Abstract:
estimation of the proportion of genetic variance explained by molecular markers (p) plays an important role in basic studies of quantitative traits, as well as in marker-assisted selection (mas), if the selection index proposed by lande and thompson (genetics 124: 743-756, 1990) is used. frequently, the coefficient of determination (r2) is used to account for this proportion. in the present study, a simple estimator of p is presented, which is applicable when a multiple regression approach is used, and progenies are evaluated in replicated trials. the associated sampling distribution was obtained and compared with that of r2. simulations indicated that, when the number of evaluated progenies is small, the statistics are not satisfactory, in general, due to bias and/or low precision. coefficient r2 was found adequate in situations where p is high. if a large number of progenies is evaluated (say, a few hundreds), then the proposed estimator appears to be better, with acceptable precision and considerably lower bias than r2. a normal approximation to the sampling distribution of is given, using taylor's expansion of the expectation and variance of this statistic. approximate confidence intervals for p, based on normal distribution, are reasonable, if the number of progenies is large. the use of in mas is illustrated for estimation of the weight given to the molecular score, when a selection index is used.

Abstract:
Estimation of the proportion of genetic variance explained by molecular markers (p) plays an important role in basic studies of quantitative traits, as well as in marker-assisted selection (MAS), if the selection index proposed by Lande and Thompson (Genetics 124: 743-756, 1990) is used. Frequently, the coefficient of determination (R2) is used to account for this proportion. In the present study, a simple estimator of p is presented, which is applicable when a multiple regression approach is used, and progenies are evaluated in replicated trials. The associated sampling distribution was obtained and compared with that of R2. Simulations indicated that, when the number of evaluated progenies is small, the statistics are not satisfactory, in general, due to bias and/or low precision. Coefficient R2 was found adequate in situations where p is high. If a large number of progenies is evaluated (say, a few hundreds), then the proposed estimator appears to be better, with acceptable precision and considerably lower bias than R2. A normal approximation to the sampling distribution of is given, using Taylor's expansion of the expectation and variance of this statistic. Approximate confidence intervals for p, based on normal distribution, are reasonable, if the number of progenies is large. The use of in MAS is illustrated for estimation of the weight given to the molecular score, when a selection index is used.

Abstract:
a phenotypic stability analysis of common bean (phaseolus vulgaris l.) grain yield (kg.ha-1) was carried out using data of the regional trial of the state of paraná during the year/harvest 1996/97. a non-linear model using the parameters proposed by toler, yij = ai + [zjb1i + (1 - zj) b2i] mj + eij, was adopted. the author proposed tests of the hypotheses h(b1i = b2i) and h(b1i = b2i = bi = 1) according to the principles of regression analysis, that allow the genotypes to be placed in five groups (a, b, c, d, and e) based on their response pattern. the parameters of the model are simultaneously estimated using iterative (non-linear) least squares through the modified gauss-newton method. the model was useful in classifying the genetic materials according to their yield and response patterns, contributing to a greater understanding of their yield behavior. the mean of the a and e groups was influenced by a negative association between and . the majority of genotypes with a double favorable response pattern (a group, convex pattern) had lower yields. genotypes with higher yields were placed mostly in the e group (concave pattern, double unfavorable). those from groups with a single-segment pattern (b, c, and d) showed variable yields. the difficulty in finding genotypes with both high yields and convex response pattern was evident.

Abstract:
five sugarcane (saccharum officinarum l.) varieties recently released by the copersucar breeding program were evaluated for yield, stability and environmental adaptability, using a methodology for phenotypic stability estimation. new varieties were compared with the check rb72454. yield was highly related with environmental improvement. varieties sp80-185, sp80-1816 and sp80-3280 were the most stable ones, showing high productivity on the best environments. sp83-5073, a variety with high sugar content and earliness, was also very stable, whereas, sp80-3480 showed higher scattering, but with high yield. based on the parameters estimated the variety sp80-185 should be indicated as check for future trials, since it was the most adapted to poorer environments and the most responsive on better ones.

Abstract:
in general terms, quantitative trait loci (qtl) mapping differs from other research tools used in genetics since it is, basically, a multiple test procedure. the use of this technique leads to problems related to the genomewise significance level and, consequently, to the power of the test. using computational data simulation the power of qtl mapping was obtained, carried out through multiple linear regression using stepwise procedures to select markers. procedures based on single marker analisys, using both the false discover rate (fdr) and the bonferroni criteria to determinate the genomewise significance level were also used. the procedure based on multiple regression, using the stepwise technique, was the most powerful in identifying markers associated to qtl's. however, in cases where its power was less intense, its advantage was the ability to detect only markers strongly associated to qtl's. in comparison to the bonferroni method, the fdr criterion was in general more powerful, and should be adopted for interval mapping procedures.

Abstract:
O mapeamento de locos envolvidos no controle gênico de caracteres quantitativos, QTL's, difere dos demais tipos de experimentos conduzidos em genética, por tratar-se, basicamente, de um procedimento de testes múltiplos. Um problema decorrente deste tipo de análise refere-se ao nível de significancia conjunto e, consequentemente ao poder da mesma. Em vistas disto avaliou-se, via simula o computacional de dados, o poder de detec o de QTL's da análise de marcas simples, utilizando os critérios da raz o de falsas descobertas (FDR) e de Bonferroni para determina o nível de significancia conjunto alfa* e da regress o linear múltipla, empregando o procedimento "stepwise" para sele o das marcas. O procedimento baseado em regress o múltipla foi mais poderoso em identificar as marcas associadas a QTL's, do que os procedimentos baseados em testes individuais, utilizando tanto o critério FDR, quanto o de Bonferroni para o controle do nível de significancia conjunto. Mesmo nos casos em que esse procedimento apresentou poder ligeiramente inferior aos demais, mostrou a grande vantagem de selecionar apenas as marcas mais fortemente ligadas a QTL's, devendo, portanto, ser preferido para sele o das marcas a serem utilizadas como covariáveis no processo de mapeamento por intervalo múltiplo. Dentre os critérios FDR e de Bonferroni, que s o aplicáveis aos métodos de mapeamento por intervalo, o primeiro mostrou-se mais poderoso, devendo portanto ser preferido.

Abstract:
O presente trabalho teve por objetivo estudar a estabilidade fenotípica da produtividade de gr os de feij o (Phaseolus vulgaris L.) com dados obtidos no Ensaio Regional Final do Estado do Paraná, durante o ano/safra 1996/97, através de modelo n o-linear, (nos parametros propostos por Toler), assim expresso: Yij = alfai + [Zjbeta1i + (1 - Zj) beta2i] mij + épsilonij. Esse autor prop s testes das hipóteses H(beta1i = beta2i) e H(beta1i = beta2i = betai = 1), as quais permitem enquadrar os genótipos em cinco grupos, conforme o padr o de resposta, a saber: A, B, C, D e E. Os parametros do modelo s o estimados conjuntamente através de quadrados mínimos iterativos (n o-lineares), empregando-se neste estudo o método de Gauss-Newton modificado. Concluiu-se que o modelo foi útil para classificar os materiais genéticos segundo suas produtividades e seus padr es de resposta, o que contribuiu para um maior discernimento de seus comportamentos. As médias dos genótipos dos grupos A e E mostraram-se influenciadas pela associa o negativa entre e . A maioria dos genótipos com padr o de resposta duplamente favorável (grupo A, padr o convexo) apresentou produtividades baixas. Os genótipos com produtividades mais elevadas enquadraram-se preferencialmente no grupo E (padr o c ncavo, duplamente desfavorável). Os genótipos dos grupos com padr o unissegmentado (B, C e D) tiveram produtividades variáveis. Ficou evidenciada a dificuldade em encontrar genótipos associando altas produtividades com padr o de resposta convexo.

Abstract:
the partial circulant diallel cross mating scheme of kempthorne and curnow (biometrics 17: 229-250, 1961) was adapted for the evaluation of genotypes in crosses at the interpopulation level. considering a random sample of n lines from base population i, and that each line is crossed with s lines from opposite population ii, there will be ns sampled crosses that are evaluated experimentally. the means of the ns sampled crosses and the remaining n(n - s) crosses can be predicted by the reduced model where yij is the mean of the cross between line i (i = 1,2,...,n) of population i and line j (j = 1',2',...,n') of population ii; μ is the general mean, and gi and gj refer to general combining ability effects of lines from populations i and ii, respectively. specific combining ability (sij) is estimated by the difference . the sequence of crosses for each line (i) is [i x j], [i x (j + 1)], [i x (j + 2)], ..., [i x (j + s -1)], starting with i = j = 1 for convenience. any j + s -1 > n is reduced by subtracting n. a prediction procedure is suggested by changing gi and gj by the contrasts i = i. - .. and j = .j - ..; the correlation coefficient (r) was used to compare the efficiency of 's and 's for selection of lines and crosses. the analysis of variance is performed with the complete model yij = μ + gi + gj + sij + ij, and the sum of squares due to general combining ability is considered for each population separately. an alternative analysis of variance is proposed for estimation of the variance components at the interpopulation level. an analysis of ear length of maize in a partial diallel cross with n = 10 and s = 3 was used for illustration. for the 30 interpopulation crosses analyzed the coefficient of determination (r2), involving observed and estimated hybrid means, was high for the reduced (g) model [r2 (ij, yij) = 0.960] and smaller for the simplified () model [r2 (ij, yij) = 0.889]. results indicated that the proposed procedure may furnish reliable estimates of

Abstract:
the objective of this study was to evaluate the efficiency of spatial statistical analysis in the selection of genotypes in a plant breeding program and, particularly, to demonstrate the benefits of the approach when experimental observations are not spatially independent. the basic material of this study was a yield trial of soybean lines, with five check varieties (of fixed effect) and 110 test lines (of random effects), in an augmented block design. the spatial analysis used a random field linear model (rfml), with a covariance function estimated from the residuals of the analysis considering independent errors. results showed a residual autocorrelation of significant magnitude and extension (range), which allowed a better discrimination among genotypes (increase of the power of statistical tests, reduction in the standard errors of estimates and predictors, and a greater amplitude of predictor values) when the spatial analysis was applied. furthermore, the spatial analysis led to a different ranking of the genetic materials, in comparison with the non-spatial analysis, and a selection less influenced by local variation effects was obtained.

Abstract:
this study reviewed the theory of estimation/prediction of treatment means, in randomized block designs, emphasizing aspects of interest to plant breeders. comparisons were made between analyses based on fixed (intrablock) and mixed (with random treatments effects - recovering intergenotypic information) linear models for identifying the determining factors that may affect the classification of genotypes. the mixed model approach, in comparison with the traditional analyses (marginal means and intrablock analysis), in general, leads to: i) more uniformly distributed treatment means; and ii) selection of different genetic treatments when the genetic variance is small relative to the environmental variance, as well as designs being non-orthogonal and unbalanced. in addition, if treatments of distinct reference populations are evaluated in the same experiment, blup prediction can lead to different ranking of means, in comparison with the intrablock analysis, even if designs are balanced and orthogonal.