Sampling bias in estimating Design II variance components with S families.

The use of several S individuals to represent an S individual permits the use of a Design II mating scheme for plants with only one pistillate flower per plant. Estimates of additive (V) and dominance (V) variance from this mating scheme will be biased upwards, when a small number (10) of individuals of each S line are used. This bias can be computed, and the additive and dominance estimates can be corrected. Of particular interest is the observation that the additive genetic variance contributes to bias in estimates of V. When S plants are non inbred and their selfedprogeny (S lines) are used to represent them in developing families for use in the Design II, $$\hat VA = \hat VA\left( {1 + 1/2m_1 } \right){\text{ and V}}_{\text{D}} {\text{ = V}}_{\text{D}} \left( {{\text{1 + }}\frac{{\text{5}}}{{{\text{4m}}_{\text{2}} }}} \right) + \left( {\frac{1}{{m_2 }} - \frac{1}{{m_1 }}} \right)V_A $$ where m is the number of individuals used to represent an S line in developing half sib-families and m is the number of individuals used to represent the S line in making up full sib-families. For example, in a 3×3 Design II, with about 10 individuals used to represent each S line in each cross, m = 10 and m = 30. When m = m = 1, $$\hat V_A = \left( {1 + 1/2} \right)V_A = \left( {1 + F} \right)V_A $$ and $$\hat V_D = V_D + \frac{5}{4}V_D = \left( {1 + F} \right)^2 V_D $$ [ABSTRACT FROM AUTHOR]