HOME HELP FEEDBACK SUBSCRIPTIONS ARCHIVE SEARCH TABLE OF CONTENTS		QUICK SEARCH:   [advanced] Author: Keyword(s): Year:  Vol:  Page:

This Article Abstract Figures Only Full Text (PDF) Free Alert me when this article is cited Alert me if a correction is posted Services Similar articles in this journal Similar articles in Web of Science Alert me to new issues of the journal Download to citation manager Citing Articles Citing Articles via HighWire Citing Articles via Web of Science (8) Citing Articles via Google Scholar Google Scholar Articles by Bouchez, A. Articles by Gallais, A. Search for Related Content PubMed Articles by Bouchez, A. Articles by Gallais, A. Agricola Articles by Bouchez, A. Articles by Gallais, A.

CROP BREEDING, GENETICS & CYTOLOGY

Efficiency of the Use of Doubled-Haploids in Recurrent Selection for Combining Ability

^a INRA-UPS-INA.PG, Station de Génétique Végétale, Ferme du Moulon, 91190 Gif Sur Yvette, France
^b INA.PG, 16 rue Claude Bernard, 75321 Paris Cedex 05, France
^c INRA-UPS-INA.PG, Station de Génétique Végétale, Ferme du Moulon, 91190 Gif Sur Yvette, France

bouchez{at}mons.inra.fr

	ABSTRACT

TOP ABSTRACT INTRODUCTION Materials and methods Results Discussion Appendix REFERENCES

 
In population improvement for combining ability, the use of selfed progenies increases genetic advance per cycle, but it can unduly increase the cycle length. Haplodiploidization (HD) can be very efficient because it induces complete homozygosity in a short period. We compared, from a theoretical approach, the potential of recurrent selection with a tester using doubled haploids (SDHT), with selection with testcrosses of S₀, S₁, or S₂ plants, with or without the use of off-season nurseries, for an annual plant like maize (Zea mays L.). With the same selection intensity, and without off-season nurseries, SDHT with a 4-yr cycle is the most efficient method. Efficiency increases with lower heritability, with an advantage in comparison to the test of S₀ plants (S₀T) of 40 to 50% at low heritability (h² < 0.15) and 12% at high heritability (h² = 0.8). Use of off-season nurseries reduces the advantage of SDHT. With a 3-yr cycle, SDHT remains the best at low heritability with a gain of 27% (for h² = 0.1) in comparison to S₀T with a 2-yr cycle. When using constant effective size, the advantage of SDHT is further reduced or suppressed at the benefit of S₀T in 2 yr. The use of HD in recurrent selection for combining ability has its biggest advantage when heritability is low. Consideration of variety development will give more advantage to HD.

Abbreviations: HD, haplodiploidization • SDHT, single-doubled-haploid descent recurrent selection for combining ability with a tester • S₀T, S₁T, S₂T, recurrent selection for combining ability with a tester with respectively S₀, S₁, S₂ plants

	INTRODUCTION

TOP ABSTRACT INTRODUCTION Materials and methods Results Discussion Appendix REFERENCES

 
FOR THE IMPROVEMENT by recurrent selection of the value of lines that can be derived from a population, haplodiploidization (HD) appears to be a very efficient process (Griffing, 1975; Gallais, 1989, 1990a, 1993b; Goldringer et al., 1996). This is due to the fact that it allows direct selection on line value, whereas by the use of partially inbred progenies, selection can be biased by heterozygosity. However, considering the improvement of combining ability of a population, the usefulness of HD may be questioned. Indeed, in the absence of epistasis, the combining ability of lines derived from an S₀ plant can be predicted from the combining ability of the S₀ plant (Gallais, 1990b). Nevertheless, HD can be efficient in increasing the variance among progenies from testcrosses and thus the heritability. HD also has the advantage of giving more uniform progenies. If the cycle length is increased in comparison with combining ability tests at the S₀ level, the genetic advance per unit of time will not necessarily be greater. As already shown by Griffing (1975), the length of HD process is a critical parameter to consider. Thus, the advantage of HD in recurrent selection for combining ability with a tester is not obvious. However, an advantage of HD in recurrent selection is to reduce the time required for varietal development by pedigree selection. Indeed, with the use of HD, if the tester is used as a parent of the new hybrids, recurrent selection is more than a method of population improvement, it becomes a method of recurrent varietal development.

Griffing (1975) has already considered some aspects of the use of HD in recurrent selection for improving combining ability; however, he considered neither the use of S₁ or S₂ progeny testcrosses, nor the possible use of off-season nurseries. Strahwald and Geiger (1988) have shown that with the use of off-season nurseries, the advantage of HD, for the development of lines tends to disappear. In a theoretical study on optimizing sugar beet breeding plans based on selection among testcross progenies, Borchardt and Geiger (1997) showed that testing S₃ lines maximizes genetic gain compared with S₁ lines or doubled haploid lines.

In our paper, we consider only the use of recurrent selection with a tester (which can be a population), with or without the use of an off-season nursery. Recurrent selection with HD is compared with recurrent selection at the S₀ plant level (i.e., without inbreeding) and with selection at the S₁ and S₂ plant level (i.e., with one or two generations of self-pollination before crossing to a tester).

The following theoretical development assumes no epistasis and no genotype x environment (G x E) interaction. Gallais (1991) has shown that epistasis is expected to have a low effect on relative efficiency of the breeding methods for combining ability. Furthermore, in a large range of realistic situations, the presence of genotype x location interaction has only a small effect on the ratio of the two phenotypic standard deviations associated to any pair of methods when selection is on average performance across locations. Interaction with an uncontrolled factor, such as years, decreases the actual heritability. Thus, here such an effect is considered through heritability. Methods are compared on the basis of the genetic advance per unit of time, at the level of the breeding population. The cost of the methods is not considered. However, it is assumed that for a given year of testing, the number of plots is fixed. Furthermore, time is considered through the cycle length. The consideration of the cost would need to assess the whole breeding plan, including varietal development (Geiger and Tomerius, 1997). For such a development, to be realistic, it would be necessary to solve the problem of response to recurrent selection on several cycles, and response to pedigree selection, which are not well resolved. Our study is valid for choosing, at a given cycle of the breeding population, the recurrent selection scheme having the greatest genetic advance per unit of time.

	Materials and methods

TOP ABSTRACT INTRODUCTION Materials and methods Results Discussion Appendix REFERENCES

 
Description of the Methods
From a practical point of view, we will consider the case of an annual crop such as maize, for which it is possible to grow off-season nurseries. Basically, a cycle of recurrent selection has four stages: (i) production of plants to be tested, i.e., the derivation of selection units: S₁, S₂ plants or doubled-haploid lines; (ii) crossing of these units to the tester, and simultaneous selfing in order to maintain tested plants; (iii) progeny testing; and (iv) intercrossing of selected units. Note that with a plant like maize, with no prolificacy, it may be difficult to self and cross simultaneously (S+TC) with the tester used as male parent. The tester can be used as a female. However, for early types, it may be impossible to produce enough seeds for trials. In this situation, many breeders prefer to produce S₁, S₂, or S₃ progenies in order to select at the S₀, S₁, or S₂ plant level, respectively, and thereafter to cross these progenies in isolation with the tester used as male parent. We assume that field testing has to take place in a normal growing season to get a representative agronomic evaluation.

The four selection stages of a cycle are scheduled differently for each selection method, according to the use of off-season nurseries and S+TC (Table 1) . As a result, each method can be applied with varying cycle lengths. With selection among S₀ plants (S₀T) and use of S+TC, the length of the cycle will be three generations, i.e., 3 yr with an annual plant without access to an off-season nursery and only 2 yr with an off-season intercrossing. It cannot be shorter, because we assumed agronomic tests will occur in a normal growing season. If S₁ progenies of the S₀ plants are used for crossing to the tester, the cycle length will be four generations long, and could last from 2 to 4 yr depending on the use of off-season nurseries; a realistic length is 3 yr. With selection among S₁ plants (S₁T), or S₂ plants (S₂T), the cycle needs one or two more generations for selfing. Depending on the use of off-season nurseries, and on the kind of progenies used to evaluate combining ability, the cycle length can vary from 2 to 5 yr for S₁T and from 3 to 6 yr for S₂T.

Expression of Genetic Advance
Consider the case of a breeding population and its tester. To simplify the notation, the combining ability of a S₀ genotype will be denoted A_T , i.e., the additive effect of the S₀ genotype crossed to a specific tester (Gallais, 1989; 1990b). The testcross value with a given tester is equivalent to a quantitative character without dominance. Note that, with this notation, if the tester is the population itself, A_T is one-half A, the classical additive effect for per se value. A general expression of the expected genetic advance per cycle has been given by Gallais (1991)

(1)

where i is the selection intensity, the degree of selection control on both sexes, cov P_TO_T is the parent-offspring covariance for testcross value, and var P_T the phenotypic variance among selection units. cov P_TO_T is equal to (1 + F)/2 ²_AT, ²_AT being the additive variance for testcross value, F the coefficient of inbreeding of selection units: F = 0 for S₀ plants or S₁ families, 1/2 for S₁ plants or S₂ families, 3/4 for S₂ plants or S₃ families and 1 for doubled haploid lines. As in our situation = 2, it results

(2)

With an experimental design with n individuals per plot and b replications, the phenotypic variance among selection units is

where ²_GBT is the genetic variance between progenies, ²_p the environmental variance between plots, ²_e the environmental variance at the plant level within plot, and ²_WGT the within progeny genetic variance. It can be shown (see appendix) that

and

²_WT being the genetic variance due to heterogeneity of the tester. When selection units are doubled-haploid lines, the within progeny genetic variance depends only on the heterogeneity of the tester, ²_WT being then zero when the tester is a homozygous line.

The general expression [1] of genetic advance per cycle can be transformed to get explicit heritabilities of the associated testing systems. Then

(3)

Assuming that the number of plants per plot is sufficiently great to neglect the contribution of the within-plot genetic variance in comparison to the between-plot environmental variance and to the genetic variance among progenies, i.e., n > 30 (Gallais, 1993a), the phenotypic variance becomes

Then, the design heritability at the S₀ level is

Heritabilities for designs with the same number of replications but different F values can be expressed in terms of h²_S0

When expressed per unit of Time t, genetic advance becomes

or

(4)

The breeding methods can be easily compared on the basis of the same number of replications. However, the optimum number of replications can vary according to the level of inbreeding. To determine this optimum, Formula [4] was transformed to express the genetic advance in terms of the number of replications and of the plot-heritability h²_S01 at the S₀ level:

(5)

It can be noted that when heritability is low, i.e., there is a great environmental variance in comparison to genetic variance, phenotypic variances under different methods can be considered as approximately equal. Then, differences in genetic advance only depend on the genetic variance among progenies multiplied by (1 + F) and divided by cycle length. At the other extreme, when heritability is high, differences in genetic advance are due to the square root of genetic variance among progenies multiplied by (1 + F)^1/2, and divided by the cycle length. These two extremes for the genetic advance in standard units of the genetic variance are easy to compute (Table 2) .

Methods are compared first on the basis of the same number of replications, and second at their optimum number. To determine such an optimum, we consider a fixed total number of plots for a given year of testing. Then, for a given number of intercrossed plants, the rate of selection with b replications is p_b = b p₁. Increasing the number of replications increases the design-heritability but decreases the selection intensity. The first effect is favorable, the second unfavorable. Then an optimum number may result. At this optimum, comparisons have been developed on the basis of the same number of intercrossed plants and on the basis of the same effective size.

	Results

TOP ABSTRACT INTRODUCTION Materials and methods Results Discussion Appendix REFERENCES

 
Selection with Same Selection Intensity
Without Off-Season Nurseries
Without off-season nurseries, considering the shortest possible schemes with same selection intensity (Fig. 1) , SDHT in 4 yr is the best method whatever the heritability. Its superiority is all the greater when the heritability is low. With low S₀-heritability , the gain in efficiency in comparison to S₀T in 3 yr is 43%, and tends towards 50% as heritability approaches zero (Table 2). With , the gain is still 27%, and for , the gain is only 12%. Gains for SDHT in 5 yr are 25% less. S₂T in 5 yr is clearly the worst whatever the heritability and at most equal to S₀T at low heritability. Other methods are relatively close to S₂T when S₀-heritability is low. When S₀-heritability increases, S₀T in 3 yr and S₁T in 4 yr are significantly better than S₂T and SDHT in 5 yr.

View larger version (27K): [in this window] [in a new window]   Fig. 1 Genetic advance per year (in genetic standard deviations) as a function of S0 heritability under different recurrent selection methods, when no off-season is used (with same selection rate )

View larger version (29K): [in this window] [in a new window]   Fig. 2 Genetic advance per year (in genetic standard deviations) as a function of S0 heritability under different recurrent selection methods, with use of off-season (with same selection rate )

Effect of the Cycle Length
As long as the cycle for SDHT is not longer than for other methods, SDHT is obviously the most efficient whatever the heritability (Fig. 3) . When its cycle is about 25% longer than that for S₁T or about 10% in comparison to S₂T, it becomes less efficient. For example, with SDHT in 4 yr and S₁T in 3 yr, the ratio of cycle length is 1.33, and then S₁T will be better than SDHT. If SDHT is in 5 yr and S₂T in 4 yr, the cycle length ratio is 1.25, and then S₂T will be better than SDHT. Note that the separations of the domains S₂T-SDHT and S₁T-SDHT are nearly vertical. This indicates a low effect of heritabilities on these boundaries, mainly for the boundary S₂T-SDHT. The boundary S₀T-SDHT clearly depends on S₀-heritability. This means that the relative cycle length of SDHT can be longer at low heritabilities than at high heritabilities. For example, with SDHT in 4 yr and S₀T in 2 yr, the ratio is 2, and then whatever the heritabilities, S₀T will be better than SDHT (approximately equal at very low heritabilities). With a shorter SDHT cycle (3 yr) and S₀T in 2 yr, with S₀-heritability less than 0.80, SDHT will be the best, whereas if h²_S0 > 0.80, it will be S₀T.

View larger version (20K): [in this window] [in a new window]   Fig. 3 Domains of efficiency for SDHT compared with S0T, S1T and S2T, according to relative cycle length (ratio of the SDHT length to the length of the compared method), and to S0 plot-heritability with (same selection intensity)

View larger version (19K): [in this window] [in a new window]   Fig. 4 Domains of efficiency for S1T compared with S0T, S2T and SDHT, according to relative cycle length (ratio of the S1T length to the length of the compared method), and to S0 plot-heritability (same selection intensity). (a) S1T > S2T and S1T < SDHT

Comparison at the Optimum
The optimum number of replications depends on the selection method, i.e. on the inbreeding coefficient (F) of selection units. Obviously, the cycle length has no influence on such an optimum. With SDHT, two replications are optimum only when h²_S0 is lower or equal to 0.2 (Fig. 5) . As the selection units have a smaller inbreeding coefficient, the optimum number of replications increases up to three for S₀T at . The optimum is relatively flat, and thus the differences in genetic advance with 1, 2, or 3 replications are small. When heritability is greater or equal to 0.5 , an evaluation based on single replicate trials ensures the best genetic advance whatever the method. For a given heritability, the optimum is approximately the same for each method. With a constant effective size, conclusions about the optimum number of replications are not changed.

View larger version (21K): [in this window] [in a new window]   Fig. 5 Genetic advance per cycle (in genetic standard deviations) as a function of the number of replications of selection units, for the same number of intercrossed plants, with the same selection intensity ( for design without replication) and with S0 plot-heritability = 0.2

	Discussion

TOP ABSTRACT INTRODUCTION Materials and methods Results Discussion Appendix REFERENCES

As far as the influence of heritability is concerned, we must note that in maize breeding for grain yield, plot heritability at the S₀ level is often about 0.40 to 0.50, leading to design–heritability greater than 0.50 with two or three replicates (Moreno-Gonzalez and Hallauer, 1982; Gallais, 1996; Sampoux and Gallais, 1996). With design heritabilities of 0.60 to 0.70 and the same selection intensity, the relative genetic gain obtained by the use of SDHT, in comparison to S₀T, is between 0 and 25%. With the same effective size, there will be no significant gain, and worse, SDHT can be lower than S₀T. Note that a gain of 10% is low in absolute value. Thus, considering HD as a costly process, its interest for the improvement of combining ability in recurrent selection is not as clear as for the improvement of line value. However, genotype x year interaction will further reduce heritability. If genotype x year interaction represents 50% of the total genetic variance, operational heritability will not be 0.60 to 0.70 but 0.30 to 0.35. Then, the advantage of SDHT will be increased. Whatever the situation, there still remains an interest in SDHT because it allows rapid development of new hybrids, particularly when off-season nurseries are not used. Moreover, HD produces completely homozygous lines, while some residual heterozygosity is possible when lines are derived by single-seed descent or pedigree selection. Then, if the HD process is expensive, it could be used every second cycle of recurrent selection to quickly develop hybrids, in alternation with the use of S₀T. S₀T in 2 yr is the shortest selection scheme available that allows separation of self-pollination and crossing to the tester. Note also that, from the point of view of the existence of genotype x year interaction, with the same expected genetic advance, a short cycle will be better than a long cycle. In 6 yr, three complete S₀T cycles can be developed, whereas only two cycles will be developed for SDHT in 3 yr. Obviously, the breeder has to consider the cost of genetic advance. However, it is sometimes efficient to invest more, even if this increases the cost of genetic advance, in order to achieve quicker varietal development, allowing success on the market, which will make the investment profitable. Use of doubled-haploids, if well controlled, is a tool to satisfy this goal.

	ACKNOWLEDGMENTS

 
The authors are very grateful to the reviewers and to Prof. Kendall R. Lamkey, Technical Editor, for their helpful suggestions and revision of the English.

Received for publication January 13, 1999.

	Appendix

TOP ABSTRACT INTRODUCTION Materials and methods Results Discussion Appendix REFERENCES

 
Derivation of Between and Within Progenies Variance
Consider, for one locus, a random mating population with alleles A^p₁, A^p₂, ... A^p_i, A^p_j and a tester population with alleles A^t₁, A^t₂, ... A^t_i, A^t_j.

The value of a genotype A^p_i, A^t_j from the population x tester cross can be written

(1)

where µ_T is the mean of all testcross progenies, ^p_i the additive effect of allele A^p_i in combination with the tester, ^t_j the additive effect of allele A^t_j in combination with the population, and ß^pt_ij the dominance effect, i.e. the interaction between two alleles, one from the population and the other from the tester.

Now consider the combining ability of a genotype A^p_i A^p_j from the S₀ population. It is

or

with

(2)

The variance among progenies will be

with

and more generally with inbred plants

(3)

The within progeny variance will be

(4)

From [1] :

According to [2], the first term is equal to 2²_AT and the last two represent variance due to the heterogeneity of the tester (²_WT). Then,

and from [4]

For a set of loci, with a population in linkage equilibrium and without epistasis, the formulae for variances remain valid, except that variance components represent summation of one-locus components over the set of loci.

	REFERENCES

TOP ABSTRACT INTRODUCTION Materials and methods Results Discussion Appendix REFERENCES

 

• Borchardt D.C., Geiger H.H. Theoretical studies on optimizing sugar beet breeding plans. In: Krajewski P., Kaczmarek Z., eds. Biometrics in Plant Breeding, Proc. 10th Meeting of the EUCARPIA section, Poznan. Wageningen, the Netherlands: EUCARPIA, 1997:61-66.
• Bordes R., Dumas de Vaux R., Lapierre A., Pollacseck M. Haplodiploidization of maize (Zea mays L.) through induced gynogenesis assisted by glossy markers and its use in breeding. Agronomie 1997;17:291-297.[Web of Science]
• Gallais A. A method of line development using haplodiploidization: The single doubled-haploid descent recurrent selection. Theor. Appl. Genet. 1988;75:330-332.[Web of Science]
• Gallais A. Optimization of recurrent selection on the phenotypic value of doubled haploid lines. Theor. Appl. Genet. 1989;77:501-504.[Web of Science]
• Gallais A. Quantitative genetics of doubled haploid populations and application to the theory of line development. Genetics 1990;124:199-206 a.[Abstract]
• Gallais A. Application of the concepts of the test value and of varietal value to the study of genetic advance in recurrent selection. Euphytica 1990;48:197-209 b.
• Gallais A. A general approach for the study of a population of test-cross progenies and consequences for the recurrent selection. Theor. Appl. Genet. 1991;81:493-503.[Web of Science]
• Gallais A. Field of efficiency of breeding methods for per se value or combining ability in plant breeding. Agronomie 1993;13:467-480 a.
• Gallais A. Efficiency of recurrent selection methods to improve the line value of a population. Plant Breeding 1993;111:31-41 b.
• Gallais A. Combined testcross and S₁ selection for the improvement of testcross and S₁ performances. Crop Sci. 1996;37:1126-1133.
• Geiger H.H., Tomerius A. Quantitative genetics and optimum breeding plans. In: Krajewski P., Kaczmarek Z., eds. Biometrics in Plant Breeding, Proc. 10th Meeting of the EUCARPIA section, Poznan, Poland. Wageningen, the Netherlands: EUCARPIA, 1997:15-26.
• Goldringer I., Brabant P., Gallais A. Theoretical comparison of recurrent selection methods for the improvement of self-pollinated crops. Crop Sci. 1996;36:1171-1180.[Abstract/Free Full Text]
• Griffing B. Efficiency changes due to use of doubled-haploids in recurrent selection methods. Theor. Appl. Genet. 1975;46:367-386.[Web of Science]
• Moreno-Gonzalez J., Hallauer A.R. Combined S₂ and crossbred family selection in full-sib reciprocal recurrent selection. Theor. Appl. Genet. 1982;61:353-358.
• Sampoux J.P., Gallais A. Expected genetic gains in testcross and S₁ performances for several populations of silage maize with combined S₁-testcross selection. Maydica 1996;41:167-179.
• Strahwald, J.F., and H.H. Geiger. 1988. Theoretical studies on the usefulness of doubled haploids for improving the efficiency of recurrent selection in spring barley. p. 1–13. In Biometrics in Plant Breeding, Proc. 5th Meeting of the EUCARPIA section, Aas, Norway. EUCARPIA, Wageningen, the Netherlands.

This article has been cited by other articles:

				A. Gallais Full-Sib Reciprocal Recurrent Selection with the Use of Doubled Haploids Crop Sci., January 28, 2009; 49(1): 150 - 152. [Abstract] [Full Text] [PDF]

				G. A. Gordillo and H. H. Geiger Alternative Recurrent Selection Strategies Using Doubled Haploid Lines in Hybrid Maize Breeding Crop Sci., May 1, 2008; 48(3): 911 - 922. [Abstract] [Full Text] [PDF]

				A. Gallais and J. Bordes The Use of Doubled Haploids in Recurrent Selection and Hybrid Development in Maize Crop Sci., December 18, 2007; 47(Supplement_3): S-190 - S-201. [Abstract] [Full Text] [PDF]

This Article Abstract Figures Only Full Text (PDF) Free Alert me when this article is cited Alert me if a correction is posted Services Similar articles in this journal Similar articles in Web of Science Alert me to new issues of the journal Download to citation manager Citing Articles Citing Articles via HighWire Citing Articles via Web of Science (8) Citing Articles via Google Scholar Google Scholar Articles by Bouchez, A. Articles by Gallais, A. Search for Related Content PubMed Articles by Bouchez, A. Articles by Gallais, A. Agricola Articles by Bouchez, A. Articles by Gallais, A.