Half-sib analysis - Animal model

Introduction

In this section we will illustrate the use of .ped files to define the genetic pedigree structure between animals. This is an alternate method of estimating additive genetic variance for these data. The variance matrix of the animals (sires, dams and lambs) for which we only have data on lambs is given by Var(u_A) = Σ_A ⊗ A^-1 where A^-1 is the inverse of the genetic relationship matrix. There are a total of 10696 (= 92 rams + 3561 ewes + 7043 lambs) animals in the pedigree. The ASReml input file is presented below. Note that this model is not equivalent to the sire/dam/litter model with respect to the animal/litter components for gfw, fd and fat.

  !CONTINUE    !RENAME !ARG 1 2   //  !DOPATH $1
  Multivariate Animal model
   tag  !P
   sire
   dam  !P
   grp    49
   sex
   brr     4
   litter 4871
   age       wwt   !m0 ywt   !m0    # !M0 identifies missing values
   gfw   !m0 fdm   !m0 fat   !m0
 coop.fmt  # read pedigree from first three fields
 coop.fmt   !MAXIT 20 !STEP 0.01
  !EXTRA 4     #  Force 4 more iterations after convergence criterion met
 !SUBSET DamTr Trait 1 2 3 0 0
 !SUBSET LitTr Trait 1 2 3 4
 wwt ywt gfw fdm fat ~ Trait Tr.age Tr.brr Tr.sex Tr.age.sex,
    !r at(Trait,1,2,4,5).age.grp   at(Trait,1,2,3,5).sex.grp  ,
 !PATH 1 // !r  xfa1(Tr).nrm(tag) xfa1(DamTr).dam xfa1(LitTr).lit  +
 !PATH 2 // !r  us(Tr).nrm(tag) xfa1(DamTr).dam us(LitTr).lit  +
 !PATH 0 //  !f Tr.grp
units.us(Trait)

The term us(Tr).tag now replaces the sire (and part of dam) terms in the half-sib analysis. This analysis uses information from both sires and dams to estimate additive genetic variance. The dam variance component is this analysis only estimates the maternal variance component. It is only significant for the weaning and yearling weights. The litter variation remains unchanged. The ASReml input file again consists of two parts, which build up to fitting unstructured variance models to Tr.tag, Tr.litter and error. We leave the Dam term as XFA1 since the correlations are all 1. A portion of the output file is

    tag  !P
    dam  !P
    age       wwt   !m0 ywt   !m0
    gfw   !m0 fdm   !m0 fat   !m0
 Reading pedigree file pcoop.fmt: skipping            0  lines
   10696 identities in the pedigree over 1 generations.
       For first parent labelled Sire, second labelled  Dam
     Sire Sire of Sire  Dam of Sire      Dam  Sire of Dam   Dam of Dam
       92            0            0     3561            0            0
 Using an adapted version of  Meuwissen  Luo GSE 1992 305-313:
 PEDIGREE [pcoop.fmt ] has    10696 identities,   29474 Non zero elements
 GIV0  NRM            10696       7    -4881.84
 QUALIFIERS: !MAXIT 20 !STEP 0.01
 QUALIFIERS: !EXTRA 4
 QUALIFIERS: !SUBSET DamTr Trait 1 2 3 0 0
 QUALIFIERS: !SUBSET LitTr Trait 1 2 3 4 0
 Notice: !SUBGROUP/!SUBSET list for LitTr is longer than declared size of Trait
 QUALIFIER: !DOPART    1 is active
 Reading coop.fmt  FREE FORMAT skipping     0 lines

 Multivariate analysis of wwt            ywt            gfw            fdm

 Multivariate analysis of fat
 Summary of 7040 records retained of 7043 read
 Notice: 3 records dropped because all traits are missing.

  Model term          Size #miss #zero   MinNon0    Mean      MaxNon0  StndDevn
   1 tag         !P  10696     0     0      3       5377      10696
   2 sire                      0     0 1.0000      48.04      92.00      25.04
   3 dam         !P  10696     0     0      1       5195      10695
   4 grp                49     0     0      1    19.8388         49
   5 sex                       0     0 1.0000      1.542      2.000     0.4982
   6 brr                 4     0     0      1     2.3588          4
   7 litter           4871     0     0      1  2448.6331       4871
   8 age                       0     0  17.00      48.64      111.0      13.87
   9 wwt            Variate   10     0  8.000      28.12      50.50      5.915
  10 ywt           Variate  2974     0  22.50      47.72      80.00      8.213
  11 gfw           Variate  2996     0 0.7000      3.040      6.700     0.8494
  12 fdm           Variate  6070     0  26.00      31.67      41.30      2.891
  13 fat           Variate  4856     0 0.5000      4.778      18.00      2.118
..

 Notice: LogL values are reported relative to a base of -20000.000
 Notice:     76 singularities detected in design matrix.
   1 LogL=-5486.37     S2= 1.00000      18085 df
   2 LogL=-5420.91     S2= 1.00000      18085 df    :   3 components restrained
   3 LogL=-4813.91     S2= 1.00000      18085 df    :   3 components restrained
   4 LogL=-3579.43     S2= 1.00000      18085 df    :   1 components restrained
   5 LogL=-2370.56     S2= 1.00000      18085 df    :   1 components restrained
   6 LogL=-1860.96     S2= 1.00000      18085 df    :   2 components restrained
   7 LogL=-1556.94     S2= 1.00000      18085 df    :   1 components restrained
   8 LogL=-1493.54     S2= 1.00000      18085 df    :   1 components restrained
   9 LogL=-1451.70     S2= 1.00000      18085 df    :   1 components restrained
  10 LogL=-1443.09     S2= 1.00000      18085 df    :   1 components restrained
..

  19 LogL=-1420.07     S2= 1.00000      18085 df    :   1 components restrained
  20 LogL=-1420.10     S2= 1.00000      18085 df    :   1 components restrained

          - - - Results from analysis of wwt ywt gfw fdm fat - - -
 Akaike Information Criterion    42928.20 (assuming 44 parameters).
 Bayesian Information Criterion  43271.52

 Model_Term                             Sigma         Sigma   Sigma/SE   % C
 Trait_1.age.grp         IDV_V   49  0.136208E-02  0.136208E-02   2.03   0 P
 Trait_2.age.grp         IDV_V   49  0.951316E-03  0.951316E-03   1.19   0 P
 Trait_4.age.grp         IDV_V   49  0.165902E-02  0.165902E-02   1.11   0 P
 Trait_5.age.grp         IDV_V   49  0.221494E-03  0.221494E-03   1.72   0 P
 Trait_1.sex.grp         IDV_V   49  0.928419      0.928419       2.90   0 P
 Trait_2.sex.grp         IDV_V   49   15.5311       15.5311       3.50   0 P
 Trait_3.sex.grp         IDV_V   49  0.280573      0.280573       3.71   0 P
 Trait_5.sex.grp         IDV_V   49   1.42344       1.42344       1.80   0 P
 units.us(Trait)              35200 effects
 Trait                   US_V  1  1   8.05905       8.05905      18.52   0 P
 Trait                   US_C  2  1   5.63073       5.63073      10.66   0 P
 Trait                   US_V  2  2   14.0103       14.0103      14.75   0 P
 Trait                   US_C  3  1  0.229120      0.229120       5.45   0 P
 Trait                   US_C  3  2  0.604319      0.604319       9.36   0 P
 Trait                   US_V  3  3  0.115554      0.115554      13.49   0 P
 Trait                   US_C  4  1  0.965394      0.965394       2.57   0 P
 Trait                   US_C  4  2   1.47917       1.47917       2.79   0 P
 Trait                   US_C  4  3  0.254480      0.254480       7.43   0 P
 Trait                   US_V  4  4   3.18843       3.18843       7.72   0 P
 Trait                   US_C  5  1  0.467651      0.467651       3.18   0 P
 Trait                   US_C  5  2   1.73841       1.73841       7.99   0 P
 Trait                   US_C  5  3  0.587357E-01  0.587357E-01   3.86   0 P
 Trait                   US_C  5  4  0.145230      0.145230       1.22   0 P
 Trait                   US_V  5  5   1.32501       1.32501      17.36   0 P
 xfa1(LitTr).lit              24355 effects
 LitTr                  XFA_V  0  1  0.100922E-02  0.100922E-02   0.00   0 ?
 LitTr                  XFA_V  0  2  0.910417      0.910417       1.60   0 P
 LitTr                  XFA_V  0  3  0.915803E-02  0.915803E-02   1.48   0 P
 LitTr                  XFA_V  0  4  0.820297      0.820297       2.20   0 P
 LitTr                  XFA_L  1  1  -1.86287      -1.86287      -3.49  -2 P
 LitTr                  XFA_L  1  2 -0.699367     -0.699367      -2.57   2 P
 LitTr                  XFA_L  1  3  0.202889E-01  0.202889E-01   1.01   0 P
 LitTr                  XFA_L  1  4 -0.446902E-01 -0.446902E-01  -0.26  -2 P
 xfa1(DamTr).dam              42784 effects
 DamTr                  XFA_V  0  1   0.00000       0.00000       0.00   0 B
 DamTr                  XFA_V  0  2   0.00000       0.00000       0.00   0 B
 DamTr                  XFA_V  0  3   0.00000       0.00000       0.00   0 B
 DamTr                  XFA_L  1  1   1.23296       1.23296       8.68   0 P
 DamTr                  XFA_L  1  2   1.40235       1.40235       7.12   1 P
 DamTr                  XFA_L  1  3  0.114810      0.114810       5.39   0 P
 dam                    NRM   10696
 xfa1(Tr).nrm(tag)            64176 effects
 Tr                     XFA_V  0  1  0.915916      0.915916       1.96  -1 P
 Tr                     XFA_V  0  2   1.14516       1.14516       1.14   0 P
 Tr                     XFA_V  0  3  0.507051E-01  0.507051E-01   4.72   0 P
 Tr                     XFA_V  0  4  0.684157      0.684157       1.92   0 P
 Tr                     XFA_V  0  5  0.113782      0.113782       1.89   0 P
 Tr                     XFA_L  1  1   1.36919       1.36919       5.62   0 P
 Tr                     XFA_L  1  2   2.36771       2.36771       7.07   0 P
 Tr                     XFA_L  1  3  0.687837E-01  0.687837E-01   1.94   0 P
 Tr                     XFA_L  1  4 -0.149794     -0.149794      -0.58   0 P
 Tr                     XFA_L  1  5  0.388888      0.388888       4.28   0 P
 tag                    NRM   10696

and from part 2

  10 LogL=-1415.11     S2= 1.00000      18085 df
  11 LogL=-1415.11     S2= 1.00000      18085 df
  12 LogL=-1415.11     S2= 1.00000      18085 df

          - - - Results from analysis of wwt ywt gfw fdm fat - - -
 Akaike Information Criterion    42932.23 (assuming 51 parameters).
 Bayesian Information Criterion  43330.17

 Model_Term                             Sigma         Sigma   Sigma/SE   % C
 Trait_1.age.grp         IDV_V   49  0.135677E-02  0.135677E-02   2.03   0 P
 Trait_2.age.grp         IDV_V   49  0.976956E-03  0.976956E-03   1.21   0 P
 Trait_4.age.grp         IDV_V   49  0.176380E-02  0.176380E-02   1.13   0 P
 Trait_5.age.grp         IDV_V   49  0.221202E-03  0.221202E-03   1.72   0 P
 Trait_1.sex.grp         IDV_V   49  0.920182      0.920182       2.89   0 P
 Trait_2.sex.grp         IDV_V   49   15.4138       15.4138       3.50   0 P
 Trait_3.sex.grp         IDV_V   49  0.280282      0.280282       3.71   0 P
 Trait_5.sex.grp         IDV_V   49   1.42102       1.42102       1.80   0 P
 units.us(Trait)              35200 effects
 Trait                   US_V  1  1   7.99624       7.99624      17.09   0 P
 Trait                   US_C  2  1   5.49377       5.49377       9.22   0 P
 Trait                   US_V  2  2   13.8642       13.8642      13.28   0 P
 Trait                   US_C  3  1  0.193135      0.193135       3.87   0 P
 Trait                   US_C  3  2  0.591702      0.591702       8.08   0 P
 Trait                   US_V  3  3  0.114192      0.114192      12.88   0 P
 Trait                   US_C  4  1  0.882617      0.882617       2.19   0 P
 Trait                   US_C  4  2   2.16587       2.16587       3.38   0 P
 Trait                   US_C  4  3  0.284696      0.284696       4.32   0 P
 Trait                   US_V  4  4   3.35060       3.35060       7.70   0 P
 Trait                   US_C  5  1  0.490299      0.490299       3.11   0 P
 Trait                   US_C  5  2   1.73925       1.73925       7.54   0 P
 Trait                   US_C  5  3  0.612316E-01  0.612316E-01   3.12   0 P
 Trait                   US_C  5  4  0.230186      0.230186       1.59   0 P
 Trait                   US_V  5  5   1.33520       1.33520      17.51   0 P
 us(LitTr).lit                19484 effects
 LitTr                   US_V  1  1   3.54347       3.54347       8.56   0 P
 LitTr                   US_C  2  1   1.50437       1.50437       3.31   0 P
 LitTr                   US_V  2  2   2.00235       2.00235       2.62   0 P
 LitTr                   US_C  3  1 -0.226319E-01 -0.226319E-01  -0.55   0 P
 LitTr                   US_C  3  2  0.616226E-01  0.616226E-01   1.07   0 P
 LitTr                   US_V  3  3  0.157954E-01  0.157954E-01   2.22   0 P
 LitTr                   US_C  4  1 -0.128867     -0.128867      -0.38   0 P
 LitTr                   US_C  4  2 -0.784696     -0.784696      -1.49   0 P
 LitTr                   US_C  4  3 -0.456359E-01 -0.456359E-01  -0.79   0 P
 LitTr                   US_V  4  4  0.733644      0.733644       1.82   0 P
 xfa1(DamTr).dam              42784 effects
 DamTr                  XFA_V  0  1   0.00000       0.00000       0.00   0 F
 DamTr                  XFA_V  0  2   0.00000       0.00000       0.00   0 F
 DamTr                  XFA_V  0  3   0.00000       0.00000       0.00   0 F
 DamTr                  XFA_L  1  1   1.21645       1.21645       7.88   0 P
 DamTr                  XFA_L  1  2   1.25861       1.25861       4.98   0 P
 DamTr                  XFA_L  1  3  0.959990E-01  0.959990E-01   3.61   0 P
 dam                    NRM   10696
 us(Tr).nrm(tag)              53480 effects
 Tr                      US_V  1  1   2.86271       2.86271       3.90   0 P
 Tr                      US_C  2  1   3.41322       3.41322       3.71   0 P
 Tr                      US_V  2  2   6.66960       6.66960       4.36   0 P
 Tr                      US_C  3  1  0.154787      0.154787       2.08   0 P
 Tr                      US_C  3  2  0.135758      0.135758       1.29   0 P
 Tr                      US_V  3  3  0.543582E-01  0.543582E-01   4.26   0 P
 Tr                      US_C  4  1  0.181664      0.181664       0.41   0 P
 Tr                      US_C  4  2 -0.261889     -0.261889      -0.42   0 P
 Tr                      US_C  4  3  0.835424E-02  0.835424E-02   0.12   0 P
 Tr                      US_V  4  4  0.614090      0.614090       1.91   0 P
 Tr                      US_C  5  1  0.501313      0.501313       2.64   0 P
 Tr                      US_C  5  2  0.921811      0.921811       3.29   0 P
 Tr                      US_C  5  3  0.234152E-01  0.234152E-01   1.00   0 P
 Tr                      US_C  5  4 -0.160268     -0.160268      -1.11   0 P
 Tr                      US_V  5  5  0.251928      0.251928       3.11   0 P
 tag                    NRM   10696
 Covariance/Variance/Correlation Matrix US Residual
   7.996      0.5218      0.2021      0.1705      0.1501
   5.494       13.86      0.4703      0.3178      0.4042
  0.1931      0.5917      0.1142      0.4603      0.1568
  0.8826       2.166      0.2847       3.351      0.1088
  0.4903       1.739      0.6123E-01  0.2302       1.335
 Covariance/Variance/Correlation Matrix US us(LitTr).lit
   3.543      0.5648     -0.9566E-01 -0.7993E-01
   1.504       2.002      0.3465     -0.6474
 -0.2263E-01  0.6162E-01  0.1580E-01 -0.4239
 -0.1289     -0.7847     -0.4564E-01  0.7336
 Covariance/Variance/Correlation Matrix XFA xfa1(DamTr).dam
   1.480      1.0000      1.0000      1.0000
   1.531       1.584      1.0000      1.0000
  0.1168      0.1208      0.9218E-02  1.0000
   1.216       1.259      0.9601E-01  1.0000
 Covariance/Variance/Correlation Matrix US us(Tr).nrm(tag)
   2.863      0.7811      0.3924      0.1370      0.5903
   3.413       6.670      0.2255     -0.1294      0.7111
  0.1548      0.1358      0.5436E-01  0.4573E-01  0.2001
  0.1817     -0.2619      0.8354E-02  0.6141     -0.4075
  0.5013      0.9218      0.2342E-01 -0.1603      0.2519

                                   Wald F statistics
     Source of Variation           NumDF              F-inc
  17 Tr.age                            5              98.78
  18 Tr.brr                           15             116.48
  19 Tr.sex                            5              59.72
  21 Tr.age.sex                        4               5.01
  24 at(Trait,1).age.grp                  49 effects fitted (       2 are zero)
  26 at(Trait,2).age.grp                  49 effects fitted (       4 are zero)
  28 at(Trait,4).age.grp                  49 effects fitted (      41 are zero)
  30 at(Trait,5).age.grp                  49 effects fitted (      22 are zero)
  32 at(Trait,1).sex.grp                  49 effects fitted (       3 are zero)
  33 at(Trait,2).sex.grp                  49 effects fitted (      17 are zero)
  35 at(Trait,3).sex.grp                  49 effects fitted (      17 are zero)
  36 at(Trait,5).sex.grp                  49 effects fitted (      38 are zero)
  44 Tr.grp                              180 effects fitted (+      65 singular)
  43 us(LitTr).lit                     19484 effects fitted (      20 are zero)
  41 xfa1(DamTr).dam                   10696 effects fitted (     384 are zero)
  39 us(Tr).nrm(tag)                   53480 effects fitted (      30 are zero)
 SLOPES FOR LOG(ABS(RES)) on LOG(PV) for Section  11
   0.19   0.53   0.62   0.41   1.03
          80  possible outliers: see .res file
 Finished: 21 Oct 2014 13:18:02.572   LogL Converged

Note that the 7 extra variance parameters have only increased the LogL value by 4.99 and so using US structures has not significantly improved the fit of the model.

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