Geoscience Reference
In-Depth Information
An interesting approach in this line could be first to explore the existence of
discontinuities and then explore the DMR in the range of body sizes between
subsequent discontinuities. Methods for the analysis of individuals' size
distribution could be particularly relevant in this case (
Andersen and
Beyer, 2006; Thibault et al., 2011
). The fit of one or several distributions to
the observed ISD on log scale allows both the detection of the number of
modes present in the data and an eventual scaling pattern between modes
(
Andersen and Beyer, 2006; Thibault et al., 2011
).
Another statistical approach that can be used to explore changes in scaling
in DMR is the fit of regressions with break points (
Muggeo, 2003, 2008
). The
use of segmented regressions in the analysis of DMR has several advantages
in comparison to other methods. First, it can be fitted to the entire range of
density-mass values, leaving aside the need to perform arbitrary pre-proces-
sing of data to define subsets where single regression would be applied.
Second, all the parameters have meaningful biological interpretation. Slopes
in log scale are estimates of the scaling exponent for different body size
ranges, and break points represent transitions in the scaling regime (see
Figure 6
). The existence of discrete changes in scaling regime has rarely
been considered, even though cases suggesting its occurrence have been
presented previously (e.g.
Ackerman et al., 2004; Marquet et al., 1995
).
Third, even novel techniques designed to make optimum use of data eventu-
ally end up discarding part of it, with a consequent loss of information (see
Clauset et al., 2009
). Segmented regression can be combined with ML esti-
mation of scaling between breaking points, thereby maximizing the use of
available data and the extraction of meaningful biological information from
the data at hand (e.g.
Figure 7
).
Considering that all the alternatives discussed herein are accessible in freely
available software—for example, R-Project (
R Development Core Team,
2007
), the best statistical practice would be to fit all or most of the alternative
models (i.e. linear, non-linear, polynomial, segmented regressions, and fits on
rank ordered data) simultaneously to obtain estimates of scaling exponents
and compare these models using suitable statistical criteria, such as AIC or
BIC (
Burnham and Anderson, 2002; Hilborn and Mangel, 1997; Zuur et al.,
2009
). The simultaneous analysis of these alternatives would then aid the
researcher in finding the best concordance between models and data.
V. DMR AND ITS DETECTION IN AMETACOMMUNITY
So far we have summarized the potential mechanisms and statistical tools
available to explain and characterize DMRs. In this section, we attempt to
illustrate the previously discussed variation in DMR with real data, as well as
to estimate the effect of the selected approach on the observed pattern.
