Inferring variance and invariance in multi-individual behavior of zebrafish (Danio rerio) responding to chemical stress

Abstract

Variance and invariance residing in multi-individual movement of zebrafish under chemical stress were addressed concurrently before and after treatment with formaldehyde. Variance was observed in movement parameters. Without treatment, linear speed was highest in groups with two-individuals, followed by those with one-and four-individuals. Following treatment, linear speed decreased significantly in groups with one-and two-individuals, but not in those with four-individuals. Inter-distances between two-individuals in groups with two-individuals decreased markedly after treatment, whereas inter-distances between two randomly selected individuals in the groups with four-individuals were not affected. The zero-and peak-values in the time-lag of autocorrelation of inter-distances decreased further after treatment in groups of two individuals relative to those in groups of four individuals. However, the empirical transition probability matrix between predefined behavioral patterns remained invariant among groups with different numbers of individuals as well as before and after treatment. Variance and invariance in multi-individual behaviors are suitable in expressing complex behaviors under chemical stress and could be a reference for detecting contaminants in the environment using indicator species.