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).