Geoscience Reference
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communities ( Carbone and Gittleman, 2002; Damuth, 1981, 1987 ), and also
for population level studies designed for the analysis of self-thinning process-
es, where changes in species or guild density are related to the mean size of its
individuals ( Latto, 1994; Yoda et al., 1963 ).
Most studies working with these bivariate relationships usually fit a linear
regression to the DMR by OLS after log-transforming data, taking the slope
as a confident estimate of the scaling parameter. However, the statistical
approaches available to perform this kind of analysis have become the focus
of attention to researchers only in the past few years ( Cohen and Carpenter,
2005; Martin et al., 2005; Packard, 2009; Packard and Birchard, 2008;
Packard et al., 2010; Reuman et al., 2009 ), and some attention has been
called to its drawbacks. The use of OLS involves some assumptions about
data structure: normality, homoscedasticity, and independence of residuals
in addition to linearity in the relationship between variables and lack of error
in the measurement of independent variables ( Cohen and Carpenter, 2005;
Neter et al., 1996; Sokal and Rohlf, 1995 ). Failure to properly fulfil these
assumptions can seriously undermine the estimation of parameters and their
biological interpretation ( Packard, 2009; Packard et al., 2010; Reuman et al.,
2009 ). Log-transforming data is expected to linearize the DMR when it
follows a power-law function. If this is the case, the transformation could
improve the statistical analysis and visualization of the relationship ( Packard
et al., 2010 ). However, accurate estimation of parameters is restricted to cases
that are well described by a power function with a correlation close to 1 (see
Packard, 2009; Packard et al., 2010 ). The fit of non-linear statistical models
to arithmetic values could represent a better approach ( Caruso et al., 2010 ),
but care should be taken to account for heteroscedastic residuals, a situation
which is common in allometric relationships ( Packard et al., 2010; Zuur et al.,
2009 ). In biology, an important source of non-independent observations is
the common shared phylogenetic history (e.g. Henri and vanVeen, 2011 ).
However, phylogenetic independent contrasts have rarely been used. Thus,
reported parameters can be biased by unaccounted errors coming from
phylogenetic correlates (e.g. Arneberg et al., 1998 ).
When polynomial fit detects non-linearity, the next step could involve the
fit of an alternative function ( Neter et al., 1996 ). Many deviations from
power-law distributions are adequately captured by a truncated power-law
distribution ( Albert and Barab´si, 2002; Bascompte and Jordano, 2007 )
M a exp
M
Mc
ð
Þ
PM
ðÞ/
5
This distribution has an exponential cut-off at high mass values, indicated by
an increase in slope steepness of the DMR. However, the opposite pattern
could also be expected, for example, when large animals have better chances
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