Repeatability and Variance Components - Which components are measured -
Figure 22. Repeatability as the variation proportion due to among-individual and within individual variation (DINGEMANSE & DOCHTERMANN 2013).
Repeatability was measured with the rptR package for R. Repeatability describes per definition assesses the variance between measurements and distinguishes them into within-group and between-group sources of variance. Therefore, it is often termed as the intra-class correlation (ICC) (Figure 22).
As far as behavioral studies are concord, repeatability measures “measures the relative consistency of some behavioral trait within individuals and the variability across individuals” (Stoffel et al. 2016). To estimate repeatability, mixed effect models are often applied. If in the case of measuring behavior, measurements derive from the same criterion, the following formula can measure repeatability (Figure 23). R=VG/(VG+VR) Repeatability is measured by variances of the group means (VG) and variances of the data-level (VR) (Nakagawa & Schielzeth 2010).
Figure 23. Linear mixed effect model approach used for whole model repeatability (A) calculations and individual Stage:Sex:Food combinations (B).
Behavioral traits - Mixed model approach -
Behaviour was modeled by using a linear mixed model as seen below (Figure 24). The model incorporates the behaviour related variable, swimming distance in this case and the hypotheses relevant fixed effects. Stage, food and sex as well as trial are predictor variables while swimming distance in this example is the response variable. The model also allows to identify significant interactions between the fixed effects. Fish_ID was included as a random effect and fish length as a control variable (covariate). The models anova table, denominator degrees of freedom of F-statistics approximated by Satterwaithe, then displayed the significant factors affecting the response variable (Kuznetsova et al. 2016). For the used example, one could precisely see if either stage, sex, food or any of their interactions had a significant effect on swimming distance. The same applies for trial and stage as single factors or interactions to identify possible trial effects between stages. Fish length as a covariate was accounted. Stepwise model simplification was applied to the models by means of removing non-significant factors according to the F-tests of the permanova, starting with the interactions, and then adjusting the model for it. Non-significant factors were of course kept in the model when being linked to a significant interaction.
Figure 24. Linear mixed effect model approach used for measured mean behavioral response and individual Stage:Sex:Food combinations.