Abstract: The breeding of Physalis peruviana is incipient in Brazil and is shown to be the most promising alternative for the development of productive genotypes with fruit quality. Therefore, the objective was to evaluate the combining ability between inbred lines of P. peruviana, thus indicating the selection of hybrids with fruit quality. Therefore, four populations from different origins were selfed for three generations and crossed in controlled hybridizations, resulting in 28 P. peruviana populations. The hybrid in relation to the parent performance, based on the effects of general and specific combining ability, was compared in a full diallel mating design (Griffing Method 1). In the analysis of variance, the factor genotype was partitioned into the following causes of variation: i) parents and F1 hybrids, ii) selfed generations and iii) Genotype × environment (GE) interaction. There were significant differences between Parents and F1 hybrids for the trait fruit polar diameter. Still, the interaction between specific combining ability x environment and, reciprocal effect x environment, was significant. However, for the Xanxerê environment, there was a reduction of approximately 3.0 mm in the polar diameter of the fruit in the hybrid Colombia x Peru and a reduction of 4.5 mm for the reciprocal (Peru x Colombia). In the comparison of the selfed generations S0 with S1, the fruit weight of the Lages population decreased by 0.380 g. There was also a reduction of 974.5 kg.ha-1 in the fruit yield of the Peruvian population. Thus, the performance of the P. peruviana populations in hybrid combinations is unpromising, indicating the existence of only one P. peruviana gene pool, with a restricted genetic basis. Abstract quality Therefore P hybridizations 2 Griffing 1. 1 . 1) variance variation i F ii iii GE (GE Still However 30 3 0 3. 45 4 5 4. Colombia. Colombia) S S1 0380 380 0.38 g 9745 974 974. kg.ha1 kgha1 kgha kg.ha kg ha kg.ha- Thus unpromising pool basis 038 38 0.3 97 ha1 03 0. 9

Resumo: O melhoramento de Physalis peruviana é incipiente no Brasil e mostra-se como a alternativa mais promissora no desenvolvimento de genótipos produtivos e com qualidade de fruto. Sendo assim, o objetivo foi avaliar a capacidade de combinação entre linhagens endogâmicas de P. peruviana, indicando, assim, híbridos comqualidade de fruto. Para tanto, quatro populações de distintas origens (Colômbia, Lages,Caçador, Peru)foram submetidas a três gerações de autofecundação e a hibridação, totalizando28 genótipos. Utilizou-se um esquema de dialelo completo (Método 1 de Griffing) a fim de comparar o desempenho dos híbridos em relação aos genitores, com base nos efeitos dacapacidade geral e da capacidade específica de combinação. Os experimentos foramconduzidos em dois locais (Lages-SC e Xanxerê-SC), sob um delineamento de blocoscasualizados, com três repetições. Na análise de variância, o fator genótipo foi decomposto nasseguintes causas de variação: i) genitores e híbridos F1’s, ii) gerações de autofecundação e iii) interação genótipo x local. Houve diferenças significativas entre Genitores e híbridos F1’s parao caráter diâmetro polar do fruto. Foram observados valores significativos para adecomposição da interação: Capacidade específica x Local e Recíproco x Local. Porém, para oambiente de Xanxerê, houve redução de aproximadamente 3,0 mm no diâmetro polar do fruto,no híbrido Colômbia x Peru, e redução de 4,5 mm, para o recíproco (Peru x Colômbia). Comrelação às autofecundações, na comparação S0 vs. S1 para as populações Lages e Peru,houve redução na massa de frutos (0,380 g) e no rendimento de frutos (974,5kg.ha-1). Porém,de maneira geral, a qualidade de fruto não foi afetada em virtude dasautofecundações. As populações não manifestam desempenho promissor quando em combinações híbridas,revelando a existência de apenas um pool gênico de P. peruviana de restritabase genética. Resumo mostrase mostra se assim P indicando tanto Colômbia, (Colômbia LagesCaçador Caçador Lages,Caçador Peruforam Peru foram hibridação totalizando totalizando2 Utilizouse Utilizou Método Griffing LagesSC SC XanxerêSC, XanxerêSC Xanxerê , Xanxerê-SC) blocoscasualizados repetições variância variação i F1s, F1s Fs F1 s, s F ii iii local Porém 30 3 0 3, frutono 45 4 5 4, Colômbia. . Colômbia) autofecundações S vs Peruhouve 0,380 0380 380 (0,38 g 974,5kg.ha1. 9745kgha1 kgha 974,5kg.ha 974 5kg ha kg (974,5kg.ha-1) Porémde dasautofecundações híbridasrevelando híbridas revelando genética Xanxerê-SC 0,38 038 38 (0,3 ha1 974,5kg.ha1 9745kgha 97 (974,5kg.ha-1 0,3 03 (0, 9 (974,5kg.ha- 0, (0 (974,5kg.ha (

RESUMO: Physalis peruviana L. (fisális) apresenta grande potencial econômico devido ao sabor diferenciado de seus frutos. A produtividade dos pomares brasileiros é baixa em função do número limitado de variedades ou cultivares disponíveis. O principal entrave na seleção de genótipos superiores é a falta de informação sobre a variabilidade genética dentro e entre as populações de fisális e, possivelmente, a base genética limitada das mesmas, que pode ser explicada pelos processos evolutivos, de domesticação e de seleção das populações naturais ou artificiais. A fisális cultivada atualmente no Brasil é tetraploide e tal poliploidia pode ter levado ao isolamento reprodutivo da espécie, o qual impede a ocorrência de hibridação intraespecífica. As populações cultivadas provêm de um pool genético comum e, além disso, sofreram um longo processo de domesticação e seleção realizadas empiricamente pelos agricultores. Porém, na Colômbia e em outros países andinos existem populações silvestres que exibem diversidade genética que, embora sejam fundamentais para a conservação da espécie, apresentam baixo potencial para o desenvolvimento de genótipos com características agronômicas superiores. A fim de criar e ampliar a variabilidade genética de fisális, os melhoristas tem empregado várias estratégias incluindo a indução de mutação, a duplicação cromossômica e a hibridação inter e intraespecífica. Além disso, a produção de linhagens duplo-haploides a partir da cultura de anterasin vitro vem demonstrando bons resultados para a seleção de híbridos. Os genótipos mutantes e/ou híbridos obtidos através dos métodos citados em associação com os de seleção genômica ampla podem gerar cultivares com características agronômicas superiores.

ABSTRACT: Physalisperuviana L. (physalis) has significant economic potential by virtue of the unique flavor of its fruit. However, the productivity of Brazilian plantations is low because of the limited number of varieties or cultivars available. The main obstacle in the selection of superior genotypes is the lack of information about genetic variability within- and between- populations and limited genetic basis that has likely resulted from evolutionary, domestication and selection processes of the natural or artificial populations. Physalis currently cultivated in Brazil is tetraploid, and such polyploidy may have led to the reproductive isolation of the species, preventing the occurrence of intraspecific hybridization. Moreover, cultivated populations derive from a common gene pool and have undergone a long process of domestication and selection carried out empirically by farmers. In Colombia and other Andean countries there are wild populations that exhibit genetic diversity which; although, fundamental for the conservation of the species, have low potential for the development of genotypes with superior agronomic traits. In order to create and expand the genetic variability of physalis, breeders have employed various strategies including induction of mutation, chromosome duplication, and interspecific and intraspecific hybridization. Furthermore, the production of double haploid lines from in vitro anther cultures has shown good results in the selection of hybrids. The mutant genotypes and/or hybrids obtained using these methods in association with those of wide genomic selection can generate cultivars with superior agronomic traits.

Abstract The objective of this work was to evaluate root phenotyping methods and the ideal phenological stage to quantify the root system of fixed and segregating common bean populations, in order to select superior genotypes. The experiment was carried out in two municipalities in the state of Santa Catarina, Brazil, and the treatments consisted of six genotypes, the Shovelomics and WinRHIZO root phenotyping methods, and the V4-4, R6, and R8 phenological stages. The simple lattice experimental design was used to evaluate the following variables: basal root angle, vertical root length, left and right horizontal root length, total root length, projected area, and root average volume and diameter. For all variables, there was a significant interaction between phenotyping methods and phenological stages, showing their influence on root system evaluation. The Shovelomics and WinRHIZO phenotyping methods are efficient in quantifying the root system of common bean plants and show specificity for phenological stages, regardless of the genotype. The quantification of the root system of fixed and segregating genotypes is analogous in both methods. The Shovelomics method is more efficient in evaluating the root system of common bean at the R8 stage, and the WinRHIZO method, at the R6 stage. populations Catarina Brazil V44, V44 V V4 4, 4 V4-4 R stages variables angle length area diameter evaluation genotype V4-

Resumo O objetivo deste trabalho foi avaliar métodos de fenotipagem de raízes e o estádio fenológico ideal para quantificação do sistema radicular de populações fixas e segregantes de feijoeiro, para selecionar genótipos superiores. O experimento foi realizado em dois municípios do estado de Santa Catarina, Brasil, e os tratamentos consistiram em seis genótipos, nos métodos de fenotipagem Shovelomics e WinRHIZO, e nos estádios fenológicos V4-4, R6 e R8. O delineamento experimental látice simples foi utilizado para avaliar as seguintes variáveis: ângulo de raiz basal, comprimento vertical das raízes, comprimento horizontal esquerdo e direito das raízes, comprimento total das raízes, área projetada, e volume e diâmetro médio de raízes. Para todas as variáveis, houve interação significativa entre os métodos de fenotipagem e os estádios fenológicos, o que mostra a influência desses na avaliação do sistema radicular. Os métodos de fenotipagem Shovelomics e WinRHIZO são eficientes para a quantificação do sistema radicular do feijoeiro e apresentam especificidade para o estádio fenológico, independentemente do genótipo. A quantificação do sistema radicular de genótipos fixos e segregantes é análoga em ambos os métodos. O método Shovelomics é mais eficiente para avaliar o sistema radicular do feijoeiro na fase R8, e o método WinRHIZO, na fase R6. superiores Catarina Brasil V44, V44 V V4 4, 4 V4-4 R R8 variáveis basal projetada genótipo V4-

Abstract According to literature, the apple cultivar SCS425 Luiza is a hybrid of Imperatriz♀ and Cripps Pink♂; however, molecular analysis of gametophytic self-incompatibility alleles showed the presence of an unexpected allele in SCS425 Luiza. This raised doubts about the fidelity of the pedigree. Thus, this study aimed to investigate the real genealogy of the SCS425 Luiza cultivar via fingerprint analysis. A total of 19 pairs of SSR primers covering 12 of the 17 chromosomes were used. ‘Imperatriz’ was tested as the female parent, and either ‘Cripps Pink’ or ‘Baronesa’ was tested as the presumed male parents. The results excluded ‘Cripps Pink’ as the male parent because most of the markers showed alleles of exclusion with Likelihood ratio (LR) value equal to zero. In contrast, when Baronesa was tested as the male parent, all alleles followed the expected segregation with very high LR values (>10.000). Therefore, it is concluded that the correct genealogy of the SCS425 Luiza cultivar is Imperatriz♀ and Baronesa♂. literature SCS SCS42 Imperatriz Pink♂ Pink however selfincompatibility self incompatibility pedigree Thus 1 used ‘Imperatriz ‘Baronesa parents (LR zero contrast >10.000. 10000 >10.000 . 10 000 (>10.000) Therefore Baronesa♂ SCS4 1000 >10.00 00 (>10.000 100 >10.0 0 (>10.00 >10. (>10.0 >10 (>10. >1 (>10 > (>1 (> (

RESUMEN La creciente demanda por cultivares de cebolla de baja pungencia ha abierto nuevos nichos de mercado. El objetivo de este estudio fue caracterizar grupos heteróticos de cebolla para el desarrollo de cultivares híbridos con baja pungencia. Se realizó un experimento de campo con un diseño de bloques al azar con dos factores (genotipo y fertilización) dispuestos en parcelas divididas en Ituporanga-SC (Brasil), en 2019. Las parcelas correspondieron a dos niveles de fertilización (con y sin azufre) y las subparcela a vinteseis genotipos de cebolla, considerando germoplasma procedente de líneas androestéreles-LA y mantenedoras-LB, poblaciones avanzadas y cultivares. Los bulbos fueron evaluados por las características: ácido pirúvico (indicador de pulgencia), contenido de azufre y rendimiento de bulbo. Los genotipos revelaron un comportamiento diferencial según el nível de fertilización adoptado. En la condición sin azufre cuatro grupos heteróticos fueron identificados, los cruzamientos LA11 × LB24 y LA15 × LB19 pueden generar variación genética y la respectiva selección negativa para la pungencia y positiva para la productividad de bulbos.

ABSTRACT The growing demand for low-pungency cultivars onion has opened new market niches. The objective of this study was to characterize heterotic onion groups to develop low-pungency hybrid cultivars. A field experiment with a randomized block design and two factors (genotype and fertilization) arranged in split plots was carried out in Ituporanga-SC (Brazil), in 2019. The plots corresponded to two fertilization levels (with and without sulfur), and the subplots corresponded to 26 onion genotypes, where the germplasm was derived from different (male-sterile-LA and maintainer-LB) lines, advanced populations and cultivars. The bulbs were evaluated for the following traits: pyruvic acid (indicator of pungency), sulfur content and bulb yield. The genotype performance differed according to the fertilization level. In the sulfur-free treatments, four heterotic groups were identified. The genetic variation in the crosses LA11 × LB24 and LA15 × LB19 could be exploited for negative selection for pungency and positive selection for bulb yield.

Abstract ‘Caviano’ is a black bean cultivar recommended for Santa Catarina, for being highly adaptable to the main grain-producing regions of the state (mean grain yield 2315 kg ha-1). Compared to previously released cultivars, Caviano has a larger root system and desirable characteristics for mechanical harvesting.

ABSTRACT. Heterosis has been one of the most studied phenomena since genetic studies were conceived. Knowledge of this phenomenon for the root distribution trait in beans (Phaseolus vulgaris L.) can favour the development of genotypes that are more tolerant to abiotic stresses. This study aimed to verify the occurrence of heterosis for the root distribution trait in hybrid F1 populations of common bean derived from crosses within and between gene groups. Thirty-six populations (six parents and 30 hybrids) were evaluated under field conditions in the agricultural years 2016/17 and 2017/18. The root distribution was assessed with the adapted Bohm method. The genotypes responded similarly to environmental changes (absence of an interaction). However, the root distribution differed significantly between the agricultural years. Comparisons between the mean of hybrids from crosses within each gene pool and the mean of parents did not reveal heterosis. The comparisons between gene groups showed significant differences only between BRS Embaixador x IPR Uirapuru, CBS 14 x IPR Uirapuru, and BAF 53 x IPR Uirapuru and the mean of parents. The absence of heterosis in the root trait can be explained by the degree of kinship between the gene groups, as well as some epistatic interactions.

ABSTRACT Genetic variability is essential for gains in breeding programs. The cyclic process of progeny recombination is a strategy to raise the chances of selecting better genotype combinations. The objective of this study was to identify superior progenies between common bean genes groups in first recurrent selection cycle for root system traits. Parents of the Andean and Middle American gene groups were hybridized in a complete diallel scheme. Thereafter, the parents and F1 and F2 populations were planted in the field. To establish the base population of recurrent selection (C0), seven segregating populations (F2) with superior performance for root system were selected and intercrossed, resulting in recombinant progenies (C1). To estimate the selection gain, the parents and C0 and C1 genotypes were compared with regard to the following variables: total root length (TRL, cm), projected root area (PRA, cm2), root volume (VOL, cm3) and number of root tips (RT). The difference between genotype combinations indicates the presence of genetic variability and effectiveness of recurrent selection. The mean genetic progress for root system-related traits was 12.9% (TRL), 12.6% (PRA), 12% (VOL) and 11.5% (RT) in the first recombination cycle. The mean phenotypic performance of seven of the C1 progenies exceeded that of their parents for all root system traits. These progenies are promising as base populations of the next selection cycle.

Resumo O objetivo deste trabalho foi caracterizar genitores e respectivas populações de macieiras quanto aos alelos S para confirmar sua genealogia e avaliar a eficiência dos marcadores moleculares utilizados. Conjuntos específicos de iniciadores foram utilizados para a identificação dos alelos S via PCR. Foram avaliadas duas populações segregantes do Programa de Melhoramento Genético de Macieira da Epagri resultantes dos cruzamentos entre ‘Fred Hough’ × ‘Monalisa’ e ‘M-11/00’ × ‘M-13/91’. As segregações esperadas são 1:1:1:1 para compatibilidade total e 1:1 para semi-compatibilidade, que pode ser confirmada pelo teste X2. O cruzamento ‘Fred Hough’ (S5S19) × ‘Monalisa’ (S2S10) foi identificado como totalmente compatível, e foram identificados dois triploides entre os híbridos. O cruzamento entre ‘M-11/00’ (S3S19) × ‘M-13/91’ (S3S5) se mostrou semi-compatível baseado nos marcadores moleculares e a segregação dos alelos S nos híbridos foi de 1:1 como esperado. A segregação dos marcadores de DNA para S2, S3, S5, S10 e S19 ocorreu juntamente com seus respectivos alelos S. Dessa forma, a caracterização dos alelos S, além de permitir identificar a compatibilidade entre os genitores, serviu para identificar contaminações em populações segregantes.

Abstract The objective of this study was to characterize the parents and respective populations of apple trees regarding S-alleles to confirm their genealogy and to evaluate the efficiency of the molecular markers used. Sixteen specific sets of primers were used for identification of apple S-alleles by PCR. Two segregating populations of the Epagri Apple Breeding Program resulting from crosses between ‘Fred Hough’ × ‘Monalisa’ and ‘M-11/00’ × ‘M-13/91’ were evaluated. The expected segregations are 1:1:1:1 for full compatibility and 1:1 for semi-compatibility, which can be confirmed by the X2 test. The ‘Fred Hough’ (S5S19) × ‘Monalisa’ (S2S10) cross proved to be fully compatible; and two triploids were identified among the hybrids as well. The ‘M-11/00’ (S3S19) × ‘M-13/91’ (S3S5) cross was characterized as semi-compatible based on DNA markers, and the segregation of the S-alleles in the hybrids was 1:1, as expected. The segregation of the DNA markers occurred together with their respective S-alleles: S2, S3, S5, S10, and S19. Thus, characterization of the S-alleles not only allowed identification of compatibility between parents but also identified contaminations in segregating populations.

ABSTRACT Apple orchards require the presence of a different genotype to pollinate the fruit producing cultivar. This is due to the process of gametophytic self-incompatibility present in most species and cultivars of the genus Malus. The fruit producing cultivar and the pollinizer must be genetically compatible to ensure fruit set and symmetrical and adequate fruit formation. The aim of this work was to evaluate five potential pollinizers for the new apple cultivar SCS426 Venice by genotyping the self-incompatibility locus (S-locus) and by controlled pollination in the field. The S-locus was screened using molecular markers and the fertilization capacity was evaluated by monitoring the fruit set after artificial pollination. Three genotypes were identified as semi-compatible (selection 135/140, cultivar SCS433 Felix 3 and SCS425 Luiza) and two as fully compatible (‘SCS431 Felix 1’ and ‘SCS434 Felix 4’) with ‘SCS426 Venice’. Regardless of the level of compatibility, all genotypes tested are efficient for the fertilization of ‘SCS426 Venice’ flowers and can be used as pollinizers in commercial orchards of this cultivar.

RESUMO Naturalmente quando concluído a condução de um experimento agrícola e estando disponível o dado coletado referente a uma variável resposta, deve ser procedida a análise de variância. Entretanto, os testes de hipóteses desta análise revelam validade somente se as pressuposições do modelo estatístico forem asseguradas. Quando tais pressuposições são violadas devem ser aplicados procedimentos com o propósito de remediar este problema. O objetivo deste trabalho foi comparar como as pressuposições do modelo estatístico podem ser logradas por métodos “clássico” e “contemporâneo” e seus reflexos sobre o teste de hipótese da análise de variância. Dados oriundos de um programa de melhoramento genético, referentes ao tempo de cocção de populações segregantes foram utilizados. Foram propostas como soluções: i) Modelos lineares clássicos com transformação de dados e ii) Modelos lineares generalizados mistos. As pressuposições de normalidade e homogeneidade foram testadas por Shapiro-Wilk e Levene, respectivamente. Ambos os métodos foram capazes de lograr as pressuposições do modelo estatístico com impacto direto nos testes de hipóteses. As transformações de dados foram eficazes em estabilizar a variância. Porém, inúmeras transformações não apropriadas, podem ser aplicadas indevidamente e atender as pressuposições, causando distorções no teste de hipótese. Os modelos lineares generalizados mistos podem exigir maior conhecimento na identificação de linhas de programação, se comparado ao método clássico, mas permitem além da separação dos efeitos fixos e aleatórios, a especificação do tipo de distribuição da variável resposta e a estruturação dos resíduos.

ABSTRACT When an agricultural experiment is completed and the data about the response variable is available, it is necessary to perform an analysis of variance. However, the hypothesis testing of this analysis shows validity only if the assumptions of the statistical model are ensured. When such assumptions are violated, procedures must be applied to remedy the problem. The present study aimed to compare and investigate how the assumptions of the statistical model can be achieved by classical linear model and generalized linear mixed model, as well as their impact on the hypothesis test of the analysis of variance. The data used in this study was obtained from a genetic breeding program on the cooking time of segregating populations. The following solutions were proposed: i) Classical linear model with data transformation and ii) Generalized linear mixed models. The assumptions of normality and homogeneity were tested by Shapiro-Wilk and Levene, respectively. Both models were able to achieve the assumptions of the statistical model with direct impact on the hypothesis testing. The data transformations were effective in stabilizing the variance. However, several inappropriate transformations can be misapplied and meet the assumptions, which would distort the hypothesis test. The generalized linear mixed models may require more knowledge about the identification of lines of programming, compared to the classical method. However, besides the separation of fixed from random effects, they allow for the specification of the type of distribution of the response variable and the structuring of the residues.

RESUMO Quando combinados distintos grupos gênicos por meio de hibridações, é necessário o conhecimento do tipo de ação gênica preponderante na expressão de um caráter. O entendimento dessa informação ampara melhoristas para a tomada de decisões nas etapas de condução e seleção de populações segregantes no decorrer do programa de melhoramento genético. Assim, o objetivo do trabalho foi determinar os efeitos da capacidade de combinação e ação gênica para a característica distribuição radicular dos grupos de feijão Andino e Mesoamericano. Seis genitores de feijão dos grupos andino e mesoamericano foram hibridados em esquema de dialelo completo, resultando em 30 híbridos F1. Os genitores e híbridos foram conduzidos a campo em delineamento látice simples. A característica alvo foi a distribuição das raízes, calculada como a quantidade relativa de raízes no solo superior. O efeito da capacidade geral de combinação foi significativamente maior em relação aos efeitos de capacidade específica de combinação (58%) e efeito recíproco (41%). As estimativas de combinações foram modificadas em função da ordem dos grupos gênicos utilizados. As combinações IPR Uirapuru x BAF53 (mesoamericano x andino), BAF53 x CBS14 (andino x andino) e CBS14 x IPR Uirapuru (andino x mesoamericano) foram as principais responsáveis por incrementar a média da característica distribuição radicular. No entanto, mesmo que realizando combinações entre grupos gênicos, a maior fração da variância genética foi relacionada a componentes aditivos (60%). Consequentemente, a ação gênica aditiva foi predominante na expressão do caráter distribuição radicular em feijão independente do grupo gênico utilizado.

ABSTRACT When different gene groups are combined by hybridization, the expression of predominant genes for a trait must be known. This understanding is fundamental to the decisions made by breeders in the stages of cultivation and selection of segregating populations during the breeding program. Thus, the objective of this study was to determine the effects of combining ability and gene action for the root distribution traits of the Andean and Mesoamerican common bean gene groups. Six common bean parents from the Andean and Mesoamerican groups were hybridized in a complete diallel mating scheme, resulting in 30 F1 hybrids. The parents and hybrids were planted in the field in a simple lattice design. The target trait was root distribution, calculated as the relative number of roots in the topsoil. The effect of the general combining ability was significantly higher than that of the specific combining ability (58%) and the reciprocal effect (41%). Particularly, the combination estimates were modified according to the order of the gene groups used. The combinations IPR Uirapuru x BAF53 (Mesoamerican x Andean), BAF53 x CBS14 (Andean x Andean), and CBS14 x IPR Uirapuru (Andean x Mesoamerican) mainly exhibited an increase in the mean root distribution. However, the highest fraction of genetic variance correlated with additive components (60%), even in crosses involving different gene groups. Consequently, the additive gene action was predominant in the expression of root distribution trait in common bean, irrespective of the gene group used.

Abstract: The objective of this study was to identify self-incompatibility (S) alleles of advanced breeding selections of apple (Malus × domestica Borkh.). The S-alleles of 42 apple genotypes were analyzed by markers using allele-specific PCR amplification and amplicons digested with restriction endonucleases. Among the screened genotypes were cultivars, advanced selections, and accessions of the Apple Germplasm Bank of Epagri (Caçador, Santa Catarina, Brazil). Two S-alleles were identified in 36 genotypes, and only one S-allele was determined in the other six genotypes. In all, eleven S-alleles were identified among all the genotypes evaluated. The S3 and S5 alleles were most frequent (30.2% and 19.8%, respectively). The identification of S-alleles using molecular markers in important apple tree genotypes is useful for determination of compatible parents for breeding programs.

ABSTRACT. The present work has aimed to assess the consideration of the appropriate variation sources of the statistical model and their impacts on the conclusions plant breeding. The Value for Cultivation and Use test was conducted to assess three common locations (Lages, Ponte Serrada, and Canoinhas) and four non-common locations (Chapecó, Guatambu, Urussanga, and Campos Novos). The grain yields of six bean genotypes were evaluated in order to represent the imbalance between the common and non-common locations. The statistical analysis considered two situations: i) union of the location factors and cultivation years, with a single variation source called environment and ii) decomposition of the mean square values of the two factors, location and year. According to the simplified analysis (environmental variation source), the F test for the genotype factor was highly significant (p = 0.0006). On the other hand, the hypothesis test for the genotype factor was not significant (p = 0.7370) when the decomposition of mean squares was used. The simplified analysis presents some erroneous points, such as the use of a mean residue to test the hypothesis of the genotype factor, since this factor is composed of several sources of variation, and there is no exact F test. However, approximate F tests can be obtained by constructing linear combinations of average squares. This fact notes the relevance of considering the appropriate sources of variation within the statistical model, with a direct impact on the conclusions and recommendations of cultivars with superior performance.

Abstract The objective was to determine the predominant genetic inheritance in the trait root distribution in common bean and define the selection strategy. An experiment involving 40 genetic constitutions (segregating and fixed populations), was developed during the agricultural years 2014/15 and 2015/16. The experiment was arranged in a Federer's augmented block design with 3 replicates. The root distribution was evaluated by Bohm method. Estimates of mean contrasts between the F4 progenies and their parents did not reveal any significant differences in any comparison. The generations F5 and F6 presented the same behavior. The distribution of the component of the additive genetic variance was similarly conducted for the segregating generations. Thus, since the predominant inheritance of the root distribution is additive, the selection of this trait is recommended to be performed at the end of the breeding program.