Modified Location Model Research Articles

Estratégias para os próximos ciclos do melhoramento intrapopulacional do maracujazeiro-azedo

ABSTRACT In breeding programs, the identification of genetic variability and knowledge of genetic constitutions existing within segregating populations are of fundamental importance for the success and continuation of the program. The present study aimed to quantify the genetic diversity among progenies of a sour passion fruit population based on morphoagronomic variables of flowers and fruits using the Ward-MLM (modified location model) procedure, which was efficient in quantifying genetic diversity and allowed the identification and consistent formation of three groups within the population. Among the groups formed, group I presented the highest means for the variables related to flowers, group II presented the highest values for the variables related to yield, and group III presented the highest means for the variables related to fruit quality. The androgynous length, nectariferous chamber length, anther surface, nectareous chamber length, and stigma surface were the variables that most contributed to the divergence between the evaluated genotypes. Crosses between groups II and III genotypes are promising for the next cycle, contributing to increased production and improvement of the physical and chemical quality of fruits.

Cacaueiros cultivados em sistema agroflorestais da Bahia revelam ampla variabilidade genética em caracteres morfoagronômicos

ABSTRACT Cacao fruits are agronomically important and show wide variability for several morphological descriptors. The present study aimed to characterize the genetic distance of 51 genotypes of Theobroma cacao L. in the cocoa-producing region of Southern Bahia (Brazil) based on morpho-agronomic descriptors. The inference of genetic similarity was performed from the phenotypic data derived simultaneously from qualitative and quantitative variables, using the Ward-MLM procedure (Modified Location Model) with the SAS® software. The distance matrix was obtained using the Gower logarithmic function. For this, 28 descriptors were evaluated, five qualitative and 23 quantitative. Furthermore, using the likelihood function procedure, the optimal number of groups was five indicating wide variability. Of 23 quantitative descriptors evaluated by fruits and leaves, 95% showed significant differences. The exception was seed width. Groups 1 and 5 were the most distant, while groups 2, 3, and 4 were closest to each other. The greatest difference between increments was 35.32 for the fifth group. The analysis of the first two canonical axes revealed that both represented 81.88% of the variation, with CAN1 and CAN2 responsible for 53.66% and 28.22% of the variation. The most promising genotypes for breeding programs belong to group 5 due to their superior performance for almost all characteristics analyzed.

MORPHO-AGRONOMIC CHARACTERIZATION AND GENETIC DIVERSITY IN PEPPERS (Capsicum spp.)

ABSTRACT Peppers and bell peppers (Capsicum spp.) are vegetables that have wide genetic variability, as well as a wide range of applications. Studies on genetic diversity help to understand the existing variability and the conservation of genetic resources, allowing breeders to select superior genotypes that meet the needs of breeding programmes. This study aimed to evaluate the genetic diversity among 15 Capsicum genotypes based on morpho-agronomic descriptors and through the Ward-MLM (Modified Location Model) procedure, as well as to indicate the most promising genotypes for breeding programmes. The research was conducted in an experimental area using a randomized block design, with three replications, using nine qualitative descriptors and ten quantitative descriptors. Analysis of variance was performed, and means were subsequently grouped by Scott-Knott’s method. There was a significant difference between genotypes for all traits evaluated, making it possible to select promising genotypes. According to the Scott-Knott grouping test, the number of seeds per fruit had the largest number of groups, with eight distinct groups, while plant height had only two groups. The genotypes GEN18 and GEN21 had the highest average values for fruit wall thickness and thus are indicated for the preparation of sauces. The genotypes GEN14 and GEN16 were the most promising for use for ornamental purposes. The Ward-MLM method made it possible to differentiate C. annuum L., C. baccatum L., C. chinense Jacq., and C. frutescens L. into different groups, and is thus a useful tool to detect genetic divergence.

Morphoagronomic characterization and genetic diversity of a Brazilian okra [Abelmoschus esculentus (L.) Moench] panel

Okra [Abelmoschus esculentus (L.) Moench] has been neglected by breeders as few cultivars have been released over the last years, which contributes to yield stagnation. Developing modern cultivars is key to increase okra production. To provide information to efficiently improve okra cultivars, this study aimed to characterize and assess the genetic diversity of a Brazilian collection by using the Ward-MLM (Modified Location Model) multivariate procedure. Both quantitative and qualitative variables can be simultaneously considered in this strategy. Forty-six okra accessions from the active germplasm bank of Embrapa Hortalicas and the open-pollinated ‘Santa Cruz 47’ were characterized according to descriptors lists. Seven groups were identified comprising seven, six, fourteen, six, five, seven, and two genotypes, respectively. Group VII was the most distant in relation to the other groups, probably because of the greatest vegetative development and lowest fruit production. Variability was observed for most morphological traits. The grouping information will be useful for germplasm conservation management and for crossing strategies. Leaf length, leaf width, petiole length, stem diameter at plant base, and first flowering height contributed the most to genetic variation. The genetic variability verified in this study suggests a high potential for breeding new okra cultivars.

Genetic variability in Brazilian Capsicum baccatum germplasm collection assessed by morphological fruit traits and AFLP markers.

Capsicum baccatum is one of the main pepper species grown and consumed in South America. In Brazil, it is commonly cultivated by family farmers, using mostly the genotypes bishop's hat genotypes (locally cambuci) and red chili pepper (dedo-de-moça). This study had the objective of characterizing 116 C. baccatum accessions from different regions of Brazil, based on morphological fruit descriptors and AFLP (Amplified Fragment Length Polymorphisms) markers. Broad phenotypic variability among the C. baccatum accessions was detected when using morphological fruit descriptors. The Ward modified location model (Ward-MLM) discriminated five groups, based mainly on fruit shape. Six combinations of AFLP primers detected polymorphism in 97.93% of the 2466 identified bands, indicating the high genetic variability in the accessions. The UPGMA coincided with the Bayesian clustering analysis and three large groups were formed, separating the wild variety C. baccatum var. praetermissum from the other accessions. There was no relation between genetic distance and geographical origin of the accessions, probably due to the intense exchange of fruits and seeds between farmers. Morphological descriptors used together with AFLP markers proved efficient in detecting the levels of genetic variability among the accessions maintained in the germplasm collections. These results can be used as an additional source of helpful information to be exploited in C. baccatum breeding programs.

Genetic divergence through joint analysis of morphoagronomic and molecular characters in accessions of Jatropha curcas.

The aim of this study was to investigate the genetic divergence between accessions of Jatropha curcas through joint analysis of morphoagronomic and molecular characters. To this end, we investigated 11 morphoagronomic characters and performed molecular genotyping, using 23 inter-simple sequence repeat (ISSR) primers in 46 accessions of J. curcas. We calculated the contribution of each character on divergence using analysis of variance. The grouping among accessions was performed using the Ward-MLM (modified location model) method, using morphoagronomic and molecular data, whereas the cophenetic correlation was obtained based on Gower's algorithm. There were significant differences in all growth-related characteristics: number of primary and secondary branches per plant, plant height, and stem diameter. For characters related to grain production, differences were found for number of fruit clusters per plant and number of inflorescence clusters per plant and average number of seeds per fruit. The greatest phenotypic variation was found in plant height (59.67- 222.33 cm), whereas the smallest variation was found in average number of seeds per fruit (0-2.90), followed by the number of fruit clusters per plant (0-8.67). In total, 94 polymorphic ISSR fragments were obtained. The genotypic grouping identified six groups, indicating that there is genetic divergence among the accessions. The most promising crossings for future hybridization were identified among accessions UFRB60 and UFVJC45, and UFRB61 and UFVJC18. In conclusion, the joint analysis of morphoagronomic characters and ISSR markers is an efficient method to assess the genetic divergence in J. curcas.

Clustering of soybean genotypes via Ward-MLM and ANNs associated with mixed models.

The objectives of this study were to use mixed models to confirm the presence of genetic variability in 16 soybean genotypes, to compare clusters generated by artificial neural networks (ANNs) with those created by the Ward modified location model (MLM) technique, and to indicate parental combinations that hold promise for obtaining superior segregating populations of soybean. A field trial was conducted between November 2014 and February 2015 at Universidade Estadual de Mato Grosso do Sul, Aquidauana, MS. The experimental design consisted of four replications of randomized blocks, each containing 16 treatments. We assessed the following agronomic traits: plant height, first pod height, number of branches per plant, number of pods per plant, number of grains per pod, hundred-grain weight, and grain yield. Mixed models were used to estimate variance components and genetic parameters, and obtain genotypic values for each trait. After verifying the presence of genetic variability for all traits, genotypic values were submitted to both a Ward-MLM procedure and ANNs to estimate genetic divergence among genotypes. The number of groups formed by both methods was the same, but there were differences in group constitutions. ANN analysis improved soybean genotypes clustering patterns compared to Ward-MLM procedure. Based on these methods, divergent crosses may be made between genotype 97R73 with genotypes AS3797 and SYN9070, whereas convergent crosses may be made between genotypes AS3797 and SYN9070.

Quantificação da divergência genética entre acessos de goibeira por meio da estratégia Ward-MLM

O presente trabalho teve como objetivo quantificar a divergência genética entre 138 acessos de goiabeira procedentes do banco de germoplasma da Universidade Estadual do Norte Fluminense Darcy Ribeiro (UENF), com base em descritores morfológicos, agronômicos e físico-químicos, por meio do procedimento Ward - Modified Location Model (MLM). Para tanto, foram avaliados 13 descritores, sendo cinco qualitativos (coloração da polpa, superfície do fruto, formato do fruto ao final do pedúnculo, largura do pescoço e uniformidade da cor da polpa) e oito quantitativos (massa média do fruto, diâmetro longitudinal do fruto, diâmetro transversal do fruto, rendimento da polpa, teor de sólidos solúveis totais, acidez do fruto, relação teor de sólidos solúveis totais e acidez do fruto e teor de ácido ascórbico). Detectou-se ampla variabilidade genética pelos dados morfológicos, agronômicos e físico-químicos nos 138 acessos de goiaba. Pelo procedimento da função da verossimilhança, determinou-se oito o número ideal de grupos, com um valor de incremento de 67,51. O grupo III foi considerado o mais distante, enquanto os grupos I, II, IV, V e VI, os mais próximos. O procedimento Ward-MLM é uma ferramenta útil para detectar divergência genética e agrupar os acessos utilizando, simultaneamente, variáveis qualitativas e quantitativas.

Evaluation and Validation of Ecogeographical Core Collections using Phenotypic Data

ABSTRACTThis study evaluated the phenotypic representativeness of core collections generated independently with ecogeographical data or with morphological data. The Spanish Phaseolus vulgaris L. collection was the target germplasm collection, and one map of ecogeographical categories and 15 morphological variables were used to create core collections. Three ecogeographical and 12 morphological core collections were produced combining different grouping methods (categories from ecogeographical land characterization map [CEM], two‐step clustering [TSC], Ward–modified location model clustering [WM], and unweighted pair‐group method using arithmetic average [UPGMA]) and allocation strategies (constant [C], proportional [P], logarithmic [L], and Gower's distance [D]). An additional morphological core collection was created using a modified least distance stepwise sampling (LDSSm) method. Core collections were evaluated with morphological data using parameters for qualitative and quantitative variables that were summarized in a new synthetic evaluation parameter (SEP). Synthetic evaluation parameter results showed that the ecogeographical core collections had high phenotypic representativeness, similar to that of morphological core collections generated by the combination of WM and TSC grouping methods and P allocation strategy. A graphical evaluation of core collections supported these results. In conclusion, ecogeographical information was confirmed as a good alternative or complement to other types of data to create reliable and representative core collections.

Classifying vegetable genetic resources—A case study with domesticated Capsicum spp.

Great variation for many traits seems to be available in Capsicum genetic resources but yet to be fully used by plant breeders. Adequate characterization of genebank accessions is needed to facilitate the utilization of germplasm by end-users. The aim of this research was to use multivariate techniques with both qualitative and quantitative descriptors in the five domesticated species of Capsicum for grouping them after assessing inter- and intra-specific variation. Key qualitative descriptors (seed color, corolla color and spot, calyx constriction, numbers of flowers per node and filament color) served for assigning most accessions to their respective species, whereas intra-specific multivariate diversity was better assessed by quantitative descriptors such as fruit length/width ratio, numbers of days to flowering, leaf width, and anther, filament and pedicel length. The modified location model an adequate method for classifying Capsicum accessions using quantitative descriptors.

Hierarchical Multiple‐Factor Analysis for Classifying Genotypes Based on Phenotypic and Genetic Data

ABSTRACTA numerical classification problem encountered by breeders and gene‐bank curators is how to partition the original heterogeneous population of genotypes into non‐overlapping homogeneous subpopulations. The measure of distance that may be defined depends on the type of variables measured (i.e., continuous and/or discrete). The key points are whether and how a distance may be defined using all types of variables to achieve effective classification. The objective of this research was to propose an approach that combines the use of hierarchical multiple‐factor analysis (HMFA) and the two‐stage Ward Modified Location Model (Ward‐MLM) classification strategy that allows (i) combining different types of phenotypic and genetic data simultaneously; (ii) balancing out the effects of the different phenotypic, genetic, continuous, and discrete variables; and (iii) measuring the contribution of each original variable to the new principal axes (PAs). Of the two strategies applied for developing PA scores to be used for clustering genotypes, the strategy that used the first few PA scores to which phenotypic and genetic variables each contributed 50% (i.e., a balanced contribution) formed better groups than those formed by the strategy that used a large number of PA scores explaining 95% of total variability. Phenotypic variables account for much variability in the initial PA; then their contributions decrease. The importance of genetic variables increases in later PAs. Results showed that various phenotypic and genetic variables made important contributions to the new PA. The HMFA uses all phenotypic and genetic variables simultaneously and, in conjunction with the Ward‐MLM method, it offers an effective unifying approach for the classification of breeding genotypes into homogeneous groups and for the formation of core subsets for genetic resource conservation.

Comparison of Several Clustering Methods in Grouping Kale Landraces

Four clustering methods were compared for classification of a collection of 148 kale landraces (Brassica oleracea L. acephala group) from northwestern Spain based on morphologic characters: the unweighted pair group method using arithmetic averages (UPGMA) and the Ward method, hierarchical cluster algorithms, and the modified location model (MLM) applied to both the UPGMA and the Ward method (UPGMA-MLM and Ward-MLM, respectively). Comparisons were based on five criteria and on subjective considerations about the structure of each method and the characteristics of the material evaluated. Although the UPGMA-MLM was superior according to the objective criteria, its slight advantage with respect to the Ward-MLM strategy did not overcome the fact that the initial UPGMA cluster generated a classification with little value. The Ward-MLM strategy generated five homogeneous groups with defined morphologic characteristics. Moreover, the Ward-MLM strategy allowed the identification of redundant landraces, which would permit the number of accessions in further critical trials to be reduced.

Genetic diversity in a germplasm collection of Brassica rapa subsp rapa L. from northwestern Spain

In Galicia (northwestern Spain), Brassica rapa subsp. rapa L. includes turnips, turnip greens, and turnip tops. The objectives of this study are (i) to determine the genetic diversity and morphological resemblances among the B. rapa landraces of northwestern Spain in order to have information relative to the resources preserved, and (ii) to evaluate their agronomic characteristics, considering the three potential products that can be harvested. A collection of 120 landraces was evaluated for 34 morphological and agronomical traits by an augmented design at two locations. Two landraces were the most promising for turnips production (MBG-BRS0183 and MBG-BRS0256), two showed the best characteristics for turnip greens (MBG-BRS0082 and MBG-BRS0184), and three were the most appropriate landraces for turnip tops production (MBG-BRS0143, MBG-BRS0173 and MBG-BRS0401). Landraces were classified into five clusters (A–E) using the Ward–MLM (Modified Location Model) strategy: (A) included plants with the worst agronomic potential, (B) included most of the turnip populations with rosette growth habit, (C) included turnip populations without rosette growth habit, having more vigorous plants than cluster B, (D) gathered the most vigorous local varieties, with the highest early vigor, fresh matter content per leaf, and number of secondary stems per plant, and (E) landraces characterized by their earliness, large flowering periods, high numbers of secondary stems, and large seed weights. As conclusion, landraces evaluated in this work displayed enough variability to differentiate among appropriate populations for each one of the distinct crops. Their classification, using the Ward–MLM strategy, grouped accessions with similar characteristics into homogeneous categories.

Comparing a Preliminary Racial Classification with a Numerical Classification of the Maize Landraces of Uruguay

Plant genetic diversity is a major component of any agricultural ecosystem. Thus, it is essential to classify genetic resources properly to conserve, evaluate, and enhance germplasm efficiently. In maize (Zea mays L.), many classification systems have been used for delineating maize races. From the 1980s, with the use of computers, numerical taxonomy became increasingly important and multivariate methods began to be used for classifying genetic resources. The objective of this study was to compare two methods of classification of Uruguayan maize landraces: (i) a preliminary racial classification obtained through visual assessment and (ii) a numerical classification. The numerical classification was conducted by means of a two-stage classification strategy: first, initial groups were formed by the Ward method and, next, the Modified Location Model (MLM) refined those groups. This classification was compared with the preliminary racial classification by four criteria. The Ward-MLM strategy generated more homogeneous groups than those corresponding to the preliminary racial classification. The numerical classification maintained the structure of the more differentiated races, but divided the Cateto Sulino race into two more homogeneous groups, each with smaller variance and more differentiated than other groups. Numerical classification produced groups with clearly distinct characteristics, in terms of the numerical variables, and better, in terms of the four criteria used, than those formed on the basis of racial classification. These results will be the basis for an improved racial classification of maize landraces of Uruguay.

Comparing a Preliminary Racial Classification with a Numerical Classification of the Maize Landraces of Uruguay

Plant genetic diversity is a major component of any agricultural ecosystem. Thus, it is essential to classify genetic resources properly to conserve, evaluate, and enhance germplasm efficiently. In maize (Zea mays L.), many classification systems have been used for delineating maize races. From the 1980s, with the use of computers, numerical taxonomy became increasingly important and multivariate methods began to be used for classifying genetic resources. The objective of this study was to compare two methods of classification of Uruguayan maize landraces: (i) a preliminary racial classification obtained through visual assessment and (ii) a numerical classification. The numerical classification was conducted by means of a two-stage classification strategy: first, initial groups were formed by the Ward method and, next, the Modified Location Model (MLM) refined those groups. This classification was compared with the preliminary racial classification by four criteria. The Ward-MLM strategy generated more homogeneous groups than those corresponding to the preliminary racial classification. The numerical classification maintained the structure of the more differentiated races, but divided the Cateto Sulino race into two more homogeneous groups, each with smaller variance and more differentiated than other groups. Numerical classification produced groups with clearly distinct characteristics, in terms of the numerical variables, and better, in terms of the four criteria used, than those formed on the basis of racial classification. These results will be the basis for an improved racial classification of maize landraces of Uruguay.

The Modified Location Model for Classifying Genetic Resources

When evaluating genetic resources and forming core subsets, gene bank accessions are classified into homogeneous and well-separated groups. The modified location model (MLM) is used in the context of a two-stage clustering strategy in which initial groups are first defined using a hierarchical clustering method (such as Ward) and then the MLM is applied to the groups that are formed (Ward-MLM). The MLM allows assuming correlations (between attributes) and variances (of the attributes) among subpopulations (SPs) to be equal (homogeneous, HOM) or different (heterogeneous, HET). The objectives of this study were (i) to compare the effect of assuming homogeneity with the effect of assuming heterogeneity of variance–covariance matrices on the classification of two simulated data sets using the Ward-MLM strategy; and (ii) to make the same type of comparison using data from maize (Zea mays L.) accessions from nine countries. When simulated HOM data were analyzed with the HOM model and the simulated HET data were analyzed with the HET model, some of the original SPs were represented in the resulting clusters but others changed and formed more separated groups. The HET model always formed the most compact and separated clusters, even for HOM data. Classification of 10 real data sets showed that the HET model produced more compact and well-separated groups than the HOM model. However, only the HOM model identified and grouped a small number of observations with very peculiar attributes. Although the HET model may suffice in most situations, the recommended strategy when classifying genetic resources would be to use both models.

The Modified Location Model for Classifying Genetic Resources

When evaluating genetic resources, data on continuous and categorical attributes of accessions is collected. The Ward method and the modified location model (MLM) (Ward-MLM strategy) classify genetic resources using a mixture of categorical and continuous variables and combine all the categorical variables into one multinomial variable (W) that is assumed to be statistically independent from the continuous variables. The main objective of this study was to examine the robustness of the MLM for recovering underlying true subpopulations when independence between variable W and the continuous variables does not hold. In addition, several scenarios, based on different degrees of overlap of the continuous and discrete variables in simulated data sets, were generated. Results showed that when the subpopulations were well-differentiated, the Ward-MLM strategy effectively predicted the true number of subpopulations and fully recovered their structure, regardless of the level of dependence between the W variable and the vector of continuous variables. When the subpopulations showed unclear boundaries and a high degree of overlap in the W variable and in the continuous variables, the Ward-MLM strategy predicted a different number of subpopulations but fully recovered the composition of the subpopulations. In this case, new groups are formed that show a balanced and consistent structure in their composition as compared with the subpopulations. The MLM proved to be a robust model under medium and strong dependence between the variable W and the vector of continuous variables and under various kinds of overlapping between subpopulations with respect to the continuous and discrete variables.

A Two‐Stage, Three‐Way Method for Classifying Genetic Resources in multiple Environments

Cluster analysis is commonly used when gene bank accessions are evaluated in different environments and several continuous and categorical attributes are measured. The objectives of this study were (i) to develop a two‐stage classification strategy for three‐way data (accession × attribute × environment) using the Modified Location Model (MLM) with categorical and continuous variables and (ii) assess this approach for classifying observations of one simulated data set (with known structure) and two experimental data sets consisting of multi‐attribute, multi‐site field trials of Caribbean and Cónico accessions of maize (Zea mays L.). Clusters were compared including and excluding the categorical variables. Results from the simulated data showed good recovery of the group structure and a balanced effect of both categorical and continuous variables on the classification. The two‐stage, three‐way MLM method formed well‐defined groups of accessions and characterized them based on the continuous as well as the categorical variables. As expected, groups formed using only continuous variables showed no clear response patterns concerning the categorical variables; however, those formed using both types of variables had clear response patterns with respect to each type. Furthermore, groups of Caribbean accessions showed dear association with geographical origin. The MLM model should be useful for classifying genetic resources evaluated in multi‐environment trials into homogeneous groups with the objective of forming core subsets. When a large number of categorical variables are combined across environments, the MLM may not improve the initial classification obtained from hierarchical clustering strategy.

Classifying Genetic Resources by Categorical and Continuous Variables

Hierarchical and nonhierarchical clustering methods are used for classifying genetic resources. In hierarchical clustering methods, all variables (categorical and continuous) can be used to form the subpopolations (groups or clusters), but in standard nonhierarchical methods only the continuous variables are incorporated in the analysis. The Location model (LM) allows classifying individuals into homogeneous subpopulations by continuous and categorical variables. In practice, the multinomial variable of the LM that arises from the combination of all the categorical variables usually shows empty cells in some subpopulations with the consequence of not allowing estimation of cell means and within‐cell variances and covariances. The main objectives of this study were (i) to develop the Modified Location model (MLM) that allows empty cells in some subpopulations under the assumption that the means and the variance‐covariance matrices depend on a given subpopulation instead of on a specific cell, (ii) to show how to use the MLM in the context of two‐stage clustering in which the Ward method is used to form the initial groups and the MLM is applied to those groups (Ward‐MLM), and (iii) to show to apply the Ward‐MLM to three different data sets to study some of its features and to compare results with other methods. The two‐stage clustering strategy of finding initial groups by the Ward method and then improving the composition of the groups by the MLM produces compact and well‐separated groups with respect to all the variables (categorical and continuous) compared with classifications obtained with only categorical variables, with only continuous variables, and with the standard Location model.