
Red Sindhi is a zebu ( Bos primigenius indicus) breed named after its region of origin, which is the north part of the Sindh province of Pakistan. ( 2003), multivariate analyses are useful for addressing relevant decisions in animal breeding programs that reach to obtain male and female animals with higher average performance with regard to previous generations by heterosis, increasing the variability of the population. Thus, multivariate statistical techniques might generate not possible interpretations if univariate statistics was used. Thus, it is essential to know genetic associations between the economic importance traits in the reason that they are correlated in magnitude and direction (Sonesson and Meuwissen 2000 Savegnago et al. Moreover, multivariate statistical techniques might reveal relationships that would not be possible with univariate statistical techniques (Usai et al. In addition, multivariate analyses are useful for addressing relevant decisions that reach male and female offspring with higher average performance related to previous generations by heterosis, increasing the variability of the population (Gianola and Sorensen 2004 Lopes et al. 2013 Jolliffe and Cadima 2016 Lopes et al. Once identified, groups of animals with desirable traits can be selected for animal breeding programs in order to enhance productivity and fertility (Karacaören and Kadarmideen 2008 Buzanskas et al. Multivariate techniques, such as cluster and principal component analyses, could be used to find the loadings or factors that explain the highest variation in the data set over dependent variables, providing a tool to build relationships that allow the clustering of animals by similar productive traits and correlations between different characteristics evaluated. In conclusion, the multivariate procedures were effective in generating the correlations among the functional traits, showing that CI is correlated with RE and all these functional traits are related with total milk yield. Total milk yield (TMY) showed 71.92% of the total variation, and age at first calving (AFC) contributed with 23.06% of the variation, being the two most important traits for the variability of the data set. Four hundred and twenty-nine females were clustered in one group, representing 76.60% of the genotypes. By cluster analysis, twelve different groups were generated from the pool of Sindhi herds analyzed, with a great homogeneity among females for the traits evaluated and only few females generating separate groups.

Clustering analysis was performed based on Tocher method, and results showed physiological relationships among functional traits. It was found that for all functional traits, first 3 principal components explained more than 90% of the total variation. Principal component analysis with correlation matrix was used to find the relationship among AFC, CI, RE, TMY, and LP. For this goal, performance data provided by the Brazilian Association of Zebu Breeders related to 560 Red Sindhi dairy cattle from 28 different herds in Brazil, born in the period from 1987 to 2011, were used. The objective of this study was to investigate the relationship among functional traits (age at first calving (AFC), calving interval (CI), reproductive efficiency (RE), total milk yield (TMY), and lactation period (LP)) in Red Sindhi breed through multivariate techniques.
