240 N kg·hm -2 ). In the reduced nitrogen rate treatment, total soil N and P contents of the maize strip reduced, whereas the total soil N, P and K contents of soybean strip and the total K content of maize strip increased compared with the zero N application treatment. With the reduced N application, the annual total grain yield, N, P and K uptake of above-ground biomass in the maizesoybean relay strip intercropping system were higher than in the monoculture, and the land equivalent ratio (LER) was 2.28. N uptake efficiency of maize in the relay strip intercropping system was 20.2% higher than in the maize monoculture, and the index of soybean was 30.5% lower than in the monoculture. The rate of soil N contribution in the relay strip intercropping system was 20.0% and 8.8% lower than in the maize and soybean monoculture, respectively. The reduced N application in the maizesoybean relay strip intercropping system was helpful to promote annual grain yield and improve N utilization efficiency.

通过田间试验研究了种植方式（玉米单作、大豆单作、玉米-大豆套作）和施氮水平（0、180、240 N kg·hm -2 ）对玉米和大豆产量、养分吸收及氮肥利用的影响.结果表明：与单作相比，玉米-大豆套作体系中玉米籽粒产量、地上部植株N、P、K吸收量及收获指数略有降低，而大豆籽粒产量、地上部植株N、P、K吸收量及收获指数显著提高.玉米-大豆套作系统的套作优势随施氮量的增加而降低，与当地农民常规施氮量(240 kg·hm -2 )相比，减量施氮（180 kg·hm -2 ）处理下玉米和大豆产量、经济系数，以及N、P、K吸收量和收获指数、氮肥农学利用率、氮肥吸收利用率显著提高，土壤氮贡献率降低；与不施氮相比，减量施氮降低了玉米带土壤的全N、全P含量，提高了大豆带土壤的全N、全P、全K含量和玉米带土壤的全K含量.减量施氮水平下，玉米-大豆套作系统的周年籽粒总产量、地上部植株N、P、K总吸收量均高于玉米和大豆单作，土地当量比（LER）达2.28；玉米-大豆套作系统的氮肥吸收利用率比玉米单作高20.2%，比大豆单作低30.5%，土壤氮贡献率比玉米和大豆单作分别低20.0%和8.8%.玉米-大豆套作减量一体化施肥有利于提高系统周年作物产量和氮肥利用率.

... 套作豆科植物相比单作能显著提高产量,主要体现在豆科植物活化土壤中难溶态磷、生物固氮供自身和共生作物吸收利用^[2,3,4] ...

2007

0.0

... 套作豆科植物相比单作能显著提高产量,主要体现在豆科植物活化土壤中难溶态磷、生物固氮供自身和共生作物吸收利用^[2,3,4] ...

2015

0.0

关佳威, 姬明飞, 王志强, 樊哲翻, 冉金枝, 邓建明. 不同种植密度条件下单混种作物的生长曲线. 草业科学, 2015, 32(8): 1243-1251.

Guan J

, Ji M

, Wang Z

, Fan Z

, Ran J

, Deng J

. The research of growth curve for monoculure and mixture planting crops grown under different density conditions. Pratacultural Science, 2015, 32(8): 1243-1251. (in Chinese)

According to metabolic scaling theory (MST), plant metabolic rate is nearly isometric to body size (biomass) for seedlings and samplings, and the scaling power is convergent to a constant 3/4 with the increasing plant size. Recently, we developed the dynamic growth model of individual sampling and seedling based on MST. However, plant individual which grown under intraspecies or interspecies competition pressure, will be strongly affected by the neighbors competition during development, it's unclear whether the growth model is suitable to the plant individuals with different pressure from intra and interspeciesneighbor competition. Therefore, three crops including spring wheat, flax, corn were selected and planted by monoculture and pair combination mixture cultivation ways, with three originally sowing densities(i.e. high, middle and low densities). We tracked the dynamic growth of individual plants in each plot for six times from germination to mature period including plant height, caudex, canopy and biomass. After fitting the growth curves based on the dynamic growth model proposed by Deng et al.(2012),we found that the growth curvesof plant individuals conform to the modelregardless of density gradient and planting way. However, the plant grows better and has bigger mature size for the species with similar nichesand in mixture cultivation plots than that in monoculture cultivation plots. Furthermore, and the growth rates and mature sizes decrease with the increasing densities or competition intensities for all species and planting ways. In a word, although the growth rate and mature size of plant vary with the competitive pressureof neighbors, growth curves of plant individual is still conformed to our growth model under different intra and interspeciescompetitive pressure. In current paper, we not only examined the growth model of small plant and the metabolic scaling theory, but also further pushing the development of metabolic theory.

代谢比例理论（Metabolic Scaling Theory）认为，植物小个体或幼苗的生物量和物质能量代谢速率之间的异速生长指数为1，而随着植物个体的逐渐增大,其代谢异速生长指数逐渐趋近于3/4。2012年，Deng等基于代谢比例理论建立了植物小个体的动态生长模型。然而，对于受到种内或种间不同竞争压力的植物个体来说，其生长过程无疑将受到邻体竞争的影响，他们是否仍然遵循上述植物小个体的动态生长模型尚不得而知。本研究针对此科学问题选取了春小麦（Triticum aestivum）、胡麻（Linum usitisimum）、玉米（Zea mays）3种作物分别进行两两组合混合种植以及单独种植，种植密度分别为高、中、低3种不同密度梯度；在作物出苗至成熟期间，分别对株高、基茎、冠幅、生物量、以及不同时期样方植物密度共进行6次跟踪测定。通过对Deng等建立的植物小个体动态生长模型的拟合分析，发现在种植密度梯度下不论单种还是混种，其植物个体的生长曲线均符合植物小个体动态生长模型，且具有相似生态位的物种混种条件下的个体生长状况要好于单种条件下的个体生长状况，而低密度条件下的生长状况亦显著优于中、高密度个体生长状况。总之，不同竞争压力下的植物个体，其生长速率和成熟大小虽有所变化，但其生长曲线均符合上述生长模型的预测。该研究不但对植物小个体生长模型和代谢理论的可靠性进行了进一步的验证，而且还使该理论的应用与发展得到进一步的完善。

... 套作豆科植物相比单作能显著提高产量,主要体现在豆科植物活化土壤中难溶态磷、生物固氮供自身和共生作物吸收利用^[2,3,4] ...

2008

0.0

杨文钰, 雍太文, 任万军, 樊高琼, 牟锦毅, 卢学兰. 发展套作大豆, 振兴大豆产业. 大豆科学, 2008(1): 1-7.

Yang W

, Yong T

, Ren W

, Fan G

, Mu J

, Lu X

. Develop relay planting soybean, revitalize soybean industry. Soybean of Science and Technology, 2008, 27(1): 1-7. (in Chinese)

... 玉米(Zea mays)-大豆带状复合种植体系以其高产、生态等特点在我国西南地区得到大面积推广^[5] ...

2016

0.0

祁军, 郑伟, 张鲜花, 唐高溶, 王祥, 朱进忠. 不同豆禾混播模式的草地生产性能. 草业科学, 2016, 33(1): 116-128.

, Zheng

, Zhang X

, Tang G

, Wang

, Zhu J

. Determination and comparison of the production performance of pastures among different spatial structure of legume-grass mixtures. Pratacultural Science, 2016, 33(1): 116-128. (in Chinese)

The seven indexes including herbage yield, dissimilarity of grass and legume relative density, relative yield total (RYT), dissimilarity of grass and legume relative yield, crude protein yield, ether extract yield and neutral detergent fiber yield were selected to study the changes of the comprehensive production performance under different legume-grass mixtures in 2012―2013. The mixture patterns included two legume-grass combinations: 5, 2 species mixture at three sowing ratios of legume︰grass (6︰4, 5︰5, 4︰6), mixed cropping and intercropping respectively. The species for mixture include Onobrychis viciaefolia, Trifolium pratense, Dactylis glomerata, Bromus inermis and Phleum pratense . The results showed that the forage yield, CP yield, EE yield, NDF yield and RYT values of legume-grass mixture (1∶1)were higher than mixed cropping in mixed 2 species-1 and mixed 2 species-1. The forage yield of mixed cropping were lower than intercropping in all species mixtures. The RYT values of all mixtures were higher than 1. The dissimilarity of grass and legume relative density, grass and legume relative yield for 2 rows legume︰2 rows grass and 3 rows legume︰3 rows grass were higher than 1 legume︰1 grass and mixed cropping. Therefore, from mixed cropping to intercropping like 1 legume︰1 grass, 2 rows legume︰2 rows grass and 3 rows legume︰3 rows grass, the forage yield and quality, the interspecific compatibility and the mixed community stability could improve. The comprehensive production performance of intercropping could further increase.

选择5种豆科与禾本科牧草建植同行与异行豆禾混播草地,混播种类为2种豆禾牧草混播、5种豆禾牧草混播,豆禾混播比例为豆禾比6∶4、5∶5和4∶6。依据2012-2013年各混播组合的牧草产量、粗蛋白产量、粗脂肪产量、中性洗涤纤维产量、相对产量总和(RYT)及豆科牧草与禾草的相对密度和相对产量相异度,分析了不同混播群落空间结构下各混播处理的生产性能变化。结果表明,混2-1(鸭茅 Dactylis glomerata+红豆草Onobrychis viciaefolia)、混2-2(无芒雀麦Bromus inermis +红豆草)的1∶1行处理具有较高的牧草产量与粗蛋白、粗脂肪和中性洗涤纤维产量,且均高于同行混播;同行混播牧草产量均低于异行混播。各混播处理RYT值均高于1,且混2-1、混2-2的1∶1行处理RYT值高于同行混播。2∶2行、3∶3行具有较高的相对密度和相对产量相异度,同行混播具有较低的相对密度和相对产量相异度。由此可见,从同行混播改为异行混播,可提高牧草产量、牧草品质和种间相容性,维持较高的群落稳定性,使豆禾混播草地的生产性能进一步增加。

... 玉米/大豆套作模式不仅能使土壤水分、养分和光资源的供给得到改善,还可以增加这些资源的可利用性,产生互利,从而提高复种系数^[6] ...

2013

0.0

徐寿军, 李志刚, 杨恒山, 陈传梅, 赵达, 郭艳锋. 大豆茎秆、叶片及豆荚生长的动态模拟. 农业工程学报, 2013, 29(20): 151-159.

Xu S

, Li Z

, Yang H

, Chen C

, Zhao

, Guo Y

. Dynamic simulation of stem, leaf and pod development on soybean. Transactions of the Chinese Society of Agricultural Engineering(Transactions of the CSAE), 2013, 29(20): 151-159. (in Chinese)

Abstract: Based on systematic observation, the organ morphogenesis model was established on soybeans. In the model, the time step was physiological development time, the growth process and the growth of the order of the stem, leaves and pods were measured by physiological development day, the model parameters were determined by genetic parameters, and the minimum nitrogen content, maximum nitrogen content, and critical nitrogen content were used to express the impact of nitrogen. In the model, internode potential length and potential thickness increased gradually with the increase of the number of soybeans internode, and reached a maximum at the ninth and seventh internode, and then decreased gradually. Therefore, the potential length of the ninth internode and potential thickness of the seventh internode were determined as potential genetic parameters that can calculate the other internodes' potential length and potential thickness. Because of similar leaf morphology on each internode on soybeans, this study only modeled the dynamic of the third fronds. Based on soybean morphological characteristics, this study simulated the pods which first appeared on the third internode. The results showed that the absolute prediction errors ranges of internode length, internode thickness, leaf length, leaf width, pod length, pod width, and pod thickness were 0.08-0.59, 0-0.10, 0.28-0.58, 0.31-0.39, 0.14-0.39, 0.09-0.21, 0.04-0.09 cm respectively with the root mean square errors (RMSE) being 0.25-0.28, 0.04-0.05, 0.47, 0.35-0.36, 0.24-0.39, 0.14-0.17, 0.06-0.07 cm, respectively. The model reflected a satisfactory prediction. Moisture had a greater impact on soybean organ morphogenesis. Because of the test conditions, this study did not establish a moisture influence factor model. The model establishment of water and nitrogen coupling soybean organ morphogenesis is the next research program. The models also need to be tested at a greater variety and a wider geographical scope.

以疆莫豆1号、蒙豆30、北豆5号为试材，在系统观测的基础上，构建了大豆茎秆、叶片和豆荚等器官的形态建成模型。模型以生理发育时间为时间步长，以生理发育日来衡量茎秆、叶片和豆荚的生长进程与生长次序，以品种遗传参数为基础来确定其他的模型参数，引入了最小含氮量、最大含氮量和临界含氮量来订正氮素的影响。不同品种不同播期的检验结果表明，节间长度的模拟误差在0.08～0.59 cm，RMSE在0.25～0.28 cm；节间粗度的模拟误差在0～0.10 cm，RMSE在0.04～0.05 cm；叶片长度的模拟误差在0.28～0.58 cm，RMSE为0.47 cm；叶片宽度的模拟误差在0.31～0.39 cm，RMSE在0.35～0.36 cm；豆荚长度的模拟误差在0.14～0.39 cm，RMSE在0.24～0.39 cm；豆荚宽度的模拟误差在0.09～0.21 cm，RMSE在0.14～0.17 cm；豆荚厚度的模拟误差在0.04～0.09 cm，RMSE在0.06～0.07 cm。模型表现出较好的预测性和可靠性。该研究可为大豆器官形态的虚拟显示提供参考。

... 同时,也是虚拟作物和作物可视化的研究基础^[7] ...

2015

0.0

邹俊林, 刘卫国, 袁晋, 蒋涛, 叶素琴, 邓榆川, 杨晨雨, 罗玲, 杨文钰. 套作大豆苗期茎秆木质素合成与抗倒性的关系. 作物学报, 2015, 41(7): 1098-1104.

Zou J

, Liu W

, Yuan

, Jiang

, Ye S

, Deng Y

, Yang C

, Luo

, Yang W

. Relationship between lignin synthesis and lodging resistance at seedlings stage in soybean intercropping system. Acta Agronomica Sinica, 2015, 41(7): 1098-1104. (in Chinese)

Stem physical characteristics are closely related to the crop lodging, increasing stem strength is available to resolve the problem of lodging. To explore the effect of intercropping soybean stem strength on the mechanism of shade tolerance and lodging resistance, we studied the relationship between lignin synthesis and lodging resistance. Three soybean cultivars with different shade tolerances were planted in maize–soybean intercropping and soybean monocropping, respectively. The lignin content, activities of phenylalanine ammonia-lyase (PAL), 4-coumarate:CoA ligase (4CL), cinnamyl alcohol dehydrogenase (CAD), peroxidase (POD) which involved in lignin synthesis in stem as well as the snapping resistance and lodging resistance index were determined at seedlings stage . The results showed that the intercropping soybean lodged seriously, the snapping resistance, lodging resistance index, lignin content and activities of the four enzymes were significantly lower than those of monocropping soybean at seedlings stage. The three soybean cultivars were affected differently by intercropping condition, the reduction of snapping resistance of Nandou 12 with strong shade tolerance was the least, its lodging resistance index, lignin content and activities of the four enzymes (PAL, 4CL, CAD, POD) also maintained a relatively high level. The lignin content of intercropping soybean seedling stem was significantly positively correlated with the snapping resistance ( r = 0.890, P r = –0.889, P

为从茎秆强度的角度探索套作大豆苗期耐阴抗倒机制，对套作大豆苗期茎秆木质素合成与抗倒性的关系进行了研究。采用耐阴性不同的 3 个大豆品种 ( 系 ) ，在大豆 - 玉米套作和大豆单作两种种植模式下，测定茎秆的木质素含量及其合成过程中的苯丙氨酸转氨酶 (PAL) 、 4- 香豆酸： CoA 连接酶 (4CL) 、羟基肉桂醇脱氢酶 (CAD) 、过氧化物酶 (POD) 等关键酶活性以及茎秆抗折力和抗倒伏指数。结果表明，套作大豆苗期倒伏严重，茎秆抗折力、抗倒伏指数、木质素含量和相关酶活性均显著低于单作。不同大豆品种受套作阴蔽影响程度不同，强耐阴性大豆南豆 12 茎秆抗折力降低幅度最小，在套作环境下其茎秆抗折力、抗倒伏指数大，茎秆木质素含量高， PAL 、 4CL 、 CAD 、 POD 活性强。相关分析表明，套作大豆苗期茎秆木质素含量与抗折力极显著正相关 ( r = 0.890 ， P ，与倒伏率极显著负相关 ( r = –0.889 ， P ，与 4CL 、 CAD 酶活性显著正相关。套作环境下，强耐阴性大豆苗期茎秆中较高的 4CL 、 CAD 活性是其维持高木质素含量的酶学基础，而高木质素含量有利于提高茎秆强度，进而增强其抗倒伏能力。

... 我国西南地区属于寡日照区域,在玉米和大豆共生期,受高位作物玉米遮阴导致苗期大豆受到一定程度的阴蔽胁迫,大豆植株茎长增加,茎粗、光合速率和地上部生物量显著下降,导致大豆易发生倒伏,从而影响大豆产量^[8,9] ...

2011

0.0

刘卫国, 蒋涛, 佘跃辉, 杨峰, 杨文钰. 大豆苗期茎秆对荫蔽胁迫响应的生理机制初探. 中国油料作物学报, 2011, 33: 141-146.

Liu W

, Jian

, She Y

, Yang

, Yang W

. Preliminary study on physiological response mechanism of soybean ( Glycine max) stem to shade stress at seedling stage. Chinese Journal of Oil Crop Sciences, 2011, 33(2): 141-146. (in Chinese)

... 05)低于单作大豆,由于光照不足亦导致大豆光合作用减弱,最终使大豆茎秆干物质积累降低^[9] ...

2016

0.0

刘婷, 刘卫国, 任梦露, 杜勇利, 邓榆川, 邹俊林, 方萍, 杨文钰. 遮荫程度对不同耐荫性大豆品种光合及抗倒程度的影响. 中国农业科学, 2016, 49(8): 1466-1475.

Liu

, Liu W

, Ren M

, Du Y

, Deng Y

, Zou J

, Fang

, Yang W

. Effects of shade degrees on photosynthesis and lodgingresistance degree of different shade tolerance soybean. Scientia Agricultura Sinica, 2016, 49(8): 1466-1475. (in Chinese)

... 但是不同耐阴性大豆品种在套作环境中的茎秆生长特性呈现较大差异,强耐阴大豆品种茎秆抗倒伏能力明显强于一般或不耐阴品种^[10] ...

2012

0.0

... 已有研究报道表明,以生理发育时间(physiological development time,PDT)为步长,可以对许多作物的形态生长动态进行模拟^[11,12,13] ...

2005

0.0

... 已有研究报道表明,以生理发育时间(physiological development time,PDT)为步长,可以对许多作物的形态生长动态进行模拟^[11,12,13] ...

2003

0.0

... 已有研究报道表明,以生理发育时间(physiological development time,PDT)为步长,可以对许多作物的形态生长动态进行模拟^[11,12,13] ...

2008

0.0

常丽英, 顾东祥, 张文宇, 杨杰, 曹卫星, 朱艳. 水稻叶片伸长过程的模拟模型. 作物学报, 2008, 34(2): 311-317.

Chang L

, Gu D

, Zhang W

, Yang

, Cao W

, Zhu

. A simulation model of leaf elongation process in rice. Acta Agronomica Sinica, 2008, 34(2): 311-317. (in Chinese)

Modeling leaf growth dynamics in rice is of significant importance for realizing virtual and digital plant growth. Based on time-course observations on leaf morphological properties (leaf length and leaf width) on main stems and tillers under different nitrogen rates and water regimes with four rice cultivars, the change patterns of leaf morphology with growth progress and environmental factors were characterized, and a dynamic model was developed to simulate time-course growth characters of different leaves on rice plant. The growth dynamics of leaf length on stem and tiller could be described with a logistic model, leaf width with conic equation, and leaf shape with exponential function and quadratic equation. The effects of nitrogen and water conditions on leaf growth were quantified by the effective values of leaf nitrogen concentration and water content. The model was validated with independent field experiment data of different nitrogen rates, and the mean RMSEs of dynamic leaf length were 3.60 cm and 3.96 cm, those of leaf width were 3.15 cm and 3.56 cm on main stem and tillers, respectively. The results indicated that the present model had a good performance in predicting morphological growth of leaf on stem and tiller in rice plant.

水稻叶片生长过程的动态模拟, 对于实现水稻生长的数字化和可视化表达具有重要的理论意义和应用价值。本研究以4个不同株型的水稻品种为试验材料, 通过对水分试验、氮素试验条件下不同叶位叶片的叶长、叶宽特征进行连续观测, 综合分析了水稻叶片几何形态指标随生育进程和环境条件的变化规律, 进而构建了水稻叶片生长过程的动态模拟模型。模型采用Logistic方程描述了水稻主茎及分蘖叶片随生长度日(GDD)的动态伸长过程; 利用二次曲线描述了叶宽随GDD的动态变化过程; 分别用幂函数和一元二次方程描述了叶形(不同叶长处的叶宽)的动态变化过程; 另外, 以叶片氮素和水分因子分别描述了不同水氮水平对叶片形态建成过程的定量影响。同时利用独立的水稻田间试验资料对所建模型进行了测试和检验, 主茎和分蘖动态变化叶长、叶宽的均方根差(RMSE)分别为3.6 cm、3.96 cm以及3.15 cm、3.56 cm。表明本模型对水稻叶片的动态伸长过程具有较好的预测性和解释性。

... 如,不同施氮水平和水分条件下水稻(Oryza sativa)的地上部器官形态特征建成^[14,15] ...

2006

0.0

石春林, 朱艳, 曹卫星. 水稻叶曲线特征的机理模型. 作物学报, 2006, 32(5): 656-660.

Shi C

, Zhu

, Cao W

. A quantitative analysis on leaf curvature characteristics in rice. Acta Agronomica Sinica, 2006, 32(5): 656-660. (in Chinese)

... 如,不同施氮水平和水分条件下水稻(Oryza sativa)的地上部器官形态特征建成^[14,15] ...

2007

0.0

徐寿军, 顾小莉, 许如根, 杨建香, 席文娟, 庄恒扬. 大麦穗和茎秆生长的动态模拟. 麦类作物学报, 2007, 27(2): 282-287.

Xu S

, Gu X

, Xu R

, Yang J

, Xi W

, Zhuang H

. Modeling spike and internode growth dynamics in barley. Journal of Triticeae Crops, 2007, 27(2): 282-287. (in Chinese)

... 不同播期条件下大麦(Hordeum vulgare)茎秆、穗的生长动态^[16] ...

2013

0.0

徐寿军, 李志刚, 杨恒山, 陈传梅, 赵达, 郭艳锋. 大豆茎秆、叶片及豆荚生长的动态模拟. 农业工程学报, 2013, 29(20): 151-159.

Xu S

, Li Z

, Yang H

, Chen C

, Zhao

, Guo Y

. Dynamic simulation of stem, leaf and pod development on soybean. Transactions of the Chinese Society of Agricultural Engineering(Transactions of the CSAE), 2013, 29(20): 151-159. (in Chinese)

... 不同大豆品种茎、叶、荚的形态建成^[17] ...

2005

0.0

陈国庆, 朱艳, 曹卫星. 冬小麦叶片生长特征的动态模拟. 作物学报, 2005, 31(11): 1524-1527.

Chen G

, Zhu

, Cao W

. Modeling leaf growth dynamics in winter wheat. Acta Agronomica Sinica, 2005, 31(11): 1524-1527. (in Chinese)

叶片形态生长特征是作物群体发育动态的重要内容，在很大程度上决定了作物冠层内的光分布、CO 2 传输及光合生产等 [1,2] ，同时也是作物生长诊断及遗传育种等多个研究领域的重要生理指标 [2] 。近年来，随着农业信息技术的飞速发展和虚拟现实技术在农业上的应用，使得建立作物形态建成模拟模型和虚拟作物生长系统成为可能，其中前者是后者的基础，也是当前数字化可视化农作系统研究的关键技术。迄今为止，关于作物叶片形态生长特征的模拟虽有报道 [3~10] ，但由于禾谷类作物的叶片形态的复杂性、可变性以及形态指标的难获取性，准确描述禾其变化特征仍是有待研究解决的一个难点 [1] 。在其描述中，叶长、叶形、叶面积是最主要的决定因素，对作物的个体和群体形态建成产生直接的影响 [1,3] 。为此，本研究以冬小麦为试材，通过对不同株型冬小麦品种不同叶位叶片生长特征的连续观察和定量分析，构建冬小麦叶片生长特征的动态模拟模型，包括叶长、叶形和叶面积生长动态，以期为虚拟小麦生长系统的建立提供技术基础。

... 以生长日(growing degree days,GDD)为步长,Logistic方程可以很好的描述小麦叶片、穗、叶鞘和节间的动态生长变化^[18,19] ...

2006

0.0

谭子辉, 朱艳, 姚霞, 田永超, 刘小军, 曹卫星. 冬小麦麦穗生长过程的模拟研究. 麦类作物学报, 2006, 26(4): 93-97.

Tan Z

, Zhu

, Yao

, Tian Y

, Liu X

, Cao W

. Modeling spike growth dynamics in winter wheat. Journal of Triticeae Crops, 2006, 26(4): 93-97. (in Chinese)

... 以生长日(growing degree days,GDD)为步长,Logistic方程可以很好的描述小麦叶片、穗、叶鞘和节间的动态生长变化^[18,19] ...

2010

0.0

王声锋, 段爱旺, 徐建新. 冬小麦株高和叶面积指数变化动态分析及模拟模型. 灌溉排水学报, 2010, 29(4): 97-100.

Wang S

, Duan A

, Xu J

. Dynamic changes and simulation model of plant height and leaf area index of winter wheat. Journal of Irrigation and Drainage, 2010, 29(4): 97-100. (in Chinese)

... 同样,以扩充的Logistic模型可以对小麦(Triticum aestivum)株高和叶面积变化动态进行模拟^[20] ...

2011

0.0

张文宇, 汤亮, 朱相成, 杨月, 曹卫星, 朱艳. 基于过程的小麦茎鞘夹角动态模拟. 应用生态学报, 2011, 22(7): 1765-1770.

Zhang W

, Tang

, Zhu X

, Yang

, Cao W

, Zhu

. Dynamic simulation of wheat stem sheath angle based on process. Chinese Journal of Applied Ecology, 201l, 22(7): 1765-1770. (in Chinese)

Based on the field experiments with different plant-type wheat ( Triticum aestivum ) cultivars and varied population densities, the time-course changes in the angle between stem and sheath (stem-sheath angle) on main stem were observed, and a process-based model was developed for simulating the growth dynamics of stem-sheath angle on the main stem by using system analysis method and dynamic modeling technology. The stem-sheath angle increased with the growth of corresponding leaves, and decreased with increasing population density. The maximum stem-sheath angle decreased with increasing leaf position, except for the first leaf on main stem. The growth dynamics of stem-sheath angle could be described with Logistic equation, and the changes in the maximum stem-sheath angle with leaf position could be quantified with two different equations. The maximal value of stem-sheath angle at the second leaf position was considered as the cultivar parameter to reflect the genetic differences, and the plant number per unit area was used to quantify the effects of population density. The independent field experiment dataset of different wheat cultivars was used to test the model, and the average RMSE between estimated and observed values was 1.7°, suggesting that the present model had good performance and reliability on predicting the growth dynamics of wheat stem-sheath angle, and provided a key module for wheat plant-type simulation and visualization.

基于不同株型品种和不同密度处理的小麦田间试验，连续观察并记录各处理不同叶位叶鞘与主茎之间的夹角，进一步利用系统分析方法和动态建模技术，构建基于过程的小麦叶片茎鞘夹角的动态模拟模型.结果表明：小麦茎鞘夹角随叶片生育进程不断加大，并随密度的增大而减小；从第2叶开始，最大茎鞘夹角随叶位的增加而减小.所建模型利用Logistic方程描述叶片茎鞘夹角随生育进程的动态变化过程，使用分段函数描述最大茎鞘夹角随叶位的动态变化，引入品种参数（第2叶茎鞘夹角的最大值）量化了茎鞘夹角在不同品种之间的差异，并利用基本苗量化了密度对茎鞘夹角的影响.基于独立的田间试验资料对所建模型进行测试与检验，结果显示茎鞘夹角模拟值与观测值之间的均方根差为1.7°.表明模型对小麦主茎叶片茎鞘夹角的动态变化过程具有较好的预测性，为小麦生长过程的可视化表达奠定了技术基础.

... 此外,利用系统分析方法和动态建模技术,成功构建小麦叶片茎鞘夹角的动态模拟模型^[21] ...

2012

0.0

陈传梅, 赵达, 李志刚, 徐寿军, 杨恒山, 郭艳锋. 大豆花芽分化和物候期的机理模型. 中国油料作物学报, 2012, 34(5): 502-507.

Chen C

, Zhao

, Li Z

, Xu S

, Yang H

, Guo Y

. Mechanism model for flower bud differentiation and phenophase of soybean. Chinese Journal of Oil Crop Sciences, 2012, 34(5): 502-507. (in Chinese)

利用作物生理发育时间恒定原理,系统构建了预测大豆花芽分化和物候期的机理模型。模型以Bate函数的特殊形式来表达温度热效应,引入温度敏感性、光周期敏感性、基本早熟性和灌浆因子4个品种遗传参数区别品种间的差异。不同地区、不同品种的花原基分化期、雌雄蕊原基分化期、胚珠花粉形成期等花芽分化阶段和出苗期、开花期、结荚期、鼓粒期、成熟期等物候期的预测结果表明,模型对大豆生育阶段的绝对模拟误差为0～4d,根均方差不超过3d。

... 大豆各发育阶段的生理发育时间的计算参照陈传梅等使用的方法^[22] ...

2016

0.0

韦还和, 孟天瑶, 李超, 张洪程, 史天宇, 马荣荣, 王晓燕, 杨筠文, 戴其根, 霍中洋, 许轲, 魏海燕, 郭保卫. 甬优籼粳杂交稻花后干物质积累模型与特征分析. 作物学报, 2016, 42(2): 265-277.

Wei H

, Meng T

, Li

, Zhang H

, Shi T

, Ma R

, Wang X

, Yang J

, Dai Q

, Huo Z

, Xu

, Wei H

, Guo B

. Dynamic model and its characteristics analysis for dry matter production after heading of Indica/Japonica hybrid rice of yongyou series. Acta Agronomica Sinica, 2016, 42(2): 265-277. (in Chinese)

This study was conducted using indica-japonica hybrid rice Yongyou 1538 and Yongyou 7176 as the material, conventional japonica rice Ningjing 3 and Wuyunjing 24, and hybrid indica rice Yangliangyou 6 and Liangyoupeijiu as the check to study the characteristics of dry matter production after heading in indica/japonica hybrid rice of Yongyou series and compare the differences in characteristics of dry matter production after heading among different types of rice variety. Results indicated that, grain yield of indica/japonica hybrid rice of Yongyou series was 11.5 t ha -1 , on an average, which was 7.8% and 10.4% higher than that of conventional japonica rice and hybrid indica rice, respectively. Dry matter accumulation of indica/japonica hybrid rice was 8.9 t ha -1 , which was19.1% and 26.9% higher than that of conventional japonica rice and hybrid indica rice, respectively.Richards' equation was fit to simulate the relationship between dry matter weight and days after heading for three types of rice variety (R 2 ≥0.990). Rate of dry matter accumulation of three types of rice variety decreased after an even increase.Maximum rate of biomass accumulation and mean rate of biomass accumulation after heading of hybrid indica rice were the highest, followed by those of conventional japonica rice, and indica / japonica hybrid rice. Days to maximum rate of dry matter accumulation after heading of indica / japonica hybrid rice was at 42–44 d after anthesis, while those of conventional japonica rice and hybrid indica rice were both at 26–28 d after anthesis. Duration of gradual increase stage and dry matter accumulation in this stage were higher in indica / japonica hybrid rice than inthe check, while mean rate of dry matter accumulation during gradual increase stage was higher inhybrid indica rice than in indica/japonica hybrid rice. The duration and dry matter accumulation during fast increase stage and slow increase stage of conventional japonica rice were the highest among three types of rice variety, while mean rate of dry matter accumulation during fast increase stage and slow increase stage of hybrid indica rice was the highest. Our results implied that greater dry matter accumulation mainly occurred in the gradual increase stage for indica/japonica hybrid rice, which was mainly attributed to the longer duration of this stage.

以甬优籼粳杂交稻甬优1538和甬优7176为试材，常规粳稻宁粳3号和武运粳24，杂交籼稻扬两优6号和两优培九为对照，研究甬优籼粳杂交稻花后干物质积累特征及比较不同类型品种花后干物质积累特征差异。结果表明: (1)两年中甬优籼粳杂交稻的平均产量为11.5 t hm -2 (11.3~11.7 t hm -2 )，较常规粳稻和杂交籼稻分别高7.8%和10.4% (两年平均值)。甬优籼粳杂交稻抽穗至成熟期的干物质积累量为8.9 t hm -2 ，较常规粳稻和杂交籼稻分别高19.1%和26.9%(两年平均值)。(2)不同类型品种花后干物质积累量与花后天数(抽穗当天为0 d)均可用Richards方程拟合( R 2 均大于0.990)；各品种花后干物重积累速率均呈先平缓增加后下降的趋势，花后最大干物重积累速率和平均干物重积累速率呈杂交籼稻>常规粳稻>籼粳杂交稻，籼粳杂交稻达最大干物重积累速率的时间大致在花后42~44 d，常规粳稻和杂交籼稻则在花后26~28 d；籼粳杂交稻在花后渐增期天数和干物质积累量显著高于常规粳稻和杂交籼稻，渐增期干物重积累速率以杂交籼稻最高。常规粳稻在花后快增期和花后缓增期天数和干物质积累量均显著高于籼粳杂交稻和杂交籼稻，快增期和缓增期干物重积累速率则以杂交籼稻最高。本研究表明甬优籼粳杂交稻花后较强的干物质积累优势主要体现在花后渐增期，而花后渐增期较强的干物质积累能力主要在于其较长的渐增期持续天数。

... 1 不同大豆品种茎秆生长动态模型的建立作物生长模型可以很好地描述作物生长发育的特征,如在水稻^[23]、玉米^[24]、大豆^[25]等作物上均有相关研究报道 ...

2010

0.0

李向岭, 赵明, 李从锋, 葛均筑, 侯海鹏, 李琦, 侯立白. 播期和密度对玉米干物质积累动态的影响及其模型的建立. 作物学报, 2010, 36(12): 2143-2153.

Li X

, Zhao

, Li C

, Ge J

, Hou H

, Li

, Hou L

. Effect of sowing-date and planting density on dry matter accumulation dynamic and establishment of its simulated model in maize. Acta Agronomica Sinica, 2010, 36(12): 2143-2153. (in Chinese)

2015

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杨萍, 李杰, 剡斌, 牛俊义. 胡麻/大豆间作体系下施氮对胡麻干物质积累和产量的影响. 中国油料作物学报, 2015(4): 489-497.

Yang

, Li

, Yan

, Liu J

. Effects of applied nitrogen on dry matter accumulation and oil flax yield in flax/soybean intercropping system. Chinese Journal of Oil Crop Sciences, 2015(4): 489-497. (in Chinese)

To optimized nitrogen management on oil flax/soybean intercropping system, field experiment was carried out to investigate N effect on dry matter accumulation and yield of 2 crops. 3 different N rates (0, 75 and 150 kg/hm2) were applied on monocropping and intercropping respectively. Results showed that fitted logistic equations of oil flax dry matter accumulation were significant at P

为改进胡麻产量和发展胡麻/大豆间作技术，采用随机区组试验，设单作模式下不施氮（T1）、施氮75kg/hm2（T2）、施氮150kg/hm2（T3）和间作模式下不施氮（T4）、施氮75kg/hm2（T5）、施氮150kg/hm2（T6）6个处理，研究了施氮量和种植模式对胡麻干物质积累规律、产量及产量构成因子的影响。结果表明，拟合的胡麻全生育期干物质积累Logistic模型均达到极显著相关水平。单作胡麻最大干物质积累速率出现在盛花期，间作种植模式下过量施氮时峰值会转移至子实期。在单作模式下，胡麻总干物质累积量和籽粒干物质累积量均随施氮量的增加而增加，以施氮量为150kg/hm2处理（T3）最高；而在间作种植模式下，施氮量为75kg/hm2处理（T5）显著高于不施氮处理（T4）和施氮量150kg/hm2的处理（T6）。在同一施氮水平下，间作种植模式下各处理开花前贮藏同化物的转运量、花后干物质积累量和花后干物质同化量对籽粒的贡献率均显著高于单作各处理，以施氮量为75kg/hm2处理（T5）最高；各处理以T5的产量最大，为3 204.80kg/hm2，且胡麻与大豆间作中得到的互利效应大于受到的竞争效应。因此，胡麻与大豆间作，即便减量施氮（75kg/hm2）仍可获得高产。

2015

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唐江华, 苏丽丽, 罗家祥, 李亚杰, 徐文修, 彭姜龙. 不同耕作方式对夏大豆干物质积累及转运特性的影响. 核农学报, 2015(10): 2026-2032.

Tang J

, Su L

, Luo J

, Li Y

, Xu W

, Peng J

. Effects of different tillage methods on dry matter accumulation and transfer characteristics of summer soybean. Acta Agriculturae Nucleatae Sinica, 2015(10): 2026-2032. (in Chinese)

... 前人的研究主要集中在大豆单作栽培模式下进行的模拟,根据Logistic方程分析不同耕作方式对夏大豆干物质积累与分配规律的影响^[26] ...

2008

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姜丽霞, 那济海, 朱海霞, 韩俊杰, 纪仰慧, 闫平, 王萍, 王晨轶, 李秀芬. 基于Logistic方程的大豆产量预报方法. 大豆科学, 2008(3): 414-419.

Jiang L

, Na J

, Zhu H

, Han J

, Ji Y

, Yai

, Wang

, Wang C

, Li X

. A method to forecast yield of soybena which based on Logistic equation. Soybean of Science and Technology, 2008(3): 414-419. (in Chinese)

基于Logistic方程建立大豆干物质累积曲线用来描述大豆干物质累积过程,由于气候条件处于非理想状态,因此对其干物质累积过程进行气象条件订正,并分析干物质累积量与气候产量的关系.在以上分析的基础上,建立大豆农业气象产量预测模式.通过计算分析温度和水分订正系数发现:在不同热量带、不同年份、不同发育时段,温度和水分订正系数不同,说明温度和水分条件是影响大豆生长发育和产量形成的重要限制因子.利用大豆主产区2004-2006年的气象和产量资料进行预报,预报精确度在95.9%左右,且预测产量与实际产量相关性较好,R2在0.903～0.948之间,通过α=0.01的显著性检验,说明模型预测的产量比较准确,模型可用.

... 根据Logistic方程建立大豆干物质累积曲线,从而预报大豆产量^[27] ...