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Problem 4.4 The following table gives the sums of squares (SS) from an analysis of variance of a random-breeding population of Drosophila melanogaster. The trait was the number of sternopleural bristles. There were 62 sires each mated to 3 dams. Each female laid eggs in one vial. The bristles of 10 female offspring of each dam were counted and the number of bristles is treated as a quantitative trait. Variation Df SS MS E(MS) Between Sires 272.121 $\sigma_{w}^{2} + \underline{\Box}\sigma_{d}^{2} + \underline{\Box}\sigma_{s}^{2}$ Between Dams 255.564 $\sigma_{w}^{2} + \underline{\Box}\sigma_{d}^{2}$ Between Sibs 1494.882 $\sigma_{w}^{2}$ (1) Complete the ANOVA table by filling up all the blank (underlined) spaces. (2) Calculate the variance components of sires ($\sigma_{s}^{2}$), dams ($\sigma_{d}^{2}$) and within family ($\sigma_{w}^{2}$). (3) Estimate the heritability using all the three formulas provided in the handout (paternal-half sib, maternal half-sib and full-sib). Note that the three estimated narrow sense heritability should be different.

          Problem 4.4 The following table gives the sums of squares (SS) from an analysis of
variance of a random-breeding population of Drosophila melanogaster. The trait was the
number of sternopleural bristles. There were 62 sires each mated to 3 dams. Each female
laid eggs in one vial. The bristles of 10 female offspring of each dam were counted and
the number of bristles is treated as a quantitative trait.
Variation	Df	SS	MS	E(MS)
Between Sires	____	272.121	____	$\sigma_{w}^{2} + \underline{\Box}\sigma_{d}^{2} + \underline{\Box}\sigma_{s}^{2}$
Between Dams	____	255.564	____	$\sigma_{w}^{2} + \underline{\Box}\sigma_{d}^{2}$
Between Sibs	____	1494.882	____	$\sigma_{w}^{2}$
(1) Complete the ANOVA table by filling up all the blank (underlined) spaces.
(2) Calculate the variance components of sires ($\sigma_{s}^{2}$), dams ($\sigma_{d}^{2}$) and within family ($\sigma_{w}^{2}$).
(3) Estimate the heritability using all the three formulas provided in the handout
(paternal-half sib, maternal half-sib and full-sib). Note that the three estimated narrow
sense heritability should be different.

Problem 4.4 The following table gives the sums of squares (SS) from an analysis of
variance of a random-breeding population of Drosophila melanogaster. The trait was the
number of sternopleural bristles. There were 62 sires each mated to 3 dams. Each female
laid eggs in one vial. The bristles of 10 female offspring of each dam were counted and
the number of bristles is treated as a quantitative trait.
Variation Df SS MS E(MS)
Between Sires 272.121 σw^2 + σd^2 + σs^2
Between Dams 255.564 σw^2 + σd^2
Between Sibs 1494.882 σw^2
(1) Complete the ANOVA table by filling up all the blank (underlined) spaces.
(2) Calculate the variance components of sires (σs^2), dams (σd^2) and within family (σw^2).
(3) Estimate the heritability using all the three formulas provided in the handout
(paternal-half sib, maternal half-sib and full-sib). Note that the three estimated narrow
sense heritability should be different.

Added by Claudia H.

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