Prediction model for basal area of Larix principis-rupprechtii plantation in Saihanba of Hebei Province, northern China
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摘要: 如何实现林分水平和单木水平预测林分断面积的兼容性，并提高不同水平断面积模型的预估精度，在森林经营过程中是一个亟待解决的科学问题。本文以华北暖温带华北落叶松人工林为研究对象，运用105块连续观测的固定样地数据，首先采用Gauss-Newton算法建立林分水平和单木水平断面积生长模型；其次分别采用不同形式的逻辑斯蒂方程对单木生存概率方程进行拟合；最后将不同水平最优预测模型进行组合并建立组合方程，采用最小二乘法估计组合方程参数，以提高对不同水平断面积的预测精度。结果表明：在约束参数法中，林分密度模型、林分断面积预测模型和单木断面积模型均具有较好的预测效果，并均能解释90%以上的变异；在分解法中采用逻辑斯蒂方程来预测单木生存概率和林分密度，经检验获得的ROC曲线下面积为0.906，表明该方程可以较好地预测林木生存概率；在组合预测法中，采用不同水平的最优模型进行组合后的预测效果最佳。在预测林分密度和断面积时，组合预测方程预测精度最高，林分水平模型预测精度次之，单木水平模型预测精度最低。组合预测法能够预测不同水平下的林分密度、立木生存概率、林分断面积及单木断面积，提高了模型预测精度，为预测林分生长动态、空间结构变化及经营效果评价等提供参考依据。Abstract: It is a scientific problem to be solved urgently in the process of forest management that how to realize area compatibility between whole-stand growth model and an individual-tree model and improve the prediction accuracy. In this paper, data from 105 permanent sample plots of Larix principis-rupprechtii plantation were used to develop both whole-stand growth model and individual-tree model. In a first step, using Gauss-Newton algorithm, a whole-stand growth model and an individual-tree model were established. In a second step, the single tree survival probability equation was fitted based on the logistic equation in different forms. Finally, the best combinations obtained in each step were compared. Regarding the disaggregation of predicted stand density, the approach based on considering the intercept of the logistic function for tree survival as a specific parameter of each sample plot and optimizing its value produced the best results. The results showed that the prediction model of stand density, stand basal area and individual basal area had a good predictive effect, and can explain more than 90% of the variance in the constraint parameter methods. In the decomposition method, survival probability of single trees and stand density were predicted based on the logistic equation. The area under the ROC curve obtained by the test was 0.906, which indicated that the equation could predict the survival probability of forest trees. In combination forecasting methods, the combination forecasting method had the best effect using different levels of optimal model. When predicting the stand density and basal area, the combination forecasting equation had the highest accuracy, and the stand level model was the second, and the accuracy of the single tree level model was the lowest. The combined forecasting method can predict the stand density, tree survival, stand basal area and tree basal area. The method improves the prediction accuracy of the model, and provides a reference for the prediction of stand growth, dynamic change of spatial structure and management effect evaluation.
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白桦(Betula platyphylla)作为我国重要的阔叶用材树种，广泛分布于东北、华北、西北及西南高山林区等14个省区[1]，其木质坚硬，质地细白，在家具、建材、造纸等方面具有广泛用途。由于白桦为异花授粉树种，自交不育，基因型高度杂合，因此群体内个体间遗传差异十分明显，主要表现在个体间的干型、生长、适应性等性状各不相同。开展白桦家系多点造林试验，对不同地点间的参试家系进行选择，可最大限度地利用家系间及家系内个体间变异，加速白桦遗传改良进程。
研究团队于1997—2000年间，依据表型性状从帽儿山、草河口、辉南、露水河、汪清、小北湖和东方红等多个种源内筛选出若干株白桦优良单株，将这些优树个体分年度定植于棚式种子园内，建立了白桦初级实生种子园。前期，对园中母树自由授粉的半同胞子代在单一地点的试验结果进行过初步分析[2]，但是这仅为单一试验点的结果且林龄尚小。然而，通过多点试验研究，不仅能够分析各家系在单一地点的生长性状，同时也能够对参试家系进行基因型与环境交互作用的分析，是筛选对不同类型环境具有特殊适应性基因型的必要手段，也是进行优良家系选择及遗传改良的重要方法之一[3-4]。在以往的白桦多点试验研究中，本团队曾就白桦杂交子代2~5年生幼龄林测定数据进行过早期选择与评价[5-7]，但也仅限于幼龄林时期，尚未对成年林分进行跟踪调查。为此，本试验开展12年生自由授粉的半同胞家系多点子代测定研究，在进行优良家系选择的同时对建园母树进行评价，为白桦种子园的改建提供参考。
1. 材料与方法
1.1 试验材料及设计
试验材料为东北林业大学白桦初级实生种子园内53株白桦母树自由授粉的半同胞子代家系。2001年采种，2002年育苗，2003年分别在黑龙江省伊春市朗乡林业局小白林场、吉林省吉林市林业科学研究院实验林场、黑龙江省尚志市帽儿山实验林场营建白桦半同胞家系测定林，3个试验点地理与气候条件见表 1。试验林按照完全随机区组设计，在帽儿山试验点为20株双行排列，在吉林与朗乡2试验点为10株单行排列，株行距2m×2m，3次重复。2015年春分别对3个地点的12年生白桦半同胞子代试验林进行全林树高、胸径调查。
表 1 3个试验点的地理气候条件Table 1. Geographical and climatic conditions of the three test sites序号
No.试验点
Test site纬度
Latitude经度
Longitude年降水量
Annual precipitation/mm年平均温度
Annual average temperature/℃无霜期
Frost-freeseason/d土壤类型
Soil type1 朗乡
Langxiang46°48′N 128°50′E 676.0 1.0 100 永冻暗棕壤
Permafrost dark brown2 帽儿山
Maoershan45°16′N 127°31′E 666.1 2.4 120 暗棕壤
Dark brown3 吉林
Jilin43°40′N 126°40′E 700.0 4.1 135 暗棕壤
Dark brown1.2 数据调查处理
1.2.1 生长性状测量
采用超声波测高仪及塔尺测量树高，采用围尺测量胸径。家系保存率按各试验点内各家系实际保存株数计算。根据白桦的二元材积表公式计算单株材积：V=0.0000051935163D1.8586884H1.0038941[8]。
1.2.2 遗传参数估计
表型变异系数(PCV)采用公式：PCV=σˉX×100%，式中：σ为性状标准差，X为性状平均值[9]。
遗传增益(G)：G=h2SˉX×100%, 式中：h2为性状遗传力，S为入选各优良家系性状平均值与参试家系相应性状平均值的差值, X为参试家系性状平均值。
1.2.3 数据处理
方差分析及多重比较(Duncan)利用SPSS16.0和Microsoft Excel等统计分析软件进行计算。
各试验地点间及试验点内均采用双因素方差分析线性模型进行分析，其模型表达式及各参数含义详见参考文献[6]。
采用南京林业大学林木多地点半同胞子代测定遗传分析R语言程序包以及R软件进行多地点半同胞子代材积育种值BLUP估计。模型建立过程根据童春发[10-11]的方法进行，详见文献[11]。
BLUP的线性混合模型公式为[11]：
yy=XXβ+ZZu+e 式中: y为材积观测值向量，X和Z分别为β和u的相关矩阵，β为固定效应，u为随机遗传效应，e为随机误差效应。
2. 结果与分析
2.1 家系生长性状的多地点联合方差分析及主要遗传参数计算
3个地点联合方差分析(表 2)表明：单株材积、树高性状在地点间和家系间以及地点与家系的交互作用均表现出极显著(P＜0.01)的差异，胸径性状在地点间和家系间也表现出极显著(P＜0.01)的差异；说明不同家系在同一地点内生长差异明显，同一个家系在不同立地条件下的生长表现也各不一致，各地点与家系间存在较为明显的互作效应。
表 2 参试家系生长性状多地点联合方差分析Table 2. Joint variance analysis of growth traits for birch families at different sites生长性状
Growth trait变异来源
Source of variationdf SS MS F P 树高
Height(H)/m地点Site 2 1755.112 877.556 490.323** ＜0.01 地点内区组Site (Block) 6 315.480 52.580 29.378** ＜0.01 家系Family 52 351.766 6.765 3.780** ＜0.01 家系×地点Family×site(G×E) 104 474.421 4.562 2.549** ＜0.01 试验误差Experiment error 4065 7275.337 1.790 总变异Total variance 4230 423725.196 胸径
Diameter at breast height (DBH)/cm地点Site 2 3674.704 1837.352 435.896** ＜0.01 地点内区组Site (Block) 6 283.320 47.220 11.203** ＜0.01 家系Family 52 389.907 7.498 1.779** ＜0.01 家系×地点G×E 104 542.376 5.215 1.237 0.053 试验误差Experiment error 4065 17134.428 4.215 总变异Total variance 4230 366062.640 单株材积Volume(V)/m3 地点Site 2 0.189 0.094 509.010** ＜0.01 地点内区组Site (Block) 6 0.017 0.003 15.243** ＜0.01 家系Family 52 0.025 ＜0.001 2.621** ＜0.01 家系×地点G×E 104 0.029 ＜0.001 1.499** ＜0.01 试验误差Experiment error 4065 0.753 ＜0.001 总变异Total variance 4230 6.436 注: *差异显著，P＜0.05; **差异极显著，P＜0.01。下同。Notes: * means significant difference at P＜0.05 level; ** means extremely significant difference at P＜0.01 level. The same below. 单个地点的方差分析(表 3)表明：树高、胸径以及单株材积在家系间均达到差异显著(P＜0.05)或极显著(P＜0.01)水平，说明不同家系间生长存在明显差别。在3个试验点中，帽儿山试验点的白桦家系树高、胸径和单株材积生长表现最好，均值分别为10.3928m、9.6489cm和0.0408m3，且变异系数较小，分别为11.79%、22.64%和34.80%，说明参试家系在帽儿山试验点不仅生长量最大，而且生长整齐度也较好。吉林试验点的参试家系各性状均值均处于中间，生长变异水平也处于中等。朗乡试验点各性状均值最小，为8.6575m、7.1091cm和0.0226m3，这与当地年均温较低，无霜期较短等气候条件有关。
表 3 不同试验点间参试家系生长性状的遗传参数Table 3. Genetic parameters for growth traits of birch families at different sites试验地点
Test site性状
Growth trait均值
Mean标准差
Standarddeviation变幅
Amplitude ofvariation变异系数
Coefficient of variation/%F P 朗乡
Langxiang树高H/m 8.6575 1.6515 9.19~9.89 19.08 2.349 ** ＜0.01 胸径DBH/cm 7.1091 2.0069 5.90~8.34 28.23 1.446* 0.02 单株材积V/m3 0.0226 0.0119 0.0156~0.0311 52.65 1.650** ＜0.01 帽儿山
Maoershan树高H/m 10.3928 1.2252 9.39~11.30 11.79 7.984** ＜0.01 胸径DBH/cm 9.6489 2.1848 8.67~10.77 22.64 1.868** ＜0.01 单株材积V/m3 0.0408 0.0142 0.0331~0.0499 34.80 3.653** ＜0.01 吉林
Jilin树高H/m 9.7268 1.5534 8.15~11.00 15.97 3.408** ＜0.01 胸径DBH/cm 9.1610 1.9483 7.73~10.21 21.27 2.293** ＜0.01 单株材积V/m3 0.0351 0.0152 0.0231~0.0453 43.30 2.892** ＜0.01 2.2 各试验点参试家系生长性状多重比较及保存率比较
由于家系间各性状均达到显著差异水平(P＜0.05)，进而进行多重比较(表 4)，初步筛选优良家系。将树高、胸径和单株材积分别在各试验点按均值高低排序后发现，由于3个试验点地理环境各有不同，基因型与环境的交互作用明显，所以53个家系在不同试验点生长表现各有差异，因此首先考虑在各试验点内进行单点优良家系初选，然后再进行3试验点间的联合选择。
表 4 各试验地点参试家系生长性状多重比较Table 4. Multiple comparisons of birch H, DBH and V for the tested lines at different sites家系
Family朗乡Langxiang 帽儿山Maoershan 吉林Jilin 树高H/m 胸径DBH/cm 单株材积V/m3 树高H/m 胸径DBH/cm 单株材积V/m3 树高H/m 胸径DBH/cm 单株材积V/m3 B1 9.65 abcd 7.43 abcde 0.0291 ab 10.23 fghijklm 9.40 bcdef 0.0384 defghijkl 9.58 bcdefghijkl 9.28 abcdef 0.0335 bcdefghij B2 7.90 hijk 6.93 abcde 0.0193 bcdefgh 10.28 efghijkl 9.64 abcdef 0.0394 cdefghijkl 8.72 lm 7.73 g 0.0265 jk B3 8.30 defghijk 6.77 abcde 0.0209 abcdefgh 10.41 bcdefghijkl 9.47 bcdef 0.0406 cdefghijk 10.07 abcdefghij 9.50 abcdef 0.0395 abcdef B4 8.86 abcdefghij 7.05 abcde 0.0251 abcdefgh 9.67 nop 8.67 f 0.0331 l 9.56 bcdefghijkl 8.39 cdefg 0.0311 cdefghijk B5 9.53 abcde 7.79 abcd 0.0280 abcd 10.13 hijklmno 9.70 abcdef 0.0382 defghijkl 10.30 abcdef 9.44 abcdef 0.0394 abcdef B6 8.27 efghijk 6.81 abcde 0.0205 bcdefgh 10.34 cdefghijkl 9.27 cdef 0.0383 defghijkl 8.69 lm 9.15 abcdef 0.0278 ijk B7 9.11 abcdefghij 6.68 abcde 0.0230 abcdefgh 9.92 lmno 8.95 ef 0.0354 ijkl 9.24 hijkl 8.25 defg 0.0295 efghijk B8 8.14 fghijk 6.27 cde 0.0172 efgh 10.44 bcdefghijkl 9.15 cdef 0.0390 cdefghijkl 8.15 m 8.43 cdefg 0.0231 k B9 8.28 defghijk 6.05 de 0.0177 defgh 9.91 lmno 9.70 abcdef 0.0366 hijkl 9.83 bcdefghijk 8.58 cdefg 0.0326 cdefghijk B10 8.81 abcdefghij 8.34 a 0.0251 abcdefgh 10.56 bcdefghij 9.60 abcdef 0.0411 cdefghijk 9.77 bcdefghijk 8.82 abcdefg 0.0343 bcdefghij B11 8.29 defghijk 6.75 abcde 0.0221 abcdefgh 10.89 abc 9.50 bcdef 0.0425 bcdefghi 9.57 bcdefghijkl 9.57 abcdef 0.0348 bcdefghij B12 9.09 abcdefghij 6.91 abcde 0.0230 abcdefgh 10.47 bcdefghijkl 9.45 bcdef 0.0404 cdefghijk 9.71 bcdefghijk 8.35 cdefg 0.0321 cdefghijk B13 8.84 abcdefghij 7.09 abcde 0.0221 abcdefgh 10.35 cdefghijkl 9.89 abcde 0.0408 cdefghijk 9.92 bcdefghijk 9.14 abcdef 0.0356 abcdefghij B14 9.15 abcdefghi 7.65 abcde 0.0275 abcdef 10.45 bcdefghijkl 9.88 abcde 0.0415 bcdefghij 9.97 bcdefghijk 9.25 abcdef 0.0366 abcdefghij B15 9.52 abcde 7.50 abcde 0.0277 abcde 10.45 bcdefghijkl 10.47 ab 0.0437 abcdefgh 11.00 a 9.78 abc 0.0453 a B16 8.96 abcdefghij 7.29 abcde 0.0237 abcdefgh 10.94 ab 9.98 abcde 0.0460 abc 10.38 abcde 9.45 abcdef 0.0410 abcd B17 8.77 abcdefghij 8.18 ab 0.0247 abcdefgh 10.21 fghijklm 9.55 bcdef 0.0387 cdefghijkl 9.74 bcdefghijk 10.13 ab 0.0376 abcdefghi B18 9.72 ab 7.55 abcde 0.0284 abc 10.32 defghijkl 9.17 cdef 0.0382 defghijkl 9.74 bcdefghijk 9.36 abcdef 0.0351 abcdefghij B19 9.27 abcdefgh 7.54 abcde 0.0254 abcdefgh 10.42 bcdefghijkl 9.57 bcdef 0.0405 cdefghijk 10.26 abcdefg 9.72 abc 0.0400 abcde B20 8.53 abcdefghij 7.02 abcde 0.0215 abcdefgh 10.10 ijklmno 9.23 cdef 0.0371 fghijkl 9.04 kl 8.47 cdefg 0.0283 hijk B21 8.06 fghijk 7.06 abcde 0.0200 bcdefgh 10.58 bcdefghij 9.51 bcdef 0.0414 bcdefghij 9.05 kl 8.69 bcdefg 0.0292 fghijk B22 9.02 abcdefghij 7.91 abc 0.0262 abcdefg 10.01 jklmno 9.32 bcdef 0.0381 efghijkl 9.32 fghijkl 8.77 abcdefg 0.0302 efghijk B23 8.71 abcdefghij 6.44 bcde 0.0200 bcdefgh 10.23 fghijklm 9.33 bcdef 0.0398 cdefghijkl 9.37 fghijkl 8.63 cdefg 0.0336 bcdefghij B24 8.75 abcdefghij 6.97 abcde 0.0229 abcdefgh 10.09 ijklmno 9.49 bcdef 0.0385 cdefghijkl 9.15 jkl 9.01 abcdefg 0.0300 efghijk B25 7.98 ghijk 6.24 cde 0.0172 fgh 10.25 fghijklm 10.01 abcde 0.0418 bcdefghi 10.09 abcdefghij 9.57 abcdef 0.0385 abcdefgh B26 9.08 abcdefghij 7.77 abcd 0.0251 abcdefgh 9.72 mnop 9.05 def 0.0369 ghijkl 9.13 jkl 9.28 abcdef 0.0350 abcdefghij B27 8.41 bcdefghijk 7.23 abcde 0.0226 abcdefgh 10.32 defghijkl 9.81 abcdef 0.0410 cdefghijk 9.52 cdefghijkl 9.17 abcdef 0.0329 cdefghijk B28 8.77 abcdefghij 6.22 cde 0.0251 abcdefgh 10.07 jklmno 10.10 abcde 0.0407 cdefghijk 10.52 ab 10.10 ab 0.0453 a B29 7.19 k 6.12 cde 0.0161 gh 10.91 abc 9.87 abcde 0.0444 abcdef 9.95 bcdefghijk 9.50 abcdef 0.0374 abcdefghi B30 9.68 abc 6.47 bcde 0.0254 abcdefgh 10.65 bcdefghi 9.58 bcdef 0.0418 bcdefghi 9.73 bcdefghijk 9.28 abcdef 0.0346 bcdefghij B31 8.91 abcdefghij 6.80 abcde 0.0228 abcdefgh 10.40 bcdefghijkl 9.66 abcdef 0.0414 cdefghij 10.39 abcde 9.71 abc 0.0416 abc B32 8.48 bcdefghijk 7.62 abcde 0.0221 abcdefgh 10.38 bcdefghijkl 9.53 bcdef 0.0399 cdefghijkl 9.29 ghijkl 8.70 bcdefg 0.0303 efghijk B33 8.94 abcdefghij 7.66 abcde 0.0258 abcdefgh 10.29 efghijkl 9.19 cdef 0.0387 cdefghijkl 10.00 bcdefghijk 9.70 abcd 0.0390 abcdefg B34 9.89 a 7.88 abcd 0.0311 a 10.87 abcd 10.16 abcd 0.0458 abc 10.50 abc 9.78 abc 0.0414 abc B35 8.30 defghijk 6.93 abcde 0.0206 bcdefgh 10.83 abcde 10.77 a 0.0486 ab 9.70 bcdefghijk 8.75 bcdefg 0.0342 bcdefghij B36 8.08 fghijk 7.04 abcde 0.0189 bcdefgh 10.70 bcdefgh 10.09 abcde 0.0444 abcdef 10.00 bcdefghijk 9.44 abcdef 0.0368 abcdefghij B37 8.25 efghijk 7.49 abcde 0.0214 abcdefgh 10.58 bcdefghij 10.00 abcde 0.0435 abcdefgh 9.87 bcdefghijk 9.28 abcdef 0.0355 abcdefghij B38 8.31 cdefghijk 7.44 abcde 0.0239 abcdefgh 9.61 op 8.96 ef 0.0339 kl 9.27 ghijkl 8.87 abcdefg 0.0313 cdefghijk B39 8.56 abcdefghij 7.58 abcde 0.0226 abcdefgh 10.17 ghijklmn 9.82 abcdef 0.0404 cdefghijk 9.61 bcdefghijkl 8.84 abcdefg 0.0334 bcdefghij B40 7.81 ijk 6.57 abcde 0.0169 gh 11.30 a 10.31 abc 0.0499 a 9.96 bcdefghijk 9.37 abcdef 0.0382 abcdefghi B41 8.12 fghijk 6.91 abcde 0.0199 bcdefgh 10.66 bcdefghi 9.37 bcdef 0.0404 cdefghijk 10.17 abcdefghi 9.34 abcdef 0.0382 abcdefghi B42 8.79 abcdefghij 7.33 abcde 0.0229 abcdefgh 10.91 abc 10.11 abcde 0.0456 abcd 9.96 bcdefghijk 9.75 abc 0.0382 abcdefghi B43 8.73 abcdefghij 7.76 abcd 0.0250 abcdefgh 10.69 bcdefgh 9.50 bcdef 0.0427 bcdefghi 9.83 bcdefghijk 9.36 abcdef 0.0356 abcdefghij B44 7.74 jk 7.11 abcde 0.0185 cdefgh 10.69 bcdefgh 10.04 abcde 0.0442 abcdefg 10.21 abcdefgh 9.61 abcdef 0.0389 abcdefgh B45 9.45 abcdef 7.41 abcde 0.0285 abc 10.69 bcdefgh 10.27 abc 0.0452 abcde 9.50 defghijkl 9.51 abcdef 0.0344 bcdefghij B46 8.93 abcdefghij 7.85 abcd 0.0245 abcdefgh 10.50 bcdefghijk 9.86 abcde 0.0418 bcdefghi 9.48 efghijkl 8.20 efg 0.0300 efghijk B47 8.66 abcdefghij 6.29 cde 0.0196 bcdefgh 9.39 p 9.37 bcdef 0.0342 jkl 9.19 ijkl 8.19 fg 0.0308 defghijk B48 9.33 abcdefg 6.54 abcde 0.0222 abcdefgh 10.73 bcdefg 10.33 abc 0.0452 abcde 9.96 bcdefghijk 9.46 abcdef 0.0364 abcdefghij B49 7.84 ijk 5.90 e 0.0156 h 10.41 bcdefghijkl 9.04 def 0.0384 defghijkl 10.11 abcdefghij 9.39 abcdef 0.0380 abcdefghi B50 8.15 efghijk 6.42 bcde 0.0183 cdefgh 10.55 bcdefghij 10.23 abcd 0.0436 abcdefgh 10.06 bcdefghij 9.66 abcde 0.0389 abcdefgh B51 8.96 abcdefghij 7.94 abc 0.0248 abcdefgh 10.45 bcdefghijkl 9.61 abcdef 0.0413 cdefghij 10.48 abcd 10.21 a 0.0439 ab B52 8.18 efghijk 7.14 abcde 0.0195 bcdefgh 9.97 klmno 9.20 cdef 0.0354 ijkl 9.06 kl 8.52 cdefg 0.0284 ghijk B53 7.83 ijk 7.13 abcde 0.0184 cdefgh 10.75 bcdef 9.67 abcdef 0.0427 bcdefghi 9.86 bcdefghijk 9.13 abcdefg 0.0352 abcdefghij 注：表中不同字母表示在P < 0.05水平上差异显著。Note: different letters mean significant difference at P < 0.05 level. 在朗乡试验点，若以各性状均值加上0.2倍标准差为选择条件，则3个性状均高于选择标准的有：B5、B14、B15、B18、B19、B22、B26和B34家系，这8个家系为生长性状最优家系，其树高、胸径和单株材积均值分别为：9.40m、7.70cm和0.0274m3, 分别高于参试家系均值的8.54%、8.30%和21.49%，仅有2个生长性状高于选择标准的有：B1、B10、B33、B43和B45家系，为生长良好家系，其树高、胸径和单株材积均值分别为：9.12m、7.72cm和0.0267m3。根据多重比较结果，朗乡试验点初步选择这13个家系为优良家系，入选率为24.53%。依据上述选择标准，在帽儿山试验点生长最优家系为B34、B35、B36、B40、B42、B45和B48，这7个家系的树高、胸径和单株材积均值为：10.86m、10.29cm、0.0464m3，分别高于参试家系均值的4.51%、6.66%和13.76%，较好家系为B15、B16、B29和B44，其树高、胸径和单株材积均值为：10.75m、10.09cm和0.0446m3，因此，这11个家系入选为帽儿山试验点的优良家系，入选率为20.75%。同样选择标准，在吉林试验点选择B15、B19、B25、B28、B31、B34、B44、B50、B51、B3、B5、B16、B33、B41和B42等15个家系为优良家系，入选率为28.30%。
进而对3个试验地点的选优结果进行比较发现：B34、B15家系在3个地点均入选为优良家系，说明这2个家系在各试验地不仅生长表现较为优异，而且生长稳定性也良好，是参试家系中的最优家系。另外，入选的优良家系中有些家系仅在2个地点表现良好，如在朗乡与吉林2试验点生长良好的是B5、B19和B33家系；在帽儿山与吉林2试验点均表现较好的是B16、B42和B44家系；在朗乡与帽儿山2试验点表现较好的是B45家系，说明这些家系虽然生长表现优良，但适应能力略低于B34、B15这2个最优家系。其余优良家系仅在其所入选地点内表现优良，说明这些家系由于基因型与环境交互作用的差异而导致的适应范围各有不同，所以仅在适宜其生长的地点表现良好。
参试的53个白桦家系在各试验点平均保存率不尽相同(表 5)。3个地点中吉林试验点的各家系保存率最好，53个家系保存率均值为69.75%，有12个家系的保存率大于80.00%，其中B9家系保存率高达96.67%，B8家系保存率最低，仅为43.33%；帽儿山试验点53个家系保存率均值为60.40%，其中保存率最高的是B14家系，为94.29%, 保存率最低的是B3家系，仅为38.57%；朗乡试验点参试家系保存率均值为54.34%，B35和B25家系的保存率最高，为90.00%，B4、B50等2个家系次之，其他49个家系的保存率均在80.00%以下，B53、B51家系保存率最低，仅为23.33%。
表 5 各试验地点参试家系保存率Table 5. Preservation rate for the tested families at different sites参试家系
Tested family保存率Preservation rate/% 3个地点保存率均值
Average preservation rate at three sites/%朗乡
Langxiang帽儿山
Maoershan吉林
JilinB1 40.00 55.71 63.33 53.01 B2 30.00 61.43 60.00 50.48 B3 66.67 38.57 46.67 50.64 B4 83.33 51.43 83.33 72.70 B5 73.33 45.71 76.67 65.24 B6 56.67 58.57 53.33 56.19 B7 33.33 62.86 70.00 55.40 B8 63.33 62.86 43.33 56.51 B9 40.00 50.00 96.67 62.22 B10 60.00 65.71 73.33 66.35 B11 26.67 62.86 76.67 55.40 B12 70.00 68.57 80.00 72.86 B13 66.67 68.57 83.33 72.86 B14 43.33 94.29 53.33 63.65 B15 30.00 50.00 53.33 44.44 B16 50.00 65.71 70.00 61.90 B17 40.00 65.71 76.67 60.79 B18 70.00 60.00 76.67 68.89 B19 76.67 51.43 63.33 63.81 B20 76.67 65.71 76.67 73.02 B21 73.33 61.43 66.67 67.14 B22 56.67 64.29 73.33 64.76 B23 33.33 54.29 90.00 59.21 B24 50.00 57.14 66.67 57.94 B25 90.00 55.71 76.67 74.13 B26 50.00 57.14 50.00 52.38 B27 50.00 60.00 70.00 60.00 B28 30.00 57.14 70.00 52.38 B29 36.67 70.00 70.00 58.89 B30 53.33 71.43 86.67 70.48 B31 36.67 65.71 60.00 54.13 B32 56.67 67.14 80.00 67.94 B33 63.33 54.29 76.67 64.76 B34 56.67 60.00 73.33 63.33 B35 90.00 67.14 66.67 74.60 B36 53.33 61.43 83.33 66.03 B37 53.33 68.57 76.67 66.19 B38 46.67 44.29 50.00 46.99 B39 63.33 50.00 60.00 57.78 B40 66.67 75.71 83.33 75.24 B41 70.00 70.00 80.00 73.33 B42 40.00 71.43 86.67 66.03 B43 70.00 70.00 76.67 72.22 B44 36.67 61.43 80.00 59.37 B45 60.00 58.57 46.67 55.08 B46 66.67 64.29 76.67 69.21 B47 53.33 44.29 70.00 55.87 B48 63.33 62.86 73.33 66.51 B49 46.67 40.00 60.00 48.89 B50 86.67 55.71 60.00 67.46 B51 23.33 60.00 76.67 53.33 B52 33.33 57.14 56.67 49.05 B53 23.33 57.14 46.67 42.38 2.3 参试家系材积性状育种值估算及优良家系选择
上述针对各试验点各家系间的树高、胸径和单株材积等3个性状单独进行了方差分析、多重比较及各试验点的优良家系初步筛选。但优良家系的评定往往应考虑多个地点的综合表现，考虑到材积是公认的反映立地质量的林木生长主要性状，并且是能够综合体现树高性状与胸径性状的高低最直接的指标。因此，在本研究中选择BLUP模型利用各家系在3个试验点的单株材积数据进行育种值估算，进而进行家系的评价和选择(表 6)。
表 6 参试家系材积性状育种值Table 6. Breeding value for volume of birch families综合排名
Comprehensive ranking家系
Family育种值
Breeding value标准误
Standard error1 B34 0.009487 0.408866 2 B15 0.008838 0.400508 3 B28 0.007473 0.404450 4 B16 0.006786 0.408455 5 B51 0.005843 0.403728 6 B40 0.005191 0.411808 7 B42 0.005067 0.408921 8 B45 0.004931 0.406538 9 B48 0.003846 0.409883 10 B35 0.003845 0.411074 11 B19 0.002876 0.408067 12 B31 0.002838 0.405394 13 B5 0.002812 0.409427 14 B43 0.002792 0.411366 15 B14 0.002778 0.410816 16 B44 0.002584 0.407243 17 B36 0.002060 0.409832 18 B29 0.001729 0.407011 19 B33 0.001726 0.409499 20 B11 0.001424 0.404868 21 B37 0.001349 0.409699 22 B17 0.001340 0.407742 23 B30 0.001311 0.410246 24 B18 0.001297 0.410728 25 B10 0.001276 0.409895 26 B50 0.001214 0.409561 27 B41 0.000381 0.411618 28 B3 0.000183 0.403408 29 B26 0.000130 0.405231 30 B13 -0.000096 0.410798 31 B53 -0.000154 0.399256 32 B1 -0.000505 0.405265 33 B46 -0.001507 0.410566 34 B25 -0.001666 0.411684 35 B39 -0.001780 0.407691 36 B12 -0.002024 0.411479 37 B22 -0.002113 0.409472 38 B23 -0.002169 0.405577 39 B27 -0.002352 0.407904 40 B32 -0.003134 0.410325 41 B24 -0.003471 0.407761 42 B49 -0.003577 0.402874 43 B21 -0.004966 0.409794 44 B20 -0.005170 0.411443 45 B7 -0.005506 0.405812 46 B38 -0.005755 0.403724 47 B6 -0.005835 0.406911 48 B9 -0.005966 0.407067 49 B4 -0.005967 0.410607 50 B2 -0.006776 0.403709 51 B47 -0.007239 0.407103 52 B52 -0.007793 0.403611 53 B8 -0.007885 0.406856 由育种值的结果可以看出，与前文多重比较选择的结果基本一致，综合排名在第1位的是B34家系，第2位的是B15家系，B28、B16、B51、B40、B42、B45、B48、B35、B19等家系次之。若以20.00%入选率为选择标准，则以上排名前11位的家系入选为优良家系，入选的优良家系材积均值分别较朗乡、帽儿山和吉林等3个地点的参试家系均值高8.29%、9.80%和13.60%，材积性状在3个地点的遗传增益分别为3.23%、7.16%和8.84%。
3. 结论与讨论
研究基因型与环境交互作用效应对林木遗传改良具有重要意义[12-13]。对3个参试地点的白桦家系生长性状遗传变异分析显示，位于小兴安岭朗乡试验点参试的白桦家系生长量明显低于另外2个试验点，但各性状的变异系数却普遍偏高。这与该试验点所处的地理位置以及特殊的气候环境密切相关，朗乡试验点位于纬度较高的小兴安岭地区，无霜期短，年均温与≥10℃年积温均较低，而参试的大部分家系原产地均处于纬度较低的张广才岭与长白山地区，原产地与造林地环境差异较大，导致参试白桦家系间产生较大分化，有部分家系生长较好，而大多数家系则长势较弱。从而导致了在朗乡试验点定植的家系各性状生长量较低，并且变异系数较高。但这也为抗逆性家系的选择提供了可能，在较恶劣环境条件下依然能保持稳定的生产力以及较高保存率的家系必然是首选，如B5、B19等家系在朗乡试验点生长性状均排在前列并且保存率均高于70.00%。另外2个试验点环境条件虽较朗乡试验点优越但家系生长依然各有差异，因此，分别依据参试家系在各试验点的生长表现，利用多重比较的结果在各试验点内进行了优良家系的初选。
早期选择可靠性及选择年龄的确定等问题一直以来都备受国内外同行关注。但是，越来越多的试验分析表明林木早期选择具有较高的可信度。如油松(Pinus tabulaeformis)、马尾松(P. massoniana)等树种的育种实践证明对生长期达1/4~1/2轮伐期的林分即可进行早期选择，并且早期选择的效率更高[14]。白桦人工林的主伐年龄为31~41年生[15]，本项研究所选取的对象为12年生白桦半同胞家系子代测定林，其林龄已达1/3轮伐期，因此，对其进行早期选择应该具有较高准确性。
对于多点造林试验，由于待测群体数量庞大，加之各造林点间的地理气候环境不尽相同，试验林的保存率也各不相同，导致观测数据复杂多样，给遗传评价和选择带来相当难度[16-17]。而育种值的估算恰恰能克服这一问题，它能体现表型值中遗传效应的加性效应部分，对群体规模大、结构复杂的不平衡数据进行统计分析时，能有效地剔除各种非遗传因素的影响，因而具有较高的选择准确性，已被广泛应用于马尾松、火炬松(Pinus taeda)、尾叶桉(Eucalyptus urophylla)等多个树种的选择中，是一种较理想的综合评价方法[18-20]。本研究采用BLUP最佳线性无偏预测模型参试家系进行多地点材积育种值估算，依据育种值高低对参试家系进行综合评价，以20.00%入选率为标准选择育种值排名前11位的家系为优良家系。同时，基于各地点白桦半同胞子代测定林生长表现分析结果，建议种子园改建时B34和B15这2个家系的采种母树为首选保留母树，B28、B16、B51、B40、B42、B45、B48、B35、B19这9个家系的采种母树为备选母树。
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图 1 不同水平最优模型残差分布
M4、M7、M9分别代表林分密度、林分断面积和单木断面积预测模型，即对应文中的公式(4)、(7)和(9)。
Figure 1. Residual distribution of different level optimal models
M4, M7, M9 represent prediction models of stand density, basal area for stand, basal area models for individual trees, which corresponding to formula (4), (7) and (9) of the paper, respectively.
表 1 建模数据与检验数据统计
Table 1 Summary statistics for modeling and validation data sets
数据
Data变量
Variable2011年调查Inventory in 2011 2016年调查Inventory in 2016 最小值
Min.最大值
Max.均值
Mean标准差
SD最小值
Min.最大值
Max.均值
Mean标准差
SD建模数据Modelling data(n=70) 林分年龄Stand age 13 42 31.5 10.22 18 47 37.0 9.21 胸径Diameter at breast height(DBH)/cm 6.27 28.02 17.17 5.61 9.06 31.52 19.45 6.13 平均高Mean height/m 4.71 16.34 11.04 2.33 6.54 19.02 12.84 2.97 林分密度/(株·hm-2)Stand density/(tree·ha-1) 900.0 3 353.0 1 927.7 958.4 500.0 2 282.0 1 295.6 611.2 林分断面积/(m2·hm-2)Stand basal area/(m2·ha-1) 8.82 67.43 36.45 12.07 11.51 90.31 42.71 17.38 立地质量Site index/m 4.66 16.81 12.36 2.91 7.06 18.56 14.14 3.43 生存概率Survival probability/% 0.35 1.00 0.77 0.17 检验数据Validation data(n=35) 林分年龄Stand age 13 40 33.5 10.43 18 47 38.0 9.46 胸径Diameter at breast height(DBH)/cm 6.87 29.11 17.58 5.07 9.12 32.42 20.24 5.97 平均高Mean height/m 5.11 17.23 11.80 2.04 7.05 18.92 13.27 3.09 林分密度/(株·hm-2)Stand density/(tree·ha-1) 900.0 3 178.0 1 802.7 907.8 500.0 2 077.0 1 226.7 578.4 林分断面积/(m2·hm-2)Stand basal area/(m2·ha-1) 9.02 70.58 37.09 12.54 10.97 85.66 45.07 15.06 立地质量Site index/m 5.24 16.33 13.11 3.13 6.98 19.24 15.37 3.55 生存概率Survival probability/% 0.41 1.00 0.74 0.19 注：n为样本数。Note：n is sample number. 
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表 2 不同水平模型参数估计与统计检验
Table 2 Parameter estimating and goodness-of-fit statistics in different levels
模型Model 参数Parameter 估计值Estimate SE R2 Bias RMSE M4 a1 0.005 1 0.003 5 0.900 2 1.952 5 2.186 3 a2 0.406 5 0.399 5 a3 1.271 3 0.526 7 M5 a1 -0.405 8 0.095 4 0.804 3 2.005 6 2.334 2 a2 -0.738 7 0.415 8 a3 -0.045 2 0.009 0 M6 b1 -0.000 8 0.000 3 0.812 3 1.280 9 3.155 0 b2 7.143 8 2.056 7 b3 3.222 4 0.684 5 M7 b1 24.978 6 1.529 1 0.914 4 0.899 7 1.833 4 b2 1.215 3 0.191 7 b3 0.799 2 0.040 5 M8 b1 0.999 3 0.000 8 0.867 1 1.008 4 2.304 1 b2 0.000 5 0.000 3 b3 -2.853 6 0.677 6 M9 c0 0.011 2 0.002 3 0.913 2 0.097 5 0.918 7 c1 -4.284 3 0.163 3 c2 4.396 3 0.151 7 c3 -24.096 1 2.385 7 M10 c0 0.000 2 0.000 1 0.908 8 0.105 8 1.007 6 c1 0.756 7 0.111 3 c2 -0.528 1 0.262 4 c3 1.093 0 0.081 3 c4 -0.042 2 0.012 1 注：M4~M10对应文中公式(4)~(10)。Note: M4-M10 correspond to formula (4)-(10) of the paper, respectively.
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表 3 不同水平生存概率模型参数估计与统计检验
Table 3 Parameter estimating and goodness-of-fit statistics in different levels of survival probability
模型Model 参数Parameter 估计值Estimate SE R2 Bias RMSE M11 f0 -3.294 0 0.780 4 0.910 4 1.022 4 2.077 1 f1 0.000 5 0.000 3 f2 0.009 2 0.002 9 f3 24.111 6 17.138 5 M12 f0 -3.663 0 0.616 0 0.904 6 1.075 8 2.332 4 f1 11.015 1 4.372 4 f2 0.036 0 0.007 8 f3 0.007 9 0.002 3 注：M11、M12对应文中公式(11)、(12)。Note: M11，M12 correspond to formula (11)，(12) of the paper, respectively.
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表 4 林分、单株生长模型与组合方程预测林分变量评价
Table 4 Evaluation statistics for predicted stand variables from the stand and individual-tree growth models and forecast combination
变量
Variable每公顷株数预测Predicted tree number per ha 林分断面积预测Predicted stand basal area RMSE RRMSE MAD RMSE RRMSE MAD 林分生长Stand growth 305.739 4 7.15 1.933 8 2.054 7 8.44 0.880 1 单木生长Individual tree growth 364.008 7 13.15 2.406 1 2.931 6 15.66 0.973 4 组合预测Combination forecast 284.446 3 5.42 1.603 2 1.664 2 -5.61 0.791 6
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