Besides estimating expected genetic gains, plant breeders must evaluate the observed gains obtained through the population improvement programme over a given period. Such evaluations help in critically analysing the efficiency of the adopted procedures and in planning any needed corrective actions for use in subsequent periods.

To estimate the genetic gains observed for yield over three
cycles of recurrent selection in population CNA-IRAT 4, we evaluated 924
S_{0:2} families in 14 trials. The first five trials, conducted in the
1992/93 cropping season in the states of Goiás, Minas Gerais,
Paraná, Roraima and Tocantins, evaluated 326 families from the first
cycle and two checks (CICA 8 and BR-IRGA 409). The following six trials,
conducted in the 1994/95 cropping season (Goiás, Piauí,
Paraná, Roraima and Tocantins), evaluated 400 families from the second
cycle and four checks (CICA 8, BR-IRGA 409, Metica 1 and Javaé). The
final three trials, conducted in the 1997/98 cropping season (Goiás,
Pará and Roraima), evaluated 200 families from the third cycle and the
same checks as for the previous cycle.

The experimental design used was triple lattice in the first cycle (two lattices 10 × 10 and two 8 × 8) and Federer’s augmented blocks (Federer, 1956) in the two following cycles. The plot comprised four rows, each 5 m long, and data on yield were obtained from the middle 4 m of the two central rows.

To estimate the genetic gains observed for yield, the method
of adjusted means was used (Breseghello *et al.*, 1998) as adapted by
Morais *et al. *(2000). This method presents more advantages mainly when
the data are imbalanced, as they are in this case.

Thus, we can separate all the group of evaluated treatments of n selection cycles in n + 1 groups: the group of checks and the n groups of families evaluated per selection cycle. Initially, the means for these n + 1 groups were estimated, and adjusted for the effects of year (in relation to the group of common checks), and the interactions site × year and blocks × site × year. Naturally, we had included the restriction that all interactions, treatment × year and treatment × site × year were components of experimental error. The genetic gains observed per selection between two successive cycles i and , whose adjusted means of the evaluated families are and are represented by:

where:

are the adjusted means of the families evaluated in cycle i and i + 1, respectively

Because the different estimates of observed genetic gains are neither independent nor homogeneous variances, the mean gain should be estimated by the method of generalized minimum squares (Hoffmam and Vieira, 1987). To estimate the matrix of covariance of observed genetic gains, the matrix of covariance of the adjusted means of the n + 1 treatment groups evaluated should first be obtained.

The average yield of the checks - 6810 kg ha^{-1} -
was significantly higher than the averages of the families in all the recurrent
selection cycles evaluated (Table 1).

The mean is a major genetic parameter to consider in population improvement. When the population mean is low, a great deal of time may be needed to raise it to a sufficiently high level. Such effort may not be compensated when using that population for improvement. For CNA-IRAT 4, the lowest mean for yield of the families, compared with the checks, can be attributed to the following factors:

- High genetic variability between and within families
- Presence of the male-sterility gene in the families
- Small number of recurrent selection cycles.

Table 1. Mean yield of checks and families in each recurrent selection cycle in the irrigated rice population CNA-IRAT 4.

Group |
Yield (kg ha |

Checks |
6810 |

First-cycle families |
5560 |

Second-cycle families |
5576 |

Third-cycle families |
5945 |

CV (%) |
18.1 |

a. Value is significantly lower than the group mean for the checks, according to Dunnett’s test at 5% of probability.

When considering only the best 10 families in each selection
cycle, the average yield was seen to be more than 7000 kg ha^{-1}. The
families of the second (7275 kg ha^{-1}) and third cycles (7283 kg
ha^{-1}) were significantly more productive than the group of checks,
according to Dunnett’s test (Dunnett, 1955, 1964) at 5% probability (Table
2). These results show the population’s genetic potential for extracting
lines with an increased high yield.

Table 2. Mean yield of checks and of the 10 best families in each recurrent selection cycle in the irrigated rice population CNA-IRAT 4.

Group |
Yield (kg ha |

Checks |
6810 |

10 best first-cycle families |
7131 |

10 best second-cycle families |
7275 |

10 best third-cycle families |
7283 |

CV (%) |
18.1 |

a. Value is significantly higher than the group mean of the checks, according to Dunnett’s test at 5% probability.

Table 3 presents the genetic gains observed for yield in the
first and second recurrent selection cycles in kilograms per hectare and as
percentage of the mean of the first-cycle families. The gain observed in the
first cycle was only 15.7 kg ha^{-1} (0.28%), that is, not significant.
The gains observed in the second cycle and the mean of the two cycles were,
respectively, 369.5 kg ha^{-1} (6.65%) and 259.9 kg ha^{-1}
(4.67%), that is, significant in that they were more than twice the value of the
respective standard deviation.

These values are greater than the estimates for the
conventional improvement programmes carried out in Brazil by several authors.
Santos *et al. *(1999) obtained a gain of only 15 kg ha^{-1}
year^{-1} (0.25%), that is, not significant, on evaluating the
performance of the irrigated rice improvement programme in the State of Minas
Gerais. Breseghello *et al. *(1999) and Rangel *et al. *(2000a)
estimated genetic gains of 54.9 kg ha^{-1} year^{-1} (0.8%) and
18.0 kg ha^{-1} year^{-1} (0.3%), respectively, for the
improvement programmes of the northeastern and central-northern regions of
Brazil.

The results of our study show that, with recurrent selection applied in genetically divergent populations, considerable gains for yield can be obtained. The maintenance of the gains across the recurrent selection cycles will be possible only if care is taken with the population such as evaluating many families (250 to 300 families); increasing the precision of evaluations of families, paying considerable attention to their management; and using an intensity of selection that makes obtaining shortterm gains possible without exhausting the population’s genetic variability.

Table 3. Estimates of observed genetic gains in yield of irrigated rice for the first (G12) and the second cycles (G23). Mean gains (Gmean) are shown in kilograms per hectare and in percentage of the mean of the first-cycle families.

Parameter |
Gain |
Standard deviation |
Gain in percentage over the first-cycle family mean |

G12 |
15.7 |
± 207.7 |
0.28 |

G23 |
369.5 |
± 129.0 |
6.65 |

Gmean |
259.9 |
± 101.3 |
4.67 |

a. Genetic gain is considered significant when its value is more than twice that of the respective standard deviation.