How To Calculate Standard Error Of Heritability
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variances of the components. Consider an example sent by another user for a bivariate analysis of a repeated trait so there is genetic variance and betweed and within animals. The variance components reported in the .asr file were Source Model terms Gamma Component Comp/SE % C Residual UnStruct 1 1.26730 1.26730 108.05 0 P Residual UnStruct 1 0.610439 0.610439 33.58 0 P Residual UnStruct 2 4.77802 4.77802 110.16 0 P Residual UnStruct 1 0.394353E-01 0.394353E-01 3.88 0 P Residual UnStruct 2 -0.274366 -0.274366 -12.47 0 P Residual UnStruct 3 1.84899 1.84899 108.08 0 P Trait.id UnStruct 1 http://www.ncbi.nlm.nih.gov/pubmed/5087357 0.303319E-01 0.303319E-01 4.05 0 P Trait.id UnStruct 1 0.277637E-01 0.277637E-01 2.50 0 P Trait.id UnStruct 2 0.158267 0.158267 5.25 0 P Trait.id UnStruct 1 0.349000E-02 0.349000E-02 0.27 0 P Trait.id UnStruct 2 -0.905091E-01 -0.905091E-01 -3.51 0 P Trait.id UnStruct 3 0.417714 0.417714 10.82 0 P Trait.ide(id) UnStruct 1 0.562876E-01 0.562876E-01 6.72 0 P Trait.ide(id) UnStruct 1 0.248613E-01 0.248613E-01 2.08 0 P Trait.ide(id) UnStruct 2 0.242284 0.242284 7.56 0 http://www.cargovale.com.au/ASReml/seherit.htm P Trait.ide(id) UnStruct 1 -0.735900E-02 -0.735900E-02 -0.70 0 P Trait.ide(id) UnStruct 2 -0.439076E-01 -0.439076E-01 -2.13 0 P Trait.ide(id) UnStruct 3 0.224123 0.224123 8.64 0 P Covariance/Variance/Correlation Matrix UnStructured 1.267 0.2481 0.2576E-01 0.6104 4.778 -0.9231E-01 0.3944E-01-0.2744 1.849 Covariance/Variance/Correlation Matrix UnStructured 0.3033E-01 0.4007 0.3101E-01 0.2776E-01 0.1583 -0.3520 0.3490E-02-0.9051E-01 0.4177 Covariance/Variance/Correlation Matrix UnStructured 0.5629E-01 0.2129 -0.6552E-01 0.2486E-01 0.2423 -0.1884 -0.7359E-02-0.4391E-01 0.2241 The variance matrix for these 18 parameters is printed in the .vvp file. This variance matrix is simply the inverse of the Average Information matrix. To calculate the heritability for the first trait, we first need the phenotypic variance. This is produced in the .pvc file by ASReml using a .pin file containing F Phen 1 7 13 H H2a 7 19 The components are for the first trait are 1 Residual 1.26730 7 Trait.id 0.303319E-01 13 Trait.ide(id) 0.562876E-01 The SUM is 1.35392. The variances for the components (from rows 1, 7 and 13 of the vvp file are) 0.137567E-03 0.265106E-06 0.561911E-04 -0.278960E-04 -0.381871E-04 0.700629E-04 Making it square and adjusting the power 1.375670E-04 0.002651E-04 -0.278960E-04 0.002651E-04 0.561911E-04 -0.381871E-04 -0.278960E-04 -0.381871E-04 0.700629E-04 Now to calculate the heritability, we must first compute the phenotypic variance (the sum of the three
to the concepts in the particular subject fields and will require an understanding of both statistics and the concerned disciplines to fully appreciate their implications. Some of these topics are briefly covered in what follows. It may be noted http://www.fao.org/docrep/003/x6831e/x6831e13.htm that quite many developments have taken place in each of the topics mentioned below and what is reported here forms only a basic set in this respect. The reader is prompted to make further reading wherever required so as to get a better understanding of the variations possible with respect to data structure or in the form of analysis in such cases. 6.1 Genetics and plant breeding 6.1.1. Estimation of heritability and how to genetic gain The observed variation in a group of individuals is partly composed of genetic or heritable variation and partly of non-heritable variation. The fraction of total variation which is heritable is termed the coefficient of heritability in the broad sense. The genotypic variation itself can be sub-divided into additive and nonadditive genetic variance. The ratio of additive genetic variance to the total phenotypic variance is called the coefficient of heritability in the narrow how to calculate sense and is designated by h2. Thus, Conceptually, genetic gain or genetic improvement per generation is the increase in productivity following a change in the gene frequency induced mostly by selection. Heritability and genetic gain can be estimated in either of two ways. The most direct estimates are derived from the relation between parents and offspring, obtained by measuring the parents, growing the offspring, and measuring the offspring. The other way is to establish a half-sib or full-sib progeny test, conduct an analysis of variance and compute heritability as a function of the variances. Understanding the theoretical part in this context requires a thorough knowledge of statistics. Formulae given below in this section are intended only as handy references. Also, there is no attempt made to cover the numerous possible variations that might result from irregularities in design. Half-sib progeny test is used for illustration as it is easier to establish and so more common in forestry. Both heritability and gain estimates apply strictly only to the experiments from which they are obtained. They may be and frequently are very different when obtained from slightly different experiments. Therefore when quoting them, it is desirable to include pertinent details of experimental design and calculation procedures. Also, it is good practice to state the statistical reliability of each heritability e
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