Principles of Plant Genetics and Breeding

524 CHAPTER 31
An important consideration for valid estimates of generation means is that there is sufficient sampling of segregating generations
(Hallauer & Miranda 1981, p. 109). Bernardo (2002, p. 138) recommends that sampled breeding populations have a minimum
of 50–100 progenies.
The advantages of generation mean analysis are:
1 It is relatively simple and statistically reliable (Mather & Jinks 1971, p. 126). Sampling errors are inherently smaller when
working with means than with variances for estimating inheritance. Smaller experiments can therefore be used to obtain the
same level of precision (Hallauer & Miranda 1981, p. 111; Campbell et al. 1997).
2 The estimation and interpretation of non-allelic interactions (epistasis) is more progressive for generation mean analysis
than for variance estimates because mean effects are less confounded with one another and because the kinds of experiments
required for analysis of means are smaller and easier to carry out than are those for variances (Mather & Jinks 1971, p. 126).
3 Populations evaluated in generation mean analysis can be used in applied breeding programs (Campbell et al. 1997).
4 It is equally applicable to both self- and cross-pollinated species (Hallauer & Miranda 1981, p. 111).
However, generation mean analysis also has several weaknesses:
1 It has limited value for quantitative traits whose parents have comparable mean performance (Bernardo 2002, p. 146).
2 As the information derived from the analysis is relevant to only a specific pair of parents, it has little application to other
populations (Hallauer & Miranda 1981, p. 111).
3 Negative effects at some loci can cancel out positive effects at other loci, causing true genetic effects to be underestimated.
Generation mean analysis does not reveal opposing effects (Bernardo 2002, p. 145). For example, a mean dominance effect
of zero due to the cancellation of opposing effects does not mean that there are no dominance effects. But it does mean that
there are no evident dominance effects and that a determination of the degree of dominance using variance components
may be necessary.
4 Generation mean analysis does not provide estimates of heritability, which are essential for estimating predicted gain from
selection (Hallauer & Miranda 1981, p. 111).
5 Finally, if epistatic effects are present, additive and dominance effects can be biased by the epistatic effects and by linkage
disequilibrium (Hallauer & Miranda 1981, p. 110).
The use of generation mean analysis should be considered as complementary, rather than as an alternative, to variance component
analyses (Mather & Jinks 1971, p. 126). However, if one estimates additive and dominance genetic effects using generation
mean analysis, and also estimates Φ2 A and Φ2 D , there may be little relation in the magnitude of the two sets of estimates (Hallauer &
Miranda 1981, p. 110). This might be expected because generation means estimate the sum of the genetic effects, whereas variances
are the squares of the genetic effects. Further, the magnitude of Φ2 A , Φ2 D , and Φ2 I may be poor indicators of the underlying
gene actions for quantitative traits (Bernardo 2002, p. 144). For example, Moll et al. (1963) found that generation mean analysis
detected epistatic effects that were not evident from estimates of Φ2 A , Φ2 D , and Φ2 E (environmental variance), but noted that variance
components may detect genetic variation not detected by generation mean analysis due to cancellation of mean effects.
Because of the weaknesses of single-plant data and the complexities of multigene quantitative traits, it may be advisable to generate
F3 progenies and selfed progenies of both the BC1P1 and BC1P2 generations (Bernardo 2002, pp. 175–177). These generations
are useful for estimating genetic variances, provided that they are developed without selection. The F3 progenies can be
grown in replicated trials, which can provide an estimate of environmental effects and genotype × environment interactions.
Hamblin and White (2000) and Walker and White (2001) provide examples in maize of using the ANOVA (analysis of variance)
of F3 progeny means to estimate Φ2 A , heritability, and predicted gain from selection.
Hallauer and Miranda (1981, p. 91) recommended the use of F3 families for estimating Φ2 A in maize. Bernardo (2002,
pp. 179–181) noted that an increase in either the number of environments or replications reduces the variance of an F3 family
mean and in turn increases heritability. Hence, selection for quantitative traits among F3 families can be effective if each family is
grown in extensive performance tests (Bernardo 2002, p. 181).
A further advantage of developing F3 progenies is that the segregation ratios within each F3 progeny can be used to confirm
applicable F2 qualitative inheritance models. Thompson et al. (1997) used F3 progeny ratios to help accurately categorize each F2 plant genotype.
An additional genetic relationship that could be used to estimate heritability and predicted gain from selection from the above
generations is that of the parent–offspring relationship between F2 individuals and F2:3 progeny means (Hallauer & Miranda 1981,
p. 110). Using least squares regression of F3 offspring means onto individual F2 parental values, the slope (b) is equal to (Φ2 A +
1
/2Φ2 D )/Φ2 P and can be interpreted as the change in breeding value per change in phenotypic value (Bernardo 2002, p. 110). As
were all the estimates of heritability previously discussed, this parent–offspring estimate is referenced to an F2 population
assumed to be in Hardy–Weinberg equilibrium and considered to be non-inbred (Bernardo 2002, p. 34). This estimate of heritability
may be biased upward by the presence of some potential amount of Φ2 D and any epistatic variance component involving
Φ2 D (Φ2 AD , etc.).