Statistical Analyses
To analyse the consistency of the core unit social network over time (H1), we used the cosine similarity metric. Cosine similarity is a measure of structural equivalence from 0 to 1 and is equal to the number of common neighbors which two nodes share divided by the geometric mean of their degrees (Newman, 2010). A cosine similarity of 1 indicates that the two nodes have exactly the same ratio and identity of associated units. A cosine of 0 indicates the two nodes do not have any shared associations (Newman, 2010). For this study, cosine similarity was used to measure the changes in associations from one time window to the next (Bonnell & Vilette, 2019). We compared cosine similarity for each core unit to the previous time window to reveal short-term variability, as well as between each window and the first time window in the data set to reveal any long-term variability that may be present.
To examine the effects of ecological conditions on group clustering and the overall connectedness of core units, we modeled how changes in fruit and young leaf abundance and rainfall influenced both node and network level measurements. For network-level measures (i.e., band level) we used linear regression with AR1 autocorrelated errors, while for node-level measures (i.e., core unit) we used a multi-level model with AR1 autocorrelated errors and core-unit identity as random effects, since nodes are repeatedly measured over time. We standardized all independent variables and calculated r-squared (R2) values to provide estimates of effect size for each model (Gelman, Goodrich, Gabry, & Vehtari, 2019).
To investigate the association between male dispersals and association patterns, we first determined whether there was temporal variability in male dispersal events. We examined the relationship between our ecological variables and the number of males transferring between core units in a given month using a Spearman rank correlation, applying a Bonferroni correction for multiple comparisons (α = 0.017). We calculated Monte-Carlo approximated p -values as these are more robust when there are ties in the data (Hájek, Šidák, & Sen, 1999). We then tested whether two core units were more likely to continue to associate after a male transferred between them than would be expected, for up to three months following the dispersal event. Here, we calculated simple association measures (AI) between the dyads with male transfers for three months following the male dispersal event. As a control, we also calculated association indices between each of the core units involved in the dispersal event, and the core units they had each been associated with during the month the male transferred. We used one-sample Wilcoxon signed-ranks tests to determine if the association index between the two core units involved in male transfers was higher than their association indices with control dyads.
All analyses were done using either SOCPROG v.2.9 (Whitehead, 2009) and R v.3.6 (R Core Team, 2019). R packages used includes: netTS (Bonnell & Vilette, 2019); BRMS (Bürkner, 2017), igraph (Csardi & Nepusz, 2006), and coin (Hothorn, Hornik, van de Wiel, & Zeileis, 2006).