Geoscience Reference
In-Depth Information
to access more resources (
Arim et al., 2010; McCann et al., 2005; Rooney
et al., 2008
). A reduction in the slope at larger sizes can be captured by the
function (see
Packard et al., 2010
)
aM
a
D
¼
D
0
þ
ð
6
Þ
These functions are presented in
Figure 5
. In some cases, a change in the slope
sign can occur. Under this circumstance, a second-order polynomial fit with
maximum (minimum) values within the range of body sizes considered prob-
ably represents the best approach (
Reuman et al., 2009
). The main concern
about polynomial fit is that parameters lack a clear biological interpretation
(
Packard et al., 2010
). However, a polynomial in the form D
cM
2
¼
a
þ
bM
þ
has either a maximum or a minimum value at M
b/2)c, which is
a biologically meaningful parameter because is estimating the value of
body size at which a transition between a positive and negative DMR is
occurring.
An additional topic to consider in this analysis is which variable (body size
or abundance) is plotted in the ordinate and which in the abscissa, two
approaches that have been widely used in the literature, but without thor-
ough discussion (
Cohen and Carpenter, 2005
). Switching dependency be-
tween both variables should not affect parameter estimation when no
random variation exists in the relationship, but this is clearly not the case
in most of the reported patterns (
Cohen and Carpenter, 2005
). Reduced
major axis (RMA) regression, major axis (MA), or OLS-bisector methods
do not need the specification of the causal direction and do not require the
¼
(
−
Mc
M
æ
P
(
M
)
∝
M
−
a
⋅
exp
-
0.5
D
=
D
0
+
aM
a
D
=
aM
a
-
1.0
-
1.5
-
2.0
1.0
1.5
2.0
2.5
3.0
3.5
4.0
Figure 5
Deviations from power-law regimes at larger sizes and equations that can
be used to estimate these trends.
