Citrullus lanatus (Thunb.) Matsum. & Nakai - Cucurbit Breeding ...

thumped (Maynard, 2001). Weights were recorded by approximation to the nearest pound. The data were
transformed to kilograms before statistical analysis.
The fruit of the giant-fruited parents in the family 'Weeks NC Giant' × 'Minilee' at Kinston were
smaller than expected, possibly due to the presence of problems of water drainage in the field during fruit
development. Therefore, the data from those families were presented in the tables , but were considered
missing data for the calculation of means by location and overall means.
We tested the F 2 data for homogeneity of variances using Bartlett's method (Ostle and Malone, 1988;
Steel et al., 1997). Since the variances were heterogeneous, we analyzed the data by family and location.
Phenotypic (P), environmental (E), genotypic (G), and additive (A) effects were estimated from
generation variances as follows (Warner, 1952; Wright, 1968):
[ ]
! 2 ( P)
= ! 2 ( F2 ) ! 2 ( E)
= ! 2 ( Pa ) + ! 2 ( Pb ) + 2 " ! 2 ( F1 )
! 2 ( G)
= ! 2 ( PH ) " ! 2 ( E)
! 2 A
( ) = 2 " ! 2 ( F2 )
4
[ ] # ! 2 ( BC P 1 a ) + ! 2 [ ( BC P 1 a ) ]
Negative estimates for genetic variances are possible with the experimental design adopted. Negative
estimates should be considered equal to zero (Robinson et al., 1955), but should be reported "in order to
contribute to the accumulation of knowledge, which may, in the future, be properly interpreted" (Dudley and
Moll, 1969). We considered negative estimates equal to zero for the calculation of the mean estimates over
families or locations. When a negative estimate was derived from another negative value (narrow-sense
heritability and gain from selection, calculated from additive variance), it was considered close to zero and
omitted.
The number of effective factors was estimated using the following five methods (Lande, 1981; Mather
and Jinks, 1982; Wright, 1968):
Lande's method I:
Lande's method II:
8 " # 2 $
%
&
( ) !
F 2
[ ] 2
µ ( P ) ! µ ( P )
b
a
2
# ( P ) + # a
2 ( P ) + 2 " # b
2 [ ( F ) 1 ] '
(
4
)
[ µ ( P ) ! µ ( P )
b
a ] 2
( F ) ( BC P ) + # 2
1 a
2
{ ( BC P ) 1 a }
[ ] ! # 2 [ ]
8 " 2 " # 2
84