Permutation-Based Multivariate Inference for Milk Composition Traits: PERMANOVA and Distance Metric Comparison

Permutation‐based multivariate statistical techniques have received increasing popularity in animal science investigations, particularly for data sets that fail to satisfy classical parametric assumptions like multivariate normality and homoscedasticity of covariance matrices. In the framework of dairy production research, milk composition traits are largely determined by different types of management and season and require appropriate robust multivariate inference models. This work used Permutational Multivariate Analysis of Variance (PERMANOVA) to evaluate differences in composition of milk fed by Holstein cows, as a function of feeding systems and periods. Means of monthly averages of milk fat (%), dry matter (%) and protein were determined based on 30 Holstein cows which were reared in a private farm located in the Tokat Province, Türkiye during the period of 2024. The 2 types of feed consumption were divided into two groups, dry forage and green alfalfa; seasonality was assessed quarterly. Of theses, PERMANOVA models were fitted under both one-way and two-way experimental design with Euclidean, Bray–Curtis and Manhattan distance as alternative commonly used choices. Milk fat and dry matter differed significantly among feeding periods, however milk protein did not (P > 0.05). Furthermore, the more permutations were conducted, the more stable and robust significance results became, which is, large all distance measures reached generally consistent conclusion as long as enough permutation was used. Generally, the results support PERMANOVA as a flexible and reliable replacement for MANOVA in the analysis of multivariate dairy data, particularly demonstrating its effectiveness at assessing differences in milk composition due to feeding and seasonality under non-normal data scenarios.