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assumption of lack of error measurement (
Reuman et al., 2009
). Com-
mendable discussions about the statistical issues involved in these analyses
as well as consideration of the underlying causality can be read elsewhere (see
Cohen and Carpenter, 2005; Reuman et al., 2009
). In general, the early
trivariate food web studies plotted mass on the y-axis, as this intuitively
depicted the flux of energy ''upwards'' through the food web, from the
smaller prey to the larger top predators (e.g.
Cohen et al., 2003; Woodward
et al., 2005a,b
), whereas most recent studies have used the converse arrange-
ment of axes (e.g.
Layer et al., 2010, 2011
).
Finally, a worthy approach could be to make an explicit analysis of the
causal structure behind the DMR (
Grace, 2006; Kline, 2005; Shipley, 2000
).
Structural equation modeling (SEM) techniques are now widely used in ecolo-
gy and have the potential to simultaneously evaluate several hypotheses
organized in a model of direct and indirect causal paths, whose causal struc-
ture intends to represent a possible theoretical explanation to observed varia-
tion (
Canavero et al., 2009; Toranza and Arim, 2010
). This approach falls
within the family of confirmatory analyses, and as such, allows for comparison
between alternative causal constructs built under different sets of assumptions.
Therefore, in this approach the analysis of DMR turns its attention towards
formally testing the underlying mechanisms instead of scaling exponent esti-
mation, and for this reason SEM should be considered as a complementary
technique in the study of DMR. It is worth mentioning that Bayesian methods
also represent a powerful tool to simultaneously evaluate a set of relationships
organized in complex causal paths (
Price et al.,2009
).
C. Multiple DMR in the Same Dataset
So far it has been assumed that the frequencies of body sizes sampled are the
outcome of a single power-law distribution. However, several parent distri-
butions could be mixed in a single empirical dataset. The mixing of different
distributions can arise for several reasons, such as deep biogeographic events
that affected differentially the observed species (
Marquet and Cofre, 1999
),
the mixing of different cohorts of individuals within the same community,
discontinuities in the body size distribution in response to landscape struc-
ture (
Holling, 1992; Skillen and Maurer, 2008
), phylogenetic inertia, and
trophic interactions (
Marquet et al., 2008; Skillen and Maurer, 2008
), to
mention a few. As stated in the previous section, the method chosen to
describe DMR should have the potential to cope with the existence of
different scaling relationships within the same system. However, none of
the discussed methods can, by itself, detect the existence of multiple scaling.
Methods for the detection of discontinuities in the body size distribution
have been extensively reviewed elsewhere (
Allen and Holling, 2008
).
