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Crop Science 43:1558-1560 (2003)
© 2003 Crop Science Society of America

NOTES

On the effectiveness of early generation selection in self-pollinated crops

Rex Bernardo*

Dep. of Agronomy and Plant Genetics, Univ. of Minnesota, 411 Borlaug Hall, 1991 Buford Circle, St. Paul, MN 55108

* Corresponding author (berna022{at}umn.edu)


   ABSTRACT
TOP
 ABSTRACT
INTRODUCTION
 Theory
 Results and Discussion
 REFERENCES
 
Breeders of self-pollinated crops often discard inferior lines at an early selfing generation so that more resources can be devoted to the further testing and selection of the more promising lines. Empirical studies have led to contradictory estimates of the correlation between the performance of lines at early and late selfing generations. Here I examine the theoretical effectiveness of early generation selection. When dominance is absent, the genetic correlation (rG) between the performance of an Ft–derived Fg line (i.e., Ft:g) and a descendant homozygous line is equal to the square root of [1 + F(t)]/2, where F(t) is the inbreeding coefficient at generation t. Dominance, when present, has little effect on rG. The minimum value of rG is high; that is, 0.707 for an F2–derived line. From a genetic standpoint, early generation selection is expected to be effective, but in practice it becomes ineffective if nongenetic effects are large.


   INTRODUCTION
TOP
 ABSTRACT
 INTRODUCTION
Theory
 Results and Discussion
 REFERENCES
 
EARLY GENERATION SELECTION in self-pollinated crops typically involves the evaluation of F2– or F3–derived lines from the cross between two inbreds. Inferior F2– or F3–derived lines are then discarded to allow the expenditure of resources on the testing and selection of the more promising lines. The F2– or F3–derived lines are far from being homozygous, and early generation selection relies on the assumption that the performance of a line at an early generation of selfing is predictive of its performance at homozygosity.

Empirical studies in different self-pollinated crops have indicated that early generation selection is sometimes effective (Mahmud and Kramer, 1951; Frey, 1954; Ntare and Aken'Ova, 1985; Sharma, 1994; St. Martin and Geraldi, 2002) and sometimes ineffective (Weiss et al., 1947; Briggs and Shebeski, 1971; Knott and Kumar, 1975; Seitzer and Evans, 1978). In soybean [Glycine max (L.) Merr.], Weiss et al. (1947) reported an average phenotypic correlation of -0.19 between the yield of F2– and F3–derived lines, and 0.15 between the yield of F3– and F4–derived lines. In contrast, Thorne (1974) reported phenotypic correlations as high as 0.85 between the yield of F3– and F6–derived soybean lines. In barley (Hordeum vulgare L.), McKenzie and Lambert (1960) reported correlations ranging from 0.11 to 0.81 between the yield of F2– and F5–derived lines. In wheat (Triticum aestivum L.), Whan et al. (1981) reported average correlations ranging from 0.29 to 0.78 for yield at different selfing generations.

The conflicting conclusions regarding the usefulness of early generation selection in self-pollinated crops have not been addressed on the basis of the following question: What are the expected genetic and phenotypic correlations between line performance at an early selfing generation and at homozygosity? My objective in this Note was to evaluate the theoretical effectiveness of early generation selection in self-pollinated crops.


   Theory
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 ABSTRACT
 INTRODUCTION
 Theory
Results and Discussion
 REFERENCES
 
Suppose Ft:g lines (t < g) are developed from the cross between two inbreds. For example, harvesting the selfed seeds from a single F2 plant leads to an F2:3 line. Bulking the selfed seeds from several F2:3 plants leads to an F2:4 line. Homozygous lines are then developed, by single-seed descent, from the same Ft (e.g., F2) plants that were selfed to develop the Ft:g lines. Selection and genetic drift are assumed absent.

Consider a quantitative trait that is controlled by several unlinked, nonepistatic loci. The coded genotypic values at an arbitrary locus, B, are a for BB, d for Bb, and -a for bb. For the sake of illustration, suppose both a and d are equal to 1 (complete dominance). In the cross between a BB parent and a bb parent, the genotypic frequencies among F2 plants are 25% BB, 50% Bb, and 25% bb. If F2 plants are selfed to form F2:3 lines, the mean genotypic values of the lines are as follows: 1 for an F2:3 line selfed from a BB F2 plant; 0.25(1) + 0.50(1) + 0.25(-1) = 0.50 for an F2:3 line selfed from a Bb F2 plant; and -1 for an F2:3 line selfed from a bb F2 plant.

Selfing a BB or bb F2:3 line until homozygosity will not change its genotypic value at the locus. But continuously selfing a Bb F2:3 line (with a mean of 0.50) will lead to either a BB line (with a mean of 1) or a bb line (with a mean of -1), each with equal probability. The genetic correlation between the performance of an F2:3 line and a descendant homozygous line is therefore obtained as the correlation between the following pairs (each with a frequency of 25%) of mean genotypic values: (1, 1) for BB; (0.50, 1) for a Bb F2:3 line and a BB homozygous line; (0.50, -1) for a Bb F2:3 line and a bb homozygous line; and (-1, -1) for bb. These values lead to a genetic correlation of 0.667.

The foregoing results for F2:3 lines can be generalized as follows. The covariance between Ft:g and Ft–derived homozygous individuals is equal to (Cockerham, 1963)

where F(t) is the inbreeding coefficient at generation t, and VA is the additive variance in the F2 population. The {infty} indicates that a large number of selfing generations are used to achieve homozygosity. The covariance between the performance of Ft:g and homozygous lines therefore does not depend on g.

The genetic variance among Ft:g lines is equal to (Cockerham, 1963)

where F(g) is the inbreeding coefficient at generation g, and VD is the dominance variance in the F2 population. Given an inbreeding coefficient of 1 at homozygosity, the genetic variance among homozygous lines is Cov({infty},{infty},{infty}) = 2VA. The genetic correlation between the performance of Ft:g lines and their descendant homozygous lines is then equal to

[1]

When dominance is absent (VD = 0), Eq. [1] reduces to

[2]

Eq. [2] is equal to the genetic correlation, for cross-pollinated crops, between the testcross (as opposed to line per se) performance of Ft:g lines and their descendant homozygous lines (Bernardo, 1991).

Phenotypic values, rather than genotypic values, are directly observable. The effectiveness of early generation selection can by judged by the correlation between the phenotypic mean of an Ft:g line and the genotypic mean of a descendant homozygous line:

where VE is the nongenetic variance on a line-mean basis. The phenotypic variance is VP = VA + VD + VE, and the heritability in the base population is h2 = VA/VP.


   Results and Discussion
TOP
 ABSTRACT
 INTRODUCTION
 Theory
 Results and Discussion
REFERENCES
 
When dominance is absent (VD = 0), the expected genetic correlation between line performance at an early generation and at homozygosity (rG) is 0.707 for F2–derived lines, 0.866 for F3–derived lines, 0.935 for F4–derived lines, and 0.968 for F5–derived lines (Table 1). The expected effectiveness of selection among Ft:g lines therefore increases as t increases. But the minimum value of rG (0.707 for F2:g lines) is high to begin with. This result indicates that, from a purely genetic standpoint, early generation selection in self-pollinated crops is expected to be effective.


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  		Table 1. Expected genetic correlation (rG) between the performance of an Ft–derived Fg line (Ft:g) and a descendant homozygous line.

 
If VA is equal to 1 in an F2 population between two inbreds, a VD of 0.50 represents complete dominance whereas a VD of 0.25 represents partial dominance. Comparisons of rG when VD is zero, 0.25, or 0.50 indicate that dominance causes only minor reductions in the effectiveness of early generation selection (Table 1). In other words, any heterosis [which is largely due to dominance effects (Davenport, 1908; Shull, 1908)] that might be observed in the early generations of selfing has only a minor effect on rG. The reductions in rG become even smaller when a line derived from generation t is selfed in bulk for additional generations, for example, from F2:3 to F2:4. These results suggest that the effects of dominance on early generation selection can be largely ignored.

The correlation between the phenotypic mean of an Ft:g line and the genotypic mean of a descendant homozygous line (rPG) is affected to a greater extent by nongenetic effects than by the selfing generation (Fig. 1). The rPG values in Fig. 1 indicate that although early generation selection is theoretically effective, the procedure could be ineffective in practice due to nongenetic effects. The rPG for an F2–derived line (assuming VD = 0) is 0.632 when the heritability (h2) is 0.80. But the rPG for an F5–derived line is 0.547 when h2 is 0.20. This example illustrates that selection can be more effective in an early than in a late generation if the VE differs between selfing generations. In practice, though, h2 is often low in early selfing generations. This is particularly true in small grains such as wheat and barley, where individual plants do not produce a sufficient amount of selfed seeds to permit replicated tests across several environments (Sneep, 1984).



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  		Fig. 1. Expected correlation (rPG) between the phenotypic mean of an Ft:g line and the genotypic mean of a descendant homozygous line as a function of the ratio (i.e., heritability, h2) of additive variance (VA) and phenotypic variance (VP). Dominance variance is assumed absent.

 
In a previous report (Bernardo, 1992), I discussed the allocation of resources during early generation testcrossing in cross-pollinated crops. Given that rG and rPG are similar (when VD > 0) or identical (when VD = 0) for line per se performance and testcross performance, the early-testing strategies for cross-pollinated crops also apply to self-pollinated crops. Specifically, the rPG values are useful for determining the probability of retaining genetically superior lines at an early selfing generation. Suppose a breeder aims to select the best line among 100 F3–derived lines, and h2 is 0.50. The value of rPG for F3–derived lines is 0.671 when VD is absent. If the breeder then selects 15 out of 100 F3–derived lines, the probability of retaining the best line is 0.84 (Bernardo, 1992).

In a broad sense, the usefulness of early generation selection does not depend only on the effectiveness of the procedure itself but on whether it is more effective than other line development methods such as single seed descent. Such comparisons are beyond the scope of this Note.

The wide range of rPG values in Fig. 1 are consistent with the wide range of correlations obtained from empirical studies (Weiss et al., 1947; McKenzie and Lambert, 1960; Thorne, 1974; Knott and Kumar, 1975; Whan et al., 1981; Ntare and Aken'Ova, 1985; Sharma, 1994). The conclusion from this Note that early generation selection in self-pollinated crops is limited primarily by nongenetic effects—rather than genetic effects—is consistent with the conclusion drawn by Mahmud and Kramer (1951) more than half a century ago: "It appeared that F3 lines should provide good estimates of the average yield potentialities of F4 segregates when some attempt is made to control genetic shift [drift] and interactions of generations with environmental factors."

Received for publication September 27, 2002.


   REFERENCES
TOP
 ABSTRACT
 INTRODUCTION
 Theory
 Results and Discussion
 REFERENCES
 




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