GENETIC CORRELATION BETWEEN TRAITS IN THE ESALQ-PB 1 MAIZE POPULATION DIVERGENTLY SELECTED FOR TASSEL SIZE AND EAR HEIGHT

Full-sib and selfed (S 1 ) progenies were obtained from sub-populations of ESALQ-PB1, divergently selected for tassel size (T+ and T–) and ear height (E+ and E–), and used for estimating genetic and phenotypic correlation coefficients between traits. The analyzed traits were: EWtotal ear weight (g/plant), PHplant height (cm), EHear height (cm), TBtassel branch number and TLtassel length. The highest genetic (r G ) and phenotypic (r F ) correlation was observed for the combination PH x EH, as expected, with average of 0.800 and 0.778, respectively over sub-populations and locations. It is apparent that divergent selection for tassel size did not affect greatly the correlation between PH and EH in the full sib progenies, but in the inbred progenies the correlation was smaller in the sub-population selected for larger tassels. Genetic correlation between PH and EH with tassel traits was always positive but ranged from 0.020 to 0.668 in Piracicaba and from 0.06 to 0.309 in Rio Verde. Genetic correlation between PH and EH with yield (EW) also was positive in the range of 0.087 to 0.503. EH showed higher correlation with EW in relation to PH x EW and differences were larger in the sub-populations divergently selected for ear height. Correlation between tassel traits with other traits was positive in most of instances and a lack of consistency was observed among sub-populations. Generally the coefficients of genetic and phenotypic correlation differed substantially from the estimates in the base population ESALQ-PB1 before divergent selection for tassel size and ear placement. Divergent selection affected the correlation between traits under unpredicted and varying magnitudes.


INTRODUCTION
Maize (Zea mays L.) is, among the cultivated species, one that has undergone a fantastic improvement in yield through artificial selection (Hallauer & Miranda Filho, 1995).Cultural practices also have greatly contributed to increase yield in the maize crops during this century.More recently, attention has been given to plant architecture toward a better efficiency in the utilization of solar energy and photosynthetic capacity (Donald, 1968;Wittner, 1974;Paterniani, 1974Paterniani, , 1981;;Miranda Filho, 1974;Sampaio, 1986).Also, intentionally or not, changes have occurred in tassel size for a better utilization of photosynthates (Mock & Pearce, 1975).
Scientia Agricola, v.58, n.1, p.119-123, jan./mar.2001 The association between traits is an important aspect to deal with in breeding programs, because genetic change in a given trait may change positively or negatively other traits (Vencovsky & Barriga, 1992).In addition, in most breeding programs the strategy is based on selection for several traits simultaneously and, therefore, knowledge on the genetic association between traits is inevitably useful for the establishment of selection criteria.The basic causes of genetic correlation are pleiotropy, and linkage disequilibrium (Falconer, 1964;Vencovsky, 1978;Hallauer & Miranda Filho, 1995).
One important application of the genetic correlation in breeding programs refers to indirect selection for traits of low heritability and consequently low direct response to selection.Selection for another trait may result in indirect response in the low heritable trait, provided the following conditions are satisfied: i) traits under consideration must be highly correlated genetically; ii) heritability of the secondary trait must be higher than the trait of higher interest (Falconer, 1964;Vencovsky & Barriga, 1992).In maize, for example, two secondary traits were identified for indirect selection to increase yield: prolificacy (Paterniani, 1981) and tassel size (Geraldi et al., 1985).
Although many authors have referred to a negative association between tassel size and yield potential (Leonard & Kiesselbach, 1932;Hunter et al., 1973;Fakorede & Mock, 1978;Lordelo & Miranda Filho, 1981;Geraldi et al., 1985), positive association of those traits also have been reported (Lordelo & Miranda Filho, 1981;Sampaio, 1986;Soares Filho, 1987).There are evidences that the correlation between yield and tassel size tends to be higher and negative under stresses caused by unfavorable environments (Soares Filho, 1987).Brunini et al. (1983) emphasized that environmental factors such as photoperiod, solar radiation and rainfall affect decisively the yield potential of a corn crop and consequently the association between traits may change if there is a differentiated variety response to the environmental factors.
Souza Júnior et al. (1985) reported on a negative correlation between tassel size and prolificacy which were explained by a larger amount of indol-acetic-acid (IAA) produced by larger tassels and causing inhibition of prolificacy, or vice-versa (Anderson, 1967).Other studies referring to the correlation of tassel size with other characters are sometimes contradictories.The correlation between tassel branch number with plant height, ear height and ear placement was reported as positive by Obilana & Hallauer (1974), Ayala Osuna et al. (1986);Miranda Filho & Andrade (2000).However, the same associations were positive in some cases and negative in other cases, as reported by Lordelo (1982), Aguilar Morán (1984), Sampaio (1986), Soares Filho (1987), and Araújo (1992).Some estimates of additive and phenotypic correlation between tassel branch number with plant height, ear height, and grain yield are summarized in TABLE 1.The objectives of this work was to study changes in the genetic correlation between traits after divergent selection for tassel size and ear height in the maize population ESALQ-PB1.Full sib progenies were obtained through biparental crosses from each sub-population.In ESALQ-PB1 (T+) and ESALQ-PB1 (T-), S 1 progenies were also obtained by selfing individual plants.The six sets totaled 921 progenies that were evaluated in 18 experiments following the completely randomized block design with three replications, at Piracicaba, SP, and Rio Verde, GO.The numbers of progenies of each set in each experiment are shown in TABLE 2.

MATERIAL AND METHODS
Experimental plots were represented by a single row 4.0 m long with 20 plants per plot (0.20 m between plants) after thinning.The following traits were analyzed: PH-plant height (cm), EH-ear height (cm), TB-tassel branch number, TL-tassel length (cm), and EW-total ear weight (g/ plant).Except for EW, the experimental units were represented by means of three plants per plot.In Rio Verde (GO), only PH, EH and TB of full sib progenies were evaluated.
The statistical model for variance and covariance analyses following the randomized complete block design is Y ij = m + p i + b j + e ij , where Y ij is the observed mean of the i th progeny in the j th replication, m is the general mean, p i is the random effect of the i th progeny, b j is the random effect of the j th replication, and e ij is the error term.In the analysis of variance the mean squares for progenies (M P ) and Error (M E ) have the following expectations: E(M P ) = σ and E(M E ) = σ 2 .In the same way, the corresponding expected mean products (P P and P E ) in the analysis of covariance have the expectations E(P P ) = cov + 3 cov P and E(P E ) = cov.In the formulations, σ 2 and cov refer to the variance and covariance of effects relative to the error term.In the same way, 2 P σ and cov P refer to the genetic variance and covariance relative to progeny effects.The coefficients of correlation were then calculated by

RESULTS AND DISCUSSION
Observed means for six traits in sub-populations of ESALQ-PB1, divergently selected for tassel size (T+ and T-) and ear height (E+ and E-) are shown in TABLE 3. The direct effect of divergent selection on means of selected traits and the correlated response on other nonselected traits can be visualized in TABLE 3. Also, Farias Neto & Miranda Filho (2000) already presented comparisons involving inbred and non-inbred progenies, leading to estimates of inbreeding depression.Therefore, our attention here focuses on results of genetic (r G ) and phenotypic (r F ) correlation (TABLE 4).

Correlation between plant height (PH) and ear height (EH)
The correlation coefficients (r G and r F ) between PH and EH were the highest among the combinations of traits in this study.Estimates of r G and r F averaged 0.800 and 0.778, ranging from 0.755 to 0.870 and 0.675 to 0.911, respectively, over sub-populations and locations.It is apparent that divergent selection for tassel size did not affect greatly the correlation between PH and EH in the full sib progenies, but in the inbred progenies the correlation was smaller in the sub-population selected for larger tassels.Also, r G and r F were smaller in the subpopulation selected for decreasing ear height.In general, a high correlation between PH and EH has been reported by many authors.Estimates of the additive genetic correlation (r A ) and phenotypic correlation summarized by Moraes (1989) averaged 0.82 and 0.78, respectively.Also, Hallauer & Miranda Filho (1995) presented a high average genetic correlation of the order of 0.81.Miranda Filho & Andrade (2000) reported on estimates of r A and r F of 0,842 and 0.803 between PH and EH in the base population ESALQ-PB1.

Correlation between plant height (PH) and ear height (EH) with tassel traits (TB, and TL)
The correlation coefficients between PH and EH with tassel branch number were always positive but not consistent among sub-populations.The highest correlations of EH with TB were observed with inbred progenies.Also, for both inbred and non-inbred progenies in Piracicaba the genetic correlation was higher in the sub-population selected for larger tassels.However, in Rio Verde, the highest positive correlation (0.301) was for EH x TB in the sub-population (T-).In general, correlation coefficients between EH and TB were higher than for PH and TB.Estimates of r A and r F in the base population ESALQ-PB1 were 0.379 and 0.339 for PH x TB and 0.436 and 0.382 for EH x TB, respectively (Miranda Filho & Andrade, 2000).The correlation of PH and EH with tassel length (TL) was estimated in only three and two sub-populations, respectively, and the estimates of r G were all positive and above 0.40, except for PH x TL in the sub-population ESALQ-PB1 (T+) with inbred progenies (r G = 0.127).Estimates of r A in the base population ESALQ-PB1 were 0.273 and 0.101 for PH x TL and EH x TB, respectively (Miranda Filho & Andrade, 2000).

Correlation between plant height (PH) and ear height (EH) with ear yield (EW)
The association of plant height and ear height with yield tends to be always positive.Hallauer & Miranda Filho (1995) reported genetic correlation of 0.26 and 0.31 for the combinations PH x EW and EH x EW, respectively, on the average of 23 experiments.The association of these traits in our experiments comprised only non-inbred progenies, where r G varied from 0.087 to 0.503 among subpopulations.EH showed higher correlation with EW than PH, and differences were larger in the sub-populations divergently selected for ear height.When looking to the sub-populations divergently selected for tassel size, a higher genetic correlation of PH and EH with EW was observed in ESALQ-PB1 (T+).Estimates of r A in the base population ESALQ-PB1 were 0.594 and 0.506 for PH x EW and EH x EW, respectively (Miranda Filho & Andrade, 2000).

Correlation between tassel traits (TB, TL) and EW
The genetic correlation coefficients between TB and TL were low but negative (r G = -0.015) in ESALQ-PB1 (T+) and positive (r G = 0.232) in ESALQ-PB1 (T-), the two sub-populations representing the divergent selection for tassel size.The later was closer to the r A estimate (0.217)    Andrade, 2000).The genetic correlation TBxEW was calculated only for full-sib progenies and was small negative (-0.022) in ESALQ-PB1 (T+) and positive (0.137 to 0.456) in the other three sub-populations.In a study with the same sub-populations in the preceding cycle of divergent selection, Araújo (1992) found the same pattern of correlation between TB and EW.The only r G estimate for TL x EW was in the sub-population ESALQ-PB1 (T+) and was small positive (0.027).Apparently, divergent selection for tassel size and ear height affected the original pattern of correlation between tassel traits and ear yield because all the estimates depart from the r A estimates of 0.207 and 0.216 for TB x EW and TL x EW, respectively, as reported by Miranda Filho & Andrade (2000) for the base population ESALQ-PB1.Falconer (1964) emphasized that selection may change significantly the pattern of correlation between traits.However, the pattern of correlation between tassel size and yield depends also on the effect of environment and tends to be positive under favorable environments (Soares Filho, 1987).Generally the coefficients of genetic and phenotypic correlation differed substantially from the estimates in the base population ESALQ-PB1 before divergent selection for tassel size and ear placement (Miranda Filho & Andrade,2000).Divergent selection affected the correlation between traits under unpredicted and varying magnitudes.
Four sub-populations were derived from ESALQ-PB1, after six cycles of divergent selection for tassel size and ear height.Sub-populations were designated by ESALQ-PB1 (E+): selection for increasing ear height end/or ear placement ESALQ-PB1 (E-): selection for decreasing ear height end/or ear placement ESALQ-PB1 (T+): selection for increasing tassel size ESALQ-PB1 (T-): selection for decreasing tassel size

TABLE 1 -
Ranges for the estimates of r A (additive genetic correlation) and r F (phenotypic correlation, family means) of tassel branch number and other quantitative traits (plant height, ear height, and grain yield).

TABLE 4 -
Estimates of the coefficients of genetic (r G , upper) and phenotypic (r F , lower) correlation in combinations of six traits in sub-populations of ESALQ-PB1 at two locations.