Determinants of Density–Body Size Scaling Within Food Webs and Tools for Their Detection - Advances in Ecological Research - page 15

A

B C

Log M

Figure 3 Possible effects of discontinuities in body size distribution in a DMR. (A)
All associations follow the same scaling with changes in the intercept due to variations
in the total amount of resources at each scale of aggregation. (B) The slope of the
DMR changes at each scale; for example, associated to an increase in predation
pressure with body size at one scale (e.g. zooplankton) but a reduction in other scales
(e.g. fishes). (C) A similar DMR is observed at each scale without a general pattern
connecting the whole body size distribution.

IV. STATISTICAL ISSUES

An important aspect of DMR is that it typically takes the form of a power-
law function. Statistical methods for estimating power-law parameters have
been extensively reviewed elsewhere ( Clauset et al., 2009; Marquet et al.,
2005; Martin et al., 2005; Newman, 2005; Packard et al., 2010; Reuman et al.,
2009; White et al., 2008 ). In this section, we present a brief update of the
available methodology in order to suggest alternative approaches to manip-
ulate frequency data generated by different distributions, and to compare the
performance of classic methods of estimation against a novel approach based
on a resampling procedure from a real dataset.

A. Frequency Distribution

Methods for the estimation of the scaling parameters in frequency distribu-
tions can be roughly classified as binned and unbinned, depending on wheth-
er or not they require grouping observations into size classes. Binned
methods consist in fitting all or part—typically the right tail—of abundance
frequency distributions to a power function of body sizes (e.g. Marquet et al.,
1995 ). The mean value of size classes and the related frequencies are used for
this purpose. In this approach, the use of a linear binning of the body size axis
has been stated to produce inaccurate and biased estimations of the expo-
nents ( Marquet et al.,2005 ). The bias originates primarily from the few
individual counts in higher size bins, which is a common problem arising