Smaller Time-Window Comparisons
We used the R package netTS (Bonnell & Vilette, 2019), that makes use
of time-aggregated windows to analyse temporal changes in social
networks. This program allows the user to alter the window size,
dependent on the types of questions being asked. A benefit of using a
shifting-window is the ability to see patterns and variation that may
not be visible in larger window size comparisons. To test the effects of
our ecological and social variables on core unit social networks, we
created 20 time-aggregated networks using a 31-day window size and
31-day window shift that spanned the full dataset (August
28th, 2017 to May 13th, 2019).
Within each time-window, a new network was created. To justify our
choice of window size, the netTS package tutorials provide guidance on
choosing a lower time scale for window-size using a bootstrap technique
(Fig. S1). This technique measures the similarity between the observed
network in a window and networks created using bootstrap samples from
within the window. The idea here is that the similarity between
bootstrapped networks and the observed network provides information
about the similarity of the observed to the full network (i.e., if
perfect sampling was possible), equivalent to the traditional
bootstrapping approach (Efron, 1992). To choose a window size above the
minimum threshold, we estimated the variability in network density, as
window sizes too large will reach asymptote (i.e., density of 1) and
window sizes too small will have densities close to 0, resulting in
lower variation (Caceres, Berger-Wolf, & Grossman, 2011). The optimal
window size, in terms of maximizing variability in edge density, for our
data was 31 days. We thus used the netTS package with a window size of
31 days to calculate and analyze social network metrics to determine the
connectedness of core units over time. At the node (core-unit) level, we
calculated degree (i.e., the number of core units associated with) and
strength (i.e., sum of all edge weights for a given node, indicating the
total association rate for a given core unit). At the network level, we
calculated edge density (i.e., the ratio of the number of edges and the
number of possible edges), clustering coefficient (i.e., number of core
units associated with that also associated with one another), and cosine
similarity (see below). At the dyad level, we calculated dyad
association measures (AI).