Crop Science 41:1513-1516 (2001)
© 2001 Crop Science Society of America
CROP BREEDING, GENETICS & CYTOLOGY
Effect of Number of Seed Bulked and Population Size on Genetic Variability When Using the Multiple-Seed Procedure of SSD
Raul Macchiavelli and
James S. Beaver*
Dep. of Agronomy and Soils, Univ. of Puerto Rico, P.O. 9030, Mayaguez, PR 00681-9030
* Corresponding author (j_beaver{at}rumac.upr.clu.edu)
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ABSTRACT
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Single-seed descent is used by grain legume breeders to maintain genetic variability in populations of advanced generation lines. To reduce labor costs, breeders often use a multiple-seed procedure in which a single pod rather than a single seed is harvested from each plant and bulked. This paper studied the distribution of the proportion of original F2 plants represented after advancing populations ranging from 100 to 600 plants from the F2 to the F6 generation when the multiple-seed procedure of SSD is used. Since the analytical solution to this problem is intractable, involving a 4-fold convolution of a hypergeometric distribution, a simulation was run in SAS to estimate this probability distribution. An increase in the size of the population advanced from the F2 to the F6 generation did not influence significantly the mean proportion of F2 plants represented in the F6 generation but decreased its variability. An increase in the number of seed per pod from two to six reduced the mean proportion of F2 plants represented in the F6 generation from 0.45 to 0.35, but did not decrease significantly the standard deviations of the distributions. Using the multiple-seed procedure, grain legume breeders could expect, on the average, that at least every third F6 line would be derived from a different F2 plant. This should generate considerable genetic variability for the selection for quantitatively inherited traits such as seed yield.
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INTRODUCTION
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SINGLE-SEED DESCENT is a method that permits plant breeders to advance generations while maintaining genetic variability (Johnson and Bernard, 1962). It is well suited to environments such as winter nurseries that are not representative of the target environment for cultivars (Fehr, 1987). As many as three generations of soybeans [Glycine max (L.) Merr.] can be grown each year in Puerto Rico, permitting advanced lines (F6) to be developed within 2 yr. Single-seed descent may permit greater genetic gain than pedigree selection because of larger genetic variances and improved selection efficiency as the result of the evaluation of advanced generation lines (Casali and Tigchelaar, 1975).
Fehr (1987) describes three procedures that use the concept of single-seed descent. The single-seed procedure permits the greatest number of F2 plants to be represented in subsequent generations. However, this labor-intensive procedure is difficult to implement when several generations are to be advanced each year. The single hill procedure ensures that most F2 plants will be represented in later generations but this approach requires more land and record keeping than single seed descent. Soybean breeders frequently use the multiple-seed procedure to avoid high labor costs associated with single-seed and single hill procedures. Pods containing 2 to 3 seed are harvested and bulked from soybean plants in segregating populations. Although it is recognized that this practice reduces genetic variability, the magnitude of the reduction has not been quantified.
Soybean breeders have used single-seed descent to improve quantitatively inherited traits such as seed yield (Empig and Fehr, 1971). Boerma and Cooper (1975) found single-seed descent to be more efficient than pedigree selection and early-generation testing for yield improvement of soybeans. Most populations advanced by soybean cultivar development programs using the multiple-seed procedure are derived from elite x elite crosses which would reduce segregation for many traits of economic importance.
Other grain legumes such as the common bean (Phaseolus vulgaris L.) can have twice as many seeds per pod than soybeans (Laing et al., 1984). Bulking pods with a greater number of seeds per pod would reduce genetic variability but there are no estimates of the magnitude of effect of bulking more than one seed per pod. The objective of this research was to estimate the effect of number of seed bulked and population size on genetic variability when the multiple-seed procedure of single seed descent is used.
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MATERIALS AND METHODS
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Under the simplifying assumptions that all seed planted produced progeny, there is no selection pressure, and the number of seeds per pod (m) remains constant, we can study the probability distribution of the number of families (N) represented in the next generation. This distribution can be derived from the multivariate hypergeometric model. Under the multiple-seed procedure of SSD, mN seed is harvested but only N seed is planted in the subsequent generation. Suppose, for example, that there are three seed per pod (m = 3). If all the N original F2 families are represented once in F3, then there has to be exactly one seed from each family selected. The probability of this event is 3-N (3N)!/N! (2N)!. Similarly, the probability that all but one F2 families are represented is 3-(N-1) (3N)!/(N - 2)! (2N)!. In order to find the probability that there are 2 families not represented in F3, we need to add the probability of the following two events: that there are one family represented with 3 seeds, N - 3 families represented with 1 seed each, 2 families not represented and that there are 2 families represented with 2 seeds each, N - 4 families represented with 1 seed each and 2 families not represented. The computations get more and more cumbersome as we consider the other possible values (i.e., 3, 4,..., etc., families not represented).
To consider what happens in further generations and remembering that the main interest is the F6, we would need to integrate appropriate conditional probabilities. For example, the probability that there are 2 F2 families not represented in F4 can be computed by adding the conditional probabilities that there are 2 F2 families not represented in F4 given one the following three conditions: that there were 2 F2 families not represented in F3, that there was 1 F2 family not represented in F3, and that all F2 families were represented in F3. Analytically this becomes intractable, and hence a simulation was necessary to perform the computations.
A SAS macro program (SAS Institute, 1990) was used to simulate the number and proportion of F2 families which were represented in F6 after bulking and randomly selecting seeds. The following algorithm was used.
- From N consecutive numbers, each repeated m times (representing N families and m seeds per pod), select randomly without replacement N numbers (representing N seeds to be advanced to the next generation).
- Repeat these N numbers m times each (representing the m seeds per pod in the next generation).
- Iterate steps 1 and 2 four times (representing the advancement from F2–F6).
- Count the number and proportion of different families represented in F6.
The scenarios considered were the 30 combinations of the following values of N (size of the F2 population): 100, 200, 300, 400, 500, and 600; and m (number of seeds per pod): 2, 3, 4, 5, 6. For each scenario, the algorithm was iterated 5000 times to obtain a reliable estimate of the probability distribution of the proportion of F2 families represented in the F6 generation.
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RESULTS AND DISCUSSION
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The mean proportion of F2 plants represented at least once declined as the population advanced from the F3 to the F6 generation (Table 1). Bulking lines from elite x elite crosses in earlier generations would result in a greater representation of the original F2 population.
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Table 1. Effect of number of seed per pod bulked and population size on genetic diversity when using the multiple-seed procedure (5000 iterations of each case).
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Increasing the size of the population from 100 to 600 plants had little effect on the mean proportion of F2 plants represented in the F6 generation (Table 1). The decrease in the mean proportion was 
0.03 when population size increased from 100 to 600 plants. However, increased population size did reduce the standard deviation and the range of the expected proportion of F2 plants that would be represented in the F6 generation. Casali and Tigchelaar (1975) observed that at low heritabilities, the possibility of maintaining larger numbers of lines with single-seed descent more than compensated for genetic progress under pedigree or mass selection. Van Oeveren and Stam (1992) found that single-seed descent produced poor results when <100 F2 plants were selected for generation advance.
Number of seed per pod bulked had a larger effect on the proportion of F2 plants represented in the F6 generation than population size. At a population size of 600, the portion of F2 plants represented in the F6 generation decreased from 0.45 to 0.35 when the bulked number of seed per pod increased from 2 to 6 (Table 1). However, number of seed per pod bulked had little effect on standard deviations and the range of the proportion of F2 plants represented in the F6 generation. Approximately 30 to 40% of the original F2 plants would be represented at least once when six seeds per pod of 600 pods were bulked and advanced to the F6 generation. Using the multiple-seed procedure, grain legume breeders could expect, on the average, that at least every third F6 line to be derived from a different F2 plant. This would generate considerable genetic variability for the selection of quantitatively inherited traits.
Soybean breeders have used the multiple-seed procedure of single-seed descent to improve traits with low heritability such as seed yield. The mean proportion of F2 plants represented in the F6 generation would only differ by 0.04 for a grain legume with three seeds per pod such as soybeans and a crop with six seeds per pod such as the common bean (Table 1).
Compared with F6 lines derived from single-seed descent, the clusters of F6 sister lines derived from the multiple-seed procedure would have less genetic variability. Single seed descent, however, permits each F2 plant to be represented only once in the F6 generation. Unlike single-seed descent, the multiple-seed procedure would allow plant breeders to benefit from divergence in segregation patterns in lines derived from the same F2 plant. For a trait controlled by only three independent pairs of alleles, 50% of the F2 plants would segregate in subsequent generations for two or more of the pair of alleles. Therefore, F6 sister lines derived from the same F2 plant would often have different genotypes.
The mean proportion of F2 plants represented in the F6 generation would change very little as population size increased. An increase in population size, however, would increase the total number of F2 plants represented in subsequent generations.
When the genetic variance of a trait is additive, the means of the generations do not change with inbreeding (Brim, 1966). In the absence of dominance, the distribution of the means of F6 lines developed from single-seed descent was found to be similar to the genotypic distribution of F2 individuals (Snape and Riggs, 1975). However, genotypic variance almost doubled from the F2 to the F6 generation. Knowledge of the minimum number of F2 plants represented in the F6 generation would permit plant breeders to adjust population size to compensate for expected loss in genetic variability.
When the objective of the plant breeding program is to advance multiple generations per year, both time and labor can become limiting factors during the harvest. Plant breeding programs that use single-seed descent must manually harvest each generation an individual seed from a large number pods. On the other hand, machinery can be used in the field to plant and harvest a larger population size to compensate, in part, for the loss in genetic variability resulting from the use of the multiple-seed procedure of SSD. Breeders of grain legumes such as common beans, which produce as many as six seeds per pod, might need to advance larger populations than are needed for soybeans.
Received for publication May 22, 2000.
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REFERENCES
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- Boerma, H.R., and R.L. Cooper. 1975. Comparison of three selection procedures for yield in soybeans. Crop Sci. 15:225–229.[Abstract/Free Full Text]
- Casali, V.W.D., and E.C. Tigchelaar. 1975. Computer simulation studies comparing pedigree, bulk, and single seed descent selection in self pollinated populations. J. Am. Soc. Hort. Sci. 100:364–367.
- Empig, L.T., and W.R. Fehr. 1971. Evaluation of methods for generation advance in bulk hybrid soybean populations. Crop Sci. 11: 51–54.
- Fehr, W. 1987. Principles of cultivar development: Volume 1, Theory and technique. Macmillan Publishing Co., New York.
- Johnson, H.W., and R.L. Bernard. 1962. Soybean genetics and breeding. Adv. Agron. 14:149–221.
- Laing, D.R., P.G. Jones, and J.H.C. Davis. 1984. Common bean (Phaeolus vulgaris L.). p. 305–351. In P.R. Goldsworthy and N.M. Fisher (ed.) The physiology of tropical field crops. John Wiley & Sons, Inc., New York.
- SAS Institute, Inc. 1990. SAS Guide to macro processing. Version 6, Second Edition. SAS Institute, Inc., Cary, NC.
- Snape, J.W., and T.J. Riggs. 1975. Genetical consequences of single-seed descent in the breeding of self-pollinated crops. Heredity 35: 211–219.
- Van Oerveren, A.J., and P. Stam. 1992. Comparative simulation studies on the effects of selection for quantitative traits in autogamous crops: early selection versus single seed descent. Heredity 69:342–351.
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ABSTRACT
INTRODUCTION
