RESUMOO presente trabalho teve por objetivo estudar a estabilidade fenotípica da produtividade de grãos de feijão (Phaseolus vulgaris L.) com dados obtidos no Ensaio Regional Final do Estado do Paraná, durante o ano/safra 1996/97, através de modelo não-linear, (nos parâmetros propostos por Toler), assim expresso: Yij = αi + [Zjβ1i + (1 -Zj) β2i] µj + εij. Esse autor propôs testes das hipóteses H(β1i = β2i) e H(β1i = β2i = βi = 1), as quais permitem enquadrar os genótipos em cinco grupos, conforme o padrão de resposta, a saber: A, B, C, D e E. Os parâmetros do modelo são estimados conjuntamente através de quadrados mínimos iterativos (não-lineares), empregando-se neste estudo o método de GaussNewton modificado. Concluiu-se que o modelo foi útil para classificar os materiais genéticos segundo suas produtividades e seus padrões 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 associação negativa entre β 1i e β 2i . A maioria dos genótipos com padrão de resposta duplamente favorável (grupo A, padrão convexo) apresentou produtividades baixas. Os genótipos com produtividades mais elevadas enquadraram-se preferencialmente no grupo E (padrão côncavo, duplamente desfavorável). Os genótipos dos grupos com padrão unissegmentado (B, C e D) tiveram produtividades variáveis. Ficou evidenciada a dificuldade em encontrar genótipos associando altas produtividades com padrão de resposta convexo. Palavras-chave: Estabilidade fenotípica, padrão de resposta, feijão. ABSTRACT NON-LINEAR MODEL REGRESSION FOR PHENOTYPIC STABILITY ANALYSIS OF BEAN GENOTYPES IN THE STATE OF PARANÁA 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 = αi + [Zjβ1i + (1 -Zj) β2i] µj + εij, was adopted. The author proposed tests of the hypotheses H(β1i = β2i) and H(β1i = β2i = βi = 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 β1i and β2i. The majority of genotypes with a double favorable response pattern (A group, convex pattern) had lower yields. Genotypes with higher yields were placed mostly ( 1 ) Recebido para a publicação em 28 de junho e aceito em 22 de novembro de 1999.

Resumo -O objetivo deste trabalho foi comparar dois métodos de regressão empregados para avaliar a estabilidade fenotípica em plantas de cana-de-açúcar, o linear, de Cruz et al., e o não-linear, de Toler & Burrows. Utilizaram-se as informações do ensaio de caracterização de 1994 do programa de melhoramento genético da Copersucar, compreendendo 13 locais e 20 genótipos de cana-de-açúcar no Estado de São Paulo. Os resultados permitiram concluir que ambos os modelos se ajustaram satisfatoriamente aos dados. As estimativas da qualidade ambiental pelos dois modelos mostraram diferenças entre seus valores, porém foram concordantes para inferir sobre os melhores e piores ambientes. Ao classificar os genótipos com base na produtividade e no padrão de resposta, no entanto, apenas dez foram coincidentes nos dois métodos. As vantagens estatísticas do método não-linear torna-o recomendável para pesquisa sobre estabilidade.Termos para indexação: Saccharum, interação genótipo-ambiente, modelos, análise de regressão. Comparison of regression methods for evaluation of phenotypic stability in sugarcaneAbstract -The purpose of this work was to compare the regression methods used for evaluating phenotypic stability in plants. The Measures of environmental quality were numerically different but agreed in general terms for the ranking of locations. However, when genotypes were classified on the bases of yield and pattern of response only ten coincided for both methods. The statistical advantages of the non-linear model makes it recommendable for studies on stability.Index terms: Saccharum, genotype environment interaction, models, regression analysis.(1) Aceito para publicação em 23 IntroduçãoA cana-de-açúcar (Saccharum spp.) é um produto de suma importância econômica e social no Brasil, em virtude dos seus derivados, principalmente o álcool e o açúcar. O Estado de São Paulo destaca-se por contribuir com cerca de 60% da produção nacional, o que equivale a aproximadamente 300 milhões de toneladas anuais (Raizer, 1998).O sucesso dessa atividade econômica está atrelado principalmente aos programas de melhoramento genético, nos quais um dos objetivos é desenvolver variedades adaptadas às diversas regiões canavieiras, visando contornar problemas relacionados a ataques de pragas e resistência às doenças, além de melhorar as características industriais das variedades.O Estado de São Paulo, por sua extensão territorial, mostra elevada diversidade edafoclimática entre as principais regiões produtoras, fazendo com que a classificação das variedades de um ambiente para outro não seja a mesma. Esse fenômeno em que a classificação dos materiais é alterada, denomina-se interação de genótipos por ambientes e suas impli-

-Rust (Puccinia psidii), ceratocystis wilt (Ceratocystis fimbriata) and cylindrocladium leaf blight (Cylindrocladium pteridis) are important diseases of eucalyptus. Planting of resistant genotypes is the most suitable control strategy of forest diseases under field condition. Resistance level of 23 Eucalyptus pellita clones was evaluated by artificial inoculations. Among the inoculated clones, 12 were resistant to rust, 16 to ceratocystis wilt and 12 to cylindrocladium leaf blight, and three of them were resistant to all three diseases. The high intra-specific variability found in this study demonstrates the importance of E. pellita as a disease resistance source to be employed for introgression of novel resistance genes in eucalyptus genetic breeding programs.

Ceratocystis wilt, caused by Ceratocystis fimbriata, is one of the most damaging diseases in eucalyptus plantations worldwide. Although there are resistant genotypes, the genetic basis of resistance is still poorly understood. In this paper we studied the resistance level by a stem inoculation experiment of genotypes of Eucalyptus grandis and E. urophylla and estimated the heritability and gains of selection in families derived from controlled interspecific crosses. In both species, highly resistant as well as highly susceptible genotypes to Ceratocystis wilt were found. Out of 21 parents assessed, twelve were resistant and nine susceptible. Estimates of individual narrow (50 %) and broad (59 %) sense heritability suggested a high degree of genetic control and low allelic dominance of the trait. There was great genetic variation among and within families, a fact that contributes to high heritability and genetic gain. A genetic gain in lesion size of up to -74.4 % was obtained from selection of the 50 best clones in the evaluated families, i.e., the mean lesion length in the progeny population can be reduced by 74,4 %.

ABSTRACT. We examined the correspondence in performance between trees selected from a family test and their respective clones from a clonal test of Eucalyptus. Full-sib families were obtained from controlled pollination among individuals of Eucalyptus grandis and between E. grandis and E. urophylla. The hybridizations did not follow a factorial scheme. The family tests were carried out at three locations in Eunápolis and Itabela counties, in Bahia, Brazil, in 2003. Four hundred and ninety-seven high-performance trees were selected, by the individual BLUP procedure, in the family tests at two years of age, based on wood volume. The clones from these trees and 14 checks were evaluated in clonal tests carried out in the same region in 2006. The wood volume of the clones was evaluated at two years of age. Trait correlation between the trees selected from the family and clonal tests was low. The estimate of the coincidence between the best trees and the best clones using an average of the different intensities of selection was only 27%. These results demonstrate that the selection of trees in the family test should not Correspondence between Eucalyptus spp be too drastic; otherwise the chance plus clones may be overlooked.

Chrysophorte cubensis induced canker occurs in nearly all tropical and subtropical regions where eucalypts are planted, causing losses in both wood quality and volume productivity, especially so in the warmer and more humid regions of Brazil. The wide inter and intra-specific genetic variability of resistance to canker among Eucalyptus species facilitates the selection of resistant plants. In this study, we evaluated resistance to this pathogen in five Eucalyptus grandis (G) and 15 E. urophylla (U) trees, as well as in 495 individuals from 27 progenies derived from crosses between the trees. In the field, six-months-old test seedlings were inoculated with C. cubensis. Lesion length in the xylem and bark was measured eight months later. The results demonstrated that xylem lesions could preferentially be used for the selection of resistant clones. Eight trees (7 U and 1 G) were susceptible, and the remainder (8 U and 4 G) resistant. Individual narrow and broad sense heritability estimates were 17 and 81%, respectively, thereby suggesting that canker resistance is quantitative and highly dependent on dominance and epistasis.

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-Eucalypts rust (Puccinia psidii) is currently one of the major diseases in commercial eucalypt plantations in