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Genetic divergence of cassava genotypes from Petrolina

ABSTRACT.

This study aimed to evaluate cassava genotypes to identify the ones with the best nutritional values for ruminant diets. Nine genotypes were used: Amansa Burro (BGM 549), Aramaris (BGM 116), Brasília, Cambadinha (BRS Guaíra), Curvelinha, Engana Ladrão (BGM 1269), Trouxinha (BGM 1468), BRS Gema de Ovo, and BRS Dourada. A completely randomized block experimental design with nine treatments (genotypes) and three blocks (replicates) were employed. The roots were analyzed for dry matter production (DMP) in tonnes per hectare, crude protein (CP), neutral detergent fiber (NDF), acid detergent fiber (ADF), starch, and in vitro dry matter digestibility (IVDMD). The multivariate analysis was carried out using Ward’s hierarchical agglomerative clustering based on Mahalanobis distance. The groups formed were evaluated by Scott-Knott test. The group formed by genotype Engana Ladrão was chosen as the best one for having the highest DMP t ha-1 and IVDMD values and the lowest NDF and ADF contents.

Keywords:
genetic dissimilarity; Manihot esculenta; Ward’s method

Introduction

Cassava (Manihot esculenta Crantz) is one of the most widely grown plants worldwide and its starch-rich roots have been the energetic base of over 700 million low-income people in several countries (Marcon, Avancini, & Amante, 2007Marcon, M. J. A., Avancini, S. R. P., & Amante, E. R. (2007). Propriedades químicas e tecnológicas do amido de mandioca e do polvilho azedo. Florianópolis: SC: Universidade Federal de Santa Catarina.).

Cassava is grown in all Brazilian states, but is particularly important in the Northeast region because it grows in poor soils, is resistant to drought, and is able to survive among weeds and pests. For that reason, the crop is present in the entire semi-arid portion of the Northeast region, where most crops cannot achieve high productivity (Cavalcanti & Araújo, 2000Cavalcanti, J., & Araújo, G. G. L. (2000). Parte aérea da mandioca na alimentação de ruminantes na região semi-árida (Circular Técnica, 7). Petrolina, PE: Embrapa Semi-Árido. Retrieved from https://ainfo.cnptia.embrapa.br/digital/bitstream/CPATSA/8858/1/CTE57.pdf
https://ainfo.cnptia.embrapa.br/digital/...
).

Nonetheless, the use of cassava roots in natura is partially limited by hydrogen cyanide contents, thus they are most often used in ruminant feed in grated form, which is a simple way of preserving cassava based on grinding sun-dried fresh roots that eliminates hydrogen cyanide due to its volatile character (Cavalcanti & Araújo, 2000Cavalcanti, J., & Araújo, G. G. L. (2000). Parte aérea da mandioca na alimentação de ruminantes na região semi-árida (Circular Técnica, 7). Petrolina, PE: Embrapa Semi-Árido. Retrieved from https://ainfo.cnptia.embrapa.br/digital/bitstream/CPATSA/8858/1/CTE57.pdf
https://ainfo.cnptia.embrapa.br/digital/...
).

Knowing the chemical and energy composition of foods determines both their value and nutritional shortcomings. The nutritional characteristics of each food must be known so that they can be properly employed. Grated cassava has 87.67% dry matter, 2.47% crude protein, 68.85% starch, 11.75% neutral detergent fiber (NDF), and 4.27% acid detergent fiber (ADF) (Rostagno et al., 2005Rostagno, H. S., Albino, L. F. T., Donzele, J. L., Gomes, P. C., Oliveira, R. D., Lopes, D. C., & Barreto, S. D. (2005). Tabelas brasileiras para aves e suínos: composição de alimentos e exigências nutricionais (2nd ed.). Viçosa, MG: Universidade Federal de Viçosa .).

Genetic divergence studies are essential to understand the genetic variability of populations and facilitate monitoring germoplasm banks (Cruz, Ferreira, & Pessoni, 2011Cruz, C. D., Ferreira, F. M., & Pessoni, L. A. (2011). Biometria aplicada ao estudo da diversidade genética. Visconde do Rio Branco, MG: Suprema Gráfica Editora. ). According to Bertini, Teófilo, and Dias (2009Bertini, C. H. C. M., Teófilo, E. M., & Dias, F. T. C. (2009). Divergência genética entre acessos de feijão-caupi do banco de germoplasma da UFC. Revista Ciência Agronômica, 40(1), 90-105. Retrieved from http://www.ccarevista.ufc.br/seer/index.php/ccarevista/article/view/410/306), genetic divergence has been studied aiming to select matrices for hybrids or from crossbreeding divergent genotypes to form new populations. Therefore, these studies produce important information for preservation and use of varieties (Toquica, Rodríguez, Martínez, Cristina Duque, and Tohme, 2003Toquica, S. P., Rodríguez, F., Martínez, E., Cristina Duque, M., & Tohme, J. (2003). Molecular characterization by AFLPs of Capsicum germplasm from the Amazon department in Colombia. Genetic Resources and Crop Evolution, 50(6), 639-647. DOI: https://doi.org/10.1023/A:1024429320771.
https://doi.org/https://doi.org/10.1023/...
).

According to Cruz, Regazzi, and Carneiro (2012Cruz, C. D., Regazzi, A. J., & Carneiro, P. C. S. (2012). Modelos biométricos aplicados ao melhoramento genético (4a. ed.). Viçosa, MG: Universidade Federal de Viçosa. ), according to some similarity or dissimilarity criterion, clustering analysis aims to divide an original group of observations into several groups.

Based on genetic similarity according to the Jaccard index, Oliveira, Baliza, Souza, Carvalho, and Assis (2012Oliveira, M. V. C., Baliza, D. P., Souza, G. A., Carvalho, S. P., & Assis, L. H. B. (2012). Caracterização de clones de mandioca utilizando marcadores microssatélites. Revista Ciência Agronômica, 43(1), 170-176. Retrieved from http://www.redalyc.org/articulo.oa?id=195320077021
http://www.redalyc.org/articulo.oa?id=19...
) investigated ten cassava clones obtained by polycrossing to detect the molecular similarity with table and industrial cultivars established on the market through microsatellite markers, which were effective to identify new cassava clones appropriate for in natura consumption but not industrial use.

The present study aims to assess the genotypes with the best nutritional value.

Material and methods

Nine cassava genotypes recommended for cultivation in the semi-arid region of the Northeast region of Brazil were evaluated (Table 1).

Table 1
Main characteristics and use of the studied cassava genotypes.

A completely randomized block experimental design with nine treatments (genotypes) and three blocks (replicates) was employed. The cassava was planted on May 4th, 2006 at Embrapa Semi-Arid in the city of Petrolina, Pernambuco State, Brazil, latitude 09°23'34"S, longitude 40°30'28"W, altitude 376 m, mean annual rainfall of 400 mm, and semi-arid tropical climate type BshW in the Köppen classification with a short wet season in the summer and mean minimum temperature of 20°C. The roots were harvested on October 26th, 2007 and mean root production, in t DM ha-1, was assessed.

No liming or fertilization was applied in the experiment since the goal was to simulate the production conditions employed in the region, where most producers do not use these practices. The meteorological data over the experimental period (Table 2 and 3) were obtained from the agrometeorological station of Bebedouro (Petrolina, Pernambuco State, Brazil 09°09'S 40°22'W).

The root samples for laboratory analyses were pre-dried in a forced air oven at 55°C and then ground with a 1 mm sieve. The resulting material was stored in airtight plastic containers.

The analyses determined values of pre-dried matter, dry matter (DM) at 105°C, crude protein (CP) according to the Lee (1995Lee, M. H. (1995). Official methods of analysis of AOAC International (16nd ed.). Trends Food Science & Technology, 6(11), 382. DOI: https://doi.org/10.1016/0924-2244(95)90022-5.
https://doi.org/https://doi.org/10.1016/...
), and NDF and ADF according to Van Soest, Robertson, and Lewis (1991Van Soest, P. J., Robertson, J. B., & Lewis, B. A. (1991). Methods for dietary fiber, neutral detergent fiber and nonstarch polysaccharides in relation to animal nutrition. Journal of Dairy Science , 74(10), 3583-3597. DOI: http://doi.org/10.3168/jds.S0022-0302(91)78551-2.
https://doi.org/http://doi.org/10.3168/j...
). Starch was determined using the amyloglucosidase α-amylase-1 method (McCleary, Gibson, & Mugford, 1997McCleary, B. V., Gibson, T. S., & Mugford, D. C. (1997). Measurement of total starch in cereal products by amyloglucosidase - α - amylase method: collaborative study. Journal of AOAC International, 80(3), 571-579. Retrieved from http://agris.fao.org/agris-search/search.do?recordID=US9747129.
http://agris.fao.org/agris-search/search...
). In vitro dry matter digestibility (IVDMD) was assessed according to the technique recommended by Tilley and Terry (1963Tilley, J. M. A., & Terry, R. A. (1963). A two stage technique for in vitro digestion of forage crops. Journal of the British Grassland Society, 18(2), 104-111. DOI: http://dx.doi.org/10.1111/j.1365-2494.1963.tb00335.x.
https://doi.org/http://dx.doi.org/10.111...
), which was modified for use in the artificial rumen fermenter DAISYII (ANKOM®) according to Holden (1999Holden, L. A. (1999). Comparison of methods of in vitro dry matter digestibility for ten feeds. Journal of Dairy Science, 82(8), 1791-1794. DOI: https://doi.org/10.3168/jds.S0022-0302(99)75409-3
https://doi.org/https://doi.org/10.3168/...
).

Table 2
Meteorological data for the period under study (part 1).

Table 3
Meteorological data for the period under study (part 2).

Prior to the multivariate analysis, the variables (t DM roots ha-1, CP, NDF, ADF, IVDMD, and starch) were submitted to Lilliefors (1967Lilliefors, H. W. (1967). On the Kolmogorov-Smirnov Test for Normality with Mean and Variance Unknown. Journal of American Statistical Association, 62(318), 399-402. Retrieved from https://www.jstor.org/stable/pdf/2283970
https://www.jstor.org/stable/pdf/2283970...
) and Bartlett (1937Bartlett, M. S. (1937). Properties of sufficiency and statistical tests. Proceedings of Royal Society of London. Series A, 160(901), 268-282. DOI: https://doi.org/10.1098/rspa.1937.0109
https://doi.org/https://doi.org/10.1098/...
) tests to verify normality and homoscedasticity, respectively.

The multivariate analyses were performed using the software R, in which Ward and Joe (1963Ward JR, Joe H. (1963). Hierarchical grouping to optimize an objective function. Journal of American Statistical Association , 58(301), 236-244. DOI: http://dx.doi.org/10.1080/01621459.1963.10500845.
https://doi.org/http://dx.doi.org/10.108...
) method was applied based on Mahalanobis distance and Rand (1971Rand, W. M. (1971). Objective criteria for the evaluation of clustering methods. Journal of the American Statistical Association, 66(336), 846-850. DOI: http://dx.doi.org/10.1080/01621459.1971.10482356.
https://doi.org/http://dx.doi.org/10.108...
) index to determine the number of groups.

The averages of the variables of the clusters formed were compared by Scott and Knott (1974Scott, A. J., & Knott, M. A. (1974). A cluster analysis method for grouping means in the analysis of variance. Biometrics, 30(3), 507-512. DOI:http://www.jstor.org/stable/2529204.
http://www.jstor.org/stable/2529204....
) test at 5% probability of type-I error.

Results and discussion

Figure 1 shows the results obtained with the hierarchical clustering analysis performed by Ward and Joe (1963Ward JR, Joe H. (1963). Hierarchical grouping to optimize an objective function. Journal of American Statistical Association , 58(301), 236-244. DOI: http://dx.doi.org/10.1080/01621459.1963.10500845.
https://doi.org/http://dx.doi.org/10.108...
) method based on Mahalanobis distance and using the Rand (1971Rand, W. M. (1971). Objective criteria for the evaluation of clustering methods. Journal of the American Statistical Association, 66(336), 846-850. DOI: http://dx.doi.org/10.1080/01621459.1971.10482356.
https://doi.org/http://dx.doi.org/10.108...
) index to determine the number of clusters. Six clusters were formed. The first was made up by genotype Gema de Ovo; the second, by genotype Dourado; the third, by genotype Engana Ladrão; the fourth, by genotypes Guaíra and Trouxinha; the fifth, by genotype Amansa Burro; and the sixth, by genotypes Brasília, Aramaris, and Curvelinha.

Figure 1
Dendogram of genetic dissimilarity of cassava genotypes.

Mahalanobis distance ranged from 3.37 to 19.63 (Table 4), which indicates the greatest similarity between Engana Ladrão and Trouxinha and the greatest difference between Guaíra and Dourado.

Table 4
Mahalanobis distance matrix of the original data for the 9 genotypes of Embrapa Semiarid, Petrolina, Pernambuco State.

Table 5 shows the mean values of t DM roots ha-1, contents of CP, NDF, ADF, and starch, and IVDMD of the clusters formed.

Cluster III had the highest (p < 0.05) t DM roots ha-1 values, while cluster IV was intermediate and clusters I, II, V, and VI had the lowest production. The results of this experiment show the production potential of genotype Engana Ladrão in the semi-arid region of the Brazilian Northeast, where Silva et al. (2009Silva, A. F., Santana, L. M. D., França, C. R., Magalhães, C. A. D. S., Araújo, C. R. D., & Azevedo, S. G. D. (2009). Produção de diferentes variedades de mandioca em sistema agroecológico. Revista Brasileira de Engenharia Agrícola e Ambiental, 13(1), 33-38. Retrieved from http://www.agriambi.com.br
http://www.agriambi.com.br...
) had previously assessed the productivity of cassava in the state of Piauí and found the highest yields for genotypes Engana Ladrão and Do Céu.

CP content was similar (p > 0.05) among all genotypes. The values found in the present study match those observed in nutritional charts of swine and poultry (Rostagno et al. 2005Rostagno, H. S., Albino, L. F. T., Donzele, J. L., Gomes, P. C., Oliveira, R. D., Lopes, D. C., & Barreto, S. D. (2005). Tabelas brasileiras para aves e suínos: composição de alimentos e exigências nutricionais (2nd ed.). Viçosa, MG: Universidade Federal de Viçosa .) and bovine feed (Valadares Filho, 2006Valadares Filho, S. D. C. (2006). Tabelas brasileiras de composição de alimentos para bovinos (2a ed.). Viçosa, MG: Universidade Federal de Viçosa .), which show cassava roots have low CP contents (between 2.2 and 3.4%). According to Van Soest (1994Van Soest, P. J. (1994). Nutritional ecology of the ruminant. Ithaca, NY: Cornell University Press. ), animal diet must contain at least 7% CP to prevent alterations in ruminal fermentation and reduction of DM intake. Therefore, using cassava roots entails adjusting the protein concentration, which will depend on the other components of the diet and the requirements of the animals.

Clusters 1 and II had the highest (p < 0.05) NDF content, while clusters V and VI had intermediate values and clusters III and IV had the lowest contents. Clusters I and V had the highest (p < 0.05) ADF content, while cluster I had intermediate values and clusters III, IV, and VI had the lowest contents. According to Buitrago (1990Buitrago A. J. A. (1990). La yuca em la alimentación animal. Cali, CO: Centro Internacional de Agricultura Tropical.), cassava skin represents between 15 and 20% of the total root weight and holds most of its fiber. It is likely that the genotypes with the highest fiber content are those with the highest proportion of skin in the root.

Clusters IV and V had the highest (p < 0.05) starch content, while clusters I, III, and VI had intermediate values and cluster II had the lowest contents. Genotype Amansa Burro (cluster V) had been reported in the literature as having high starch content (Borges, Fukuda, & Rossetti, 2002Borges, M. D. F., Fukuda, W. M. G., & Rossetti, A. G. (2002). Avaliação de variedades de mandioca para consumo humano. Pesquisa Agropecuária Brasileira. 37(11), 1559-1565. DOI: http://dx.doi.org/10.1590/S0100-204X2002001100006
https://doi.org/http://dx.doi.org/10.159...
).

Table 5
Root production in tons of dry matter per hectare (PMS), crude protein (CP), neutral detergent fiber (NDF), acid detergent fiber (ADF), starch and in vitro dry matter digestibility (IVDMD) of the groups formed.

Clusters III and IV had the highest (p < 0.05) IVDMD values, followed by cluster VI, clusters I and II, and cluster V. The results obtained are in accordance with Alves de Brito, Rodella, and Deschamps (2003Alves de Brito, C. J. F., Rodella, R. A., & Deschamps, F. C. (2003). Perfil químico da parede celular e suas implicações na digestibilidade de Brachiaria brizantha e Brachiaria humidicola. Revista Brasileira de Zootecnia, 32(6), 1835-1844. DOI: https://doi.org/10.1590/S1516-35982003000800005
https://doi.org/https://doi.org/10.1590/...
), who reported the increase in cell-wall components reduces its degradability by ruminants, which is confirmed by the correlation between IVDMD and NDF and ADF, i.e., an increase in fiber content leads to a reduction in IVDMD. However, starch content did not impact IVDMD (Table 6).

Table 6
Correlation between in vitro dry matter digestibility (IVDMD) with starch, neutral detergent fiber (NDF) and acid detergent fiber (FDA).

Conclusion

Genotype Engana Ladrão stands out nutritionally among the genotypes assessed for having the highest DMP t ha-1, lowest content of NDF and ADF, and highest IVDMD.

Aknowledgements

The authors thank the Federal Rural University of Pernambuco and CAPES for their support

Referências

  • Alves de Brito, C. J. F., Rodella, R. A., & Deschamps, F. C. (2003). Perfil químico da parede celular e suas implicações na digestibilidade de Brachiaria brizantha e Brachiaria humidicola. Revista Brasileira de Zootecnia, 32(6), 1835-1844. DOI: https://doi.org/10.1590/S1516-35982003000800005
    » https://doi.org/https://doi.org/10.1590/S1516-35982003000800005
  • Araujo, J. C., & Almeida, C. O. (2013). Inventário de variedades de mandioca lançadas pela Embrapa Mandioca e Fruticultura no período de 1996 a 2009 (Circular Técnica, 107). Cruz das Almas, BA: Embrapa. Retrieved from https://ainfo.cnptia.embrapa.br/digital/bitstream/item/119005/1/CircularTecnica-107.pdf
    » https://ainfo.cnptia.embrapa.br/digital/bitstream/item/119005/1/CircularTecnica-107.pdf
  • Bartlett, M. S. (1937). Properties of sufficiency and statistical tests. Proceedings of Royal Society of London. Series A, 160(901), 268-282. DOI: https://doi.org/10.1098/rspa.1937.0109
    » https://doi.org/https://doi.org/10.1098/rspa.1937.0109
  • Bertini, C. H. C. M., Teófilo, E. M., & Dias, F. T. C. (2009). Divergência genética entre acessos de feijão-caupi do banco de germoplasma da UFC. Revista Ciência Agronômica, 40(1), 90-105. Retrieved from http://www.ccarevista.ufc.br/seer/index.php/ccarevista/article/view/410/306
  • Borges, M. D. F., Fukuda, W. M. G., & Rossetti, A. G. (2002). Avaliação de variedades de mandioca para consumo humano. Pesquisa Agropecuária Brasileira 37(11), 1559-1565. DOI: http://dx.doi.org/10.1590/S0100-204X2002001100006
    » https://doi.org/http://dx.doi.org/10.1590/S0100-204X2002001100006
  • Buitrago A. J. A. (1990). La yuca em la alimentación animal Cali, CO: Centro Internacional de Agricultura Tropical.
  • Cavalcanti, J., & Araújo, G. G. L. (2000). Parte aérea da mandioca na alimentação de ruminantes na região semi-árida (Circular Técnica, 7). Petrolina, PE: Embrapa Semi-Árido. Retrieved from https://ainfo.cnptia.embrapa.br/digital/bitstream/CPATSA/8858/1/CTE57.pdf
    » https://ainfo.cnptia.embrapa.br/digital/bitstream/CPATSA/8858/1/CTE57.pdf
  • Cruz, C. D., Ferreira, F. M., & Pessoni, L. A. (2011). Biometria aplicada ao estudo da diversidade genética Visconde do Rio Branco, MG: Suprema Gráfica Editora.
  • Cruz, C. D., Regazzi, A. J., & Carneiro, P. C. S. (2012). Modelos biométricos aplicados ao melhoramento genético (4a. ed.). Viçosa, MG: Universidade Federal de Viçosa.
  • Holden, L. A. (1999). Comparison of methods of in vitro dry matter digestibility for ten feeds. Journal of Dairy Science, 82(8), 1791-1794. DOI: https://doi.org/10.3168/jds.S0022-0302(99)75409-3
    » https://doi.org/https://doi.org/10.3168/jds.S0022-0302(99)75409-3
  • Lee, M. H. (1995). Official methods of analysis of AOAC International (16nd ed.). Trends Food Science & Technology, 6(11), 382. DOI: https://doi.org/10.1016/0924-2244(95)90022-5.
    » https://doi.org/https://doi.org/10.1016/0924-2244(95)90022-5.
  • Lilliefors, H. W. (1967). On the Kolmogorov-Smirnov Test for Normality with Mean and Variance Unknown. Journal of American Statistical Association, 62(318), 399-402. Retrieved from https://www.jstor.org/stable/pdf/2283970
    » https://www.jstor.org/stable/pdf/2283970
  • Marcon, M. J. A., Avancini, S. R. P., & Amante, E. R. (2007). Propriedades químicas e tecnológicas do amido de mandioca e do polvilho azedo Florianópolis: SC: Universidade Federal de Santa Catarina.
  • McCleary, B. V., Gibson, T. S., & Mugford, D. C. (1997). Measurement of total starch in cereal products by amyloglucosidase - α - amylase method: collaborative study. Journal of AOAC International, 80(3), 571-579. Retrieved from http://agris.fao.org/agris-search/search.do?recordID=US9747129
    » http://agris.fao.org/agris-search/search.do?recordID=US9747129
  • Oliveira, M. V. C., Baliza, D. P., Souza, G. A., Carvalho, S. P., & Assis, L. H. B. (2012). Caracterização de clones de mandioca utilizando marcadores microssatélites. Revista Ciência Agronômica, 43(1), 170-176. Retrieved from http://www.redalyc.org/articulo.oa?id=195320077021
    » http://www.redalyc.org/articulo.oa?id=195320077021
  • Rand, W. M. (1971). Objective criteria for the evaluation of clustering methods. Journal of the American Statistical Association, 66(336), 846-850. DOI: http://dx.doi.org/10.1080/01621459.1971.10482356.
    » https://doi.org/http://dx.doi.org/10.1080/01621459.1971.10482356.
  • Rostagno, H. S., Albino, L. F. T., Donzele, J. L., Gomes, P. C., Oliveira, R. D., Lopes, D. C., & Barreto, S. D. (2005). Tabelas brasileiras para aves e suínos: composição de alimentos e exigências nutricionais (2nd ed.). Viçosa, MG: Universidade Federal de Viçosa .
  • Scott, A. J., & Knott, M. A. (1974). A cluster analysis method for grouping means in the analysis of variance. Biometrics, 30(3), 507-512. DOI:http://www.jstor.org/stable/2529204.
    » http://www.jstor.org/stable/2529204.
  • Silva, A. F., Santana, L. M. D., França, C. R., Magalhães, C. A. D. S., Araújo, C. R. D., & Azevedo, S. G. D. (2009). Produção de diferentes variedades de mandioca em sistema agroecológico. Revista Brasileira de Engenharia Agrícola e Ambiental, 13(1), 33-38. Retrieved from http://www.agriambi.com.br
    » http://www.agriambi.com.br
  • Tilley, J. M. A., & Terry, R. A. (1963). A two stage technique for in vitro digestion of forage crops. Journal of the British Grassland Society, 18(2), 104-111. DOI: http://dx.doi.org/10.1111/j.1365-2494.1963.tb00335.x.
    » https://doi.org/http://dx.doi.org/10.1111/j.1365-2494.1963.tb00335.x.
  • Toquica, S. P., Rodríguez, F., Martínez, E., Cristina Duque, M., & Tohme, J. (2003). Molecular characterization by AFLPs of Capsicum germplasm from the Amazon department in Colombia. Genetic Resources and Crop Evolution, 50(6), 639-647. DOI: https://doi.org/10.1023/A:1024429320771.
    » https://doi.org/https://doi.org/10.1023/A:1024429320771.
  • Valadares Filho, S. D. C. (2006). Tabelas brasileiras de composição de alimentos para bovinos (2a ed.). Viçosa, MG: Universidade Federal de Viçosa .
  • Van Soest, P. J., Robertson, J. B., & Lewis, B. A. (1991). Methods for dietary fiber, neutral detergent fiber and nonstarch polysaccharides in relation to animal nutrition. Journal of Dairy Science , 74(10), 3583-3597. DOI: http://doi.org/10.3168/jds.S0022-0302(91)78551-2.
    » https://doi.org/http://doi.org/10.3168/jds.S0022-0302(91)78551-2.
  • Van Soest, P. J. (1994). Nutritional ecology of the ruminant Ithaca, NY: Cornell University Press.
  • Ward JR, Joe H. (1963). Hierarchical grouping to optimize an objective function. Journal of American Statistical Association , 58(301), 236-244. DOI: http://dx.doi.org/10.1080/01621459.1963.10500845.
    » https://doi.org/http://dx.doi.org/10.1080/01621459.1963.10500845.

Publication Dates

  • Publication in this collection
    22 May 2023
  • Date of issue
    2023

History

  • Received
    03 Mar 2021
  • Accepted
    15 Feb 2022
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