The development of base populations goes through an initial stage of selecting parental materials and, later, of repeated crosses that seek to liberate additional genetic variability to be taken advantage of in subsequent selection cycles. Hanson (1959) concluded that at least one, although preferably four recombination cycles, should precede the selfpollinating generations to permit breaking linkage groups and, thus, increasing recombination. For rice, Fujimaki (1979), following Hanson’s suggestions (1959), recommends three recombination cycles before the population is selfpollinated and enters the selection stage.
Studies were done on rice to determine the relationship between the number of recombination cycles and the average performance of derived individuals and the population’s genetic variation. They showed that no advantages exist in carrying out recombination cycles, or more than one recombination cycle, between F_{2} plants, because neither the mean nor the genetic variance increases for the various traits evaluated (MarínGaravito, 1994; CabezasSantacruz, 1995; Ospina et al., 1997).
In Brazil, no records exist of studies that have been developed to evaluate the efficiency of carrying out recombination cycles with base populations of rice, and their relationships with the released genetic variability. This is important, considering that additional recombination cycles demand more time and resources. Hence, a study was developed to evaluate the effect of 0, 1, 2, 3 and 4 recombination cycles on the mean, and on the genetic variability, of the irrigated rice population CNA5 for different traits. The idea was to help improve the efficiency of the recurrent selection programme for rice in Brazil (Cordeiro, 2001; Cordeiro et al., 2003).
Embrapa Arroz e Feijão synthesized population CNA5 according to the methodology of Rangel and Neves (1997), using as components population CNA1, which was the source of the malesterility gene; commercial cultivars Metica 1, BRIRGA 409 and CICA 8; sources of multiple resistance to the fungal diseases blast and grain discoloration, that is, Colombia 1, IR342 and Basmati 370; and the traditional cultivars De Abril, Paga Dívida, Quebra Cacho and Brejeiro.
After synthesis, the original population CNA5/0/0 was recombined once, twice, three and four times, obtaining, respectively, populations CNA5/0/1 (one recombination cycle), CNA5/0/2 (two recombination cycles), CNA5/0/3 (three recombination cycles) and CNA5/0/4 (four recombination cycles). From each of the five populations, 60 fertile plants were harvested individually, totalling 300 families that were advanced to generation S_{0:2}. The S_{0:2} families were evaluated in five triple lattices (8 × 8), conducted under conditions of irrigation by flooding, with control of the water layer, at two sites (Goianira and Lambari) in the 1998/99 cropping season. The treatments of each experiment were 60 families from the same crossing cycle and four checks (Metica 1, BRIRGA 409, CICA 8 and Javaé). The plots were two rows, 2 m long, spaced at 0.3 m, with 100 seeds per linear metre. Yield data were later collected.
The seeds, harvested in bulk from each S_{0:2} family, were used to evaluate the S_{0:3} generation in the 1999/00 cropping season, using the same experimental procedures as described for the S_{0:2} generation.
Analyses of variance were carried out for each individual site, each individual generation, site per generation, two sites per generation and all treatments (sites and generations). The effects of sites and generations were considered fixed and that of family, random.
To confirm change in the family mean with the increase in the number of recombination cycles, linear regression equations were estimated, where yield was the dependent variable and the number of recombination cycles the independent. Using estimate b obtained for the trait grain yield, genetic gain due to the recombination cycles carried out was also estimated as a percentage [G_{j} (%)], using the following equation:
where:
is the linear regression coefficient obtained in treatment j
is the estimated mean corresponding to the population with 0 (zero) recombination cycles in treatment j (intercept of the regression equation).
Based on the mathematical expectations of the mean squares, the following estimates were obtained:
1. Average phenotypic variance among the families from recombination cycle i in treatment j (site and generation), that is,
where:
QMF_{ij} is the mean square of the families from recombination cycle i, in treatment j (site and generation)
r is the number of replications
2. Genetic variance among families from recombination cycle i in treatment j (site and generation):
where:
QME is the mean square of the error of the joint analysis involving all treatments QMF_{ij} and r as previously defined. In addition, the intervals of confidence associated with the estimates of the genetic variances between families were estimated, using the equations of Scheffé (1959) and Wricke and Weber (1986).
3. Broadsense heritability in the mean of families, using the equation of Ramalho et al. (1993):
where:
is the heritability estimated as a percentage relative to the families from cross i in treatment j
and as previously defined
The lower and superior limits of the estimates were calculated by the equations of Knapp et al. (1985), using a 5% level of significance.
4. Realized heritability , calculated according to the equations of Fehr (1987) and Ramalho et al. (1993):
where:
GS_{ij'} is the performance for yield in generation j' of the five and ten best and worst families from recombination cycle i and selected from generation j minus the general mean of families from recombination cycle i in generation j'
ds_{ij} is the selection differential (this is the mean of the five and ten best and worst families selected from generation j derived from recombination cycle i minus the general mean of families in recombination cycle i)
m_{ij} and m_{ij'} are the general means of families from recombination cycle i in generations j and j' respectively
j is the generation in which the selection of the five and ten best and worst families was carried out and which, in this case, corresponds to S_{0:2}
j' is the generation in which the families selected in generation j were evaluated, and which, in this case, corresponds to S_{0:3}
5. Realized genetic gain, estimated by using the equation of Ramalho et al. (1993):
where:
GR(%) is the realized genetic gain described as a percentage
MF_{ij'} is the mean of the five or ten most productive families from recombination cycle i, selected in the S_{0:2} generation and evaluated in the S_{0:3} generation
m_{ij} is the general mean of the families from recombination cycles i in the S_{0:3} generation
We attempted to detect changes in the genetic gains made and in the means of the five and ten most productive families, using variation in the number of recombination cycles. We estimated linear regression equations, with genetic gain (expressed as a percentage or mean yield) as a dependent variable and the number of recombination cycles as an independent variable. We took into account data from Lambari and Goianira and, later, the mean of these sites.
Most of the sources of variation were significant (P = 0.001) in the combined analyses involving all sites and generations. The differences obtained for sites and for the interactions checks × generations and checks × generations × sites were not significant.
The interactions families × sites and families × generations were significant, indicating that the performance of families was not consistent across sites and generations.
Other alternatives for evaluating the effect of the number of recombination cycles on population formation are available. One is to confirm if changes in the mean of families occur with the recombination cycles. The estimates of the linear regression coefficient b were positive and different from zero for all treatments, suggesting that average yield increased with the number of recombination cycles. The greatest response for yield was obtained in the S_{0:2} generation in Lambari, with a value of b of 21.9. This value corresponds to a genetic gain of 5.83% per crossing cycle on the intercept estimated in the regression equation (Table 4).
Low estimates of b were obtained for the S_{0:3} generation in Lambari 10.6 g per plot) and Goianira (8.6 g per plot). However, these values represent expressed genetic gains of 2.77% and 2.34%, respectively. Averaging across the four treatments, the b estimate was 14.9 g per plot (Table 4), representing an increase in the mean of families of 3.91%. These results differ from those obtained by MarínGaravito (1994) who worked with families from the irrigated rice population of CNAIRAT 2 with zero, one, two and three recombination cycles, and did not detect significant differences for yield in the family means.
In principle, these results show the advantage of carrying out more than one recombination cycle, although there is a need to question them. The first question is related to the purpose of crossing to help increase the mean of the trait grain yield. Considering the same genetic grouping and the absence of selection, changes in allelic frequencies are not expected, as what a cross provides is the occurrence of new genotypic combinations. This could cause an increase in the expression of the trait if in the genetic control of the same involved, for example, epistatic changes. Not much information exists on this aspect of the rice crop, but what is available indicates that it is predominantly an additive effect (Morais, 1992). Should this be true, then explaining the increase in the average yield by the recombination cycle only would not be possible.
Table 4. Yield means (g per plot) of irrigated rice families for different numbers of recombination cycles. Experiments were conducted at Lambari and Goianira, Brazil, in the S_{0:2} (1998/99 cropping season) and S_{0:3} generations (1999/00 cropping season).
Parameter 
Treatment 
Mean


Lambari 
Goianira 

S_{0:2} 
S_{0:3} 
S_{0:2} 
S_{0:3} 

Recomb cycles (no.) 





0 
396.0 
401.8 
417.3 
382.8 
399.5 
1 
375.0 
364.2 
393.5 
353.8 
371.6 
2 
417.3 
410.3 
436.6 
384.5 
412.2 
3 
444.0 
420.3 
446.3 
391.6 
425.5 
4 
471.2 
427.0 
483.5 
406.8 
447.1 
a^{a} 
376.7 
383.4 
398.4 
366.8 
381.3 
b^{b} 
21.9 
10.6 
18.5 
8.6 
14.9 
R^{2}(%) 
83.0 
47.0 
76.0 
49.3 
69.5 
P^{c} 
0.02 
0.18 
0.04 
0.16 
0.05 
Family mean 
420.7 
404.7 
435.4 
383.9 
411.2 
Mean of checks 
675.2 
649.5 
623.8 
569.5 
629.5 
a. Where a is the intercept of the linear regression equation.
b. Where b is the linear regression coefficient.
c. Level of significance, according to the t test.
Another question is that during recombination, problems of sampling would occur, that is, the possibility of changes in allelic frequencies would exist.
In this study, 60 families per recombination cycle were evaluated. To evaluate a higher number would have been very difficult. Even in the literature, studies with similar objectives used smaller numbers of families. It should be pointed out that the problem of sampling is more serious during recombination than in evaluation. Because recombination was carried out using male sterility, each recombination cycle is expected to increase the frequency of alleles of the malesterile parent. The original malesterile parent was ‘IR36’, widely grown in Asia because of its particularly high productivity. As a result, it probably carried many of the favourable alleles of the normal line and thus may have increased the population mean. Good evidence of this is offered by Ferreira et al. (2000), who worked at the molecular level with population CNA5, which originated from one and three recombination cycles. They observed that, in each recombination cycle, a return to the genetic ‘background’ of the malesterile parent occurred, causing deviations in the population’s allelic frequencies. At four loci analysed, a marked increase in the frequency of alleles from the malesterile parent was observed.
A final question is what would be the effect of natural selection during each recombination cycle, where no artificial selection is carried out. As mentioned above, the formation of population CNA5 involved 23 progenitors (taking into account that population CNA1 was the source of male sterility) and including elite, traditional and exotic cultivars that, when recombined, generated a very large variability in the population. Considering that the individual that leaves the most number of descendants, that is, has the greatest number of seeds, is the most adapted, then, the most adapted cultivars probably benefit from natural pollination in the field, thereby increasing, in this case, the families’ average yield.
The literature reports response to the action of natural selection, the most notable result in this regard having been observed in barley. Allard (1988) observed, after 50 successive generations of selfpollination in a segregating population, a genetic gain for yield close to 1% per generation. In contrast, several studies, involving mixtures of cultivars, showed the action of natural selection in that, after a few generations, only one or two cultivars predominated (Cardoso and Vieira, 1976). Ferreira et al. (2000) confirmed that some alleles present in the parental materials are lost after the third recombination cycle. The authors commented that this finding may indicate that the recombination strategy, using genetic male sterility, may favour certain progenitors.
Another alternative to confirm the effect of recombination cycles is to evaluate the genetic variability available for selection. Some studies consider crossing as a way of breaking linkage blocks and releasing greater variability (Hanson, 1959; Fujimaki, 1979; Lamkey et al., 1995).
The largest estimates of genetic variance were obtained for the group of families originating from the population with zero recombination cycles at the two sites and in the two generations. These estimates were usually located outside the intervals of confidence for the other groups or family types. These, in their turn, acquired estimates of similar magnitudes, with, in some cases, the increase in the number of recombination cycles presenting a tendency to reduce variability (Table 5).
Ferreira et al. (2000) observed a reduction of alleles with the increase in recombination cycles, characterizing a premature loss of genetic variability in the population and showing that some parental materials are favoured in random crossing with malesterile plants. These results agree with those obtained by MarínGaravito (1994) and CabezasSantacruz (1995), who also observed increases in genetic variances for several traits in the irrigated rice population CNAIRAT 2 when carrying out recombination cycles.
The estimates of heritability varied from 85.55% (Lambari, S_{0:3}) to 97.18% (Lambari, S_{0:2}) and from 74.30% (Goianira, S_{0:3}) to 96.94% (Goianira, S_{0:2}), indicating the presence of large genetic variability for yield within each generation. Similar values were obtained by Rodríguez et al. (1998) and Santos (2000). The estimates of broadsense heritability were not only high, but also very close. Thus, with regard to the estimates of phenotypic variances, the estimates of genetic variances for all family groups (except those originating from the population with zero recombination cycles) presented the same pattern of performance. Hence, they did not present evidence that increasing the number of recombination cycles promoted greater variability (Table 5).
One could conclude, therefore, that increasing the number of recombination cycles did not increase genetic variability in the irrigated rice population CNA5. This corroborates findings in the literature on recurrent selection programmes that report the lack of advantage in carrying out recombination cycles (or more than one recombination cycle) between F_{2} plants of the base population before selfpollination and evaluation (Meredith and Bridge, 1971; Bos, 1977; Altman and Busch, 1984; Guimarães and Fehr, 1989; MarínGaravito, 1994; CabezasSantacruz, 1995; Ospina et al., 1997; Uphoff et al., 1997).
This study also evaluated the efficiency of selection for yield, testing families across two generations. For this purpose, the five and ten best and worst families were selected from each group representing the numbers of recombination cycles in the S_{0:2} generation. Their response to that selection was confirmed in the S_{0:3} generation for Lambari and Goianira, and in the mean of the two sites. Subsequently, estimates of realized heritability were obtained, which is the measure that really reflects the results of selection (Table 6).
The estimates of realized heritability were lower than the estimates of broadsense heritability cited above. Santos (1996), when evaluating S_{0:2} and S_{0:3} families of the irrigated rice population CNAIRAT 4 in southern Minas Gerais, also obtained estimates of realized heritability that were lower than the estimates for broadsense heritability. The difference is mainly associated with the effects of the interactions families × site and families × generations that inflate the genetic variance estimates, which does not occur with realized heritability. In most cases, the estimates of realized heritabilities found made it possible to foresee that selection carried out in one environment provided gains for yield in the other for all family types (Table 6).
Table 5. Estimates of genetic variance and broadsense heritability , and their respective intervals of confidence for the trait grain yield. The S_{0:2} and S_{0:3} families of irrigated rice derived from population CNA5 were evaluated for different numbers of recombination cycles at Lambari and Goianira, Brazil.
Generation (and season) 
Site/parameter^{a} 

Lambari 
Goianira 

S_{0:2 }(1998/99) 




0 
26358.04 (18734.6039828.78) 
97.18 (96.0498.12) 
24205.65 (16774.6237977.64) 
96.94 (95.7097.96) 
S_{0:3 }(1999/00) 




0 
18844.86 (13316.7028720.04) 
96.10 (94.5397.40) 
13305.14 (9373.6420368.13) 
94.57 (92.3896.38) 
a. The values in brackets indicate the lower and upper limits of the confidence intervals (á = 0.05).
Table 6. Estimates, in percentage, of realized heritability , with the selection of the five and ten best and worst families for the trait grain yield. The estimates are for different numbers of recombination cycles carried out with the irrigated rice population CNA5 at Lambari and Goianira, Brazil. The means of the two sites are also given.
Site 
Recomb. cycles 
Families 

5 best 
5 worst 
10 best 
10 worst 

Lambari 
0 
59.39 
36.89 
67.58 
44.37 
1 
30.31 
50.79 
17.49 
51.88 

2 
50.00 
62.54 
48.08 
61.58 

3 
23.05 
52.08 
13.31 
33.11 

4 
35.70 
27.16 
41.63 
27.50 

Mean 
39.69 
45.89 
37.62 
43.69 

Goianira 
0 
28.59 
26.05 
58.12 
39.18 
1 
33.30 
43.40 
36.29 
18.28 

2 
78.76 
81.51 
76.70 
62.28 

3 
16.44 
33.40 
20.57 
38.61 

4 
47.39 
86.21 
66.53 
73.87 

Mean 
40.89 
54.11 
51.64 
46.44 

Mean of the sites 
0 
88.07 
35.75 
71.46 
42.25 
1 
22.90 
58.57 
38.10 
46.36 

2 
69.48 
60.59 
70.98 
73.19 

3 
8.72 
55.24 
20.56 
52.46 

4 
34.20 
56.74 
62.15 
49.35 

Mean 
44.67 
53.38 
52.65 
53.32 
Finally, what is most important in verifying the efficiency of recombination cycles is the comparison of genetic gains with selection. In this sense, for each family type, the realized genetic gains were estimated, based on the selection of the five and ten most productive S_{0:2} families and the response to selection in S_{0:3}. Results indicated that although the estimates of R_{2} were not large, the estimates of the linear regression coefficients b were always negative. This shows a tendency of a reduced increase in genetic gain, and in the mean of the best families, with the increase in the number of recombination cycles (Tables 7, 8 and 9). It is noteworthy that, for any number of recombination cycles carried out, we could select families with higher yield, as in the case of the families originating from zero recombination cycles, which presented one of the lowest means. These results agree with those of Piper and Fehr (1987), Guimarães and Fehr (1989) and Uphoff et al. (1997), who argue that the increase in the number of recombination cycles did not increase genetic gain for yield in soybeans. Consequently, it should not be recommended as an efficient methodology for recurrent selection programmes.
Table 7. Realized genetic gain (GR%) and means of yield (g per plot) of the five and ten best families selected in the S_{0:2} generation. Their responses to selection in the S_{0:3} generation are shown according to the different numbers of recombination cycles carried out with the CNA5 population of irrigated rice at Lambari, Brazil, 1998/99 and 1999/2000 cropping seasons.
Parameter 
5 best families 
10 best families 

GR (%) 
Mean 
GR (%) 
Mean 

Recomb cycles (no.) 




0 
47.41 
592.26 
41.45 
568.32 
1 
15.49 
420.64 
7.18 
390.37 
2 
24.93 
512.65 
19.45 
490.16 
3 
8.65 
456.61 
4.45 
438.96 
4 
23.04 
525.34 
19.63 
510.78 
a^{a} 
35.02 
521.07 
27.71 
493.02 
b^{b} 
5.56 
9.79 
4.64 
6.65 
R^{2} (%) 
36.00 
5.47 
25.20 
2.37 
P^{c} 
0.264 
0.698 
0.372 
0.800 
a. Where a is the intercept of the linear regression equation.
b. Where b is the linear regression coefficient.
c. Level of significance, according to the t test.
Another aspect worth highlighting is related to the time dedicated to recombination. Considering that, for 0, 1, 2, 3 and 4 recombination cycles, about 1, 1.5, 2.0, 2.5 and 3.0 years, respectively, are needed, then the results obtained for families originating from zero recombination cycles are much more expressive and show, once again, that recombination in the base population in the present study was not advantageous.
Moreover, everything indicates that the methodology of manual chain crossing, used before conducting recombination cycles at random in the field, seems efficient and sufficient to form a base population. It permits the selection of superior families without the additional need for recombination cycles. Thus, it makes the recurrent selection programme for rice faster while requiring fewer resources.