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a Dep. of Agronomy and Plant Genetics, Univ. of Minnesota, 411 Borlaug Hall, 1991 Upper Buford Cir., St. Paul, MN 55108
b Institut National de la Recherche Agronomique, Station de génétique végétale, Ferme du Moulon, 91190 Gif-sur-Yvette, France
* Corresponding author (bernardo{at}umn.edu)
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ABSTRACT |
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 TOP ABSTRACT INTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONREFERENCES |
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INTRODUCTION |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONREFERENCES |
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The number of progenies selected and recombined in recurrent selection typically ranges from NSel = 10 to 30 (Kenworthy and Brim, 1979; Hallauer, 1992; Weyhrich et al., 1998). Reducing NSel while keeping N constant would increase both the selection differential and the response achieved in the next cycle of selection. A low NSel, however, could lead to a reduced genetic variance and, consequently, a lower response in future cycles of selection (Rawlings, 1979). Theoretical results as well as empirical studies with model species have indicated that NSel values of 30 to 45 are required to maintain medium-term and long-term response to selection (Robertson, 1960; Frankham et al., 1968; Jones et al., 1968). But empirical studies in maize (Zea mays L.) (Weyhrich et al., 1998; Guzman and Lamkey, 2000) and in soybean [Glycine max (L.) Merr.] (Brim and Burton, 1979) have indicated little advantage in selecting and recombining more than NSel = 10 progenies, at least in the short term (e.g., five cycles).
Regardless of NSel, breeders usually assign equal fitness to the selected individuals in recurrent selection. Fitness refers to the number of progenies contributed by an individual to the next generation. Suppose NSel = 10 individuals are selected from N = 400 individuals. If a population size of N = 400 is to be maintained across cycles, the NSel = 10 individuals are typically recombined in such a way that each selected individual contributes 2N/NSel = 80 gametes to the next cycle. It seems arbitrary, however, to have the 10th-best individual contribute 80 gametes but to have the 11th-best individual not contribute any gametes to the next generation. Varying the fitness of the selected individuals could potentially increase the response to selection. In this scheme, the N individuals in a given cycle will be ranked according to the probability that they would produce superior progenies. The NSel individuals will then be recombined in a way that the best individual will have a higher fitness than the second-best individual, the second-best individual will have a higher fitness than the third-best individual, and so on. Depending on the criterion for defining superiority, some individuals will effectively have a fitness of zero.
Our objective in this study was to determine if varying the fitness of selected individuals increases the short-term, medium-term, and long-term response to recurrent selection. Specifically, we developed and evaluated an optimum method (Unequal Fitness) and a simplified method (Better Half) for determining the appropriate fitness of selected individuals. Optimizing the fitness of selected individuals needs to be more advantageous than simply reducing NSel to increase the selection response. We therefore studied the joint effects of having different numbers of selected individuals and different fitness of selected individuals in recurrent selection. We studied both recurrent selection based on phenotypic data and marker-assisted recurrent selection (MARS).
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MATERIALS AND METHODS |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONREFERENCES |
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We conducted 1000 repeats of each simulation experiment and averaged the results across the repeats. Selection responses were expressed in terms of units of the genetic standard deviation in cycle 0. The statistical significance (P = 0.05) of differences in selection response was determined with z-tests, using the variances of the selection response across the 1000 repeats of an experiment.
Genotypic and Phenotypic Values
In this study, genotypic and phenotypic values were defined in terms of testcross performance, which is appropriate for maize. But the results regarding the number and fitness of selected parents should generally apply to per se performance as well. Details of the procedures we used to simulate genotypic and phenotypic values have been described in previous articles (Bernardo, 2004; Bernardo and Charcosset, 2006). Each repeat of an experiment differed in the genetic map, the genotypes of the individuals sampled, and their phenotypic values.
The base population for both phenotypic recurrent selection and MARS was a simulated F2 generation formed by selfing the F1 between two parental inbreds. The F2 population was segregating at 100 codominant marker loci and l = 10, 40, or 100 QTL. The sizes of the chromosomes and of the entire genome (1749 cM) corresponded to those in a published maize linkage map (Senior et al., 1996). The genome was divided into 100 bins of 1749/100 
17 cM. A marker was assumed randomly located (according to a uniform distribution) within ± 5 cM of the midpoint of each bin. The l QTL were randomly located among the 10 chromosomes according to a uniform distribution over the total genome. In each simulated cycle of selection, F2 (in cycle 0) or S0 individuals (after cycle 0) were selfed and testcrossed to an unrelated inbred tester. Testcross genotypic values were simulated according to metabolic control theory as outlined by Bost et al. (1999) and Bernardo and Charcosset (2006). The effects of the l QTL followed a geometric distribution, where few QTL had large effects and many QTL had small effects. Specifically, the first QTL had the largest effect, the second QTL had the second-largest effect, and the lth QTL had the smallest effect. The first parent had the favorable allele at even-numbered QTL and the less-favorable allele at odd-numbered QTL. Coupling and repulsion linkages were therefore generated at random, given that QTL positions were randomly assigned without regards to the magnitude of QTL effects.
Random nongenetic effects were added to the genotypic values to obtain phenotypic values. The random nongenetic effects had a normal distribution with a mean of zero and were scaled so that broad-sense heritability among testcrosses, on an entry-mean basis, was H = 0.20, 0.50, or 0.80 in the initial F2 population. The amount of nongenetic variance (VE), for each level of H, was constant across cycles of selection. Although the true values of the genetic variance (VG) and VE were known, these parameters were estimated in each cycle of phenotypic recurrent selection. Estimates of VG and VE in each cycle were later used in calculating the fitness of selected individuals.
Estimation of Marker Effects and Marker-Assisted Recurrent Selection
In MARS, markers associated with the trait were identified and their effects were estimated only in the initial F2 population (i.e., cycle 0). First, multiple regression of phenotypic value on the number of marker alleles (0, 1, or 2) from the first parental inbred was performed on a chromosome-by-chromosome basis. Significant markers on each chromosome were identified by backward elimination. Second, multiple regression coefficients were obtained by jointly analyzing all the markers found significant in the per-chromosome analysis. Standard procedures were used to handle any singularities encountered in multiple regression analysis (Press et al. 1992, p. 56). Relaxed significance levels (
= 0.20, 0.30, and 0.40), which have been found to maximize the response to MARS (Hospital et al., 1997), were used.
In practice, cycle 0 of MARS in maize involves marker-assisted selection in regular selection seasons and locations (Koebner, 2003; Johnson, 2004). Selection in cycle 0 was therefore based on both phenotypic and marker data. In contrast, cycles 1 to 3 of MARS in maize are conducted in an off-season (e.g., winter) nursery, where phenotypic evaluations are not meaningful but three generations can be grown in 1 yr (Koebner, 2003; Johnson, 2004). Selection in cycles 1 to 3 was therefore based on markers alone. We simulated the following procedures in MARS. In cycle 0, a marker score (Lande and Thompson, 1990) for each family was calculated from the multiple regression coefficients for the markers with significant effects. This marker score was then combined with the individual's phenotypic value in a least-squares selection index as outlined by Lande and Thompson (1990), but with the restriction that the weight for the phenotypic value was always positive (Hospital et al., 1997). In cycles 1 to 3, only the marker scores were calculated.
Equal Fitness and Better Half Methods
In the Equal Fitness method, the N individuals in each cycle were ranked according to their phenotypic mean (phenotypic recurrent selection), selection index value (cycle 0 in MARS), or marker score (cycles 1 to 3 in MARS). The top NSel individuals were selected, without considering whether the means of the poorest selected individual and of the best nonselected individual were significantly different. The number of pairwise crosses among the NSel selected individuals was NCross = NSel(NSel – 1)/2 (Fig. 1
); selfs and reciprocal crosses were excluded. Each of the NCross pairwise crosses had an equal number or nearly equal number of progenies in the next cycle of selection. Suppose NSel = 4 individuals were selected out of N = 100. In this situation, each of the NCross = 6 crosses contributed [|N/NCross|] = [|100/6|] = [|16.67|] = 16 progenies to the next cycle, where the [| |] symbol denotes the integer function. Given that 6 crosses x 16 progenies per cross would lead to only 96 progenies, a total of 100 – 96 = 4 crosses were selected at random. Each of these four random crosses then contributed one additional progeny to the next cycle. On the other hand, NCross sometimes exceeded N, e.g., N = 100, NSel = 20, and NCross = 20(19)/2 = 190. In this situation, 100 out of the 190 crosses were selected at random, and each of these 100 crosses contributed one progeny to the next cycle.
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Unequal Fitness
In the Unequal Fitness method, the number of progenies contributed by cross i was proportional to the probability that the cross would produce superior progeny. This probability was denoted by pi. In this study a progeny was considered superior if it had a genotypic mean in the top 1% of the population. This percentage corresponded to that of the best individual in the most common population size (N = 100) we studied. In preliminary studies, we also considered upper-tail probabilities of 5 and 0.1%. Upper-tail probabilities of 5, 1, or 0.1% did not affect the usefulness of the Unequal Fitness method relative to the Equal Fitness and Better Half methods (results not shown). Compared with less-stringent probabilities, an upper-tail probability of 0.1% led to a slightly higher short-term response but a slightly lower long-term response.
Suppose cycle k has a mean of µCycle k (Fig. 2 ) and a genetic variance of VG(Cycle k). The dotted vertical line in Fig. 2 depicts the threshold above which the top 1% of individuals in cycle k are found. Two individuals in cycle k are crossed to form Cross 1, and the progenies in Cross 1 have a mean (µ1) greater than µCycle k but a genetic variance less than VG(Cycle k). A second pair of individuals in cycle k are crossed to form Cross 2, and the progenies in Cross 2 have a mean (µ2) greater than µ1 but a genetic variance less than that in Cross 1. The probability of progenies exceeding the 1% threshold is depicted by p1 in Cross 1 and p2 in Cross 2 (Fig. 2). Given that p2 is greater than p1, the number of progenies contributed by Cross 2 would be greater than the number of progenies contributed by Cross 1.
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Unequal Fitness in Phenotypic Recurrent Selection
In phenotypic recurrent selection, the threshold in cycle k was estimated as T = µCycle k + zT [VG(Cycle k)]1/2, where µCycle k was the estimated mean phenotypic value in cycle k; VG(Cycle k) was the estimate of VG in cycle k; and zT was the one-sided z-value for the threshold (2.326 for 1%). Suppose vj was the phenotypic value of individual j whereas vj' was the phenotypic value of individual j'. The mean of cross i was predicted as µi = µCycle k + H [1/2 (vj + vj') – µCycle k], where H was the estimate of broadbase heritability in cycle k. The genetic variance in cross i was predicted as VG(i) = [1 – 1/(2NParents)]VG(Cycle k) = 0.75VG(Cycle k) (Lande, 1980), where NParents was equal to 2 because each pairwise cross was formed by mating two individuals. In phenotypic recurrent selection, the crosses between the NSel individuals therefore differed in their predicted means but had the same predicted genetic variance.
The probability of superior progenies in cross i was then a function of zi = (T – µi)/[VG(i)]1/2. Assuming a standard normal distribution, pi was equal to the one-sided probability that corresponded to zi. The number of progenies to be contributed by cross i was determined through the following steps. First, the relative fitness of each cross (i.e., among the NSel individuals) was calculated as pi' = pi/
pi. Second, the minimum, nonzero pi' among all crosses was determined. If the minimum pi' was less than 1/N (i.e., the minimum contribution to the next cycle was one progeny), then this minimum pi' was set equal to zero. Steps 1 and 2 were then repeated until the minimum, nonzero pi' was greater than 1/N. Third, the number of progenies from each cross was calculated as Ni = [|Npi'|]. Finally, the total number of progenies was calculated as Ni. If, due to rounding error, Ni was less than N, then adjustments similar to those for the Equal Fitness method were made.
Unequal Fitness in Marker-Assisted Recurrent Selection
The availability of marker-effect information in MARS permitted the modeling of the variance in a given cross in addition to its mean. The procedures for the Unequal Fitness method in phenotypic recurrent selection and in MARS therefore differed only in the calculation of the predicted mean and genetic variance in a cross. Procedures for calculating T, zi, pi, pi', and Ni in MARS were similar to those used for phenotypic recurrent selection.
In MARS, µCycle k and VG(Cycle k) were calculated from selection index values in cycle 0 and from marker scores in cycles 1, 2, and 3. Suppose cross i was created by crossing individuals j and j' in cycle k. In cycle 0, the predicted mean of cross i (µi) was calculated as the mean selection index value of individuals j and j'. Likewise, µi in cycles 1, 2, and 3 was calculated as the mean marker score of individuals j and j'.
Three methods were used to model the genetic variance within cross i: Expected Variance, Immediate Variance, and Equal Variance. Suppose the favorable allele at a significant marker was denoted by + and the less favorable allele was denoted by –. The estimated marker effect at the mth significant marker was bm. In the Expected Variance method, the variance at the locus was modeled as 2pqb2m (Falconer, 1981, p. 116), where p was the frequency of the + allele and q was the frequency of the – allele. The variance due to the mth marker was therefore 0.5b2m if the parental genotypes of cross i were ++ and – – or were +– and +– (i.e., allele frequencies of 0.5); 0.375b2m if the parents were ++ and +– or were +– and – – (i.e., allele frequencies of 0.75 and 0.25); and zero if both parents were homozygous for the same allele (i.e., allele frequencies of 1 or 0). The expected variance in cross i was then calculated as the sum of variances across significant markers, assuming that the selected markers were independent.
The Expected Variance method modeled the genetic variance expected on random mating among the progenies of the cross, but it did not model the genetic variance expressed immediately in the cross. For example, the progenies from mating a ++ individual and a – – individual would all have the +– genotype. At this locus, the progenies will all have the same genotypic value in the cross [i.e., immediate VG(i) = 0] but will have an expected variance greater than zero on random mating. In the Immediate Variance method, the variance due to the mth marker was calculated as 0.5b2m if both parents were +–; 0.25b2m if the parents were ++ and +– or were +– and – –; and zero for all other pairs of parental genotypes. The immediate variance in cross i was calculated as the sum of variances across significant markers.
In the Equal Variance method, VG(i) was assumed constant across all crosses. Specifically, VG(i) was modeled using the variance among selection index values in cycle 0 and among marker scores in cycles 1 to 3.
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RESULTS AND DISCUSSION |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONREFERENCES |
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Among the 60 comparisons for short-term response (i.e., four genetic models, three levels of H, and cycles 1–5), the maximum response with the Unequal Fitness method was numerically higher than the maximum response with Equal Fitness method in 28 instances (47%; Fig. 3 ). The maximum response with the Better Half method was numerically higher than the maximum response with the Equal Fitness method in 42 instances (70%). Yet even with the large number of repeats (1000) of the simulation experiments, most of the differences were statistically insignificant (P = 0.05). The maximum response with the Unequal Fitness method was significantly higher than the maximum response with the Equal Fitness method in only two instances (3%). The maximum response with the Better Half method was significantly higher than the maximum response with the Equal Fitness method in only eight instances (13%). Overall, these results indicated that simply reducing NSel is superior to varying the fitness of selected individuals in short-term phenotypic selection. The appropriate NSel in phenotypic selection will be discussed later in the Rule-of-Thumb for NSel section.
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= 0.20, 0.30, or 0.40) for detecting QTL and considered a population size (N = 100) typically used in MARS (Hospital et al., 1997; Johnson, 2001). The use of relaxed significance levels typically led to the detection of 20 to 40 markers with significant effects for the quantitative trait (results not shown). In a previous study we found that for the 100 QTL, N = 100, H = 0.20 genetic model, the use of = 0.30 led to an average of 37 markers declared significant (Bernardo and Charcosset, 2006). But the variance due to these significant markers was twice the amount of VG, indicating an overestimation of QTL effects (Beavis, 1994). Given these previous results, we initially speculated that estimating the effects of 20 to 40 markers from a population size of N = 100 would not lead to sufficiently precise predictions of genetic variances. The results for the 10 QTL, N = 100 model, the 40 QTL, N = 100 model, and the 100 QTL, N = 100 model confirmed this speculation. However, a larger population size of N = 400 (i.e., 40 QTL, N = 400 model) still did not lead to any advantage of the Unequal Fitness method over the Equal Fitness method in MARS. This result suggests that even larger population sizes should be used, although in practice population sizes larger than 400 would be prohibitive. This result may also suggest that the contribution of differences in genetic variances to the fitness of crosses is intrinsically limited when compared to that of the mean, but we were unable to confirm this speculation, which deserves further investigation.
Medium- and Long-Term Response
For medium-term (cycles 6–15) response to phenotypic selection, the Better Half and Unequal Fitness methods were usually superior to the Equal Fitness method (Fig. 3). Consider the genetic model of 40 QTL, N = 100, and H = 0.20 (Table 1). In cycles 1 to 5 (short-term response), the three methods lead to similar maximum responses. But in cycle 10 (medium-term response), the maximum responses with the Better Half (5.14) and Unequal Fitness methods (5.09) were both significantly higher than the maximum response with the Equal Fitness method (4.90).
Among 90 comparisons for medium-term response (i.e., three genetic models, three levels of H, and cycles 6–15), the maximum responses with the Unequal Fitness or Better Half methods were numerically higher than the maximum response with the Equal Fitness method in 82 instances (91%; Fig. 3). Furthermore, the maximum response with the Unequal Fitness method was significantly higher than the maximum response with the Equal Fitness method in 42 instances (47%), whereas the maximum response with the Better Half method was significantly higher than the maximum response with the Equal Fitness method in 59 instances (66%). The advantage of the Better Half method was greatest in the middle cycles of medium-term selection (cycles 9–12). Across all cycles, the maximum responses were usually numerically higher with the Better Half method than with the Unequal Fitness method, although most of the differences were insignificant. Overall, these results indicated that the Better Half method is useful for increasing the response to medium-term selection.
For long-term response (cycles 16–30), the superiority of the Better Half and Unequal Fitness methods over the Equal Fitness method tended to diminish toward the later cycles of selection (Fig. 3). Again consider the genetic model of 40 QTL, N = 100, and H = 0.20 (Table 1). Compared to the Equal Fitness method, the Better Half method continued to have significantly higher maximum responses in cycles 20 and 25. By cycle 30, however, the maximum response with the Better Half method was no longer significantly higher than the maximum response with the Equal Fitness method. For this genetic model, the maximum responses with the Unequal Fitness method in cycles 20, 25, and 30 were not significantly higher than the maximum responses with the Equal Fitness method. Among 135 comparisons for long-term response (i.e., three genetic models, three levels of H, and cycles 16–30), the maximum response with the Better Half method was significantly higher than the maximum response with the Equal Fitness method in 62 instances (46%; Fig. 3). The maximum response with the Unequal Fitness method was significantly higher than the maximum response with Equal Fitness method in only 37 instances (27%).
Based on theory, we expected the Unequal Fitness method to be superior to the Better Half method. It was unclear why the Unequal Fitness method was not superior to the Better Half method. The Better Half method depends on rankings of selected individuals, whereas the Unequal Fitness method depends on estimates of their mean performance. In practice, ranks are generally considered more robust and less prone to error than estimates of mean performance, and this robustness may have contributed to the superiority of the Better Half method over the Unequal Fitness method. From a practical standpoint, the Better Half method is also simpler and easier to apply in a breeding program than the Unequal Fitness method.
There was no clear difference among methods in the variance of the selection response (i.e., across the 1000 repeats of the simulation experiments). In general, the effect of the Equal Fitness, Unequal Fitness, and Better Half methods on the variance of the response was minor compared with the effects of the cycle of selection (larger variance of response at later cycles), heritability (larger variance of response at lower H), and NSel (larger variance of response at lower NSel). Consider the 40 QTL, N = 100 genetic model. For NSel = 20 and H = 0.80, the variance of the response in cycle 1 was 1.60 with Equal Fitness, 1.60 with Unequal Fitness, and 1.59 with the Better Half method. For the Better Half method, this variance of the response in cycle 1 increased to 1.76 when H was reduced from 0.80 to 0.20, and it increased further to 2.02 when H was reduced from 0.80 to 0.20 and NSel was reduced from 20 to 3. With H = 0.80 and NSel = 20, the variance of the response increased from 1.59 in cycle 1 to 2.54 in cycle 30.
The effective population size is maximized when the selected parents contribute equal numbers of gametes to the next generation (Falconer, 1981, p. 67). For a given NSel, the effective population size is therefore larger with the Equal Fitness method than with the Unequal Fitness and Better Half methods. The results therefore indicated that, for a given NSel, the reduction in effective population size due to variable fitness in the Unequal Fitness and Better Half methods has only a very limited effect on the variance of the response.
Rule-of-Thumb for NSel
If changing NSel is preferable to varying the fitness of selected individuals, particularly in short-term selection, what value of NSel should be used? To maximize the genetic gain within cycle 0, the optimum number of selected individuals should be NSel = 1 (i.e., select the best individual in cycle 0 and develop an inbred or a cultivar directly from it). To maximize the genetic gain achieved in cycle 1, the best two individuals in cycle 0 should be selected and crossed to form cycle 1; selecting the third-best cycle 0 individual would decrease the selection differential and, consequently, decrease response to selection achieved in cycle 1. So if the number of selected individuals should be NSel = 1 to identify the best individual in cycle 0 and NSel = 2 to maximize the gain achieved in cycle 1, would the appropriate number of selected individuals be NSel = 3 for selection until cycle 2, NSel = 4 for selection until cycle 3, NSel = 5 for selection until cycle 4, and NSel for selection until cycle NSel – 1?
This rule-of-thumb for determining the optimum NSel is depicted by the dotted diagonal lines in Fig. 4 , for NSel = 2, 3, 4, 5, 10, 15, 20, 25, 30, 35, and 40 and for cycles of selection equal to NSel – 1 until cycle 29. The size of the plotted circles in Fig. 4 is proportional to the number of times, across the different genetic models studied, a particular NSel led to the maximum response in a given cycle of selection, with NSel being constant across cycles of selection. For the Equal Fitness method, the rule-of-thumb gave good predictions of the optimum NSel, particularly for short-term selection. In medium- to long-term selection, the optimum NSel varied mostly between NSel = 10 and 30. Nevertheless, the rule-of-thumb provided good approximations of the mean of the optimum NSel values for medium- and long-term selection. This rule-of-thumb obviously recognizes that for short-term recurrent selection where maintaining genetic variance is not of primary concern, selecting only a few individuals in each cycle would maximize the selection differential and the short-term response. On the other hand, in long-term selection a large number of individuals should be kept in each cycle to maintain genetic variance and sustain the response to selection. As we mentioned in the previous section, selecting a large number of individuals would also lead to less variability in the response.
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We were unable to derive an analytic proof for this simple rule-of-thumb. How useful it will be in practice remains to be seen, as breeders usually do not specify in advance how many cycles of recurrent selection will be conducted in a breeding population. Yet to the extent that the duration of a recurrent selection program is planned, this rule-of-thumb should provide a useful guide for determining NSel. As we previously mentioned, the number of individuals selected in recurrent selection programs typically ranges from NSel = 10 to 30 (Kenworthy and Brim, 1979; Hallauer, 1992; Weyhrich et al., 1998). These values of NSel are larger than those we are recommending for short-term selection. Perhaps part of the reason for these larger NSel values is because selection programs are initiated without specifying the number of cycles to be conducted, larger NSel values are used so that sufficient genetic variance will be retained should selection be continued in the long-term. We argue, however, that the low NSel values we recommend for short-term selection are consistent with those used in inbred development. Maize inbreds are usually developed from the cross between only two inbreds (Hallauer, 1992). We reason that if breeders can successfully develop elite inbreds from the cross of only two parental inbreds, then NSel values of 2 to 5 are reasonable for short-term recurrent selection.
In MARS, the NSel values that led to the maximum response ranged from 2 to 10 but were mostly between 2 and 4 (Table 2). These numbers of selected individuals are lower than those used in MARS in maize (Edwards and Johnson, 1994). Given that MARS comprises four cycles of selection, the rule-of-thumb indicates that NSel = 5 should be used in MARS. The differences in response in MARS with NSel = 2, 3, 4, or 5 were usually small (results not shown). Consider the genetic model of 40 QTL, N = 100. When heritability was H = 0.20, the response to MARS with the Equal Fitness method was 1.31 with NSel = 2, 1.36 with NSel = 3, 1.43 with NSel = 4, and 1.42 with NSel = 5. When the heritability increased to H = 0.80, the response was 3.10 with NSel = 2, 3.10 with NSel = 3, 3.09 with NSel = 4, and 3.04 with NSel = 5.
In conclusion, simply reducing NSel is superior to varying the fitness of selected individuals in short-term phenotypic selection. Varying the fitness of selected individuals is most useful in medium-term recurrent selection. We recommend the Better Half method over the Unequal Fitness method because of its simplicity and because it remained superior to the Equal Fitness method over more cycles of selection. Varying the fitness of selected individuals is not useful in marker-assisted recurrent selection, which is short-term. As a rule-of-thumb, we suggest that NSel should be roughly equal to the number of cycles for which selection will be conducted.
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ACKNOWLEDGMENTS |
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Received for publication January 26, 2006.
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