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log 10 (predator mass) and log 10 (PPMR) is positive (or negative) and that the
predator species feeds on relatively larger (or smaller) prey as it grows. A
zero slope means no change in relative prey size during individual growth,
suggesting no intraspecific variation in PPMR. The analysis revealed that
there were significant interspecific differences in the regression slope at sites
16, 18, and 20 ( Figure 5 ). The most distinct differences were again found at
site 20, including the largest sample size ( Table 1 ). The species specificity of
the slope may become clearer if sufficient data were available for the other
sites.
C. Application
We have argued (see Section III.C ) that the species-based allometric and
size-based spectrum models should employ species-based (species-averaged
or link-averaged PPMR) and individual-based (individual-predator or indi-
vidual-link) PPMRS, respectively. The present analysis evaluates how these
PPMRs could be improved by including the effects of species identity and
body size. First, it is necessary to incorporate the body-mass effects on
PPMR, irrespective of the type of model being used. Given that prey-
predator interactions occur at an individual level, the fact that individual-
based PPMRs are improved by incorporating the body-size effect might
indicate that PPMRs affect trophic interaction-related behaviour in a non-
linear way. Further, the incorporation of species-averaged body mass
improves the explanation of species-based PPMRs ( Table 2 ). This means
that PPMR should be size dependent in species-based allometric food-web
models that omit intraspecific variation. We also showed both body mass
and species identity are crucial, especially for individual-predator and indi-
vidual-link PPMRs ( Table 2 ), from which it may be inferred that size-based
community-spectrum models should incorporate both species-identity and
body-mass effects.
Our argument, in part, counters the initial motivation of constructing
size-based community-spectrum models, which aimed to reduce the com-
plexity of size-structured food webs by overlooking interspecific variability.
However, we recommend that the incorporation of both species identity
and body-mass effects would provide the most useful inferences from which
future research could better understand and predict food-web dynamics.
Indeed, this line of argument has also been presented in the recent study of
functional response (e.g. Brose et al., 2008b; Rall et al., 2011; Vucic-Pestic
et al., 2010 ) and food-web modelling (e.g. Andersen and Beyer, 2006;
Blanchard et al., 2009; Hartvig et al., 2011 ). An important question to be
addressed in future studies is which approach is better, species-based allo-
metric modelling or size-based spectrum modelling. We cannot yet answer
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