Published online 18 December 2007
Published in Crop Sci 47:S-190-S-201 (2007)
© 2007 Crop Science Society of America
677 S. Segoe Rd., Madison, WI 53711 USA
The Use of Doubled Haploids in Recurrent Selection and Hybrid Development in Maize
A. Gallaisa,* and
J. Bordesb
a INRA-UPS-CNRS-INAPG, Station de Génétique Végétale, Ferme du Moulon, 91190 Gif sur Yvette, France
b UMR Amélioration des Plantes, INRA-UBP, 234 Avenue du Brezet, 63000 Clermont-Ferrand, France
* Corresponding author (gallais{at}moulon.inra.fr).
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ABSTRACT
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Progress made around the in situ gynogenesis technique allows production in a great number of maize (Zea mays L.) doubled-haploid (DH) lines. Doubled haploids are now largely used in maize breeding. To optimize their use in breeding schemes, it is first required to know whether genetic variation expressed at the level of DH lines is the same as at the level of lines from self-fertilization. In several experiments, with evaluation for testcross performance, good agreement appears between variance expressed in selfed progenies and DH variance for grain yield. Recurrent selection (RS) for testcross performance using doubled haploids (DH-RS) can then be compared to the use of Sn (SnT) plants (S0, S1, S2, ...). From a theoretical approach by numerical application, it was shown that, with the same selection intensity and without off-season nurseries, DH-RS in four years gives the highest genetic advance per year. With the use of off-season nurseries, the same investment in trials and the same rate of reduction of effective population size, to have the advantage of DH-RS the cycle length must be reduced to three years and for traits of low heritability. In an experiment comparing two cycles of RS-S0T selection in four years to one cycle of DH-RS (in three or four years), considering the expected gain per year with a DH-RS cycle in four years, there was an advantage to RS-S0T, whereas with a three-year cycle for the DH method both methods were expected to be equivalent. The observed genetic gains were similar for one DH-RS cycle and the two RS-S0T cycles in four years. In conclusion, there is not a greater advantage from using doubled haploids in RS. However, DH-RS has the advantage of simultaneously producing lines that are directly usable as parents of a hybrid. From a theoretical approach, it is shown that DH-RS is expected to be the best method at the level of genetic advance in variety development, even for medium heritabilities. Furthermore, the whole process appears to be less costly than conventional methods. Use of doubled haploids can thus be very efficient in maize breeding.
Abbreviations: DH, doubled-haploid • RS, recurrent selection • S0T, S1T, S2T, recurrent selection for testcross performance with S0, S1, and S2 plants, respectively • SSD, single-seed descent • VD, variety development
Received for publication April 4, 2007.
The Use of Doubled Haploids in Recurrent Selection and Hybrid Development in Maize
A. Gallaisa,* and
J. Bordesb
a INRA-UPS-CNRS-INAPG, Station de Génétique Végétale, Ferme du Moulon, 91190 Gif sur Yvette, France
b UMR Amélioration des Plantes, INRA-UBP, 234 Avenue du Brezet, 63000 Clermont-Ferrand, France
* Corresponding author (gallais{at}moulon.inra.fr).
Progress made around the in situ gynogenesis technique allows production in a great number of maize (Zea mays L.) doubled-haploid (DH) lines. Doubled haploids are now largely used in maize breeding. To optimize their use in breeding schemes, it is first required to know whether genetic variation expressed at the level of DH lines is the same as at the level of lines from self-fertilization. In several experiments, with evaluation for testcross performance, good agreement appears between variance expressed in selfed progenies and DH variance for grain yield. Recurrent selection (RS) for testcross performance using doubled haploids (DH-RS) can then be compared to the use of Sn (SnT) plants (S0, S1, S2, ...). From a theoretical approach by numerical application, it was shown that, with the same selection intensity and without off-season nurseries, DH-RS in four years gives the highest genetic advance per year. With the use of off-season nurseries, the same investment in trials and the same rate of reduction of effective population size, to have the advantage of DH-RS the cycle length must be reduced to three years and for traits of low heritability. In an experiment comparing two cycles of RS-S0T selection in four years to one cycle of DH-RS (in three or four years), considering the expected gain per year with a DH-RS cycle in four years, there was an advantage to RS-S0T, whereas with a three-year cycle for the DH method both methods were expected to be equivalent. The observed genetic gains were similar for one DH-RS cycle and the two RS-S0T cycles in four years. In conclusion, there is not a greater advantage from using doubled haploids in RS. However, DH-RS has the advantage of simultaneously producing lines that are directly usable as parents of a hybrid. From a theoretical approach, it is shown that DH-RS is expected to be the best method at the level of genetic advance in variety development, even for medium heritabilities. Furthermore, the whole process appears to be less costly than conventional methods. Use of doubled haploids can thus be very efficient in maize breeding.
Abbreviations: DH, doubled-haploid • RS, recurrent selection • S0T, S1T, S2T, recurrent selection for testcross performance with S0, S1, and S2 plants, respectively • SSD, single-seed descent • VD, variety development
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INTRODUCTION
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Until the 1990s, the low efficiency of the different techniques for the derivation of doubled-haploid (DH) maize (Zea mays L.) lines prevented the use of this tool on the scale of a conventional selection program. Production of large numbers of DH lines by induced in situ gynogenesis (Coe, 1959) is now successful in maize, whatever the genotype (Lashermes and Beckert, 1988; Chalyk, 1994; Deimling et al., 1997; Bordes et al., 1997). Therefore, doubled haploids can be routinely used in maize breeding, in population improvement and variety development (VD). The DH method is already used in many applied breeding programs (Seitz, 2005). The problems that remain to be solved are (i) knowing whether genetic variation is expressed in the same way in DH as in lines from self-fertilization, (ii) optimizing the use of doubled haploids in population improvement and VD. For its optimal use in maize breeding, it is important to know whether the use of testcross progenies from doubled haploids in recurrent selection (RS) is more efficient than the use of testcross progenies from S0, S1, or S2 plants. Furthermore, when considering the whole strategy of VD, the place of doubled haploids has to be determined. Should it be integrated within RS or just used for VD? To answer this question, experimental and theoretical studies were developed.
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Variation among DH Lines Versus Variation among Conventional Inbred Lines
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Field comparisons of doubled haploids and conventional lines have already been attempted in maize for agronomic traits. Thomson (1954) and Chase (1974) found about the same variation among spontaneous doubled haploids as among selected and unselected conventional inbred lines. Murigneux et al. (1993) and Marhic et al. (1998) did not find important differences between DH lines derived by anther culture and lines from pedigree selection or single-seed descent (SSD) evaluated for their per se value or their testcross performances. Until now, few studies have considered the genetic variance from DH lines derived by in situ gynogenesis, which appears to be the most successful technique of DH derivation. Lashermes and Beckert (1988) have shown that DH lines derived by this method were quite similar to conventional inbred lines for different morphological traits, both evaluated for per se performance. The most extensive study was that of Seitz (2005), who compared testcross performance of such lines with conventionally derived lines, and concluded that variation was the same. We have also developed an experiment aimed at comparing variation among DH lines, S1 families, and SSD families derived from the same population (Bordes et al., 2006b).
Development of Genetic Material
The material used in this study is fully described by Bordes et al. (2006b). To identify the haploid plants from gynogenesis, in the absence of an available inductor with an easily observed dominant marker, we have used a recessive marker (a glossy gene, gl6), which was thus introduced in the material from which we intended to derive doubled haploids. With this aim, a glossy population was developed from 48 inbred lines with two cycles of random mating. From this population, 150 S1 families were first produced and then DH and SSD lines were derived from them. The SSD lines (S5 families) were derived with only one family per S1. The DH lines were produced from haploid lines obtained by gynogenesis using a haploid inductor derived from WS 14 (Lashermes and Beckert 1988). Haploid plants were identified by the glossy phenotype when the first ligulate leaf appeared. Chromosome doubling was induced by colchicine treatment at the three ligulate leaf stage (Bordes et al., 1997). After chromosome doubling, 261 DH lines were obtained from only 94 S1 families, with one to eight DH lines per S1.
For their evaluation, these S1 families, DH lines, and SSD lines were crossed with the German flint inbred line D171 to produce the testcross progenies. Progeny evaluation trials were conducted in one year at three locations. In each location, the progenies of the same family (S1, DH, and SSD) were distributed in sets of 56 entries and evaluated in a complete randomized block design with two replications and two-row plots, 5.5 m long and 0.80 m between rows. Plant density was approximately 82,000 plants ha–1. At harvest, grain yield (adjusted to 15.5% moisture) was measured for all plots.
Theory
With a population assumed in linkage equilibrium, in the absence of selection and with no effect of the DH process, an equality between the means of the three types of testcross progenies (from S1, DH, and SSD lines) is expected. If the variation is expressed in the same way at the level of DH lines as at the level of Sn derived lines, in the absence of epistasis, the covariance between two relatives X and Y can be written
 | [1] |
where 
XY is the coefficient of kinship between individuals X and Y, and 
AT2 is the additive variance defined at the level of testcross progenies (Gallais, 1991). Note that as the testcross value can be considered an additive trait, there is no component due to dominance. Thus the following relationships between genetic variances and covariances (Gallais, 1991) are expected: var DH = 2 var S1; var DH 
var SSD; cov DH-S1 = cov S1-SSD = cov DH-SSD = var S1. Furthermore, the absence of epistasis can be tested at the level of DH lines by comparing genetic variances between and within S1 (Gallais, 1991).
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Results
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The similar population mean grain yield observed for DH, SSD, and S1 populations indicates the absence of directional selection in the development of DH and SSD populations (Table 1
). The four possible estimates of the genetic variance among S1 populations (GS12) were quite comparable: 29.8 for GS12 (grain yield being expressed in 100 kg ha–1), 24.01 for cov S1-DH, 22.1 for cov S1-SSD, and 23.7 for cov SSD-DH. Thus, we have used a pooled estimate to compare genetic variance among doubled haploids (GDH2) and GS12. It appeared that estimate of genetic variance among doubled haploids was significantly higher than that among S1 with a ratio GDH2 / GS12 = 1.8, close to 2 as expected in the absence of epistasis. A comparison (at threshold 0.10) between the observed value for GDH2 and that predicted by twice GS12 showed no significant differences. This is like a test of absence of epistasis, which was also shown by comparing genetic variances of DH lines between and within S1 (Bordes et al., 2006a). Results of these two tests show consistency in the expression of genetic variation at the level of DH lines and of S1 families. In contrast, the comparison between the observed value for GSSD2 and that predicted by twice GS12 showed significant difference, with too low an observed value (data not shown). Thus some factors have reduced the genetic variation at the level of SSD lines. During the process of SSD, unconscious selection of plants with mean value rather than random choice could explain such a reduction in variation. It is quite probable that plants with an extreme flowering date have not been considered. This kind of selection has not changed the mean of the population, but has affected the variance for such a trait and traits related to flowering date such as grain yield.
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Conclusions
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These results indicate that for an important agronomic trait like grain yield, the DH technique by in situ gynogenesis allows production of inbred lines showing similar genetic variation to conventional inbred lines. The greatest conformity of relative variances DH versus S1 as compared to relative variances SSD versus S1 lets us conclude that the DH production of lines through in situ gynogenesis technique is less subject to selection bias than the SSD method of production lines. Our results confirm those from Seitz (2005). It appears, thus, that in a selection program with early S1 tests, derivation of inbred lines by gynogenesis technique from the best S1 families can advantageously replace selfing technique.
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Use of Doubled Haploids in Recurrent Selection
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For the improvement by RS of the per se value of lines, which can be derived from a population, the use of doubled haploids appears to be a very efficient process (Griffing, 1975; Gallais, 1988, 1990, 1993; Goldringer et al., 1996). This is due to the fact that it allows direct selection on the value of lines, whereas by the use of partially inbred progenies, selection can be biased by heterozygosity. Considering the improvement of combining ability of a population, however, the usefulness of doubled haploids may be questioned. Indeed, in the absence of epistasis, the combining ability of an S0 plant (i.e., the value of its progeny from crossing with a tester) gives directly the combining ability with the tester of lines that can be derived from such a plant (Gallais, 1991). Furthermore DH allows through the increase in variance among progenies increased genetic advance per cycle, but it also increases the length of the selection cycle. Therefore, the genetic advance per unit of time will not necessarily be greater. The use of off-season nurseries can greatly affect the genetic advance per unit of time and the ranking of various methods. We have developed theoretical and experimental studies for comparing the use of DH methods versus testing of S0, S1, or S2 plants.
Theoretical Approach
Description of the Methods
The theoretical approach is based on the Bouchez and Gallais (2000) study with further developments. Table 2
describes the four methods considered, with S0 plants (RS-S0T), S1 plants (RS-S1T), S2 plants (RS-S2T), and doubled haploids (RS-DH). The selection stages of a cycle are scheduled differently according to the use of off-season nurseries and of simultaneous selfing and crossing to the tester as female (S+TC). However, it is easier to self first and thereafter cross these progenies in isolation with the tester taken as male parent. We assume that field testing has to take place in a normal growing season to get a representative agronomic evaluation. As a result, each method can be applied with varying cycle lengths. With the test of S0 plants and use of S+TC, the length of the cycle will be three years without off-season nursery, and only two years with off-season intercrossing. It cannot be shorter, as we assume 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 will be four generations long, and could last from two to four years depending on the use of off-season nurseries; a realistic length being three years. With the testing of S1 or S2 plants the cycle needs one or two more generations for selfing.
In the application of RS with doubled haploids, several lines can be derived from an S0 plant using doubled haploids. The best approach will be to derive only one line per S0 plant, which is equivalent to the classical SSD method (Gallais, 1988, 1989). When using doubled haploids, cycle length depends mostly on the length of the DH process. Without off-season generation, if we consider that the whole DH process takes two years, the total cycle length will be two years longer than with S0 testing, or one year longer than with S1 testing. If DH lines can be developed from S0 plants within one year, then DH-RS becomes comparable to RS-S1T for cycle length. With maximum use of off-season resources, all four stages of RS-S0T or RS-S1T can be realized within two years, while DH-RS as RS-S2T will take at least one more year.
Expression of Genetic Advance
The genetic advance per year can be written (Bouchez and Gallais, 2000)
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AT2 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 DH lines; var PT is the phenotypic variance among testcross progenies and is the cycle length in years.
This general expression can be transformed in terms of heritability at the level of S0 testcross progeny means (hS02):
 | [3] |
The methods being characterized by their inbreeding coefficient F and their cycle length t, they can be compared according to their expected genetic advance per unit of time for a given selection intensity.
Selection Intensities
Bouchez and Gallais (2000) have compared the methods at the same selection intensity and on the basis of the same effective size of the population of intercrossed plants. Comparison at the same selection intensity, favors the schemes with the most inbred selection units. Indeed, as an example, the selection of N completely homozygous individuals leads to an effective size which is half that with the selection of N non-inbred individuals. This is thus equivalent to applying a greater selection intensity. Furthermore, when comparing methods with different cycle length and different tools, it also appears necessary to consider the investment. To simplify, we have compared the methods for the same investment in plots per year and the same rate of reduction of effective population size. Such constraints allow the determination of selection intensity according to the method. As an example consider two cycles with S0 plants. With 200 plants per cycle and a selected proportion of 15%, the effective population size is 30 in the first cycle and 15 in the second cycle (in expectation). In the same duration a four-year DH-RS can be developed by studying 400 DH lines, and to have an effective population size of 15, it is necessary to select 30 DH lines leading to a selection rate of 7.5% (Table 3
).
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Table 3. Example of computation of selection intensities for the different methods to have the same effective population size for a given time and with the same investment in trials per year.
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Results
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Results with the same selection intensities have been reported by Bouchez and Gallais (2000). Without off-season nurseries, DH-RS in four years appears as the best method whatever the heritability. S2T in five years is 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 three years and S1T in four years are significantly better than S2T and DH-RS in five years.
With the use of off-season nurseries (Fig. 1
), whatever the heritability, S1T in two years obviously becomes more competitive than all other methods. It is followed by DH-RS in three years for medium to low heritabilities), S0T in two years, and S1T and S2T in three years. DH-RS in four years is the least efficient, especially for high heritabilities. The relative efficiencies are given in Table 4
for some given heritabilities, taking S0T in two years as a reference. Among the four most comparable schemes, with the maximum realistic use of off-season nurseries (i.e., S0T in two years, S1T in three years, S2T in three years, and DH-RS in three years), DH-RS in three years gives a gain of 27% as compared to S0 for hS02 = 0.10, whereas it is equal for hS02 = 0.80. S2T in three years is only about 10% less than DH-RS in three years whatever the heritability. DH-RS in four years is at most equal to S0T in two years at low heritability and is 25% less at high heritability. These results show the strong effect of the cycle length on the genetic advance per unit of time and underline the strong effect of off-season nurseries.
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Figure 1. Genetic advance per year, in genetic standard deviations, according to S0 heritability, with the use of off-season generations and the same selection intensity (PS0= 0.05).
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Table 4. Relative efficiency of five recurrent selection methods according to the S0 heritability (hS02), in reference to S0T in 2 yr, and with the same selection intensity.
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Considering always using of winter nurseries, with the same investment in plots per year and the same reduction in effective population size per year, the ranking of the method tends to be the same as when methods are compared with the same selection intensity (Fig. 2
), although they are more similar in their relative efficiencies. The best method is always S1 in two years, however, its advantage over S0 in two years at hS02 = 0.50 is only 15%, and is not better than DH-RS in three years for S0 heritability lower than 0.50. At low hS02 DH-RS in three years is the best method (Fig. 3
). For medium hS02, relative efficiency of DH in four years is very similar to that of S0 in two years or S1 in three years.
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Figure 2. Genetic advance per year in standard deviations according to S0 heritability, with the use of off-season generations, the same investment in trials per year and the same effective population size for a given duration.
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Figure 3. Relative efficiency of the methods according to S0 heritability, with the use of off-season generations, the same investment in trials per year and the same effective population size for a given duration.
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Conclusion
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With the use of off-season nurseries, DH-RS in a three-year cycle maintains its advantage mainly at low heritability values. It is thus necessary to have a well-controlled DH process to have DH-RS among the best methods for genetic advance per unit of time. Indeed, the use of off-season nurseries and the simultaneous selfing and crossing increase genetic advance per unit of time of conventional methods. With the constraints of same investment in trials and same reduction in genetic base the expected advantage of using DH is reduced at medium, realistic heritabilities. Thus, considering DH production as a costly process, its value for the improvement of combining ability in RS is not clear.
Experimental Approach
We have tried to compare the two schemes, RS using S1 families (i.e., S0 plants and RS using DH). In a period of four years, with the use of off-season nurseries, one cycle of DH-RS was developed in four years whereas two cycles of S0 selection were developed. Note that it would have been possible to develop the DH method in three years (Bordes et al., 2006b).
Selection Process
The population was the same as in our experiment aimed at comparing genetic variances in doubled haploids and in selfed progenies. The S1 families (which represent S0 plants) and DH lines were crossed with the German flint inbred line D171 to produce the testcross progenies. A common selection rate of 20% was applied for each selection method. Consequently, for S1 family selection, 30 S1 were selected from the 150 derived from the initial population on the basis of their testcross value and intercrossed. To initiate the second selection cycle, again 150 S1 progenies were derived at random from the first cycle population, and after their evaluation, 30 were selected and intercrossed to obtain the second cycle population. For DH selection, after evaluation of the testcross progenies from the 261 DH lines derived from the initial population, to try to maintain a similar genetic base, 52 DH lines were selected and also intercrossed. The expected population size with S0-RS was 30 in the first cycle and 15 in the second cycle. The expected inbreeding coefficient with DH-RS was 0.0247 leading to an effective population of 20 instead of 15 as for the second cycle of S0 selection. Thus, with the objective of comparing the methods with the same population size we should have selected a proportion of 15.3% instead of 20%; this means multiplying selection intensity by 1.1. However with the consideration of the same reduction in effective population size per year, the expected effective population size for DH-RS was that for a cycle in three years.
Progeny evaluation trials were conducted in only one year at three locations. In each location, progenies were arranged in sets of 56 entries and evaluated using a complete randomized block design with two replications. Population density was approximately 82,000 plants ha–1. Grain yield was adjusted to 15.5% grain moisture. For the evaluation of genetic advance, the tester used (the German flint inbred line UH002), was different from that used for selection; however, the two were related. Progenies were evaluated over a period of two years, in 2002 and 2003 in five locations.
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Results and Discussion
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The predicted genetic advance per year was 265 kg ha–1 in S0-RS versus 225 kg ha–1 in four years DH-RS (after correction for the difference in the effective population size) (Table 5
). This means an expected advantage of 18% of S0-RS as compared to DH-RS. Considering DH-RS in three years with the same selection intensity and the same investment as in four years, would be an advantage of DH-RS in three years (+13%). However for the same decrease in effective population size per year, the expected genetic advance per year is 270 kg ha–1 which is quite similar to the expected genetic advance with two S0-RS cycles. Thus, as predicted from our theoretical study, according to the S0 heritability observed, DH-RS in four years is expected to be less efficient than S0-RS, whereas DH-RS in three years is expected about as efficient as S0-RS.
After correction for difference in genetic base of both populations, the total realized gains are quite comparable: 175 kg ha–1 with S0-RS versus 182 kg ha–1 with DH-RS. With DH-RS in three years, with the same investment per year and the same effective population size, the genetic advance per year would have been 220 kg ha–1 (i.e., +26%). This is a significant advantage of DH in three years (the difference with predicted results could be due to realized heritabilities lower than the estimated heritabilities). Compared to expected gains, the lower realized gains could be due to genotype x year (or site) interactions, but also to the change of tester.
In the two years of evaluation, the estimation of genetic variances in initial and improved populations showed no significant change due to the breeding methods (Table 5). In spite of the change in tester, the genetic variance estimated for each cycle of S1 selection was similar to the genetic variance of S1 progenies used for the evaluation of observed genetic gain.
In our experiment, the cycle length for the DH selection method was four years. It would have been possible to reduce it to three years in two ways: first by deriving haploids from S0 plants; second, by suppressing the DH multiplication stage due to the low number of kernels produced by doubled haploids. Improvement of the parameters governing the DH process (haploid induction, haploid identification, and artificial chromosome doubling) would also contribute to making it shorter.
In conclusion, the experimental results tend to confirm the theoretical results. With medium to high heritabilities, there is no expected advantage of DH-RS in four years, whereas there could exist an advantage of DH-RS in three years (for the same investment per year in plots and same effective population size). We do not know of any other experiments comparing DH-RS with other methods. Note that if, as expected, the production of DH is more expensive than the production of S1 or S2 families, even with the same investment in trials, DH-RS would be more costly than the S1 or S2 method. Considering strictly the same investment in S0-RS as in DH-RS would allow increasing the number of evaluated S0. Consequently, for the same effective population size, this would allow increasing selection intensity and then genetic advance per cycle. This could cancel the possible advantage of DH-RS in three years. Therefore we can conclude that, in terms of benefits/costs ratio, use of DH in RS is not very competitive as compared to selection of S0 or S1 plants.
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Variety Development
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Pedigree selection of new lines is long and costly because it is necessary to select for combining ability with a tester. To initiate such a scheme, the testcross value is frequently evaluated on F2 plants or S1 families. Then, the use of DH has several advantages: (i) it saves time, (ii) it allows a better use of genetic variation, and (iii) it increases selection efficiency by increasing genetic variance among families and decreasing the residual variance. Moreover, when the line used as tester is a putative parent of hybrids, the selected lines can be directly used for the development of new hybrids. Indeed, if the tester is an elite line, then RS for testcross performance leads directly to new hybrids: after testing the DH testcross progenies it is only necessary to identify the best one or two, whereas with the S1 method it is necessary to add the whole process of VD from the best S1 families. Therefore, from an applied plant breeding point of view we have to consider the whole process of population improvement and VD.
Considering the expected value of the new selected varieties from a given cycle of population improvement, it is the sum of genetic advance due to population improvement and of the genetic advance due to VD. Assuming no change in genetic variances during the first cycles of selection, the total genetic advance can be written in terms of all parameters, the genetic advance per cycle of RS (
Gpop1), the genetic advance due to VD (GV), the duration of a cycle of RS (tpop), the duration of VD (tv):
 | [4] |
t being the number of years from the beginning of selection.
To simplify the consideration of VD, we have considered the case of derivation by SSD and with the use of DH. Both have the same potential and they give the potential of pedigree selection. The contribution of VD was then estimated as GV = iVDhL2GL, with iVD being the selection intensity for VD; hL2, the heritability at the level of homozygous lines; and GL2 = 2AT2, the total genetic variance among testcross progenies from homozygous lines. The proportion selected was 0.03%; in practice it is probably higher. However, this parameter does not affect the differences among the selection methods. To take into account the increase in the number of replications generally observed in the last stages of selection, we have doubled this number, which leads to the increase of heritability. The duration for the derivation of variety was equal to the length of the RS cycle + 1 yr with the DH method and + 5, 4, and 3 yr in the case of S0, S1, and S2 selection, respectively. The case of three years could correspond to the derivation of DH lines (see Appendix); four years could correspond to the derivation by SSD from S2 and S3; and five years more probably for the derivation of lines from S1. It must be noted that the conditions considered for computing genetic advance do not affect the differences among methods which depend only on the genetic advance due to population improvement.
The assumption of no change in genetic variance during the first cycles does not appear too strong. Indeed, this is supported by various experimental results showing no significant change for the first three or four cycles (Hallauer and Miranda, 1981). Furthermore, we have tested the effect of reduction in variance, by using the Bulmer (1980) formula: var A' = var A[1 – i(i – x)0.5h2], where var A (var A') is the additive variance before and after selection, i is the selection intensity, and x the abscissa of the truncation point. The results showed a decrease in the total genetic advance, but the ranking of the methods was the same as with the assumption of linearity (data not shown).
In all situations, it appears for the first three or four cycles of DH-RS an advantage of DH-RS in three years. Comparing only RS-S0 and DH-RS (Fig. 4
), whatever the heritability, we always have the ranking: DH 3 yr + 1 yr VD > DH 4 yr + 1 yr VD = S0 2 yr + 3 yr VD > S0 2 yr + 4 yr VD > S0 2 yr + 5 yr VD. Furthermore, only doubled haploids in three years allows the total genetic advance to be higher than genetic advance due to population improvement. Due to the duration of the process, VD from S0 in more than three years is always the less efficient method.
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Figure 4. Expected total genetic advance at the level of variety development (VD) from DHT-RS versus S0T-RS. Predicted results for S0T-RS in 2 yr + 3 yr for VD are the same as for DHT-RS in 4 yr and one year more for VD. For the computation we have considered constraints given in Table 3, and hS02= 0.50. Lines for DHT 4 yr + VD one year and S0T 2 yr + VD 3 yr are the same.
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Even the S1 method in two years with an extra duration for VD of only four years is not competitive with doubled haploids in three years (Fig. 5
). Doubled haploids in four years is the second method only for the first cycle, afterward S1 method will be more efficient. If VD is developed in three years (possible by the use of doubled haploids), then DH selection in three years is the best during the first cycles and then afterward S1 selection becomes the best. In comparison to S2 in three years DH selection in three years is always the best (results not shown). The conclusion is that, excluding S1 selection in two years, which can be hard to manage, at the level of the total genetic advance, the use of a three-year cycle for the DH method gives a clear advantage to the DH method.
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Figure 5. Expected total genetic advance at the level of variety development (VD) from DHT-RS versus S1T-RS. For the computation we have considered constraints given in Table 3, and hS02 = 0.50.
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When the derivation of doubled haploids is not well controlled, it could be used only for VD. Assuming that it is possible to develop varieties in three years, this increases the efficiency of S0, S1, or S2 methods, but these methods will remain generally less efficient than DH methods in three years with only one more year for VD.
The total cost of methods of VD could also be taken into consideration, although for a plant breeder what is important is to develop the best variety as quickly as possible to put it on the market as early as possible, which will make the investment profitable (Bouchez and Gallais 2000). With the existing cost ratios practiced in Europe we have attempted, as an example, to estimate the cost of the two methods experimentally studied: DH-RS in four years with one year more for VD, and S0-RS in two years with 4 additional years for VD (see Appendix for an example). In RS, it appears that the use of doubled haploids is more costly than the use of S0 or S1 (+26%) (Table 6
). This is clearly dependent on the DH lines' cost and thus on laboratory organization. However variety cost development is definitively lower than with SSD (–17%). Therefore, as a whole, when considering RS and VD, the use of DH is less costly and more efficient than conventional methods. Comparison of the methods for the same total investment will allow to study more DH lines, leading to an increase in the selection intensity and thus to an increase in the genetic advance per year. As the cost of DH derivation could still decrease, this would still give more advantage to the DH method.
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Table 6. An example of costs in euros for two cycles of S0T-RS and one cycle of DHT-RS including the cost of variety development (VD) for each breeding method, with the same number of evaluated progenies in recurrent selection (RS; 300).
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Conclusion
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It appears that the DH process with in situ gynogenesis can be considered as a system of inbreeding that does not alter genetic variation. This is also confirmed by a good agreement between theoretical and experimental results at the level of genetic advance by RS. Considering only population improvement, on a per year basis, with one cycle in four years, for medium to high heritabilities, the DH method appears to be approximately equivalent to the S0 method. For the DH method to be better, it is necessary to develop one cycle in three years. However, for medium to high heritabilities, S1-RS in two years is still expected to be more efficient. Considering population improvement and VD simultaneously, the DH system has the advantage of producing potential hybrid cultivars at each cycle. Thus, if the genetic advance per unit of time is evaluated from the point of view of VD, there is a clearer advantage to using the DH method if one cycle of RS can be developed in three years. However, it must be noted that the most efficient method would be S1-RS in two years followed by VD in three years by derivation of doubled haploids from the best S1 families, although this scheme could be hard to manage for maize. With the use of doubled haploids in RS, VD can be considered as integrated in the process of RS, which becomes a recurrent VD. In practice RS is not applied by random intercrossing; indeed, it is rather a cumulation of pedigree selection cycles. However, such an organization of selection does not change the main conclusions. Using doubled haploids, with derivation of doubled haploids from the F1, shortens the process of hybrid development and increases the genetic advance per unit of time or even of means. Furthermore, it allows efficient use of marker-assisted selection. Indeed the combination of the use of doubled haploids and molecular markers is a powerful tool at the disposal of the plant breeder to bring together in the same genotype the favorable alleles of detected quantitative trait loci in a population of crosses.
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APPENDIX
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Description of the Derivation of Variety from S0T-RS (or SnT-RS) and from DHT-RS
The following proposals are just given as examples of possible schemes. We have used these proposals for the computation of costs.
From S0-RS Program by Selfing
Thirty S1s have been selected as a result of the RS program. The best 15 are selected and then SSD lines are derived with 10 lines per S1, leading to 150 lines to study. A first evaluation of these 150 Sn families can be realized before S6 (in S4 for example). This first evaluation will be developed with the same trial network as in RS (three sites, two replications per site). The best 20 S4 lines are selected and then next year, they are studied with more accuracy, with five sites and three replications per site. On the basis of two-year evaluation, the best line is selected to develop a new hybrid with the tester. The whole process could be managed in four years.
From Sn-RS Program by Doubled Haploids
From an Sn family (n = 0, 1, or 2), crossing with the inductor is realized in the following winter after the evaluation of testcross progenies in the RS program. In the following summer, chromosome doubling is developed, followed by crossing to the tester in winter. Testcross progenies can then be evaluated in the summer of the next two years. Therefore, the whole process, with two years evaluation of testcross progenies, takes three years.
From DH-RS Program by DH
Among the 30 selected DH lines from the DH-RS program, the best 20 are selected and re-evaluated in a trial network similar to that used in the second step of the selection of the best SSD lines. The best DH lines will be selected on the basis of two-year evaluation. Therefore these lines will be evaluated during two years in different environments. This process needs only one more year than the duration of a DH-RS cycle.
Received for publication April 4, 2007.
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REFERENCES
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ABSTRACT
INTRODUCTION
