Reference Publications

Study on heritability of growth in the juvenile sea urchin Strongylocentrotus nudus

Journal of Shellfisheries Research, August, 2004 by Liu Xiaolin, Chang Yaqing, Xiang Jianhai, Ding Jun, Cao Xuebin

TABLE 1.
Analysis of variance for components of phenotypic variation.

    Source of          Degree of         Sum of
    Variance         Freedom (df)     Squares (SS)

Dams                F x M - 1         S[S.sub.M]
Sires               F - 1             S[S.sub.F]
Dams/sires          F x (M - 1)       S[S.sub.M(F)]
Offspring (error)   F x M x (n - 1)   SS

Total               N - 1             S[S.sub.T]

    Source of        Mean Square        Expected Mean
    Variance            (MS)            Square E (MS)

Dams
Sires               M[S.sub.F]      [[sigma].sup.2]  
                                      [k.sub.2] [[sigma].
                                      sup.2.sub.M]   [k.
                                      sub.3]   [[sigma].
                                      sup.2.sub.F]
Dams/sires          M[S.sub.M(F)]   [[sigma].sup.2]  
                                      [k.sub.1] [[sigma].
                                      sup.2.sub.F]
Offspring (error)   MS              [[sigma].sup.2]

Total

TABLE 2.
Relationships between the covariance of full and half-sibs and
causal components of phenotypic variance.

      Component of                  Covariance
        Variance                    Components

[[sigma].sup.2.sub.F]       CO[V.sub.HS]
[[sigma].sup.2.sub.M]       CO[V.sub.FS] - CO[V.sub.HS]
[[sigma].sup.2.sub.E]       [V.sub.P] - CO[V.sub.FS]
[[sigma].sup.2.sub.T] =     [V.sub.P]
  [[sigma].sup.2.sub.F]  
  [[sigma].sup.2.sub.M]  
  [[sigma].sup.2]
[[sigma].sup.2.sub.F]       CO[V.sub.FS]
  [[sigma].sup.2.sub.M]

      Component of                           Causal
        Variance                           Components

[[sigma].sup.2.sub.F]       1/4 [V.sub.A]
[[sigma].sup.2.sub.M]       1/4[V.sub.A]   1/4[V.sub.NA]   [V.sub.EC]
[[sigma].sup.2.sub.E]       1/2 [V.sub.A]   3/4[V.sub.D]   [V.sub.ES]
[[sigma].sup.2.sub.T] =     [V.sub.A]   [V.sub.NA]   [V.sub.EC]  
  [[sigma].sup.2.sub.F]       [V.sub.ES]
  [[sigma].sup.2.sub.M]  
  [[sigma].sup.2]
[[sigma].sup.2.sub.F]       1/2 [V.sub.A]   1/4[V.sub.D]   [V.sub.EC]
  [[sigma].sup.2.sub.M]

      Component of                        Calculation of
        Variance                      Component of Variance

[[sigma].sup.2.sub.F]       {M[S.sub.F]- [(M[S.sub.M(F)] - M[S.sub.E])
                              /[k.sub.1] x [k.sub.2] - M[S.sub.E]}
                              /[k.sub.3]
[[sigma].sup.2.sub.M]       (M[S.sub.M(F)] - M[S.sub.E])/[k.sub.1]
[[sigma].sup.2.sub.E]       M[S.sub.E]
[[sigma].sup.2.sub.T] =
  [[sigma].sup.2.sub.F]  
  [[sigma].sup.2.sub.M]  
  [[sigma].sup.2]
[[sigma].sup.2.sub.F]  
  [[sigma].sup.2.sub.M]

TABLE 3.
Body weight and test diameter of offspring at 3 and 5 months of age.

             Body Weight (g)       Test Diameter (mm)

 Growth               Standard    Standard
 Phase     Average    Deviation   Average    Deviation

3 months   0.014484    0.0103      2.916       0.945
5 months   1.366       0.377       8.492       2.841

TABLE 4.
Analysis of variance for components of phenotypic variation
of Strongylocentrotus nudus at 3 and 5 months of age.

                              Body Weight

   Source of       Degrees of        Mean
   Variance       Freedom (df)    Square (MS)     F-Value

3 months
  Dam                   62       4.08340 x        9.893 **
                                   [10.sup.-3]
  Sire                  20       7.26634 x       17.605 **
                                   [10.sup.-3]
  Dams within           42       2.56772 x        6.221 **
    sires                          [10.sup.-3]
  Full-sibs           2210       4.12753 x
    within dams                    [10.sup.-4]
  Total               2272
5 months
  Dams                  59          0.79976       7.580 **
  Sire                  20          1.31728      12.485 **
  Dams within           39          0.53436       5.065 **
    sires
  Full-sibs           2045          0.10551
    within dams
  Total               2104

  Body Weight                   Test Diameter

   Source of         Mean                       Expected Mean
   Variance       Square (MS)    F-Value        Square E (MS)

3 months
  Dam               6.01406      6.737 **
  Sire             10.71717     12.006 **   [[sigma].sup.2]  
                                              [k.sub.2] [[sigma].
                                              sup.2.sub.M]  
                                              [k.sub.3][[sigma].
                                              sup.2.sub.M]
  Dams within       3.77449      4.228 **   [[sigma].sup.2]  
    sires                                     [k.sub.1] [[sigma.
                                              sup.2.sub.M]
  Full-sibs         0.89266                 [[sigma].sup.2]
    within dams
  Total
5 months
  Dams              69.16935     8.570 **
  Sire             108.2978     13.418 **   [[sigma].sup.2]  
                                              [k.sub.2] [[sigma].
                                              sup.2.sub.M]  
                                              [k.sub.3][[sigma].
                                              sup.2.sub.F]
  Dams within       49.10348     6.084 **   [[sigma].sup.2]  
    sires                                     [k.sub.1] [[sigma.
                                              sup.2.sub.M]
  Full-sibs          8.07108                [[sigma].sup.2]
    within dams
  Total

** P < 0.01; S = sires; D = dams; [K.sub.1] is the weighed mean
offspring number of females, [K.sub.2] = is the weighed offspring
number of females within sire, [K.sub.3] is the weighed mean
offspring number of sires.

TABLE 5.
Relationships between the covariance of full and half-sibs and causal
components of phenotypic variance.

Component of                   Causal        Covariance
Variance                     Components      Components

[[sigma].sup.2.sub.F]     1/4 [V.sub.A]      [Cov.sub.HS]
[[sigma].sup.2.sub.M]     l/4[V.sub.A]       [Cov.sub.FS]
                            1/4 [V.sub.NA]     - [Cov.sub
                              [V.sup.EC]       .HS]
[[sigma].sup.2]           1/2[V.sub.A]       [V.sub.P] -
                              3/4[V.sub.D]     [Cov.sub.
                              [V.sub.EW]       FS]
[[sigma].sup.2.sub.P] =   [V.sub.A]          [V.sub.P]
  [[sigma].sup.2.sub.F]     [V.sub.NA]  
  [[sigma].sup.2.sub.M]       [V.sub.EC]
  [[sigma].sup.2]             [V.sub.EW]
[[sigma].sup.2.sub.F]     1/2[V.sub.A]       CO[V.sub.FS]
  [[sigma].sup.2.sub.M]       1/4[V.sub.D]
                              [V.sub.EC]

                               Result of Component of Variance

                                   3 Month               5 Month

Component of                                Test      Body       Test
Variance                   Body Weight    Diameter   Weight    Diameter

[[sigma].sup.2.sub.F]     4.13895 x       0.06027    0.00678   0.50447
                            [10.sup.-5]
[[sigma].sup.2.sub.M]     6.16974 x       0.08308    0.01280   1.22465
                            [10.sup.-5]
[[sigma].sup.2]           4.275 x         0.89264    0.10551   8.07108
                            [10.sup.-4]
[[sigma].sup.2.sub.P] =   5.40587 x       1.03598    0.12509   9.80020
  [[sigma].sup.2.sub.F]     [10.sup.-4]
  [[sigma].sup.2.sub.M]
  [[sigma].sup.2]
[[sigma].sup.2.sub.F]     1.03087 x       0.14335    0.01958   1.72912
  [[sigma].sup.2.sub.M]     [10.sup.-4]

TABLE 6.
Heritabilitics in narrow sense ([h.sup.2]) and standard
error ([[sigma].sub.h.sup.2]).

                                   3 Months of Age

                         Body Weight                Diameter

[h.sup.2.sub.S]    ** 0.306 [  or -] 0.055   ** 0.233 [  or -] 0.046
[h.sup.2.sub.D]    ** 0.457 [  or -] 0.071   ** 0.321 [  or -] 0.046
[h.sup.2.sub.FS]   ** 0.381 [  or -] 0.063   ** 0.277 [  or -] 0.051

                                   5 Months of Age

                         Body Weight                Diameter

[h.sup.2.sub.S]    ** 0.217 [  or -] 0.042   ** 0.206 [  or -] 0.041
[h.sup.2.sub.D]    ** 0.409 [  or -] 0.064   ** 0.500 [  or -] 0.072
[h.sup.2.sub.FS]   ** 0.313 [  or -] 0.054   ** 0.353 [  or -] 0.058

** Denotes very significance between [h.sub.2] with
zero (P < 0.01); [t.sub.0.01] [infinity] = 2.576.