家系模型之Echidna篇

大家好，欢迎来到IT知识分享网。

家系模型，也称为亲本模型，是遗传评估的经典模型，常用于优良家系的选择和优良亲本的评估。家系分为半同胞家系和全同胞家系，前者可来自种源试验或自由授粉设计，后者多数来自析因交配、双列交配、巢式交配等设计。

1 示例数据

示例数据Pine_provenance.csv共有4个种源，36个半同胞家系。田间试验设计为随机完全区组设计，5个区组，每个小区测量2~6株。

2 统计模型

对于种源-家系试验，典型的统计模型如下：

$$y_{ijkl}=\mu +P_j+F_{k(j)}+B_i+B{F}_{ik(j)}+{\epsilon }_{ijkl}.$$

3 分析代码

程序代码(.es)如下：

!RXL !WORKSPACE 2 !OUT !RE !ARG 1 Title: Pine_provenance. #treeid,female,male,prov,block,plot,height,diameter,volume Treeid !I Female !I Male * Prov !I Block * Plot * height diameter volume !*10 Provenance.csv !SKIP 1 !SLN !YHT !DDF 1 !MAXIT 20 !DOPART $1 !PART 1 height ~ mu Prov !f mv, # Specify fixed model !r Female*Block # Specify random model residual units PREDICT Prov Female !present Prov Female VPREDICT F Pheno Female + Female.Block + Residual # sum of variances F Additive Female*4 # Multiply component by 4 H h2i Additive Pheno # Heritability 

4 主结果

程序运行的主结果文件(.esr)如下:

... Summary of 914 data records Variable Levels Miss Zero Min Max Distribution or Mn SD Sk Kt Treeid 914 0 0 1 914 Male 2 0 914 0 0 Female 36 0 0 1 36 Prov 4 0 0 1 4 77 267 306 264 Block 5 0 0 1 5 192 187 188 179 168 Plot 240 0 0 1 240 height 1 0 0 4.00 15.20 10.48 1.79 -0.40 0.21 diameter 1 0 0 5.00 31.20 18.31 4.40 -0.24 -0.13 volume 1 0 0 0.03000 4.29300 1.18093 0.66110 0.74 0.71 * This job may use 8 processor cores. * 1 LogL= -935.00 2.477 910 DF 2 LogL= -934.25 2.502 910 DF 3 LogL= -934.12 2.529 910 DF 4 LogL= -934.12 2.527 910 DF 5 LogL= -934.12 2.527 910 DF ... Akaike Information Criterion 1876.24 (assuming 4 parameters). Bayesian Information Criterion 1895.50 Analysis of height Wald F statistics Source of Variation NumDF DenDF F-inc P-inc mu 1 3566.99 Prov 3 10.01 Model_Term Order Gamma Sigma Z_ratio %C Block 5 0.E-01 0. 1.20 0 P Female 36 0.E-01 0. 2.26 0 P Female.Block 180 0.E-01 0. 2.29 0 P Residual_units 914 1.00000 2.52703 19.22 mv 0 effects fitted. Block 5 effects fitted. Female 36 effects fitted. Female.Block 180 effects fitted. Warning: If job runs slow, see if !EQN 2 or !EQN 3 is faster. Finished: Sat Feb 29 10:45:37 2020 LogL Converged prov.HS1/prov.HS 

5 遗传力计算

.evp文件里含有遗传力的计算结果，具体如下：

 Warning: The analysis was performed on the GAMMA scale. Check all parameters have been converted to the Sigma scale. 1 Residual 2.5270 0.13147 2 Block 0.10749 0.89924E-01 3 Female 0.18950 0.83980E-01 4 Female.Block 0.19762 0.86236E-01 F Pheno Female + Female.Block + Residual 5 Pheno 2.9141 0.14791 F Additive Female*4 6 Additive 0.75801 0.33592 H h2i Additive Pheno h2i = Additive 6/Pheno 5 = 0.26011 0.11018 Notice: The parameter estimates are followed by their approximate standard errors. 

6 模型效应值

此模型估计的种源效应值如下：

Model_Term, Class, Solution, StndError Prov, 10, 0.0 , 0.0 Prov, 11, -1., 0. Prov, 12, -0., 0. Prov, 13, -1., 0. mu, 1, 11., 0. 

模型估算的母本一般配合力或者家系效应值在.ess文件里，部分结果如下：

Model_Term, Class, Solution, StndError Female, 170, -0., 0. Female, 191, -0.0, 0. Female, 192, 0., 0. Female, 196, -0., 0. Female, 197, 0., 0. Female, 198, -0., 0. Female, 200, 0., 0. Female, 201, -0., 0. Female, 202, -0.0, 0. ... 

7 模型预测

与ASReml类似，Echidna也可进行模型项的预测，本例中，部分的家系预测值(.epv)如下:

 Predicted values of height Notice: Some PREDICT qualifier combinations may not work properly. ---- ---- ---- ---- 1 ---- ---- ---- ---- Block is ignored. Predicted_Value Stnd_Error Ecode Prov Female 11.42950 0.33923 E 10 191 11.75801 0.34975 E 10 192 9.38584 0.33593 E 11 196 10.20207 0.32912 E 11 197 9.39586 0.32880 E 11 198 10.11352 0.33504 E 11 200 9.65586 0.33591 E 11 201 9.81746 0.32424 E 11 202 10.23119 0.33101 E 11 203 10.13957 0.32423 E 11 204 9.76929 0.33423 E 11 205 9.89575 0.33136 E 11 206 9.70434 0.32851 E 11 207 10.52994 0.32528 E 12 210 10.87955 0.32769 E 12 211 ... 

与ASreml相比，Echidna的predict功能还不够稳定。