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文冠果不同果型种实性状的概率分布与选择

汪子洋 黄炎子 王俊杰 周祎鸣 王青 于震 关文彬

汪子洋, 黄炎子, 王俊杰, 周祎鸣, 王青, 于震, 关文彬. 文冠果不同果型种实性状的概率分布与选择[J]. 北京林业大学学报, 2017, 39(9): 17-31. doi: 10.13332/j.1000-1522.20170162
引用本文: 汪子洋, 黄炎子, 王俊杰, 周祎鸣, 王青, 于震, 关文彬. 文冠果不同果型种实性状的概率分布与选择[J]. 北京林业大学学报, 2017, 39(9): 17-31. doi: 10.13332/j.1000-1522.20170162
WANG Zi-yang, HUANG Yan-zi, WANG Jun-jie, ZHOU Yi-ming, WANG Qing, YU Zhen, GUAN Wen-bin. Probability distribution and selection of seed and fruit traits of different fruit types of Xanthoceras sorbifolium[J]. Journal of Beijing Forestry University, 2017, 39(9): 17-31. doi: 10.13332/j.1000-1522.20170162
Citation: WANG Zi-yang, HUANG Yan-zi, WANG Jun-jie, ZHOU Yi-ming, WANG Qing, YU Zhen, GUAN Wen-bin. Probability distribution and selection of seed and fruit traits of different fruit types of Xanthoceras sorbifolium[J]. Journal of Beijing Forestry University, 2017, 39(9): 17-31. doi: 10.13332/j.1000-1522.20170162

文冠果不同果型种实性状的概率分布与选择

doi: 10.13332/j.1000-1522.20170162
基金项目: 

文冠果植物新品种测试指南及已知品种数据库项目 2014009

详细信息
    作者简介:

    汪子洋。主要研究方向:生物多样性保护与利用。Email :782813968@qq.com  地址: 100083北京市海淀区清华东路35号北京林业大学自然保护区学院

    责任作者:

    关文彬,教授。主要研究方向:生物多样性保护与利用。Email: swlab@bjfu.edu.cn  地址:同上

  • 中图分类号: S718.54

Probability distribution and selection of seed and fruit traits of different fruit types of Xanthoceras sorbifolium

  • 摘要: 文冠果是无患子科单属种,其种群野生濒危,生境破碎化严重且具有自交不亲和性。文冠果有“千花一果”之称,为提高其产量,测量了4年生文冠果实生园1 051个单株的坐果序数、坐果数、果实质量、种子质量、壳质量、平均单粒质量共6个种实性状并对各种实性状按不同果型进行了单因素方差分析和分布拟合。结果表明:不同果型之间果实质量、种子质量、壳质量、平均单粒质量4个种实性状之间差异极显著,而坐果序数和坐果数2个种实性状之间差异不显著。所有种实性状均符合威布尔分布,其中果实质量、种子质量、壳质量、坐果序数和坐果数5个种实性状均符合左偏威布尔分布,说明丰产是个“小概率”事件;平均单粒质量近似正态分布,说明实验园整体种子大小较为稳定,极大值与极小值的出现概率均比较低。基于威布尔概率分布建立了早期性状选择的模型,模型预测大桃型、倒卵型、尖柱型、凸桃型、短桃型、柱型在种子质量和平均单粒质量上选择概率均比较高,可作为丰产果型,其中大桃型为丰产的最理想果型;小柱型、小桃型和短柱型的种子质量和平均单粒质量的选择概率较低,不适合作为丰产选优果型。因此可根据该分布的特性对不同果型进行选择,为进一步的育种选优提供理论支持。

     

  • 图  1  不同果型轮廓模拟线

    Figure  1.  Simulated contour lines of different fruit types

    图  2  不同果型种子质量和平均单粒质量的差异

    不同小写字母表示不同果型在P<0.01水平上差异显著。

    Figure  2.  Variations in seed yield and average single grain mass for different fruit types

    Different lowercase letters mean significant difference among different fruit types at P < 0.01 level.

    图  3  种实性状的威布尔分布拟合

    Figure  3.  Weibull distribution fitting of seed and fruit traits

    图  4  种子质量威布尔参数变化趋势

    Figure  4.  Seed mass changing trend of Weibull parameters

    图  5  平均单粒质量威布尔参数变化趋势

    Figure  5.  Changing trend of Weibull parameters of average single grain mass

    图  6  威布尔分布中kzq的关系

    z为曲线在某一点的概率密度;q为选择部分的面积,即其所占的概率。下同。

    Figure  6.  Relationship between k and z and q in Weibull distribution

    z means the probability density of curve at a certain point; q means the area of the chosen part, i. e. the probability. The same below.

    图  7  种子质量和平均单粒质量概率累积分布曲线

    Figure  7.  Probability cumulative distribution curves of seed mass and average single grain mass

    表  1  不同果型文冠果种实性状的均值与标准差

    Table  1.   Mean and standard deviation of phenotypic traits of different fruit types of Xanthoceras sorbifolium

    果型
    Fruit type
    株数
    Trees number
    果实质量
    Fruit mass/g
    种子质量
    Seed mass/g
    壳质量
    Shell mass/g
    平均单粒质量
    Average single grain mass/g
    坐果序数
    Infructescence number
    坐果数
    Fruit number
    1308236.322±12.697133.344±7.119102.978±5.670.957±0.0115.94±0.3137.92±0.448
    2133239.394±19.502123.02±10.194116.375±9.8161.037±0.0186.21±0.538.06±0.704
    364336.187±35.192184.276±19.109151.912±16.2861.08±0.0227.17±0.7718.77±0.937
    493323.530±30.358168.866±15.695154.664±15.0731.183±0.0216.74±0.618.76±0.85
    5139318.627±23.551177.091±13.266141.535±10.431.088±0.0167.14±0.508.75±0.629
    638245.275±32.908124.968±17.515120.306±15.6591.245±0.034.29±0.5314.92±0.636
    716221.643±34.755119.288±18.069102.355±17.6041.034±0.0486.31±1.2678.00±2.123
    86227.62±32.911127.383±18.788100.237±15.1311.345±0.0964.83±0.8725.50±1.088
    967269.255±24.992144.764±14.045124.492±11.3151.062±0.0276.25±0.6018.12±0.792
    1021325.828±51.86174.148±28.963151.68±23.6221.183±0.0505.81±0.9257.19±1.032
    1157259.291±30.49134.274±15.947125.018±14.7731.184±0.0275.40±0.5726.54±0.761
    12109336.123±32.861182.877±17.225153.247±16.3151.138±0.0176.94±0.6848.58±0.855
    总体Total1051276.929±7.894150.248±4.279126.681±3.7271.068±0.0076.31±0.1768.04±0.235
    P0.002**0.001**0.001**0.000**0.2150.312
    注:*表示该列内各果型之间在P<0.05水平上差异显著,**表示该列内各果型之间在P<0.01水平上差异显著。Notes: * means significant difference among different fruits at P<0.05 level; ** means significant difference among different fruits at P<0.01 level.
    下载: 导出CSV

    表  2  不同果型种实性状的威布尔分布拟合

    Table  2.   Weibull distribution fitting of different fruit types

    果型编号Fruit type No.果实质量Total mass种子质量Seed mass粒数Grain number
    αβR2αβR2αβR2
    11.744 7238.907 30.900 11.609 6139.911 70.923 51.519 9151.782 50.941 9
    21.711 6249.666 70.942 61.729 2130.624 70.923 11.698 6133.602 70.951 9
    31.573 7337.515 30.808 41.460 4213.911 70.775 61.466 3189.655 70.762 2
    41.433 5381.180 70.949 01.469 4194.908 50.969 61.376 5180.380 80.884 5
    51.814321.281 60.923 81.745 8180.106 90.943 61.752 5173.967 80.951 4
    62.346 5225.220 30.917 42.340 5112.779 10.898 92.111 996.160 40.939 5
    91.647 7334.577 30.971 01.505 3182.665 00.919 31.501 0164.926 80.949 3
    111.080 7257.100 00.971 21.107 8131.864 90.974 01.075 4115.099 60.957 8
    121.731 5310.185 30.917 91.732 1161.522 90.898 11.665 0156.194 10.948 7
    果型编号Fruit type No.单粒质量Single grain mass坐果序数Fruit ordinal number坐果数Fruit number
    αβR2αβR2αβR2
    16.291 31.024 50.949 71.577 95.273 10.902 01.688 07.068 40.895 2
    26.526 51.120 40.920 32.465 44.147 50.910 22.200 95.675 50.870 7
    37.225 01.159 50.964 81.348 77.187 10.899 21.632 38.802 80.889 0
    47.455 61.252 00.917 31.626 56.068 50.854 51.539 68.459 90.779 1
    57.892 91.179 90.943 71.594 27.424 70.967 21.743 39.209 80.963 5
    67.058 91.362 70.846 31.760 04.515 30.917 61.802 45.692 60.927 2
    95.378 71.194 00.919 61.609 36.048 70.835 51.675 88.283 60.818 7
    1110.113 11.234 00.811 31.390 15.896 80.905 31.575 66.343 40.914 5
    128.399 11.233 80.977 61.732 85.689 10.932 11.897 76.864 50.925 7
    下载: 导出CSV

    表  3  种实性状的选择概率与选择强度

    Table  3.   Selection of percentage and intensity of yield traits

    q/%果实质量
    Fruit mass
    种子质量
    Seed mass
    平均单粒质量
    Average single grain mass
    壳质量
    Shell mass
    p/gkp/gkp/gkp/gk
    90750.002 1400.004 00.810.821 736.00.004 4
    701560.003 4840.006 30.982.129 073.00.007 4
    502330.004 51270.008 11.103.791 9108.00.009 9
    402750.005 01500.009 01.154.735 0127.00.011 1
    303240.005 51780.010 01.205.857 1148.00.012 5
    203860.006 22130.011 11.267.474 1176.00.014 1
    104780.007 22660.012 81.3410.166 0216.00.016 4
    55600.008 03130.014 11.4012.653 4251.00.018 3
    45850.008 23260.014 51.4213.582 8262.00.018 9
    36160.008 53440.014 91.4414.566 0276.00.019 6
    26570.008 93680.015 61.4615.605 3294.00.020 5
    17250.009 54070.016 61.5118.464 9323.00.022 0
    0.87460.009 74190.016 91.5219.084 1331.00.022 4
    0.67720.009 94350.017 31.5319.719 8343.00.023 0
    0.48090.010 24560.017 81.5521.041 9358.00.023 7
    0.28660.010 74900.018 61.5823.157 2383.00.024 9
    0.19210.011 15220.019 31.6125.439 3407.00.026 1
    注:p为选择值,k为选择强度。下同。Notes: p means selection value, k means selection intensity. The same below.
    下载: 导出CSV

    表  4  不同果型果实质量的选择概率和选择强度

    Table  4.   Selection of percentage and intensity of fruit mass for different fruit types

    q/%小柱型Small pillar type小桃型Small peach type尖柱型Pointed pillar type
    p/gkp/gkp/gk
    90660.002 4680.002 4820.001 8
    701330.004 01380.003 91760.002 8
    501940.005 32030.005 22680.003 6
    402280.006 02380.005 83200.004 0
    302660.006 82790.006 53810.004 4
    203150.007 73310.007 34580.004 9
    103860.008 94070.008 55740.005 6
    54490.010 04750.009 56790.006 2
    44680.010 34950.009 87100.006 3
    34910.010 75210.010 17500.006 5
    25230.011 25550.010 68040.006 8
    15740.012 06100.011 38920.007 2
    q/%大桃型Big peach type短柱型Short pillar type凸桃型Convex peach type
    p/gkp/gkp/gk
    90800.001 8940.001 8870.002 3
    701870.002 71830.003 21460.004 7
    502960.003 22630.004 31930.006 9
    403600.003 53070.004 82180.008 2
    304350.003 83570.005 52450.009 6
    205320.004 24190.006 22770.011 3
    106830.004 75100.007 33220.013 8
    58210.005 05890.008 23600.016 1
    48630.005 26130.008 53720.016 8
    39150.005 36430.008 83850.017 6
    29880.005 56830.009 34040.018 8
    11 1070.005 77470.010 04330.020 6
    q/%倒卵型Inverted egg type短桃型Short peach type柱型Pillar type
    p/gkp/gkp/gk
    90860.002 0330.003 5860.001 9
    701800.003 21000.003 81720.003 2
    502690.004 11840.004 02520.004 2
    403180.004 62380.004 12960.004 7
    303750.005 13060.004 23460.005 3
    204480.005 74000.004 34090.006 0
    105560.006 65570.004 45030.006 9
    56520.007 37110.004 55850.007 8
    46810.007 57590.004 56100.008 0
    37180.007 88220.004 56410.008 3
    27670.008 19090.004 56830.008 7
    18460.008 61 0570.004 67500.009 3
    下载: 导出CSV

    表  5  不同果型种子质量的选择概率与选择强度

    Table  5.   Selection of percentage and intensity of seed mass for different fruit types

    q/%小柱型Small pillar type小桃型Small peach type尖柱型Pointed pillar type
    p/gkp/gkp/gk
    90360.004 4370.004 6470.003 2
    70750.007 0730.007 71070.004 7
    501120.008 91070.010 21670.005 8
    401340.009 91250.011 42020.006 4
    301580.011 01460.012 82440.006 9
    201890.012 31730.014 52970.007 6
    102360.014 12130.016 93800.008 5
    52780.015 52470.018 84540.009 2
    42900.015 92580.019 44770.009 5
    33060.016 52710.020 15060.009 7
    23270.017 22880.021 05450.010 1
    13620.018 33170.022 56100.010 6
    q/%大桃型Big peach type短柱型Short pillar type凸桃型Convex peach type
    p/gkp/gkp/gk
    90430.003 5510.003 4440.004 7
    70980.005 21010.005 6740.009 6
    501530.006 41470.007 5970.013 8
    401850.007 01720.008 41100.016 3
    302220.007 62010.009 41230.019 0
    202700.008 42380.010 71390.022 4
    103450.009 42910.012 51620.027 6
    54120.010 23390.013 91810.032 0
    44330.010 53530.014 41870.033 5
    34590.010 83710.014 91940.035 2
    24940.011 13940.015 62030.037 4
    15520.011 74330.016 82180.041 1
    q/%倒卵型Inverted egg type短桃型Short peach type柱型Pillar type
    p/gkp/gkp/gk
    90420.003 8180.006 5450.003 5
    70930.005 7530.007 4900.005 9
    501440.007 1960.007 91320.007 8
    401730.007 81230.008 11550.008 8
    302080.008 61570.008 31810.009 9
    202520.009 52040.008 52140.011 2
    103190.010 72810.008 82620.013 0
    53800.011 73560.009 13050.014 5
    43980.011 93800.009 13180.014 9
    34210.012 34100.009 23340.015 5
    24530.012 74520.009 33560.016 2
    15050.013 55240.009 53910.017 4
    下载: 导出CSV

    表  6  不同果型平均单粒质量的选择概率与选择强度

    Table  6.   Selection of percentage and intensity of average single grain mass for different fruit types

    q/%小柱型Small pillar type小桃型Small peach type尖柱型Pointed pillar type
    p/gkp/gkp/gk
    900.730.938 70.800.817 70.860.902 1
    700.882.555 00.972.400 81.022.639 7
    500.984.543 71.074.151 41.114.490 7
    401.025.626 91.125.355 81.165.922 4
    301.077.266 21.166.513 11.207.327 1
    201.129.273 11.228.627 01.259.466 8
    101.1812.251 71.2811.272 41.3112.704 3
    51.2315.288 31.3414.548 31.3616.068 7
    41.2415.963 21.3515.163 21.3716.824 2
    31.2617.385 41.3716.456 91.3918.424 8
    21.2818.908 61.3917.839 71.4120.151 2
    11.3222.280 31.4320.891 41.4422.994 4
    q/%大桃型Big peach type短柱型Short pillar type凸桃型Convex peach type
    p/gkp/gkp/gk
    900.940.838 70.900.907 91.000.784 2
    701.102.337 11.052.656 31.192.271 9
    501.204.118 81.144.706 91.303.898 5
    401.255.372 31.185.982 31.365.134 7
    301.296.594 41.227.542 21.416.400 4
    201.348.445 11.269.437 51.478.253 2
    101.4111.760 11.3213.037 91.5410.960 9
    51.4614.750 01.3716.878 61.6013.837 5
    41.4715.419 21.3817.752 91.6214.926 2
    31.4916.834 81.3918.665 51.6416.085 5
    21.5118.358 61.4120.611 71.6617.319 0
    11.5521.758 21.4423.855 21.7020.023 9
    q/%倒卵型Inverted egg type短桃型Short peach type柱型Pillar type
    p/gkp/gkp/gk
    900.800.751 21.000.893 70.950.886 4
    701.002.018 01.122.535 21.102.650 7
    501.133.463 81.204.780 21.194.767 6
    401.194.353 01.235.997 71.236.101 3
    301.255.408 81.278.047 51.277.746 2
    201.316.652 11.309.972 21.3210.330 9
    101.408.917 71.3514.102 51.3713.630 2
    51.4711.058 21.3918.437 71.4217.804 1
    41.4911.737 01.4019.691 71.4318.759 9
    31.5212.815 01.4121.021 11.4419.759 7
    21.5513.967 81.4222.429 71.4621.898 4
    11.6016.065 31.4527.173 71.4925.481 0
    下载: 导出CSV

    表  7  不同果型壳质量的选择概率与选择强度

    Table  7.   Selection of percentage and intensity of shell mass for different fruit types

    q/%小柱型Small pillar type小桃型Small peach type尖柱型Pointed pillar type
    p/gkp/gkp/gk
    90410.004 0450.003 7580.003 0
    70870.006 3880.006 41140.005 2
    501300.008 11270.008 61650.006 9
    401540.009 01490.009 81930.007 8
    301830.010 11730.011 02250.008 8
    202180.011 22030.012 52640.010 0
    102720.012 82480.014 73220.011 7
    53200.014 22870.016 53730.013 2
    43350.014 62990.017 03890.013 6
    33530.015 13130.017 64080.014 1
    23780.015 73330.018 54330.014 8
    14180.016 73650.019 94740.015 9
    q/%大桃型Big peach type短柱型Short pillar type凸桃型Cenvex peach type
    p/gkp/gkp/gk
    90560.003 0580.003 1680.003 5
    701160.004 91130.005 41100.007 2
    501730.006 41610.007 31430.010 7
    402040.007 11880.008 31600.012 6
    302400.007 92170.009 41780.014 8
    202860.008 92540.010 72000.017 6
    103540.010 33090.012 72310.021 9
    54150.011 43560.014 32570.025 6
    44330.011 83700.014 72640.026 7
    34560.012 23880.015 32730.028 0
    24870.012 74120.016 12860.030 1
    15370.013 64500.017 43050.033 1
    q/%倒卵型Inverted egg type短桃型Short peach type柱型Pillar type
    p/gkp/gkp/gk
    90610.003 4380.004 0580.003 1
    701070.006 7850.005 91090.005 6
    501440.009 61330.007 31540.007 7
    401640.011 21610.008 11780.008 7
    301860.013 01930.008 82060.010 0
    202120.015 22340.009 72390.011 4
    102490.018 42980.010 92890.013 6
    52810.021 23560.011 83310.015 3
    42910.022 13730.012 13440.015 9
    33020.023 13950.012 53600.016 6
    23180.024 54250.012 93810.017 4
    13420.026 84750.013 64150.018 8
    下载: 导出CSV
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  • 收稿日期:  2017-05-03
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