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基于Logistic和Gompertz模型的小叶杨幼苗生长组合优化模型

葛会硕 宋跃朋 苏雪辉 张德强 张晓宇

葛会硕, 宋跃朋, 苏雪辉, 张德强, 张晓宇. 基于Logistic和Gompertz模型的小叶杨幼苗生长组合优化模型[J]. 北京林业大学学报, 2020, 42(5): 59-70. doi: 10.12171/j.1000-1522.20190296
引用本文: 葛会硕, 宋跃朋, 苏雪辉, 张德强, 张晓宇. 基于Logistic和Gompertz模型的小叶杨幼苗生长组合优化模型[J]. 北京林业大学学报, 2020, 42(5): 59-70. doi: 10.12171/j.1000-1522.20190296
Ge Huishuo, Song Yuepeng, Su Xuehui, Zhang Deqiang, Zhang Xiaoyu. Optimal growth model of Populus simonii seedling combination based on Logistic and Gompertz models[J]. Journal of Beijing Forestry University, 2020, 42(5): 59-70. doi: 10.12171/j.1000-1522.20190296
Citation: Ge Huishuo, Song Yuepeng, Su Xuehui, Zhang Deqiang, Zhang Xiaoyu. Optimal growth model of Populus simonii seedling combination based on Logistic and Gompertz models[J]. Journal of Beijing Forestry University, 2020, 42(5): 59-70. doi: 10.12171/j.1000-1522.20190296

基于Logistic和Gompertz模型的小叶杨幼苗生长组合优化模型

doi: 10.12171/j.1000-1522.20190296
基金项目: 中央高校基础研究基金(2017ZY30、2015ZCQ-LY-01),国家自然科学基金(11501032)
详细信息
    作者简介:

    葛会硕。主要研究方向:概率论与数理统计。Email:huishuo_ge@163.com  地址:100083 北京市海淀区清华东路35号北京林业大学

    责任作者:

    张晓宇,副教授,硕士生导师。主要研究方向:概率论与数理统计。Email:xyzhang@bjfu.edu.cn  地址:同上

  • 中图分类号: S758.5

Optimal growth model of Populus simonii seedling combination based on Logistic and Gompertz models

  • 摘要: 目的  通过对我国小叶杨幼苗的株高生长规律及生长模型的研究,为其生长预估及科学育苗提供参考。 方法  以来自我国16个产区的小叶杨幼苗作为研究对象,通过试验地调查及测量等方法获取基础数据,以时间维度建立生长模型分析小叶杨幼苗株高的生长规律。选取具有生物学意义的生长方程,根据模型拟合优度与评价指标选取最优基础生长模型,并在最优模型的基础上构建适合不同产区幼苗生长的组合优化生长模型。 结果  (1)不同产区的样本株高的综合最优基础模型分别为Logistic方程和Gompertz方程,其中Logistic模型的R2和预测精度分别在0.847 9和92.23%以上,Gompertz模型的R2和预测精度分别在0.891 5和92.60%以上。(2)在此基础上构建的组合优化模型对我国7个产区的小叶杨幼苗生长呈现出较大的F值(α = 0.01)和较高的预测精度,其中门源回族自治县样本的预测精度提高了0.90%,富平县和都兰县的样本预测精度分别提高了0.37%和0.34%,且模型显著相关。(3)通过组合优化模型参数发现16个产区样本平均在17.73 d达到生长速率最大点。 结论  小叶杨幼苗的生长受地理位置和气候等条件的影响,通过建立符合不同产区小叶杨幼苗生长的模型,有利于提高生长模型的精度和适用性,不仅能为幼苗研究提供科学基础,也为进一步的全基因组关联分析奠定基础。

     

  • 1  我国16个产区的小叶杨幼苗样本生长曲线对比图

    A. 河北赤城产区;B. 陕西富民产区;C. 陕西富县产区;D. 青海贵德产区;E. 陕西高陵产区;F. 宁夏中宁产区;G. 陕西岚皋产区;H. 陕西麟游产区;I. 青海门源产区;J. 内蒙古包头产区;K. 河南嵩县产区;L. 北京陶然亭产区;M. 青海都兰产区;N. 青海兴海产区;O. 河南伊川产区;P. 河北张家口产区。表示4月29日、5月20日和6月4日小叶杨幼苗实际株高;表示6月17日小叶杨幼苗实际株高。A, Chicheng production area of Hebei; B, Fumin production area of Shaanxi; C, Fu production area of Shaanxi; D, Guide production area of Qinghai; E, Gaoling production area of Shaanxi; F, Zhongning production area of Ningxia; G, Langao production area of Shaanxi; H, Linyou production area of Shaanxi; I, Menyuan production area of Qinghai; J, Baotou production area of Inner Mongolia; K, Songxian production area of Henan; L, Taoranting production area of Beijing; M, Dulan production area of Qinghai; N, Xinghai production area of Qinghai; O, Yichuan production area of Henan; P, Zhangjiakou production area of Hebei. indicates the actual plant height of P. simonii seedlings on April 29, May 20 and June 4; indicates the actual plant height of P. simonii seedlings on June 17.

    1.  Comparison in growth curves of P. simonii seedling samples in 16 production areas of China

    表  1  小叶杨株高的描述性统计分析

    Table  1.   Descriptive statistical analysis on seedling height of P. simonii

    产地
    Production area
    4月29日
    April 29th
    6月17日
    June 17th
    产地
    Production area
    4月29日
    April 29th
    6月17日
    June 17th
    河北赤城
    Chicheng County, Hebei Province
    15.52 ± 0.61 29.30 ± 0.55 河南嵩县
    Song County, Henan Province
    14.69 ± 1.25 28.37 ± 1.33
    陕西富平
    Fuping County, Shaanxi Province
    17.16 ± 1.02 43.51 ± 0.89 陕西麟游
    Linyou County, Shaanxi Province
    15.07 ± 1.00 29.84 ± 0.78
    陕西富县
    Fu County, Shaanxi Province
    16.67 ± 0.88 35.11 ± 1.20 青海都兰
    Dulan County, Qinghai Province
    13.41 ± 0.79 25.11 ± 0.56
    青海贵德
    Guide County, Qinghai Province
    11.15 ± 1.23 18.39 ± 0.82 青海兴海
    Xinghai County, Qinghai Province
    14.12 ± 0.73 28.35 ± 0.24
    陕西高陵
    Gaoling District, Shaanxi Province
    16.86 ± 0.45 27.02 ± 0.76 陕西岚皋
    Langao County, Shaanxi Province
    15.07 ± 1.57 27.35 ± 1.44
    宁夏中宁
    Zhongning County, Ningxia Hui Autonomous Region
    15.19 ± 0.90 28.73 ± 0.67 河北张家口
    Zhangjiakou City, Hebei Province
    12.35 ± 1.22 27.65 ± 1.03
    青海门源
    Menyuan Hui Autonomous County, Qinghai Province
    12.31 ± 0.43 20.24 ± 0.56 内蒙古包头
    Baotou City, Inner Mongolia Autonomous Region
    12.87 ± 0.57 22.56 ± 0.43
    河南伊川
    Yichuan County, Henan Province
    16.73 ± 0.68 29.01 ± 0.78 北京陶然亭
    Taoranting, Beijing
    18.10 ± 0.60 26.73 ± 0.48
    下载: 导出CSV

    表  2  生长模型表达式

    Table  2.   Expression of growth model

    模型 Model逻辑斯谛 Logistic理查兹 Richards韦布尔 Weibull冈珀茨 Gompertz
    表达式 Expression $\scriptstyle {y} = \frac{k}{ {1 + { {\exp }^{(a - bt)} } } }$ $\scriptstyle y = a{(1 - {{\exp }^{ - ct}})^b}$ $\scriptstyle y = a(1 - {{\exp }^{ - b{t^c}}})$ $\scriptstyle y = (a{{\exp }^{ - b{{\exp }^{ - ct}}}})$
    注:k代表最大生长量;a代表初始株高;b代表生长率;c代表最大生长天数;t代表时间。Notes: k represents the maximum growth amount; a represents initial plant height; b represents growth rate; c represents the maximum growth days; t represents time.
    下载: 导出CSV

    表  3  16个产区样本株高的Logistic模型参数估计

    Table  3.   Logistic model parameter estimation of plant height in 16 production areas

    产地
    Production area
    k/cma/cmb/%最大生长速率点
    Maximum growth rate point
    下渐近线
    Lower asymptote
    河北赤城 Chicheng County, Hebei Province 28.403 6 2.118 2 0.118 0 (17.95, 14.20) 3.048 8
    陕西富平 Fuping County, Shaanxi Province 40.705 2 2.422 2 0.117 5 (20.61, 20.35) 3.317 2
    陕西富县 Fu County, Shaanxi Province 27.633 4 1.399 7 0.093 7 (14.93, 13.81) 5.467 6
    青海贵德 Guide County, Qinghai Province 18.479 6 2.465 5 0.143 8 (17.14, 9.23) 1.447 1
    陕西高陵 Gaoling District, Shaanxi Province 25.859 0 1.344 1 0.081 8 (16.43, 12.92) 5.348 5
    宁夏中宁
    Zhongning County, Ningxia Hui Autonomous Region
    30.556 7 2.776 6 0.150 1 (18.49, 15.27) 1.790 6
    陕西岚皋 Langao County, Shaanxi Province 26.462 2 2.037 8 0.120 8 (16.86, 13.23) 3.050 8
    陕西麟游 Linyou County, Shaanxi Province 30.480 9 1.875 9 0.104 2 (18.00, 15.24) 4.049 7
    青海门源
    Menyuan Hui Autonomous County, Qinghai Province
    19.417 6 1.834 5 0.126 1 (14.54, 9.70) 2.673 8
    内蒙古包头
    Baotou City, Inner Mongolia Autonomous Region
    22.159 1 1.885 5 0.106 5 (17.70, 11.07) 2.919 6
    河南嵩县 Song County, Henan Province 28.768 0 1.648 3 0.077 0 (21.40, 14.38) 4.641 3
    北京陶然亭 Taoranting, Beijing 35.709 8 0.478 8 0.026 7 (17.93, 17.85) 13.660 0
    青海都兰 Dulan County, Qinghai Province 23.386 5 2.933 5 0.163 9 (17.89, 11.69) 1.181 5
    青海兴海 Xinghai County, Qinghai Province 24.462 6 2.997 6 0.172 3 (17.39, 12.23) 1.162 8
    河南伊川 Yichuan County, Henan Province 26.129 0 1.545 3 0.093 0 (16.61, 13.06) 4.592 5
    河北张家口 Zhangjiakou City, Hebei Province 28.173 6 2.070 8 0.104 2 (19.87, 14.08) 3.154 5
    注:下渐近线为k/(1 + exp(a)),最大生长速率点是(a/b, k/2),a/b是生长天数,k/2是相应的株高。Notes: k/(1 + exp(a)) is the lower asymptote, the maximum growth rate point is (a/b, k/2), a/b is the growth days, k/2 is the corresponding plant height.
    下载: 导出CSV

    表  4  我国16个小叶杨幼苗样本产区的地理特征

    Table  4.   Geographical characteristics of P. simonii seeding samples of 16 production areas in China

    产地
    Production area
    经度
    Longitude
    纬度
    Latitude
    海拔
    Altitude/m
    年均温度
    Annual average temperature/℃
    年均降雨量
    Average annual rainfall/mm
    河北赤城 Chicheng County, Hebei Province 115º15′ ~ 116º16′E 40º18′ ~ 41º13′N 945 6.8 404.9
    陕西富平 Fuping County, Shaanxi Province 102°12′ ~ 102°28′E 25°04′ ~ 25°21′N 400 15.8 846.5
    陕西富县 Fu County, Shaanxi Province 108°17′ ~ 109°25′E 35°26′ ~ 36°13′N 944 16.9 500.0
    青海贵德 Guide County, Qinghai Province 109°27′ ~ 117°12′E 20°05′ ~ 25°18′N 3 000 2.3 1 777.0
    陕西高陵 Gaoling District, Shaanxi Province 109°04′ ~ 110°13′E 34°31′ ~ 36°18′N 400 15.6 732.9
    宁夏中宁
    Zhongning County,Ningxia Hui Autonomous Region
    105°15′ ~ 106°04′E 37°05′ ~ 37°30′N 2 955 9.5 202.1
    陕西岚皋 Langao County, Shaanxi Province 108°53′ ~ 109°01′E 32°01′ ~ 32°33′N 1 500 16.0 1 050.0
    陕西麟游 Linyou County, Shaanxi Province 108°43′ ~ 108°52′E 32°03′ ~ 32°30′N 1 486 17.0 1 000.0
    青海门源
    Menyuan Hui Autonomous County, Qinghai Province
    107°11′ ~ 108°01′E 34°19′ ~ 34°34′N 1 271 9.1 680.0
    内蒙古包头
    Baotou City, Inner Mongolia Autonomous Region
    102°00′ ~ 102°03′E 37°03′ ~ 38°00′N 2 866 0.8 520.0
    河南嵩县 Song County, Henan Province 111º24′ ~ 112º22′E 33º35′ ~ 34º21′N 1 966.6 14.0 800.0
    北京陶然亭 Taoranting, Beijing 115°07′ ~ 117°04′E 39°04′ ~ 41°06′N 44 12.6 483.9
    青海都兰 Dulan County, Qinghai Province 98°06′ ~ 98°34′E 36°19′ ~ 37°08′N 3 180 2.7 179.1
    青海兴海 Xinghai County, Qinghai Province 99°01′ ~ 100°43′E 34°37′ ~ 36°10′N 3 924 1.5 359.0
    河南伊川 Yichuan County, Henan Province 112°36′ ~ 114°01′E 34°36′ ~ 35°52′N 277 15.0 620.0
    河北张家口 Zhangjiakou City, Hebei Province 113°42′ ~ 116°19′E 39°21′ ~ 42°07′N 1 400 10.0 400.0
    下载: 导出CSV

    表  5  16个产区样本株高的Logistic模型的评价指标

    Table  5.   Evaluating indices of Logistic model for sample plant height in 16 production areas

    产地
    Production area
    R2赤池信息准则
    An information criterion (AIC)
    贝叶斯信息准则
    Bayesian information criterion (BIC)
    MSEF
    河北赤城 Chicheng County, Hebei Province 0.929 6 − 18.745 7 − 17.973 1 0.291 6 198.77
    陕西富平 Fuping County, Shaanxi Province 0.903 8 1.934 7 2.707 2 1.062 3 145.49
    陕西富县 Fu County, Shaanxi Province 0.936 5 − 26.658 2 − 25.885 6 0.177 8 220.42
    青海贵德 Guide County, Qinghai Province 0.945 7 − 38.140 8 − 37.368 3 0.086 7 257.71
    陕西高陵 Gaoling District, Shaanxi Province 0.910 0 − 21.812 2 − 21.039 6 0.240 8 155.54
    宁夏中宁
    Zhongning County, Ningxia Hui Autonomous Region
    0.986 0 − 32.686 7 − 31.914 1 0.122 0 1 000.40
    陕西岚皋 Langao County, Shaanxi Province 0.939 5 − 25.353 9 − 24.581 3 0.192 9 231.45
    陕西麟游 Linyou County, Shaanxi Province 0.921 0 − 15.111 9 − 14.339 3 0.366 0 177.20
    青海门源
    Menyuan Hui Autonomous County, Qinghai Province
    0.958 5 − 46.320 3 − 45.547 7 0.052 0 337.58
    内蒙古包头
    Baotou City, Inner Mongolia Autonomous Region
    0.925 1 − 26.512 1 − 25.739 5 0.179 5 186.96
    河南嵩县Song County, Henan Province 0.847 9 − 5.651 4 − 4.878 8 0.661 2 92.07
    北京陶然亭 Taoranting, Beijing 0.340 2 12.550 9 13.323 5 2.062 6 21.21
    青海都兰 Dulan County, Qinghai Province 0.167 0 30.447 2 31.219 8 6.312 2 5.24
    青海兴海 Xinghai County, Qinghai Province 0.949 9 − 30.416 3 − 29.643 8 0.140 6 279.36
    河南伊川 Yichuan County, Henan Province 0.922 9 − 22.971 8 − 22.199 2 0.223 9 181.49
    河北张家口 Zhangjiakou City, Hebei Province 0.903 9 − 11.891 6 − 11.119 0 0.447 6 145.63
    注:R2 = 1 − (SSE/SST),其中SST为总平方和,SSE为残差平方和。MSE = SSE/nk,其中n是样本的数目,k是参数个数. Notes: R2 = 1 − (SSE/SST), where SST is the sum of total squares, SSE is the sum of residual squares. MSE = SSE/nk, where n is the number of samples and k is the number of parameters. AIC = ln(SSE/n) + 2k; BIC = ln(SSE/n) + k·ln(n); Fα = 8.86 (P < 0.01); Fα = 4.16 (P < 0.05).
    下载: 导出CSV

    表  6  16个产区样本株高的Gompertz模型参数估计

    Table  6.   Gompertz model parameter estimation of sample plant height in 16 production areas

    产地
    Production area
    k/cma/cmb/%最大生长速率点
    Maximum growth rate point
    下渐近线
    Lower asymptote
    河北赤城Chicheng County, Hebei Province 28.498 8 1.518 5 0.102 9 (14.75, 14.24) 0.296 5
    陕西富平 Fuping County, Shaanxi Province 40.956 1 1.659 6 0.098 3 (16.88, 20.47) 0.213 3
    陕西富县 Fu County, Shaanxi Province 27.778 5 0.911 3 0.081 3 (11.20, 13.88) 2.308 7
    青海贵德 Guide County, Qinghai Province 18.497 3 1.938 5 0.130 6 (14.84, 9.24) 0.017 7
    陕西高陵 Gaoling District, Shaanxi Province 26.153 8 0.791 9 0.067 8 (11.67, 13.07) 2.876 0
    宁夏中宁
    Zhongning County, Ningxia Hui Autonomous Region
    31.960 0 2.057 9 0.105 0 (19.59, 15.98) 0.012 7
    陕西岚皋 Langao County, Shaanxi Province 26.524 4 1.498 7 0.107 2 (13.98, 13.26) 0.301 8
    陕西麟游 Linyou County, Shaanxi Province 30.660 6 1.265 9 0.088 8 (14.25, 15.33) 0.883 9
    青海门源
    Menyuan Hui Autonomous County, Qinghai Province
    19.438 5 1.416 3 0.115 6 (12.25, 9.71) 0.315 1
    内蒙古包头
    Baotou City, Inner Mongolia Autonomous Region
    22.271 4 1.291 3 0.091 5 (14.11, 11.13) 0.586 1
    河南嵩县 Song County, Henan Province 29.587 9 0.915 1 0.058 4 (15.66, 14.79) 2.435 9
    北京陶然亭 Taoranting, Beijing 40.219 3 0.095 0 0.016 9 (5.61, 20.10) 13.39 2
    青海都兰 Dulan County, Qinghai Province 23.398 8 2.377 5 1.150 0 (2.06, 11.69) 0.000 4
    青海兴海 Xinghai County, Qinghai Province 24.470 4 2.487 1 0.159 6 (15.58, 12.23) 0.000 1
    河南伊川 Yichuan County, Henan Province 26.318 5 0.991 4 0.079 0 (12.54, 13.15) 1.777 6
    河北张家口 Zhangjiakou City, Hebei Province 28.412 9 1.362 9 0.086 3 (15.79, 14.20) 0.570 8
    下载: 导出CSV

    表  7  16个产区样本株高的Gompertz模型的评价指标

    Table  7.   Evaluating indices of Gompertz model for sample plant height in 16 production areas

    产地
    Production area
    R2AICBICMSEF
    河北赤城 Chicheng County, Hebei Province 0.999 8 − 110.733 0 − 109.960 0 0.000 9 89 725.28
    陕西富平 Fuping County, Shaanxi Province 0.999 8 − 87.620 2 − 86.847 6 0.003 9 58 988.08
    陕西富县 Fu County, Shaanxi Province 0.999 5 − 99.736 9 − 98.964 3 0.001 8 29 681.81
    青海贵德 Guide County, Qinghai Province 1.000 0 − 153.014 0 − 152.241 0 6.613 3 47 580.73
    陕西高陵 Gaoling District, Shaanxi Province 0.999 0 − 87.153 6 − 86.381 1 0.004 0 13 339.15
    宁夏中宁 Zhongning County, Ningxia Hui Autonomous Region 0.891 5 8.561 7 9.334 3 1.607 4 129.05
    陕西岚皋 Langao County, Shaanxi Province 0.999 9 − 119.867 3 − 119.094 0 0.000 5 19 685.19
    陕西麟游 Linyou County, Shaanxi Province 0.999 7 − 96.046 1 − 95.273 5 0.002 3 40 480.97
    青海门源Menyuan Hui Autonomous County, Qinghai Province 0.999 9 − 144.849 3 − 144.076 0 0.000 1 2 272.73
    内蒙古包头 Baotou City, Inner Mongolia Autonomous Region 0.999 7 − 109.285 0 − 108.513 0 0.001 0 47 610.94
    河南嵩县 Song County, Henan Province 0.998 0 − 68.400 9 − 67.628 3 0.013 0 7 053.93
    北京陶然亭 Taoranting, Beijing 0.990 6 − 60.268 9 − 59.496 3 0.021 7 1 483.19
    青海都兰 Dulan County, Qinghai Province 0.167 0 30.447 2 31.219 8 6.312 2 5.24
    青海兴海 Xinghai County, Qinghai Province 1.000 0 − 171.298 0 − 170.525 0 0.000 02 95 643.44
    河南伊川 Yichuan County, Henan Province 0.999 4 − 95.756 1 − 94.983 5 0.002 3 24 605.57
    河北张家口 Zhangjiakou City, Hebei Province 0.999 6 − 92.047 2 − 91.274 6 0.002 9 32 600.28
    下载: 导出CSV

    表  8  16个产区样本株高的组合优化模型参数估计和拟合优度值

    Table  8.   Parameter estimation of combinatorial optimization model for sample plant height in 16 production areas

    产地
    Production area
    标准差1
    Standard deviation 1 (σ1)
    标准差2
    Standard deviation 2 (σ2)
    权重1
    Weight 1 (w1)
    权重2
    Weight 2 (w2)
    R2
    河北赤城 Chicheng County, Hebei Province 0.038 3 0.054 6 0.456 0 0.544 0 0.988 8
    陕西富平 Fuping County, Shaanxi Province 0.151 2 0.236 2 0.444 9 0.555 1 0.986 2
    陕西富县 Fu County, Shaanxi Province 0.098 1 0.127 7 0.467 1 0.532 9 0.988 6
    青海贵德 Guide County, Qinghai Province 0.002 3 0.003 2 0.458 7 0.541 3 0.991 0
    陕西高陵 Gaoling District, Shaanxi Province 0.233 3 0.307 3 0.465 7 0.534 3 0.983 8
    宁夏中宁
    Zhongning County, Ningxia Hui Autonomous Region
    0.005 9 0.008 7 0.451 9 0.548 1 0.940 1
    陕西岚皋 Langao County, Shaanxi Province 0.021 5 0.029 6 0.459 9 0.540 1 0.989 9
    陕西麟游 Linyou County, Shaanxi Province 0.108 4 0.152 8 0.457 4 0.542 6 0.987 3
    青海门源
    Menyuan Hui Autonomous County, Qinghai Province
    0.004 5 0.005 8 0.468 2 0.531 8 0.992 4
    内蒙古包头
    Baotou City, Inner Mongolia Autonomous Region
    0.046 6 0.065 3 0.458 1 0.541 9 0.987 8
    河南嵩县 Song County, Henan Province 0.770 7 1.085 1 0.457 5 0.542 5 0.974 9
    北京陶然亭 Taoranting, Beijing 2.526 6 2.711 7 0.491 2 0.508 8 0.772 1
    青海都兰 Dulan County, Qinghai Province 0.001 1 0.001 6 0.455 3 0.544 7 0.167 0
    青海兴海 Xinghai County, Qinghai Province 0.000 5 0.000 7 0.458 5 0.541 5 0.991 6
    河南伊川 Yichuan County, Henan Province 0.123 7 0.166 4 0.463 1 0.536 9 0.986 7
    河北张家口 Zhangjiakou City, Hebei Province 0.135 6 0.201 3 0.451 1 0.548 9 0.985 5
    下载: 导出CSV

    表  9  16个产区样本株高的组合优化模型评价指标

    Table  9.   Evaluating indices of combinatorial optimization model for sample plant height in 16 production areas

    产地 Production areaAICBICMSEF
    河北赤城 Chicheng County, Hebei Province − 44.890 2 − 44.117 6 0.056 9 1250.38
    陕西富平 Fuping County, Shaanxi Province − 25.299 7 − 24.527 1 0.193 6 1 011.90
    陕西富县 Fu County, Shaanxi Province − 51.182 5 − 50.409 9 0.038 4 1 226.29
    青海贵德 Guide County, Qinghai Province − 63.943 7 − 63.171 1 0.017 3 1 555.40
    陕西高陵 Gaoling District, Shaanxi Province − 46.053 7 − 45.281 1 0.052 9 865.28
    宁夏中宁 Zhongning County, Ningxia Hui Autonomous Region − 42.869 4 − 3.514 3 0.720 0 233.53
    陕西岚皋 Langao County, Shaanxi Province − 50.971 3 − 50.198 7 0.038 9 1 388.53
    陕西麟游 Linyou County, Shaanxi Province − 40.957 4 − 40.184 8 0.072 7 1 099.15
    青海门源 Menyuan Hui Autonomous County, Qinghai Province − 70.957 4 − 70.184 8 0.011 1 1 844.85
    内蒙古包头 Baotou City, Inner Mongolia Autonomous Region − 52.303 8 − 51.531 2 0.035 8 1 151.26
    河南嵩县 Song County, Henan Province − 30.787 2 − 30.014 7 0.137 4 557.67
    北京陶然亭 Taoranting, Beijing − 9.7482 3 − 8.975 6 0.511 8 61.42
    青海都兰 Dulan County, Qinghai Province 30.447 2 31.219 8 6.312 2 5.24
    青海兴海 Xinghai County, Qinghai Province − 56.062 9 − 55.290 3 0.028 3 1 659.63
    河南伊川 Yichuan County, Henan Province − 47.888 1 − 47.115 5 0.047 1 1 051.28
    河北张家口 Zhangjiakou City, Hebei Province − 38.504 1 − 37.731 5 0.084 8 966.69
    下载: 导出CSV

    表  10  16个产区样本株高的Logistic模型、Gompertz模型和组合优化模型评价指标对比

    Table  10.   Comparison in evaluation indices of Logistic model, Gompertz model and combinatorial optimization model in 16 production areas

    产地
    Production area
    逻辑斯蒂
    Logistic
    冈珀茨
    Gompertz
    组合优化模型
    Combinatorial optimization model
    均方误差
    MSE
    均方绝对误差
    MAE
    均方误差
    MSE
    均方绝对误差
    MAE
    均方误差
    MSE
    均方绝对误差
    MAE
    河北赤城 Chicheng County, Hebei Province 3.312 4 0.143 4 0.008 0 0.089 6 0.013 0 0.114 1
    陕西富平 Fuping County, Shaanxi Province 40.960 0 3.150 1 9.075 9 3.012 6 9.448 4 3.073 8
    陕西富县 Fu County, Shaanxi Province 9.363 6 1.037 1 0.949 7 0.974 5 1.007 6 1.003 8
    青海贵德 Guide County, Qinghai Province 1.000 0 0.432 7 0.176 9 0.420 6 0.181 6 0.426 2
    陕西高陵 Gaoling District, Shaanxi Province 6.812 1 0.073 1 0.030 3 0.174 0 0.016 1 0.127 0
    宁夏中宁
    Zhongning County, Ningxia Hui Autonomous Region
    0.028 9 0.818 6 0.708 8 0.841 9 0.691 2 0.831 4
    陕西岚皋 Langao County, Shaanxi Province 5.760 0 1.092 8 1.116 2 1.056 2 1.151 8 1.073 2
    陕西麟游 Linyou County, Shaanxi Province 1.345 6 1.215 6 1.697 2 1.302 8 1.594 9 1.262 9
    青海门源
    Menyuan Hui Autonomous County, Qinghai Province
    4.202 5 1.405 3 1.938 8 1.392 4 1.955 7 1.398 5
    内蒙古包头
    Baotou City, Inner Mongolia Autonomous Region
    5.062 5 0.644 7 0.346 4 0.588 6 0.377 4 0.614 3
    河南嵩县 Song County, Henan Province 34.222 0 1.408 5 1.384 9 1.176 8 1.646 2 1.283 0
    北京陶然亭 Taoranting, Beijing 16.000 0 1.097 9 1.389 6 1.178 8 1.297 5 1.139 1
    青海都兰 Dulan County, Qinghai Province 3.865 2 3.036 5 2.084 0 1.443 6 2.096 2 1.447 8
    青海兴海 Xinghai County, Qinghai Province 0.950 6 0.566 4 0.314 0 0.560 3 0.317 1 0.563 1
    河南伊川 Yichuan County, Henan Province 6.105 8 0.238 5 0.025 3 0.159 0 0.038 4 0.195 9
    河北张家口 Zhangjiakou City, Hebei Province 3.482 0 0.754 8 0.754 2 0.868 5 0.667 7 0.817 1
    下载: 导出CSV

    表  11  16个产区样本株高的Logistic模型、Gompertz模型和组合优化模型预测精度和时间复杂度对比

    Table  11.   Comparison in prediction accuracy and time complexity of Logistic model, Gompertz model and combinatorial optimization model in16 production areas

    产地
    Production area
    逻辑斯蒂
    Logistic
    冈珀茨
    Gompertz
    组合优化模型
    Combinatorial optimization model
    预测精度
    Prediction accuracy/%
    时间
    Time/s
    预测精度
    Prediction accuracy/%
    时间
    Time/s
    预测精度
    Prediction accuracy/%
    时间
    Time/s
    提高百分比
    Percentage increase/%
    河北赤城
    Chicheng County, Hebei Province
    0.994 9 0.402 0 0.996 8 0.736 8 0.996 0 1.060 9
    陕西富平
    Fuping County, Shaanxi Province
    0.922 3 0.403 9 0.926 0 0.622 8 0.929 7 0.985 9 0.37
    陕西富县
    Fu County, Shaanxi Province
    0.962 2 0.399 5 0.964 6 0.702 4 0.964 8 1.123 5 0.02
    青海贵德
    Guide County, Qinghai Province
    0.976 6 0.406 5 0.977 2 0.647 0 0.977 5 1.068 4 0.03
    陕西高陵
    Gaoling District, Shaanxi Province
    0.997 1 0.396 1 0.993 2 0.611 3 0.995 0 1.011 4
    宁夏中宁
    Zhongning County, Ningxia Hui Autonomous Region
    0.973 2 0.398 7 0.972 5 0.652 4 0.972 0 1.040 3
    陕西岚皋
    Langao County, Shaanxi Province
    0.958 6 0.406 8 0.960 0 0.600 3 0.961 0 1.052 5 0.10
    陕西麟游
    Linyou County, Shaanxi Province
    0.959 9 0.411 5 0.957 1 0.558 1 0.956 6 1.077 2
    青海门源
    Menyuan Hui Autonomous County, Qinghai Province
    0.927 5 0.418 3 0.928 3 0.672 3 0.932 8 1.023 6 0.90
    内蒙古包头
    Baotou City, Inner Mongolia Autonomous Region
    0.970 8 0.407 2 0.973 4 0.569 9 0.972 9 1.066 2
    河南嵩县
    Song County, Henan Province
    0.949 7 0.409 2 0.958 3 0.539 7 0.956 4 1.074 0
    北京陶然亭
    Taoranting, Beijing
    0.961 2 0.406 0 0.958 5 0.639 2 0.958 1 0.978 3
    青海都兰
    Dulan County, Qinghai Province
    0.937 9 0.409 4 0.938 3 0.610 3 0.941 7 1.008 1 0.34
    青海兴海
    Xinghai County, Qinghai Province
    0.976 8 0.414 7 0.977 1 0.553 4 0.977 5 0.993 0 0.04
    河南伊川
    Yichuan County, Henan Province
    0.990 8 0.406 6 0.993 9 0.598 4 0.992 5 0.958 3
    河北张家口
    Zhangjiakou City, Hebei Province
    0.973 0 0.404 0 0.969 1 0.527 1 0.970 0 1.091 5
    下载: 导出CSV
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出版历程
  • 收稿日期:  2019-07-15
  • 修回日期:  2019-12-30
  • 网络出版日期:  2020-05-11
  • 刊出日期:  2020-07-01

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