F phenvar 1 + 2 # pheno var F genvar 1 * 4 # geno var H herit 4 3 # heritabilityThe .pin file specifies the functions to be calculated. The user re-runs ASReml with the -P command line option specifying the .pin file as the input file. ASReml reads the model information from the .asr and .vvp files and calculates the requested functions. These are reported in the .pvc file.

where

F

can be used, as in the Coopworth data example, see UserGuide. For example, after fitting a model like

ywt ~ mu sex age !r sire

ASReml will have estimated two variance components, Sire and Residual respectively. To calculate heritability, the .pin file is

F phenvar 1 + 2 # pheno var F genvar 1 * 4 # geno var H herit 4 3 # heritabilityF phenvar 1 + 2 gives a third component which is the sum of the variance components, that is, the phenotypic variance, and

F genvar 1 * 4 gives a fourth component which is the sire variance component multiplied by 4, that is, the genotypic variance.

H

This calculates v

H herit 4 3

calculates the heritability as the ratio of component 4 (from second line of .pin) to component 3 (from first line of .pin), that is, genetic variance / phenotypic variance.

R

This calculates the correlation r = v

R

calculates all the correlations in the lower triangular row-wise matrix represented by components

For example, after fitting a trivariate sire model gfw fd lwt ~ Trait Tr.sex !r Tr.sire, the Residual matrix is in positions 1:6 and the Sire matrix is in positions 7:12. A .pin file is

F phenvar 1:6 + 7:12 # defines 13:18 F addvar 7:12*4 # defines 19:24 H heritgfw 19 13 H heritfd 21 15 H heritlwt 24 18 R phencorrAB 13 14 15 R phencorrAC 13 16 18 R phencorrBC 15 17 18 R gencorr 7:12In the example

R phencorrAB 13 14 15

calculates the phenotypic correlation for the first two traits from components 13, 14 and 15, and

R gencorr 7:12

calculates the set of three genetic correlations.

Bivariate sire model sire !I ywt fat bsiremod.asd ywt fat ~ Trait !r Trait.sire 1 2 1 0 # ASReml will count units Trait 0 US 3*0 Trait.sire 2 Trait 0 US 3*0 sirewhich estimates six variance components

Source Model terms Gamma Component Comp/SE % C Residual UnStruct 1 26.2197 26.2197 18.01 0 U Residual UnStruct 1 2.85090 2.85090 9.55 0 U Residual UnStruct 2 1.71556 1.71556 18.00 0 U Tr.sire UnStruct 1 16.5262 16.5262 2.69 0 U Tr.sire UnStruct 1 1.14422 1.14422 1.94 0 U Tr.sire UnStruct 2 0.132847 0.132847 1.88 0 UA .pin file to calculate heritabilities and correlations is

F phenvar 1:3 + 4:6 F addvar 4:6 * 4 H heritA 10 7 H heritB 12 9 R phencorr 7 8 9 R gencorr 4:6Labelling the initial six components

V1 | error variance for ywt |

V2 | error covariance for ywt and fat |

V3 | error variance for fat |

V4 | sire variance component for ywt |

V5 | sire covariance for ywt and fat |

V6 | sire variance for fat |

V7 | phenotypic variance for ywt |

V8 | phenotypic covariance for ywt and fat |

V9 | phenotypic variance for fat |

V10 | additive genetic variance for ywt |

V11 | additive genetic covariance for ywt and fat |

V12 | additive genetic variance for fat |

H heritB 12 9 calculates the heritabilty for fat

R phencorr 7 8 9 calculates the phenotypic correlation

R gencorr 4:6 calculates the genetic correlation

The result is:

7 phenvar 1 42.75 6.297 8 phenvar 2 3.995 0.6761 9 phenvar 3 1.848 0.1183 10 addvar 4 66.10 24.58 11 addvar 5 4.577 2.354 12 addvar 6 0.5314 0.2831 h2ywt = addvar 10/phenvar 7= 1.5465 0.3574 h2fat = addvar 12/phenvar 9= 0.2875 0.1430 phencorr = phenvar /SQR[phenvar *phenvar ]= 0.4495 0.0483 gencor 2 1 = Tr.si 5/SQR[Tr.si 4*Tr.si 6]= 0.7722 0.1537