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has. In a size-class-based food web, in-degree is the number of size classes a
focal size class feeds upon and out-degree is the number of size classes which
feed upon a focal size class. The sum of in-degree and out-degree links a node
has thus represents the total number of direct links it has in the food web.
These measures require food web data and therefore can only be employed in
the grouping comparisons using aggregations D* and F*. Species-averaged
body masses or size-class masses were used for the focal entities. As in past
studies which have investigated these patterns (e.g. Digel et al., 2011; Thierry
et al., 2011 ), we include in the analysis nodes which do not have any in or
out links.
D. Statistical Analyses
1. Modelling Response Variables
To assess the strength of size structuring of the different aggregations, we
needed to calculate the allometric relationships listed in Table 2 . However,
for some of the response variables at certain aggregations, there was non-
independence between sample points in the raw datasets (multiple predator
individuals within a species and multiple prey items from a single predator;
Barnes et al., 2010; Costa, 2009 ). To overcome this issue, we employed linear
mixed-effect models (LMMs) with random intercepts and slopes ( Pinheiro
and Bates, 2000; Zuur et al., 2009 ) using the nlme library ( Pinheiro et al.,
2008 )inR( R Development Core Team, 2009 ). Focal mass was used as a
fixed effect, and depending on the response variable examined and the level
of aggregation used, up to two levels of nested random effects (predator
species and predator individual) were included in the models to account for
the non-independence. LMMs were not used in cases where data were
aggregated such that non-independence was eliminated, and ordinary least
square (OLS) regression models were used instead. Some of the response
variables showed unimodal relationships with focal species mass, and in these
cases, we entered a quadratic term in the regressions. If one aggregation in a
comparison of a response variable suffered from non-independence while the
other did not, a LMM was used on both regardless. The type of model used
for each comparison is indicated in Table 2 .
2. Comparison of Response Variables
To check for differences for both the resolution and grouping comparisons, the
slope estimates were used for the each of the different study systems calculated
in the LMM or OLS regressions. To determine if altering resolution or
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