Test of interaction in the analysis of molecular variance

Abstract

The genomic diversity, expressed in the differences between molecular haplotypes of a group of individuals, can be divided into components of variability between and within some factor of classification of the individuals. For such variance partitioning, molecular analysis of variance (AMOVA) is used, which is constructed from the multivariate distances between pairs of haplotypes. The classical AMOVA allows the evaluation of the statistical significance of two or more hierarchical factors and consequently there is no interaction test between factors. However, there are situations where the factors that classify individuals are crossed rather than nested, that is, all the levels of a factor are represented in each level of the other one. This paper proposes a statistical test to evaluate the interaction between crossed factors in a Non-Hierarchical AMOVA. The null hypothesis of interaction establishes that the molecular differences between individuals of different levels of a factor are the same for all the levels of the other factor that classifies them. The proposed analysis of interaction in a Non- Hierarchical AMOVA includes: calculation of the distance matrix and partition of it into blocks, subsequent calculation of residuals and analysis of non-parametric variance on the residuals. Its implementation is illustrated in simulated and real scenarios. The results suggest that the proposed interaction test for the Non-Hierarchical AMOVA presents high power.