Genetic variance and covariance components related to intra- and interpopulation recurrent selection in maize (Zea mays L.)

Abstracts

New genetic variance and covariance components related to intra- and interpopulational recurrent selection methods have been theoretically developed by Souza Jr. (Rev. Bras. Genet. 16: 91-105, 1993) to explain the failure of these methods to concomitantly develop hybrid and per se populations. Intra- and interpopulation half-sib progenies of 100 genotypes were sampled from maize (Zea mays L.) populations BR-106 and BR-105 to estimate variance and covariance components and to compare the expected responses to reciprocal (RRS), intrapopulational (HSS), and modified (MRS) recurrent selection in interpopulation hybrid, populations per se, and to determine heterosis. Four sets of 100 progenies, two intra- and two interpopulational, were evaluated in partially balanced 10 x 10 lattices arranged in split-blocks with two replications in two years (1991/92 and 1992/93) and two locations in Piracicaba, SP. Data for ear weight, plant and ear height, and ear by plant height ratio were recorded. Populations and interpopulation crosses were high yielding and showed high breeding potential for production of hybrids from inbred lines. Mid parent and the highest parent heterosis were relatively high, but lower than values reported for these populations under other environmental conditions. Additive variance estimates of populations per se and interpopulation crosses confirmed the high potential of these materials. The magnitude of the variance estimates for the deviations from intra- and interpopulation additive effects (<img src="http:/img/fbpe/gmb/v21n4/1918f1.jpg" alt="1918f1.jpg (1262 bytes)" align="middle"> for BR-106 and <img src="http:/img/fbpe/gmb/v21n4/1918f3.jpg" alt="1918f3.jpg (1259 bytes)" align="middle">for BR-105) and covariance between additive effects with these deviations (<img src="http:/img/fbpe/gmb/v21n4/1918f2.jpg" alt="1918f2.jpg (2022 bytes)" align="middle"> for BR-106 and <img src="http:/img/fbpe/gmb/v21n4/1918f4.jpg" alt="1918f4.jpg (1995 bytes)" align="middle"> for BR-105) indicated that these new components can significantly influence the effectiveness of breeding methods. Genetic component estimates for BR-105 had relatively small errors, with <img src="http:/img/fbpe/gmb/v21n4/1918f4.jpg" alt="1918f4.jpg (1995 bytes)" align="middle"> negative for all traits. Estimates of <img src="http:/img/fbpe/gmb/v21n4/1918f1.jpg" alt="1918f1.jpg (1262 bytes)" align="middle">and <img src="http:/img/fbpe/gmb/v21n4/1918f2.jpg" alt="1918f2.jpg (2022 bytes)" align="middle"> had relatively larger errors for BR-106. The MRS method was more effective than the RRS and HSS methods in producing hybrids from inbred lines. The choice of a population tester for the MRS method based on population means per se may be incorrect. The additional use, when possible, of intra- and interpopulation additive genetic variances from each population would be more appropriate.

Novos componentes genéticos de variância e covariância relacionados aos métodos de seleção recorrente intra- e interpopulacional foram desenvolvidos teoricamente por Souza Jr. (Rev. Bras. Genet. 16: 91-105, 1993) para explicar porque estes métodos têm falhado em melhorar o híbrido e as populações per se conjuntamente. Progênies de meio-irmãos intra- e interpopulacionais foram produzidas a partir de 100 genótipos amostrados das populações de milho BR-106 e BR-105 para estimar estes componentes de variância e covariância e comparar as respostas esperadas para os métodos de seleção recorrente recíproca (RRS), intrapopulacional (HSS) e modificada (MRS) sobre o híbrido interpopulacional, as populações per se e a heterose. Quatro grupos de 100 progênies, dois intra- e dois interpopulacionais, foram avaliados em látices 10 x 10, parcialmente balanceados, arranjados segundo um delineamento em faixas com duas repetições, nos anos agrícolas 1991-1992 e 1992-1993 e em dois locais da região de Piracicaba, SP. Foram avaliados os seguintes caracteres: peso de espiga, alturas de planta e espiga e a razão altura de planta sobre altura de espiga. As populações e os híbridos interpopulacionais apresentaram alta produtividade e grande potencial para a produção de híbridos de linhagens. As heteroses em relação à média populacional e à melhor população foram relativamente altas, mas abaixo dos valores relatados para estas populações sob outras condições ambientais. As estimativas da variância aditiva para as populações per se e para os cruzamentos interpopulacionais confirmaram o grande potencial desses materiais para o melhoramento. As magnitudes das estimativas da variância para os desvios dos efeitos aditivos intra- e interpopulacionais (<img src="http:/img/fbpe/gmb/v21n4/1918f1.jpg" alt="1918f1.jpg (1262 bytes)" align="middle"> para BR-106 e <img src="http:/img/fbpe/gmb/v21n4/1918f3.jpg" alt="1918f3.jpg (1259 bytes)" align="middle"> para BR-105) e para a covariância entre os efeitos aditivos com esses desvios (<img src="http:/img/fbpe/gmb/v21n4/1918f2.jpg" alt="1918f2.jpg (2022 bytes)" align="middle"> para BR-106 e <img src="http:/img/fbpe/gmb/v21n4/1918f4.jpg" alt="1918f4.jpg (1995 bytes)" align="middle"> para BR-105) indicaram que estes novos componentes podem influenciar significativamente a eficiência dos métodos de melhoramento. As estimativas dos componentes genéticos para BR-105 apresentaram erros relativamente pequenos, com <img src="http:/img/fbpe/gmb/v21n4/1918f4.jpg" alt="1918f4.jpg (1995 bytes)" align="middle"> negativo para todos os caracteres. As estimativas de <img src="http:/img/fbpe/gmb/v21n4/1918f1.jpg" alt="1918f1.jpg (1262 bytes)" align="middle"> e <img src="http:/img/fbpe/gmb/v21n4/1918f2.jpg" alt="1918f2.jpg (2022 bytes)" align="middle"> apresentaram erros relativamente grandes para BR-106. O método MRS foi mais eficiente que RRS e HSS para a produção de híbridos de linhagens. A escolha da população testadora para o método MRS baseada apenas nas médias das populações per se pode ser incorreta. Quando possível, a utilização adicional das variâncias genéticas aditivas intra- e interpopulacionais de cada população seria mais apropriada.

Genetic variance and covariance components related to intra- and interpopulation recurrent selection in maize (Zea mays L.)

Carlos Alberto Arrabal Arias¹ and Cláudio Lopes de Souza Júnior²

¹ Centro Nacional de Pesquisa de Soja, Embrapa, Caixa Postal 481, 86001-970 Londrina, PR, Brasil. Send correspondence to C.A.A.A.

E-mail: [e-mail].

² Departamento de Genética, Escola Superior de Agricultura "Luiz de Queiroz", ESALQ/USP.

ABSTRACT

New genetic variance and covariance components related to intra- and interpopulational recurrent selection methods have been theoretically developed by Souza Jr. (Rev. Bras. Genet. 16: 91-105, 1993) to explain the failure of these methods to concomitantly develop hybrid and per se populations. Intra- and interpopulation half-sib progenies of 100 genotypes were sampled from maize (Zea mays L.) populations BR-106 and BR-105 to estimate variance and covariance components and to compare the expected responses to reciprocal (RRS), intrapopulational (HSS), and modified (MRS) recurrent selection in interpopulation hybrid, populations per se, and to determine heterosis. Four sets of 100 progenies, two intra- and two interpopulational, were evaluated in partially balanced 10 x 10 lattices arranged in split-blocks with two replications in two years (1991/92 and 1992/93) and two locations in Piracicaba, SP. Data for ear weight, plant and ear height, and ear by plant height ratio were recorded. Populations and interpopulation crosses were high yielding and showed high breeding potential for production of hybrids from inbred lines. Mid parent and the highest parent heterosis were relatively high, but lower than values reported for these populations under other environmental conditions. Additive variance estimates of populations per se and interpopulation crosses confirmed the high potential of these materials. The magnitude of the variance estimates for the deviations from intra- and interpopulation additive effects ( for BR-106 and for BR-105) and covariance between additive effects with these deviations ( for BR-106 and for BR-105) indicated that these new components can significantly influence the effectiveness of breeding methods. Genetic component estimates for BR-105 had relatively small errors, with negative for all traits. Estimates of and had relatively larger errors for BR-106. The MRS method was more effective than the RRS and HSS methods in producing hybrids from inbred lines. The choice of a population tester for the MRS method based on population means per se may be incorrect. The additional use, when possible, of intra- and interpopulation additive genetic variances from each population would be more appropriate.

INTRODUCTION

Production of hybrids from inbred lines is the main goal of maize breeding programs. Their commercial use depends on the grain yield of the inbred lines and of the hybrid itself. Inbred line and hybrid improvements are indirectly evaluated in populations per se and population crosses, respectively. Thus, efficient production of commercial hybrids and improvement of populations per se and of interpopulational crosses are required. Intra- and interpopulation recurrent selection methods have been devised to improve populations per se and interpopulational crosses, respectively (Moll and Stuber, 1971). Intrapopulational selection studies reported by Coors and Mardones (1989), Moll and Hanson (1984), and Helms et al. (1989) efficiently improved population per se but they were not suitable for interpopulational cross improvement. Interpopulational selection studies reported by Moll and Stuber (1971), Eberhart et al. (1973), Darrah et al. (1978), Moll et al. (1978), Martin and Hallauer (1980), Smith (1983), Moll and Hanson (1984) and Keeratinijakal and Lamkey (1993) showed significant responses in the interpopulational cross and in one of the populations, with a small or negative response for the other population. Therefore, these methods do not satisfy all the objectives of an improvement program for hybrid production from inbred lines.

Souza Jr. (1993) partitioned the interpopulational additive variance ( and ) into intrapopulational additive variances ( and ), genetic variances of deviations from inter- and intrapopulation additive effects ( and ), and covariances between them (Cov_(A1t12) and Cov_(A2t21)). He concluded that negative Cov_(A2t21) values can cause the small selection response observed for one of the populations. He suggested an intrapopulational method for the low productive population and an interpopulational method for the other. The less productive population was the tester for itself and for the other population.

The objective of the present study was to estimate variance and covariance components and compare the expected responses of some combinations of intra- and interpopulational selection methods obtained with two Brazilian maize populations.

MATERIAL AND METHODS

Two maize populations (BR-106 and BR-105) that showed excellent general combining ability (Naspolini Filho et al., 1981) were used. BR-106 is a variety with yellow, dent kernels, short height, and early maturity, obtained by intercrossing tall and late varieties (Centralmex, Dent Compost and Maya) with BR-108 (Tuxpeño-1), which has short plants and early maturity. BR-105 (Suwan-DMR) has orange, flint kernels, short plants, early maturity, is resistant to downy mildew (Peronosclerospora sorghi), and has low inbreeding depression (Souza Jr. et al., 1993).

One hundred individual S₀ plants were sampled from each population and selfed to increase the seed number. Seeds to sow a 4-meter row were sampled from each S₁ progeny, which represented each of the S₀ plants from BR-106. These half-sib progenies were then grown as females and crossed with pollen from self and from BR-105 in two isolated detasseling blocks. Two similar detasseling blocks included BR-105 as females and crossed with pollen from self and BR106. S₁ seeds obtained from each S₀ plant were used to produce a half-sib progeny. Thus, 100 intra- and interpopulation half-sib progenies from each of the 100 S₀ plants were produced. In 1991/92 and 1992/93, these progenies were evaluated at two sites near Piracicaba, SP. Intra- and interpopulation half-sib progenies were evaluated in a 10 x 10 partially balanced lattice with two replications. The half-sib progenies were arranged in split-blocks (Steel and Torrie, 1960) with the main plot representing each S₀ plant. The two types of progenies for each S₀ plant were arranged into sub-plots. The sub-plots were 4 m rows spaced 1.00 m apart with 0.20 m between plants within rows, with a total of 20 plants per sub-plot (50,000 plants per hectare) after thinning. The control was the simple hybrid ICI8452 raised in border plots. The traits studied were yield (mean weight of unhusked ear after correction for stand variation, Y), plant height (PH), ear height (EH), calculated as a mean of five competitive plants per sub-plot, and the ratio of ear height and plant height (r).

Analysis of variance was performed in a split-block design with corrected means obtained from partially balanced lattices. An analysis of variance for each progeny was performed as randomized complete blocks with corrected means within progeny types and populations. The mean error was calculated from individual analysis for each environment or site with years combination. Intra- (A) and interpopulation (E) mean squares (M) and mean products (P) between them were obtained using the relation: M_{(A + E)} = M_A + M_E + 2P_AE (Kempthorne, 1966), and provided the estimates for all desired variances and covariances. Thus, estimates of genetic variance and covariance among progenies ( and , respectively) were obtained from progeny mean squares (M_p), mean product (P_p), progeny by environment interaction mean square (M_{p x e}), and mean product (P_{p x e}), as follows: = (M_p - M _{p x e})/nk and = (P_p - P_{p x e})/nk. Estimates of genetic variance and covariance among progeny by environment interactions ( and , respectively) were obtained including residual mean square (M_r) and mean product (P_r) as follows: = (P_{p x e} - M_r)/k and = (P_{p x e} - P_r)/k. The phenotypic variance among progeny means ( = + /k + /nk = M_p/nk) was obtained for all traits, where is an estimate of the mean residual variance, and n and k are the numbers of environments and replications, respectively. The desired parameters were estimated with these variances and covariances. The estimates and their genetic interpretations were obtained according to the relations given by Souza Jr. (1993) for each population, as follows:

Population BR-106:

= 4 = 2pq [a + (q-p)d]²

= 4 = 2pq [a + (v-u)d]²

= 4 [ -2 + ] = 8pq (p-u)²d²

= 2 [ - ] = 2pq (p-u) [a + (q-p)d]d

Population BR-105:

= 4 = 2uv [a + (v-u)d]²

= 4 = 2uv [a + (q-p)d]²

= 4 [ -2 + ] = 8uv (p-u)²d²

= 2 [ - ] = 2uv (u-p)[a + (v-u)d]d

where p and q, u and v are the frequencies of favorable and unfavorable alleles in populations 1 and 2, respectively, a is half of the difference of the genotypic values of the homozygotes, and d is the genotypic value of the heterozygote.

The expected selection responses for the interpopulation cross, populations per se, and heterosis, were calculated as shown in Tables I and ^II, for three distinct selection schemes: interpopulational or reciprocal recurrent selection (RRS), intrapopulational selection of half-sib progenies (HSS), and intra- and interpopulational or modified recurrent selection (MRS). The latter method (MRS) was suggested by Souza Jr. (1993). It used one of the populations as the tester for itself and for the other population. MRS(a) and MRS(b) represent the testers BR-105 (less productive) and BR-106 (more productive), respectively. Half-sibs and S₁ progenies were the evaluation and recombination units, respectively. Selection intensity was 20% (i = 1.40) for all schemes.

RESULTS AND DISCUSSION

Means obtained for BR-106, BR-105, the interpopulation cross, mid-parent and highest parent heterosis are shown in Table III. The control hybrid had a mean of 8.32 t/ha for ear weight (Y). The mean grain yields for BR-106, BR-105 and the interpopulational cross were 7.40, 6.84, and 7.58 t/ha, respectively. These values were considered high, but the interpopulational cross mean was very low in comparison with previous data. The low mean for the 1 x 2 cross (expected to be similar or greater than 2 x 1) was an important contributing factor. High-parent heterosis (h_HP) and mid-parent heterosis (h_MP) for Y (Table III) were below the values 17.9% and 19.2%, respectively, reported by Souza Jr. et al. (1993), and the values obtained in 1986-1987 (14.0% and 26.4%), 1990-1991 (3.7% and 9.6%), and 1992-1993 (14.3% and 15.4%), for the same populations (Santos et al., 1994). The observed heterosis values in this study were intermediate to those from other studies. Heterosis (h_HP and h_MP) was lower for other traits.

Analysis of variance was calculated by the split-block model (Table IV). The environment effects (E) were significant for the most traits in BR106 and BR-105; so, there were distinct environmental conditions for the trials. Genotype (G) was significant for all traits in both populations, and indicated presence of significant additive genetic variance among progenies for all traits. Genotype by environment interaction (G x E) was not significant for the studied traits, and demonstrated uniform genotype performance among environments. Progeny type (P) was significant only for Y in BR-105, where the genetic divergence level between populations used as reciprocal testers was sufficiently high. The released genetic divergence was not great enough to make P significant for the remaining traits in BR-105 and for the more productive population BR-106. Progeny type by environment interaction (P x E) was significant for Y in both populations, suggesting that the divergence level was not uniform for all environments. Genotype by progeny interaction (G x P) was significant for all traits only for BR-105. The G x P effect measures whether the use of an intra- or interpopulation tester produced different evaluations for the genotypes, which occurred in BR-105, while tester type was not important for BR-106. The triple interaction (G x P x E) was significant for Y and EH in BR-106, and only for r in BR-105. Its significance indicates that G x P interaction or tester effect was not uniform from one environment to another, which was true mainly for population BR-106.

Analysis of variance for each progeny type (intra- and interpopulation) and analysis of covariance between them for each population are presented in Table V. Individual analysis confirmed the presence of significant additive genetic variance between progenies for all traits in the evaluated populations. The progeny by environment interaction was significant for Y, EH and r for the interpopulation progenies (12) in BR-106, and only for r in interpopulation progenies (21) in BR-105.

Mean squares and mean products for progeny (P), progeny by environment interaction (P x E), and mean error obtained from Table V were used to calculate the estimates for all variance and covariance genetic components shown in Table VI. Estimates for intra- and interpopulation additive genetic variances in population BR-106 were below the corresponding estimates in BR-105 for all traits. The intrapopulation estimates of additive variances for ear weight ( and ) were above the average of 58 estimates ( = 309.0) reported by Vencovsky et al. (1988) for Brazilian populations. Our PH and EH estimates were below the average of 16 Brazilian population estimates, 321.0 and 218.0, respectively, reported by Miranda Filho (1985). The interpopulation estimate for yield [ = 1/2 (+ ) = 401.9] was greater than those obtained by Miranda Filho and Paterniani (1983), Souza Jr. and Miranda Filho (1989), and Souza Jr. et al. (1993), which were 158.0, 260.5, and 141.1, respectively. They were also above the average estimate (203.9) reported by Vencovsky et al. (1988). PH and EH estimates ( = 131.8 and 79.2, respectively) were below that reported by Souza Jr. and Miranda Filho (1989), which were 255.3 and 88.1, respectively. These results confirm the great potential of these populations for yield improvement, while plant and ear height were relatively homogeneous.

Estimates for genetic variances of the deviations from inter- and intrapopulation additive effects () and genetic covariances of the intrapopulation additive effects with the deviations from inter- and intrapopulation additive effects [] showed relatively small errors only for BR-105 (Table VI). Their genetic expectations (Souza Jr., 1993) showed that is directly related to heterosis, and and are related to genetic divergence between populations and the dominance level of the traits.

Interpopulation additive variances (Souza Jr., 1993) were as follows:

= + + 4 , for population BR-106;

= + + 4 , for population BR-105

Thus, if + 4 ¹ 0 then ¹ , for the BR-106 population. This is true when ¹ |4 |. From these relationships, it is possible to verify that when is positive or negative with magnitude smaller than ()/4, then > . Otherwise, if is negative with magnitude greater than ()/4, this variance relationship becomes < . The same relationship can be verified for the BR-105 population. For example, ear weight (Y) had a negative estimate for , that was greater than ()/4 making < for BR-106, while was also negative but with magnitude smaller than ()/4 making > . The traits PH, EH and r of population BR-106 showed similar results in relation to Y. For BR-105, only the ratio r = EH/PH was similar to Y, while PH and EH showed < , that is similar to the relationship shown by all traits in BR-106 (Table VI).

According to their genetic significance, and are expected to show opposite signs in genetically divergent populations. These estimates were all negative in this research, which is not expected theoretically (Table VI). However, the negative estimates obtained for BR-106 showed relatively high errors, and possibly they are null. Conversely, the errors associated with for BR-105 were relatively small, indicating that this parameter was truly negative.

Using data from Souza Jr. (1983) for BR-106 and ESALQ-PB1 populations, the following estimates for , , and were obtained: 37.6, 47.0, 24.2 and -19.4 (g/plant)². These results indicated that the parameter could really be the main cause of the small indirect response showed by intra- and interpopulation recurrent selection. Its sign and its relative magnitude in comparison with determine if an intra- or interpopulation method is the best choice for each population (Table I).

The values obtained for the ratios / and / for BR-106 were: 5.4 and -9.2, respectively, for Y, 5.9 and -12.3 for PH, -50.0 and -12.5 for EH, and -5.6 and -16.0 for r. The same ratios obtained for BR-105 were 1.0 and -5.0 for Y, 1.1 and -4.2 for PH, 1.2 and -4.0 for EH, and 1.1 and -4.7 for r, respectively. Souza Jr. (1993) calculated these ratios in a numeric evaluation with different dominance levels and different divergences between populations in a theoretical study. The expected value for Y (d/a @ 1.0) for the ratio / between divergent populations is 2.14, and for PH and EH (d/a @ 0.5) is 8.93. The observed values for Y (5.40) and PH (5.89) were similar, while EH (-50.0) had an opposite sign and a greater magnitude than expected. The same relationship calculated from data from Souza Jr. (1983) for Y (6.28) and EH (8.67) was similar, while PH (-6.96) showed an opposite sign. Expectations (Souza Jr., 1993) for the ratio / were 5.0 for Y and 16.5 for PH and EH. The signs of these values agree with those observed in this research. The same ratio calculated with data from Souza Jr. (1983) was 3.85, 4.67 and -12.81 for Y, PH and EH, one of which (-12.18) had a different sign. For the ratio / the expectation was 10.0 for Y and 13.89 for PH and EH. Compared with values obtained in this study (-9.2, -12.3 and -12.5) and by Souza Jr. (1983) (9.8, 12.0 and 42.5 for Y, PH and EH, respectively), the signs were all inverted in the first case, probably because must be null. The ratio / expected (Souza Jr., 1993) between divergent populations was -6.3 for Y and -11.8 for PH and EH. These values were -5.0, -4.2, and -4.0 in this study, and -9.3, -14.8 and 437.9 in Souza Jr. (1983) for Y, PH and EH, respectively. The sign differed only for EH in this last case. The similarity between expected and observed values for these ratios was larger when the errors associated with the parameters and were smaller.

Estimates for parameter by environment interactions (Table VII) showed relatively small errors in a few cases in BR-106 (Y and r for and EH for ) and in BR-105 ( and for r). These results were expected according to the significance level for progeny by environment interaction (P x E) mean square shown in Table V.

The expected responses obtained for Y (Table VIII) showed that the intrapopulation recurrent selection method (HSS) and the modified recurrent selection method (a) (MRS(a), with population BR-105 as tester) were similar. Both were inferior to the reciprocal recurrent selection (RRS) and modified recurrent selection (b) (MRS(b), with population BR-106 as tester) methods, for improving the interpopulation cross (I.C.). RRS and MRS(a) were similar and inferior to HSS and MRS(b) for improving the BR-106 population; RRS and MRS(b) were similar and inferior to HSS and MRS(a) for BR-105, and finally HSS and MRS(a) were inferior to MRS(b) and RRS for heterosis (Table VIII). Thus, the method MRS(b) was the best option, since MRS(b) and RRS were superior to the other methods in improving I.C. and heterosis, and MRS(b) showed additional superiority in relation to RRS for improving the BR-106 population.

These results may be compared to data obtained by Souza Jr. (1983) with ESALQ-PB1 and BR-105 populations. A similar method was applied to estimate the quadratic parameters and the expected responses to RRS, HSS, MRS(a) and (b) methods. The expected responses obtained for Y (g/plant/cycle) were: 12.25 (9.9%) for I.C., 12.73 (20.8%) for ESALQ-PB1, 7.49 (6.6%) for BR105, and 2.14 (26.3%) for heterosis obtained by the RRS method; 10.57 (8.6%), 11.76 (10.0%), 8.87 (7.9%) and 0.25 (3.1%) for I.C., ESALQ-PB1, BR105 and heterosis, respectively, using the HSS method; 11.77 (9.5%), 12.73 (10.8%), 8.87 (7.9%) and 0.97 (11.9%), respectively, for MRS(a), with BR105 as tester, and 11.05 (8.9%), 11.76 (10.0%), 7.49 (6.6%) and 1.42 (17.5%), respectively, using the MRS(b) with ESALQ-PB1 as tester. Comparisons of these expected responses can be outlined by the efficiency relationship of the methods: HSS @ MRS(b) < MRS(a) @ RRS for the interpopulation cross (I.C.); HSS = MRS(b) < RRS = MRS(a) for ESALQ-PB1; RRS = MRS(b) < HSS = MRS(a) for BR-105, and HSS < MRS(a) < MRS(b) < RRS for heterosis. These results showed that the MRS(a) method was superior for producing hybrids from inbred lines, since it obtained a small response only for heterosis, that was calculated in relation to the mean of parental populations per se. Expected responses to interpopulation cross, populations per se, and heterosis for PH, EH and r showed similar results in relation to those observed for Y, except for r in population BR-106 (Gs11), where HSS was similar to MRS(b) and inferior to RRS and MRS(a).

The MRS method was superior to RRS and HSS for hybrid production from inbred lines in the two data sets studied. Choosing of the best tester (MRS(a), the population with lower mean, or MRS(b), the population with greater mean for Y), based only on mean population values as suggested by Souza Jr. (1993), would not be the best option. Furthermore, estimating all these parameters is impractical and normally subject to large associated errors. A more practical and efficient form of choosing a population tester for the MRS method would be the intra- and interpopulation means with the additional use, when possible, of intra- ( and ) and interpopulation ( and ) additive variances, which showed relatively small errors and are easily estimated.

ACKNOWLEDGMENTS

This paper was approved for publication by the Technical Director of Embrapa Soja as manuscript number 006/97. The authors are grateful to CAPES and CNPq for financial support.

RESUMO

Novos componentes genéticos de variância e covariância relacionados aos métodos de seleção recorrente intra- e interpopulacional foram desenvolvidos teoricamente por Souza Jr. (Rev. Bras. Genet. 16: 91-105, 1993) para explicar porque estes métodos têm falhado em melhorar o híbrido e as populações per se conjuntamente. Progênies de meio-irmãos intra- e interpopulacionais foram produzidas a partir de 100 genótipos amostrados das populações de milho BR-106 e BR-105 para estimar estes componentes de variância e covariância e comparar as respostas esperadas para os métodos de seleção recorrente recíproca (RRS), intrapopulacional (HSS) e modificada (MRS) sobre o híbrido interpopulacional, as populações per se e a heterose. Quatro grupos de 100 progênies, dois intra- e dois interpopulacionais, foram avaliados em látices 10 x 10, parcialmente balanceados, arranjados segundo um delineamento em faixas com duas repetições, nos anos agrícolas 1991-1992 e 1992-1993 e em dois locais da região de Piracicaba, SP. Foram avaliados os seguintes caracteres: peso de espiga, alturas de planta e espiga e a razão altura de planta sobre altura de espiga. As populações e os híbridos interpopulacionais apresentaram alta produtividade e grande potencial para a produção de híbridos de linhagens. As heteroses em relação à média populacional e à melhor população foram relativamente altas, mas abaixo dos valores relatados para estas populações sob outras condições ambientais. As estimativas da variância aditiva para as populações per se e para os cruzamentos interpopulacionais confirmaram o grande potencial desses materiais para o melhoramento. As magnitudes das estimativas da variância para os desvios dos efeitos aditivos intra- e interpopulacionais ( para BR-106 e para BR-105) e para a covariância entre os efeitos aditivos com esses desvios ( para BR-106 e para BR-105) indicaram que estes novos componentes podem influenciar significativamente a eficiência dos métodos de melhoramento. As estimativas dos componentes genéticos para BR-105 apresentaram erros relativamente pequenos, com negativo para todos os caracteres. As estimativas de e apresentaram erros relativamente grandes para BR-106. O método MRS foi mais eficiente que RRS e HSS para a produção de híbridos de linhagens. A escolha da população testadora para o método MRS baseada apenas nas médias das populações per se pode ser incorreta. Quando possível, a utilização adicional das variâncias genéticas aditivas intra- e interpopulacionais de cada população seria mais apropriada.

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(Received June 6, 1997)

Publication Dates

• Publication in this collection
  01 Mar 1999
• Date of issue
  Dec 1998

History

• Received
  06 June 1997