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and Warren (2007)
, whereby the value for individual-link PPMR was compa-
rable with link-averaged PPMR. Second, the species-averaged PPMR value
was similar to the link-averaged PPMR, whereas
Woodward and Warren
(2007)
showed that the former was lower by about one order of magnitude
than the latter. We observed that individual-predator PPMR was lower by
about one order of magnitude than individual-link PPMR, while having a
similar value to link-averaged PPMR. However, this pattern cannot be di-
rectly compared with that of
Woodward and Warren (2007)
, because they
provided individual-predator PPMR of a single predator, rather than of all
predators in the community.
B. Mechanisms
What mechanism makes a PPMR value higher or lower than another PPMR?
Why are the patterns that are observed different between studies? Here, we
show that there are two potential major effects, specifically averaging and
sampling effects. We show that these effects may generate variation among
different PPMR definitions, and we suggest that the combination of the two
effects may have led to the difference between the earlier study (
Woodward and
Warren, 2007
)andours.
Woodward and Warren (2007)
attributed the lower
value for species-averaged PPMR to the averaging effect. Species-averaged
PPMR assumes that all sizes of a predator population feed equally on prey of
all sizes. However, this is unlikely when evaluating the other definitions of
PPMR, because in reality, intraspecific variations exist in predator-prey inter-
actions. In particular, smaller predator individuals are unlikely to consume
larger prey individuals. The averaging effect arises from unrealistic links be-
tween smaller predator and larger prey that are inevitably incorporated in the
procedure of species averaging and may lead to the underestimation of PPMR
(
Woodward and Warren, 2007; Yvon-Durocher et al., 2011b
).
Yet, their explanation of the averaging effect is based on a verbal model,
and more formal arguments would be required to confirm the logic. More
importantly, the averaging effect may not be the only effect making PPMR
scale-dependent. In fact, the species-averaged and link-averaged PPMRs had
similar values in our analysis (
Figure 2
), indicating that there may be a
counter-effect to increasing the former PPMR and compensating for the
averaging effect. As a result, it is still uncertain whether species averaging
always results in lower PPMR values. Here, using simple mathematics and
numerical simulations, we illustrate that species averaging may, or may not,
result in lower PPMR and that the sampling effect also plays a major role.
Suppose that species-averaged and individual-predator PPMRs of the
same predator species feeding on a prey species are compared. For simplicity,
we assume that body-mass variation does not exist in prey that interact