Construction of Apple Leaf Area Estimation Model

doi:10.6048/j.issn.1001-4330.2023.03.017

Abstract

Abstract:

【Objective】 This study aims to establish an accurate and non-destructive model for apple leaf area estimation.【Methods】 Leaves were collect from vegetative and bourse shoots considering their length for Fuji and Gala apple trees.Leaf morphological parameters, such as leaf length (LL), leaf width (LW) and leaf area (LA), were obtained by digital scanner.17 candidate models with or without constant were evaluated by determination coefficient (R²), root mean square error (RMSE) and Akakchi Information Criterion (AIC).【Results】 Leaf morphological characteristics of 5,207 leaves were obtained, and among those leaf are had the highest coefficient of variation by 51.59%.Leaf morphologies were significantly affected by shoot types and cultivars The LL, LW and LA of long shoots were significantly larger than those of short shoot, and those were significantly higher in vegetative shoot than bourse shoot when the shoots belong to same category determined by shoot length.Leaves in Gala were more slender than those in Fuji.The accuracies of following selected models where LL and LW were used as independent variables can meet the requirements for leaf area estimation in apple trees, including model 5: LA = a(LL×LW), model 6: LA = a(LL+LW)², model 9: LA = aLL²+bLW², model 16: LA = a(LL×LW)^b, and model 17: LA = (LL×LW)^b., but model need to be established for each shoot type and cultivar.Those models had both LL and LW variables were more reliable than those models only had LL or LW solely.Among shoot types, regarding the accuracy of selected models, bourse was the highest, short shoot was higher than that of long shoot, and vegetative long shoot was the lowest.The all-data model 5 (R²= 97.72%, RMSE = 1.756,6 cm²) and 17 (R²= 97.37%, RMSE =1.831,9 cm²) were available to estimate the leaf area no matter of cultivars or shoot types with same model coefficients.The accuracies of the models 5 and 17 were not improved by adding constant.The model coefficients for model 5 and 17 were 0.712,3 and 0.910,8, respectively.The minimum number of samples was 241 and 3,939 for model 7 and 17, respectively; to have relative errors lower than 5%.【Conclusion】 The selected models in current study can be used for leaf area estimation irrespective of cultivars and shoot types, without the need of establishing model for each type of shoot and cultivar.The addition constant had no effect on selected model accuracy, and there is a minimum number of samples for model were required to have lower relative error.

Key words: apple; leaf area; model; akachi information criteria

摘要：

【目的】建立准确、无损的适宜于苹果不同品种和枝梢类型的叶面积估算模型。【方法】以富士及嘎啦不同长度的营养枝梢和果台枝梢叶片为试材,采用数字扫描仪获取叶片长度(LL)、宽度(LW)和叶面积(LA)等叶片形态参数,并采用决定系数(R²)、均方根误差(RMSE)、赤池信息准则(AIC)对建立的17个有常数项和无常数项叶面积模型精度进行筛选和适宜性评价。【结果】共获得5 207枚叶片形态参数,其中叶面积变异系数最大,达51.59%。叶片形态受品种及枝梢类型的显著影响,其中长枝梢叶片长、宽和叶面积显著大于同类型短枝梢叶片,而营养枝梢叶片长、宽和叶面积显著大于同长度果台枝梢,嘎啦叶片相比富士更为细长。以LL和LW复合变量为自变量的模型5:LA = a(LL×LW)、模型6:LA = a(LL+LW)²、模型9:LA = aLL²+bLW²、模型16:LA = a(LL×LW)^b、模型17:LA = (LL×LW)^b的精度可满足富士和嘎啦各类枝梢叶面积的估算,但需针对各品种和枝梢类型单独建模。同时包含LL和LW双变量的叶面积模型精度高于单一LL或LW变量的模型。无论富士还是嘎啦,对于不同类型枝梢,果台叶面积模型精度最高,短枝梢均比长枝梢精度高,营养长枝梢拟合精度最低。模型5和17可适用于富士和嘎啦各类枝梢叶面积的估算。模型5和17的R²分别为97.72%和97.37%,RMSE分别为1.756 6和1.831 9 cm²,模型系数分别为0.712 3和0.910 8。满足模型5和17精度所需的最低样品数量为241与3 939枚叶片。【结论】筛选的叶面积模型可用于各品种和各个类型枝梢叶片面积估算,无需针对单个品种及枝梢独立建模,且模型无需添加常数项。叶片数量影响叶面积模型精度,需满足最低临界值。

关键词: 苹果, 叶面积, 模型, 赤池信息准则

CLC Number:

S661.1

WANG Kai, LI Xiuling, Fazal Haider, BAI Ru, FENG Jianrong, YANG Weiwei. Construction of Apple Leaf Area Estimation Model[J]. Xinjiang Agricultural Sciences, 2023, 60(3): 664-674.

王凯, 李秀玲, 白茹, 冯建荣, 杨伟伟. 富士和嘎啦苹果叶片面积估算模型构建[J]. 新疆农业科学, 2023, 60(3): 664-674.

Figures/Tables 9

References 39

[1]	安树康. 梨叶面积最佳预测模型筛选[J]. 甘肃农业大学学报, 2003, 38(4): 463-466.
	AN Shukang. Selection of optimal prediction model for pear leaf area[J]. Journal of Gansu Agricultural University, 2003, 38(4): 463-466.
[2]	张钰, 钟海霞, 潘明启. 等. 马奶子葡萄叶面积评估模型的建立[J]. 新疆农业科学, 2020, 57(1): 63-68. DOI
	ZHANG Yu, ZHONG Haixia, PAN Mingqi, et al. Establishment of evaluation model for leaf area of grape[J]. Xinjiang Agricultural Sciences, 2020, 57(1): 63-68. DOI
[3]	Ngao J, Martinez S, Marquier A, et al. Spatial variability in carbon- and nitrogen-related traits in apple trees: the effects of the light environment and crop load[J]. Journal of Experimental Botany, 2021, 72(5): 13.
[4]	刁明, 戴剑锋, 罗卫红. 等. 温室甜椒叶面积指数形成模拟模型[J]. 应用生态学报, 2008, 19(10): 2277-2283.
	DIAO Ming, DAI Jianfeng, LUO Weihong, et al. A simulation model for the formation of leaf area index of sweet pepper in greenhouse[J]. Journal of Applied Ecology, 2008, 19(10): 2277-2283.
[5]	冯冬霞, 施生锦. 叶面积测定方法的研究效果初报[J]. 中国农学通报, 2005, 21(6): 150-152,155.
	FENG Dongxia, SHI Shengjin. A preliminary report on the effect of the method for leaf area determination[J]. Chinese Agricultural Science Bulletin, 2005, 21(6): 150-152,155.
[6]	张新平, 董洁, 张芳芳. 等. 几种常用的树木叶面积测量方法比较[J]. 中国城市林业, 2016, 14(2): 38-42.
	ZHANG Xinping, DONG Jie, ZHANG Fangfang, et al. Comparison of several commonly used tree leaf area measurement methods[J]. China Urban Forestry, 2016, 14(2): 38-42.
[7]	谭峰, 高艳萍. 基于图像的植物叶面积无损测量方法研究[J]. 农业工程学报, 2008, 24(5): 170-173.
	TAN Feng, GAO Yanping. 2008. Study on nondestructive measurement method of plant leaf area based on image[J]. Transactions of the CSAE, 2008, 24(5): 170-173.
[8]	柳觐, 倪书邦, 宫丽丹. 等. 澳洲坚果叶面积测定方法比较[J]. 中国农学通报, 2014, 30(25): 142-147.
	LIU Jian, NI Shubang, GONG Lidan, et al. Comparison of determination methods of macadamia leaf area[J]. Chinese Agricultural Science Bulletin, 2014, 30(25): 142-147.
[9]	张鑫, 孟繁疆. 植物叶面积测定方法的比较研究[J]. 农业网络信息, 2008,(12): 14-15, 31.
	ZHANG Xin, MENG Fanjiang. Comparative study on methods for determination of leaf area in plants[J]. Agricultural Network Information, 2008, (12): 14-15, 31.
[10]	安佳佳, 李茂富, 黄绵佳. 等. 香蕉叶面积回归模型的建立[J]. 广西农业科学, 2009, 40(6): 724-727.
	AN Jiajia, LI Maofu, HUANG Mianjia, et al. Establishment of regression model of banana leaf area[J]. Guangxi Agricultural Sciences, 2009, 40(6): 724-727.
[11]	Zanetti S, Pereira L, Sartori M, et al. Leaf area estimation of cassava from linear dimensions[J]. Anais da Academia Brasileira de Ciencias, 2017, 89(3):1729-1736. DOI URL
[12]	Williams L, Martinson T. Nondestructive leaf area estimation of ‘Niagara’ and ‘DeChaunac’ grapevines[J]. Scientia Horticulturae, 2003, 98(4): 493-498. DOI URL
[13]	李先明, 秦仲麒, 涂俊凡. 等. 7个早熟梨品种叶面积回归方程的建立[J]. 江西农业学报, 2011, 23(5): 36-39.
	LI Xianming, QIN Zhongqi, TU Junfan, et al. Establishment of regression equation for leaf area of seven early ripening pear cultivars[J]. Acta Agriculturae Jiangxi, 2011, 23(5): 36-39.
[14]	只佳增, 杜浩, 周劲松. 等. 基于叶型特征的云南特色香蕉叶面积模型分析[J]. 江西农业学报, 2020, 32(10): 57-61.
	ZHI Jiazeng, DU Hao, ZHOU Jinsong, et al. Analysis of area model of Yunnan characteristic banana leaf based on leaf shape characteristics[J]. Acta Agriculturae Jiangxi, 2020, 32(10): 57-61.
[15]	张萌, 张德安, 鲁晓燕. 等. 枣树叶面积估算模型构建[J]. 果树学报, 2020, 37(12): 1964-1973.
	ZHANG Meng, ZHANG Dean, LU Xiaoyan, et al. A model for estimation of leaf area of jujube[J]. Journal of Fruit Science, 2020, 37(12): 1964-1973.
[16]	Gyves E M, Rouphael Y, Cristofori V, et al. A non-destructive, simple and accurate model for estimating the individual leaf area of kiwi (Actinidia deliciosa)[J]. Fruits, 2007, 62(3): 171-176. DOI URL
[17]	Demirsoy H. Leaf area estimation in some species of fruit tree by using models as a non-destructive method[J]. Fruits, 2009, 64(1): 45-51. DOI URL
[18]	Pompelli F, Antunes C, Ferreira G, et al. Allometric models for non-destructive leaf area estimation of Jatropha curcas[J]. Biomass and Bioenergy, 2012, 36: 77-85. DOI URL
[19]	Keramatlou I, Sharifani M, Sabouri H, et al. A simple linear model for leaf area estimation in Persian walnut (Juglans regia L.)[J]. Scientia Horticulturae, 2015, 184: 36-39. DOI URL
[20]	Koubouris G, Bouranis D, Vogiatzis E, et al. Leaf area estimation by considering leaf dimensions in olive tree[J]. Scientia Horticulturae, 2018, 240: 440-445. DOI URL
[21]	杨伟伟, 陈锡龙, 刘航空. 等. 矮化中间砧短枝富士苹果高纺锤树形冠层结构与光能截获的三维模拟[J]. 中国农业科学, 2014, 47(23): 4680-4694. DOI
	YANG Weiwei, CHEN Xilong, LIU Hangkong, et al. Three-dimensional simulation of high spindle canopy structure and light energy interception in short Fuji apple with dwarfing interstock[J]. Scientia Agricultura Sinica, 2014, 47(23): 4680-4694. DOI
[22]	张玉星. 果树栽培学各论(第3版)[M]. 北京: 中国农业出版社. 2005.
	ZHANG Yuxing. Monodicy on fruit cultivation (The 3th Ed.)[M]. Beijing: China Agriculture Press, 2005.
[23]	施月园, 王彦君, 金光泽. 等. 小兴安岭8种阔叶树在不同叶生长期的叶面积经验模型[J]. 林业科学, 2019, 55(9): 22-30.
	SHI Yueyuan, WANG Yanjun, JIN Guangze, et al. Empirical model of leaf area of eight broad-leaved trees during different leaf growth periods in the Xiaoxingan Mountains[J]. Scientia Silvae Sinicae, 2019, 55(9): 22-30.
[24]	Core R, Rdct R, Team R, et al. A Language and Environment for Statistical Computing[J]. Computing, 2015, 1:12-21.
[25]	Ramkhelawan E, Rai B. Leaf area estimation by non-destructive methods in sour orange (Citrus aurantium L.)[J]. Hortscience, 1990, 67:203-206.
[26]	Williams L, Martinson T E. Nondestructive leaf area estimation of 'Niagara' and 'DeChaunac' grapevines[J]. Scientia Horticulturae, 2003, 98(4):493-498. DOI URL
[27]	蒋有条, 黄保健, 余抗. 等. 西瓜叶面积的测量方法[J]. 园艺学报, 1985, 1(2): 107-112.
	JIANG Youtiao, HUANG Baojian, YU Kang, et al. A method for measuring the leaf area of watermelon[J]. Acta Horticulturae Sinica, 1985, 1(2): 107-112.
[28]	龚建华, 向军. 黄瓜群体叶面积无破坏性速测方法研究[J]. 中国蔬菜, 2001, 1(4): 7-9.
	GONG Jianhua, XIANG Jun. Study on non-destructive rapid measurement of cucumber population leaf area[J]. China Vegetables, 2001, 1(4): 7-9.
[29]	Rouphael Y, Colls G, Fanasca S, et al. Leaf area estimation ofsunflower leaves from simple linear measurements[J]. Photosynthetica, 2017, 45(2) : 306-308. DOI URL
[30]	卜海东, 顾蔚, 齐永平. 等. 基于图像处理华中五味子叶面积的回归测算[J]. 植物生理学通讯, 2008, 44(3):543-547.
	BU Haidong, GU Wei, QI Yongqi, et al. Regression estimation of cotyledon area in central China based on image processing[J]. Plant Physiology Communications, 2008, 44(3): 543-547.
[31]	朱宏光, 赵金龙, 温远光. 等. 尾叶桉和巨尾桉叶面积的测算模型研究[J]. 安徽农业科学, 2010, 38(31): 17568-17570,17584.
	ZHU Hongguang, ZHAO Jinlong, WEN Yuanguang, et al. Study on the estimation model of leaf area of Eucalyptus urophylla and Eucalyptus grandis[J]. Journal of Anhui Agricultural Sciences, 2010, 38(31): 17568-17570,17584.
[32]	王士杰, 姜晓莉, 张国锋. 等. 人参叶面积预测模型建立[J]. 东北农业科学, 2016, 41(6):109-112.
	WANG Shijie, JIANG Xiaoli, ZHANG Guofeng, et al. A prediction model of ginseng leaf area was established[J]. Journal of Northeast Agricultural Sciences, 2016, 41(6): 109-112.
[33]	姜喜, 周禧琳, 党艳青. 等. 阿拉尔市二十种树木叶片形态分析[J]. 塔里木大学学报, 2017, 29(4): 64-69.
	JIANG Xi, ZHOU Xilin, DANG Yanqing, et al. Analysis on leaf morphology of twenty species of trees in Alar city[J]. Journal of Tarim University, 2017, 29(4): 64-69.
[34]	解雅麟, 雷相东, 王海燕. 等. 长白落叶松叶面积回归模型及比叶面积估计[J]. 林业科学研究, 2019, 32(4):57-63.
	XIE Yalin, LEI Xiangdong, WANG Haiyan, et al. Leaf area regression model and specific leaf area estimation of Larix olgensis[J]. Forest Research, 2019, 32(4): 57-63.
[35]	Willaume M, Lauri P, Sinoquet H, et al. 2004. Light interception in apple trees influenced by canopy architecture manipulation[J]. Trees-structure and Function, 2004, 18(6): 705-713. DOI URL
[36]	Yang W, Ma X, Ma D, et al. Modeling canopy photosynthesis and light interception partitioning among shoots in bi-axis and single-axis apple trees (Malus domestica Borkh.)[J]. Trees, 2021, 35(3): 845-861. DOI
[37]	谢龙飞, 董利虎, 李凤日. 等. 人工长白落叶松立木叶面积预估模型[J]. 应用生态学报, 2018, 29(9):2843-2851. DOI
	XIE Long Fei, DONG Lihu, LI Fengri, et al. Predicting models of leaf area for trees in Larix olgensis plantation[J]. Chinese Journal of Applied Ecology, 2018, 29(9): 2843-2851. DOI
[38]	B. Helsel, N. M. Cowen. Optimum sample size for measurement of leaf area in oats (Avena sativa L.)[J]. Cereal research communications, 1983, 11(1).
[39]	Antunes W C, Pompelli M F, Carretero D M, et al. Allometric models for non‐destructive leaf area estimation in coffee (Coffea arabica and Coffea canephora)[J]. 2008, 153(1): 33-40.

模型类型 Model types	序号 Order	模型 Model equations	序号 Order	模型 Model equations	变量 Variable
线性模型 Linear models	1	LA = aLL	1c	LA= aLL+c	LL
	2	LA = aLW	2c	LA =aLW+c	LW
	3	LA =aLL²	3c	LA =aLL²+c	LL²
	4	LA = aLW²	4c	LA = a LW²+c	LW²
	5	LA = a (LL×LW)	5c	LA = a (LL×LW)+c	LL×LW
	6	LA = a (LL+LW)²	6c	LA = a (LL+LW)²+c	LL+LW
	7	LA = a (LL+LW)³	7c	LA = a (LL+LW)³+c	LL+LW
	8	LA = aLL+ bLW	8c	LA = aLL+ bLW+c	LL,LW
	9	LA = aLL²+bLW²	9c	LA = aLL²+bLW²+c	LL²,LW²
非线性模型 Non-linear models	10	LA = aLL^b	10c	LA = aLL^b+c	LL
	11	LA =LL^b	11c	LA =LL^b+c	LL
	12	LA = aLW^b	12c	LA = aLW^b+c	LW
	13	LA = LW^b	13c	LA =LW^b+c	LW
	14	LA = a (LL+LW)^b	14c	LA = a (LL+LW)^b+c	LL+LW
	15	LA = (LL+LW)^b	15c	LA = (LL+LW)^b+c	LL+LW
	16	LA = a (LL×LW) ^b	16c	LA = a (LL×LW)^b+c	LL ×LW
	17	LA = (LL×LW) ^b	17c	LA = (LL×LW)^b+c	LL×LW

模型类型 Model types	序号 Order	模型 Model equations	序号 Order	模型 Model equations	变量 Variable
线性模型 Linear models	1	LA = aLL	1c	LA= aLL+c	LL
	2	LA = aLW	2c	LA =aLW+c	LW
	3	LA =aLL²	3c	LA =aLL²+c	LL²
	4	LA = aLW²	4c	LA = a LW²+c	LW²
	5	LA = a (LL×LW)	5c	LA = a (LL×LW)+c	LL×LW
	6	LA = a (LL+LW)²	6c	LA = a (LL+LW)²+c	LL+LW
	7	LA = a (LL+LW)³	7c	LA = a (LL+LW)³+c	LL+LW
	8	LA = aLL+ bLW	8c	LA = aLL+ bLW+c	LL,LW
	9	LA = aLL²+bLW²	9c	LA = aLL²+bLW²+c	LL²,LW²
非线性模型 Non-linear models	10	LA = aLL^b	10c	LA = aLL^b+c	LL
	11	LA =LL^b	11c	LA =LL^b+c	LL
	12	LA = aLW^b	12c	LA = aLW^b+c	LW
	13	LA = LW^b	13c	LA =LW^b+c	LW
	14	LA = a (LL+LW)^b	14c	LA = a (LL+LW)^b+c	LL+LW
	15	LA = (LL+LW)^b	15c	LA = (LL+LW)^b+c	LL+LW
	16	LA = a (LL×LW) ^b	16c	LA = a (LL×LW)^b+c	LL ×LW
	17	LA = (LL×LW) ^b	17c	LA = (LL×LW)^b+c	LL×LW

项目 Item	中位数 Median value	最大值 Maximum value	最小值 Minimum value	平均值 Average value	变异系数 CV(%)
叶片长度 Leaf length(cm)	7.17	15.24(嘎啦营养长枝)	1.50(嘎啦果台)	7.17	31.72
叶片宽度 Leaf width(cm)	4.14	7.99(嘎啦营养长枝)	4.14(嘎啦短果枝)	4.14	26.14
叶柄长度 Petiole length(cm)	2.95	5.46(富士营养短枝)	0.47(富士短果枝)	2.89	29.62
叶片面积 Leaf area(cm²)	21.52	73.94(嘎啦营养长枝)	1.95(嘎啦果台)	22.69	51.59
长宽比 Leaf length/Leaf width ratio	1.71	3.13(嘎啦营养短枝)	0.79(富士果台Bourse)	1.73	19.27
圆度 Roundness	0.13	0.41(富士营养短枝)	0.07(嘎啦营养短枝)	0.14	24.34

项目 Item	中位数 Median value	最大值 Maximum value	最小值 Minimum value	平均值 Average value	变异系数 CV(%)
叶片长度 Leaf length(cm)	7.17	15.24(嘎啦营养长枝)	1.50(嘎啦果台)	7.17	31.72
叶片宽度 Leaf width(cm)	4.14	7.99(嘎啦营养长枝)	4.14(嘎啦短果枝)	4.14	26.14
叶柄长度 Petiole length(cm)	2.95	5.46(富士营养短枝)	0.47(富士短果枝)	2.89	29.62
叶片面积 Leaf area(cm²)	21.52	73.94(嘎啦营养长枝)	1.95(嘎啦果台)	22.69	51.59
长宽比 Leaf length/Leaf width ratio	1.71	3.13(嘎啦营养短枝)	0.79(富士果台Bourse)	1.73	19.27
圆度 Roundness	0.13	0.41(富士营养短枝)	0.07(嘎啦营养短枝)	0.14	24.34

品种 Cultivar	枝梢类型 Shoot type	叶长 Leaf length (cm)	叶宽 Leaf width (cm)	叶柄长 Petiole length (cm)	叶面积 Leaf area (cm²)	叶长/宽比 Leaf length/ Leaf width ratio	圆度 Roundness
富士	果台	3.95^f	3.03^g	1.65^e	9.48^h	1.31^f	0.19^a
Fuji	长果枝	7.00^bc	4.37^b	2.93^b	22.64^d	1.61^cd	0.14^d
	短果枝	6.33^d	3.90^d	2.78^c	19.06^f	1.62^cd	0.15^c
	营养长枝	7.13^bc	4.37^b	2.91^b	24.22^c	1.64^c	0.15^c
	营养短枝	6.56^d	4.05^c	2.86^c	21.48^de	1.60^d	0.16^b
嘎啦	果台	4.77^e	3.20^f	2.09^d	11.60^g	1.49^e	0.16^b
Gala	长果枝	8.26^a	4.40^b	3.25^a	25.99^b	1.89^a	0.11^g
	短果枝	7.28^b	3.84^de	3.30^a	20.63^e	1.90^a	0.12^f
	营养长枝	8.44^a	4.56^a	3.21^a	28.56^a	1.86^ab	0.13^e
	营养短枝	6.94^c	3.71^e	2.65^c	20.11^ef	1.85^b	0.13^e
P值	品种Cultivar	***	ns	***	***	***	***
P values	枝类Shoot type	***	***	***	***	***	***
	品种×枝类	***	***	***	***	**	ns