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Genetic divergence among accessions of Manihot spp.

ABSTRACT.

The aim of this study was to perform a morphological and morphoagronomic analysis of wild Manihot species from a Brazilian semiarid region for inclusion in the collection at the Center for Agricultural Sciences, Federal University of Paraíba. To characterize the 55 accessions, 12 quantitative and 18 qualitative descriptors were used. A dissimilarity matrix was generated by Mahalanobis generalized distance (D²), and clusters were identified by the UPGMA method. It was possible to verify the formation of 8 dissimilar groups based on morphological characters and 5 groups based on morphometric characters, indicating the presence of genetic diversity among accessions. The evaluated morphometric variable with the greatest relative contribution was the length between the central lobe. Based on the dissimilarity matrix, the accessions 16 x 48 were the most genetically distant accessions, followed by 47 x 49. The accessions 4 Monteiro, 16 Soledad, 38 Boa Vista, 3 Pedra Lavrada, 7 Junco, 10 Barra de Santa Rosa, 21 Monteiro, and 39 Junco are the most promising and can be used as parents in breeding programs for this forage species.

Keywords:
germplasm bank; agronomic descriptors; morphological descriptors

Introducion

The cassava is a naturally occurring plant in the Caatinga, belonging to the family Euphorbiaceae, genus Manihot, and is found in several areas of the northeastern semiarid region. It has great persistence to the drought, presents a system of tuberous roots that are very developed and able to accumulate solid reserves and water, and is one of the first species of the Caatinga to develop foliage soon after the beginning of the rainy season. It is used for the maintenance of herds of domestic animals.

The Manihot tree species of the northeast region and the herbaceous species of the midwest region have weak barriers to reproductive isolation, which has led to extensive natural hybridization that makes the taxonomy and delineation of these species difficult. The use of morphometric and morphological descriptors can be used as a tool for differentiation through phenotypic characteristics, allowing easy identification and differentiation using a germplasm bank in the field, which is needed due to the high degree of diversity of the species.

One use for the germplasm of the species is to estimate the genetic divergence to predict promising crossings (Krishnamurthy et al., 2013Krishnamurthy, S. L., Rao, A. M., Reddy, K. M., Ramesh, S., Hittalmani, S., & Rao, M. G. (2013). Limits of parental divergence for the occurrence of heterosis through morphological and AFLP marker in chilli (Capsicum annuum L.). Current Science, 104(6), 738-746.), which can be achieved using morphological and agronomic characters Vieira et al. (2013Vieira, E. A., Fialho, J. F., Faleiro, F. G., Bellon, G., Fonseca, K. G., Silva, M. S., Paula-Morães, S. V., & Carvalho, L. J. C. B. (2013). Caracterização fenotípica e molecular de acessos de mandioca de indústria com potencial de adaptação às condições do Cerrado do Brasil Central. Semina: Ciências Agrárias, 34(2), 567-582. DOI: 10.5433/1679-0359.2013v34n2p567
https://doi.org/10.5433/1679-0359.2013v3...
). Among the phenotypic descriptors, the ones with agronomic importance are most influenced by the environment. Additionally, they help to identify adapted accessions with productive potential.

In view of the above, the objective of this study was to evaluate the genetic diversity and potential of cassava by means of morphometric and morphological characteristic analysis for breeding program inclusion via the germplasm bank.

Material and methods

For the purpose of characterization, 55 accessions of cassava at the reproductive stage of maturation between the end of flowering and the beginning of fruiting were selected for evaluation. Three plants per accession, located in the central line, all belonged to the Germplasm Active Bank (GAB) of the Federal University of Paraíba. The accessions in the BAG came from the Brazilian semiarid region, specifically from the municipalities of Soledade, Juazerinho, Pocinhos, Boa Vista, Sumé, Monteiro, Barra de Santa Rosa, Picuí, Pedra Lavrada, Junco do Seridó, Cubati, Barra de Santana, and along the BR 230 between the municipalities of Boa Vista and Pocinhos (in the State of Paraíba, Brazil) and Taquaritinga do Norte and Santa Cruz do Capibaribe (in the State of Pernambuco, Brazil).

The accessions were spaced with 1.0 m between rows and with 1.0 m between plants, allowing the plants to express full development, avoiding intergenotypic competition, and ensuring vegetative material for analysis as well as duplication for research. For characterization, 12 morphological descriptors and 18 agronomic descriptors were used according to the methodology described by Fukuda, Guevara, Kawuki, and Ferguson (2010Fukuda, W. M. G., Guevara, C. L., Kawuki, R., & Ferguson, M. E. (2010). Selected morphological and agronomic descriptors for the characterization of cassava. Ibadan, NI: International Institute of Tropical Agriculture (IITA). ).

The quantitative data were submitted to normality adjustment using the equation: x" = (x + 0.5). The quantitative traits were submitted to analysis of variance, and the means were grouped according to the Scott and Knott (1974Scott, A. J., & Knott, M. A. A. (1974). Cluster analysis method for grouping means in the analysis of variance. Biometrics, 30(3), 507-512. DOI: 10.2307/2529204
https://doi.org/10.2307/2529204...
) criterion at 5% probability. Then, the dissimilarity was analyzed by generalized Mahalanobis distance (D²), and clusters were determined by the UPGMA method (Sneath & Sokal, 1973Sneath, P. H., & Sokal, R. R. (1973). Numerical taxonomy: The principles and practice of numerical classification. San Francisco, US: W.H. Freeman.). A bootstrap analysis was performed to verify and provide statistical support to the internal nodes of the dendrograms generated by the UPGMA clustering method using the Genes program (Cruz, 2006Cruz, C. D. (2006). Programa Genes: análise multivariada e simulação. Viçosa, MG: UFV. DOI: 10.1590/S1415-47571998000100022
https://doi.org/10.1590/S1415-4757199800...
). The dendrogram cutoff point and group definition were generated by the hierarchical method described by Mojena (1977Mojena, R. (1977). Hierarchical grouping methods and stopping rules: an evaluation. The Computer Journal, 20, 359-363. DOI: 10.1093/comjnl/20.4.359
https://doi.org/10.1093/comjnl/20.4.359...
).

The validation of the clusters was determined by the cophenetic correlation coefficient (Sokal & Rohlf, 1962Sokal, R. R., & Rohlf, F. J. (1962). The comparison of dendrograms by objective methods. Taxon, 11(2), 33-40.). The quantification of the relative contributions of the morphometric characteristics in the genetic divergence was estimated using the methodology proposed by Singh (1981Singh, D. (1981). The relative importance of characters affecting genetic divergence. The Indian Journal of Genetic and Plant Breeding, 41(2), 237-245.).

Results and discussion

For accessions included in the cut dendrogram, the correlation was approximately 70% based on the morphological characters (Figure 1), and the formation of 8 groups of dissimilarity was observed, indicating diversity between the accessions evaluated; 26 accessions of the 55 evaluated belonged to group VIII. Group VI and group I presented only a single isolated individual, and the group I accession was the most genetically distant when compared to the others. The other groups, although less populous, showed variability among accessions from the same place of origin.

Figure 1
UPGMA dendrogram obtained from the dissimilarity matrix (D2) of the 55 Manihot spp. accessions based on 12 morphological descriptors. The cophenetic correlation coefficient was 0.74. The dotted line represents the cutoff point based on the methodology proposed by (Mojena, 1977Mojena, R. (1977). Hierarchical grouping methods and stopping rules: an evaluation. The Computer Journal, 20, 359-363. DOI: 10.1093/comjnl/20.4.359
https://doi.org/10.1093/comjnl/20.4.359...
). Bootstrap values are expressed in percent for 100 repetitions.

Similar results were obtained by Campos et al. (2010Campos, A. L., Zacarias, A. J., Costa, D. L., Neves, L. G., Barelli, M. A. A., Sobrinho, S. P., & Luz, P. B. (2010). Avaliação de acessos de mandioca do banco de germoplasma da UNEMAT Cáceres - Mato Grosso. Revista Tropica - Ciências Agrárias e Biológicas, 4(2), 44-54. DOI: 10.0000/rtcab.v4i2.156
https://doi.org/10.0000/rtcab.v4i2.156...
) who evaluated the characterization of 53 genotypes of the genus Manihot using group analysis based on qualitative and quantitative characteristics, which have been shown to be useful in the study of diversity, serve to support the improvement of and the appropriate use in breeding programs and express the variability present in a germplasm bank based on multiple character evaluations. The least dissimilarity was between accessions Junco 7 and Barra de Santa Rosa 10, and the greatest dissimilarity was between Junco 7 and Pedra Lavrada 3. This genetic distance probably occurs because the accessions originate from opposing localities, making it impossible to exchange genetic material between them.

The cophenetic correlation coefficient obtained for the comparison of the dissimilarity distance matrix and the cophenetic distance matrix was (r = 0.74*) with low distortion and low stress (Table 1), which is considered high and adequate, indicating a good correlation between distance and cluster matrices. Cruz and Carneiro (2006Cruz, C. D., & Carneiro, P. C. S. (2006). Modelos biométricos aplicados ao melhoramento genético (2. ed.). Viçosa, MG: UFV.) stated that the higher the cophenetic correlation and the lower the distortion of the cluster, the better the agreement between the original values of dissimilarity and those represented by the dendrogram is, suggesting a good reliability of the data generated.

Table 1
Cophenetic correlation of 12 morphological characters evaluated in 55 accessions of Manihot spp.

The percentages of distortions (4.79%) and stress (21.90%) are classified as good according to the Kruskal (1964Kruskal, J. B. (1964). Multidimensional scaling by optimizing goodness of fit to a nonmetric hypothesis. Psychometrika, 29(1), 1-27. DOI: 10.1007/BF02289565
https://doi.org/10.1007/BF02289565...
) scale and show a good fit between the genetic similarity matrix and the graphical representation of the dendrogram (Table 1).

The analysis of the results of the phenotype classes and their respective frequencies affirmed that the accessions belonging to the GAB presented genetic variability. No variability was detected only for the growth character of stipules; all the accessions evaluated presented short stipules, and the other characters had wide variability. These results allow the formation of the hypothesis that these accessions have a broad genetic base, which can be explained by the fact that they are a wild species. According to Asare, Galyuon, Sarfo, and Tetteh (2011Asare, P. A., Galyuon, I. K. A., Sarfo, J. K., & Tetteh, J. P. (2011). Morphological and molecular based diversity studies of some cassava (Manihot esculenta Crantz) germplasm in Ghana. African Journal of Biotechnology, 10(63), 13900-13908. DOI: 10.5897/AJB11.929
https://doi.org/10.5897/AJB11.929...
), the morphological characteristics are useful for preliminary evaluation since they offer an easy and fast approach to evaluate the extent of diversity.

It was observed that of the 55 evaluated accessions, 28 (50.91%) presented a cylindrical plant type. A dark green leaf color was observed in 90.91%, five lobes were observed in 85.45%, a straight growth habit was observed in 52.73%, and a branching level greater than 5 was observed in 41.82% (Table 2). This wide phenotypic variability is because the genotypes are of different origins. These factors can be taken into account for the choice of accessions in future breeding programs, as they will provide better management qualities, increased photosynthesis, a greater production of leaves and, consequently, more forage production. Silva et al. (2016Silva, R. S., Moura, E. F., Farias Neto, J. T., Sousa, N. R., Moura, M. F., & Sampaio, J. E. (2016). Genetic divergence among accessions of cassava (Manihot esculenta Crantz) sampled in the Tapajós region, State of Pará, using agronomic characters and microsatellite markers. Semina: Ciências Agrárias, 37(5), 2989-3004. DOI: 10.5433/1679-0359.2016v37n5p2989
https://doi.org/10.5433/1679-0359.2016v3...
) observed differences in all the phenotypic characteristics evaluated, reporting the variability of agronomic traits similar to those in this study, proving their efficiency in diversity studies. Vieira, Fialho, Silva, Fukuda, and Faleiro (2008Vieira, E. A., Fialho, J. F., Silva, M. S., Fukuda, W. M. G., Faleiro, F. G. (2008). Variabilidade genética do banco de germoplasma de mandioca da Embrapa cerrados acessada por meio de descritores morfológicos. Científica, 36(1), 56-67. DOI: 10.15361/1984-5529.2008v36n1p56
https://doi.org/10.15361/1984-5529.2008v...
) verified differences in all the quantitative traits, similar to those in this study, which revealed the existence of differences in the agronomic potential of the genotypes and supported the wide variability once accessions from different origins were evaluated.

In the formation of the distinct groups (Figure 2), the variable with the largest number of groups was DMC, comprising six groups with averages varying from 10.73 mm for accession 53 to 36.49 mm for accession 16. This characteristic confers the plant capacity of support and sustentation of the same, mainly because it is a shrub-arbor species.

For plant height (AP), number of axillary buds (NGA), number of floral branches (NRF), and number of senescent leaves (NFS) three groups were formed (a, b and c). Of the 55 accessions evaluated, for the variable plant height, 11 accessions were grouped in group (a) and were considered larger plants with values ranging from 226.30 cm in accession 24 to 155.30 cm in accession 1. Twenty-seven accessions in group b (medium sized) ranged from 147.50 cm in accession 33 and 115.00 cm in accession 43. The smaller plants were in group c with 17 accessions varying between 100.40 cm in accession 34 and 58.60 cm in accession 53.

According to Rós, Hirata, Araújo, and Narita (2011Rós, A. B., Hirata, A.C. S., Araújo, H. S., & Narita, N. (2011). Crescimento, fenologia e produtividade de cultivares de mandioca. Pesquisa Agropecuária Tropical, 41(4), 552-558. DOI: 10.5216/pat.v41i4.11075
https://doi.org/10.5216/pat.v41i4.11075...
), plant height is an important feature for the adequacy of spacing, for weed competition potential and for the use of branches as propagation material, as taller and densely branched plants generally tend to have a higher potential for foliage production. Taller plants, however, are also more susceptible to bedding, which may hinder the material harvesting process and decrease photosynthetic activity.

The lowest number of groups formed were in the number of flowers (NFlores), number of fruits (NFrutos), and length between leaf lobes (CLBF), with only 2 groups per variable. The number of flowers and fruits should be taken into account when a cross between an accession and propagated specimen of the same species is desired by means of seeds.

Table 2
Characteristics of the phenotype classes (morphology) evaluated and frequency of accessions in each class.

For the number of branches (NR), number of leaves (NFs), diameter of the base of the leaf petiole (DBPF), mean leaf petiole diameter (DMPF), central lobe length (CLC), and upper lobe width LSLC), 4 groups were formed. For leaf petiole length (CPF), upper leaf petiole diameter (DSPF), and length between leaf median lobes (CLMF), 5 groups were formed. These characteristics are important in choosing the parents because, when used as fodder, they may provide a greater yield of dry matter.

The greatest values found for length between the median lobes of the leaves were those belonging to group a, ranging from 28.30 cm in accession 3 and 24.15 cm in accession 30, and this character could be selected from a possible parent. Ledo et al. (2011Ledo, C. A. S., Alves, A. A. C., Silveira, T. C., Oliveira, M. M., Santos, A. S., & Tavares Filho, L. F. Q. (2011). Caracterização morfológica da coleção de espécies silvestres de Manihot (Euphorbiaceae - Magnoliophyta) da Embrapa Mandioca e Fruticultura (Boletim de Pesquisa e Desenvolvimento, 53). Cruz das Almas, BA: Embrapa Mandioca e Fruticultura. ) stated that the relationship between the length and width of the central lobe as well as the width of the central lobe influence the photosynthetic rate and, consequently, leaf mass production.

The median width of the central lobe (LMLC) consisted of 8 distinct groups with higher values, ranging from 16.00 cm in accession 15 and 18.50 in for accession 18, both of which belonged to group a (4 accessions). The lowest values were found in accessions 48 and 53 at 3.80 and 3.30 cm, respectively. Narrow leaf lobes allow less shading between the leaves of the same plant, which allows a better distribution and use of solar rays for photosynthesis.

Figure 2
The averages of 18 morphometric characters evaluated in 55 accessions (Manihot spp.) AP = plant height; NGA = number of axillary buds; DMC = mean stem diameter (mm); NR = number of branches; NFolhas = number of leaves; NFL number of flowers, NRFL- number of floral bouquets; NFR = number of fruits; NFS = number of senescent leaves; CPF = leaf petiole length (cm); DBPF = diameter of the leaf petiole base (mm); DMPF = mean leaf petiole diameter (mm); DSPF = upper leaf petiole diameter (mm); CLC = central lobe length (cm); LMLC = median lobe width (cm); LSLC = upper lobe width (cm); CLMF = length between the leaf lobes (cm); CLBF = length between the leaf lobes. *Means followed by the same letter in the columns do not differ statistically from the genetic group by the Scott-Knott test at 5%.

It was possible to detect differences in the variation, with the variable length between the central lobes representing 19.17%. It is a characteristic of great importance in regard to the use of the species as forage since the size of leaf can infer a greater percentage of leaf mass (Table 3).

Following the criterion of relevance, the number of axillary buds contributed 19.06%, plant height contributed 16.86% and the median central lobe width contributed 13.44%. The number of productive buds has great importance for branching and thus can contribute to the increase of productivity of greens and dry mass, which are the parts of the plant most used in animal feed.

The variables base diameter and mean diameter of the leaf petiole can be ruled out in future breeding studies since they contributed only 0.66 and 0.44%, respectively, in the study of the diversity among the accessions.

The matrix of genetic dissimilarity generated from morphometric data is shown in (Figure 3), showing the proximity and distance between the accessions evaluated. The most similar pair of accessions were 47 x 49 (1.464), which could be discarded in the parental choice if used only for genetic proximity, reducing its contribution to the breeding program. The most dissimilar pair of accessions among all the accessions were 16 x 48 (209.592), which makes them the most suitable to be used as parents of Manihot spp. for the genetic mapping of genes of interest.

Table 3
Relative contribution of traits to diversity (Singh, 1981Singh, D. (1981). The relative importance of characters affecting genetic divergence. The Indian Journal of Genetic and Plant Breeding, 41(2), 237-245.) based on the generalized Mahalanobis distance.

Figure 3
Matrix of genetic dissimilarity obtained by the generalized Mahalanobis distance based on the morphometric characters of the 55 accessions of Manihot ssp. Areia, Paraíba State, Brazil.

The cluster produced by the UPGMA method was subjected to a cut of approximately 79%, allowing the formation of 5 well-distributed, distinct groups (Figure 4). The divergence between and among the groups, including individuals from the same locality belonging to different genetic groups presenting different characteristics, can be used for future breeding work. Bootstrap values with 89 and 92% dissimilarity provided reliability in the formation of dendrogram branches. According to Cruz (2006Cruz, C. D., & Carneiro, P. C. S. (2006). Modelos biométricos aplicados ao melhoramento genético (2. ed.). Viçosa, MG: UFV.), these values represent a true significant junction, inferring the consistency and adaptation of the dendrogram to represent dissimilarity between the accessions.

Figure 4
UPGMA dendrogram obtained from the dissimilarity matrix (D2) of the 55 Manihot spp. accessions based on 18 agronomic characters. The cophenetic correlation coefficient was 0.85. The dotted line represents the cutoff point based on the methodology proposed by (Mojena, 1977Mojena, R. (1977). Hierarchical grouping methods and stopping rules: an evaluation. The Computer Journal, 20, 359-363. DOI: 10.1093/comjnl/20.4.359
https://doi.org/10.1093/comjnl/20.4.359...
). Bootstrap values for 100 repetitions are expressed in percent.

Campos et al. (2010Campos, A. L., Zacarias, A. J., Costa, D. L., Neves, L. G., Barelli, M. A. A., Sobrinho, S. P., & Luz, P. B. (2010). Avaliação de acessos de mandioca do banco de germoplasma da UNEMAT Cáceres - Mato Grosso. Revista Tropica - Ciências Agrárias e Biológicas, 4(2), 44-54. DOI: 10.0000/rtcab.v4i2.156
https://doi.org/10.0000/rtcab.v4i2.156...
) evaluated the genetic divergence among 53 accessions of the Manihot genus using 28 morphoagronomic descriptors and verified the formation of ten genetic groups. They concluded that the genus presents a high degree of variability, being therefore very diversified, and demonstrated that these variables present high variability when analyzing the species of the Manihot genus.

Araujo, Ledo, Martins, and Santos (2012Araújo, J. S., Ledo, C. A. S., Martins, M. L. L., & Santos, A. S. (2012). Diversidade genética em acessos de espécies silvestres de Manihot, mediante caracterização morfológica. Cruz das Almas, BA: Embrapa Mandioca e Fruticultura.) evaluated 10 quantitative and 22 qualitative characteristics similar to those used in this study in 145 accessions of two wild species of Manihot and verified the formation of 3 groups of dissimilar genotypes by the UPGMA method. These results showed the presence of genetic diversity among the evaluated genotypes, demonstrating the efficacy of the morphological descriptors for the characterization and determination of the genetic diversity.

The cophenetic correlation coefficient (Table 4) was 0.85%, indicating a high correlation between distance and cluster matrices. The higher the correlation value, the less distortion caused by the grouping exists (Manly, 2019Manly, B. F. J. (2019). Métodos estatísticos multivariados: uma introdução (4. ed.). Porto Alegre, RS: Bookman. ). The percentages of distortions (11.42%) and stress (23.80%), according to the Kruskal (1964Kruskal, J. B. (1964). Multidimensional scaling by optimizing goodness of fit to a nonmetric hypothesis. Psychometrika, 29(1), 1-27. DOI: 10.1007/BF02289565
https://doi.org/10.1007/BF02289565...
) scale, are classified as good, showing a good fit between the genetic similarity matrix and the graphical representation of the dendrogram.

Table 4
Cophenetic correlation of 18 morphoagronomic characters evaluated in the 55 accessions (Manihot spp.).

Conclusion

In this work, it was observed that there was genetic variability between the accessions evaluated based on the morphological and morphometric characteristics. These characteristics should be considered in the choice of the potential parents for a genetic improvement programs and for forage purposes.

The accessions 4 Monteiro, 16 Soledade, 38 Boa Vista, 3 Pedra Lavrada, 7 Junco, 10 Bar of Santa Rosa, 21 Monteiro, and 39 Junco are the most promising parental accessions.

References

  • Araújo, J. S., Ledo, C. A. S., Martins, M. L. L., & Santos, A. S. (2012). Diversidade genética em acessos de espécies silvestres de Manihot, mediante caracterização morfológica Cruz das Almas, BA: Embrapa Mandioca e Fruticultura.
  • Asare, P. A., Galyuon, I. K. A., Sarfo, J. K., & Tetteh, J. P. (2011). Morphological and molecular based diversity studies of some cassava (Manihot esculenta Crantz) germplasm in Ghana. African Journal of Biotechnology, 10(63), 13900-13908. DOI: 10.5897/AJB11.929
    » https://doi.org/10.5897/AJB11.929
  • Campos, A. L., Zacarias, A. J., Costa, D. L., Neves, L. G., Barelli, M. A. A., Sobrinho, S. P., & Luz, P. B. (2010). Avaliação de acessos de mandioca do banco de germoplasma da UNEMAT Cáceres - Mato Grosso. Revista Tropica - Ciências Agrárias e Biológicas, 4(2), 44-54. DOI: 10.0000/rtcab.v4i2.156
    » https://doi.org/10.0000/rtcab.v4i2.156
  • Cruz, C. D. (2006). Programa Genes: análise multivariada e simulação Viçosa, MG: UFV. DOI: 10.1590/S1415-47571998000100022
    » https://doi.org/10.1590/S1415-47571998000100022
  • Cruz, C. D., & Carneiro, P. C. S. (2006). Modelos biométricos aplicados ao melhoramento genético (2. ed.). Viçosa, MG: UFV.
  • Fukuda, W. M. G., Guevara, C. L., Kawuki, R., & Ferguson, M. E. (2010). Selected morphological and agronomic descriptors for the characterization of cassava Ibadan, NI: International Institute of Tropical Agriculture (IITA).
  • Krishnamurthy, S. L., Rao, A. M., Reddy, K. M., Ramesh, S., Hittalmani, S., & Rao, M. G. (2013). Limits of parental divergence for the occurrence of heterosis through morphological and AFLP marker in chilli (Capsicum annuum L.). Current Science, 104(6), 738-746.
  • Kruskal, J. B. (1964). Multidimensional scaling by optimizing goodness of fit to a nonmetric hypothesis. Psychometrika, 29(1), 1-27. DOI: 10.1007/BF02289565
    » https://doi.org/10.1007/BF02289565
  • Ledo, C. A. S., Alves, A. A. C., Silveira, T. C., Oliveira, M. M., Santos, A. S., & Tavares Filho, L. F. Q. (2011). Caracterização morfológica da coleção de espécies silvestres de Manihot (Euphorbiaceae - Magnoliophyta) da Embrapa Mandioca e Fruticultura (Boletim de Pesquisa e Desenvolvimento, 53). Cruz das Almas, BA: Embrapa Mandioca e Fruticultura.
  • Manly, B. F. J. (2019). Métodos estatísticos multivariados: uma introdução (4. ed.). Porto Alegre, RS: Bookman.
  • Mojena, R. (1977). Hierarchical grouping methods and stopping rules: an evaluation. The Computer Journal, 20, 359-363. DOI: 10.1093/comjnl/20.4.359
    » https://doi.org/10.1093/comjnl/20.4.359
  • Rós, A. B., Hirata, A.C. S., Araújo, H. S., & Narita, N. (2011). Crescimento, fenologia e produtividade de cultivares de mandioca. Pesquisa Agropecuária Tropical, 41(4), 552-558. DOI: 10.5216/pat.v41i4.11075
    » https://doi.org/10.5216/pat.v41i4.11075
  • Scott, A. J., & Knott, M. A. A. (1974). Cluster analysis method for grouping means in the analysis of variance. Biometrics, 30(3), 507-512. DOI: 10.2307/2529204
    » https://doi.org/10.2307/2529204
  • Silva, R. S., Moura, E. F., Farias Neto, J. T., Sousa, N. R., Moura, M. F., & Sampaio, J. E. (2016). Genetic divergence among accessions of cassava (Manihot esculenta Crantz) sampled in the Tapajós region, State of Pará, using agronomic characters and microsatellite markers. Semina: Ciências Agrárias, 37(5), 2989-3004. DOI: 10.5433/1679-0359.2016v37n5p2989
    » https://doi.org/10.5433/1679-0359.2016v37n5p2989
  • Singh, D. (1981). The relative importance of characters affecting genetic divergence. The Indian Journal of Genetic and Plant Breeding, 41(2), 237-245.
  • Sneath, P. H., & Sokal, R. R. (1973). Numerical taxonomy: The principles and practice of numerical classification San Francisco, US: W.H. Freeman.
  • Sokal, R. R., & Rohlf, F. J. (1962). The comparison of dendrograms by objective methods. Taxon, 11(2), 33-40.
  • Vieira, E. A., Fialho, J. F., Faleiro, F. G., Bellon, G., Fonseca, K. G., Silva, M. S., Paula-Morães, S. V., & Carvalho, L. J. C. B. (2013). Caracterização fenotípica e molecular de acessos de mandioca de indústria com potencial de adaptação às condições do Cerrado do Brasil Central. Semina: Ciências Agrárias, 34(2), 567-582. DOI: 10.5433/1679-0359.2013v34n2p567
    » https://doi.org/10.5433/1679-0359.2013v34n2p567
  • Vieira, E. A., Fialho, J. F., Silva, M. S., Fukuda, W. M. G., Faleiro, F. G. (2008). Variabilidade genética do banco de germoplasma de mandioca da Embrapa cerrados acessada por meio de descritores morfológicos. Científica, 36(1), 56-67. DOI: 10.15361/1984-5529.2008v36n1p56
    » https://doi.org/10.15361/1984-5529.2008v36n1p56

Publication Dates

  • Publication in this collection
    03 July 2020
  • Date of issue
    2020

History

  • Received
    10 Aug 2018
  • Accepted
    27 Sept 2019
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