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more resources until all preys are available. A lower limit to handling and
consume prey could also be considered. However, as this lower limit typically
increases with body size at lower rates than the upper limit (e.g.
Cohen et al.,
1993, 2003
), for the actual formulation, we focus on the upper constrain
without loss of generality. Prey distribution can be modelled as one or several
normal distributions on log scale—or any other distribution type. The cu-
mulative probability distribution of prey directly estimates the fraction of all
resources that a predator of a given size can consume. So f(M) can be
estimated as
R
m
¼
ðÞ¼
ðÞ
R
T
where R
T
is the total amount of resources present in the community and
CDF is the cumulative density function for a normal distribution, with mean
and standard deviation of the prey distribution evaluated in m. Fitting a
normal distribution from a real community provides a close estimation of the
proportion of prey that predators of different sizes can consume (see
Figure 1
). We can incorporate the change in the amount of available
resources with body size in Eq.
(2)
fM
CDF m
R
T
a
1
M
a
exp E
D
CDF m
ðÞ
ð
kT
Þ
ð
3
Þ
=
Cumulative probability is a monotonic increasing function, and as a conse-
quence, access to new resources with increasing body size counteracts the rise
in energetic demands. If the increase in resources is larger than that in
metabolic demand even a positive DMR can be expected. A component of
several DMRs previously reported is a positive relationship, at least within
some ranges of body sizes (
Blackburn and Gaston, 1997; Gaston, 2000
).
However, few studies have made an explicit analysis of this component of
the DMR (
Ackerman et al., 2004; Reuman et al., 2009
).
Consumption of individuals has the potential to reduce prey density. If the
predation rate experienced by a population changes with body size, it should
also be considered as a determinant of the DMR. The counterpart of gape
limitation is a reduction in predation pressure as individuals become larger
(
Hopcraft et al., 2009; Sinclair et al., 2003
). However, predators can also
exhibit a preference for larger prey (
Mittelbach, 1981; Schmitt and
Holbrook, 1984; Werner and Hall, 1974
). In addition, it was reported an
increase in the number of parasites and diseases with the body size of
potential host (
Lafferty et al., 2006, 2008
). All these empirical patterns
indicate that the degree of consumption experienced by a population is
affected by the body size of its individuals. Predation can be incorporated
as an increase in the energetic cost of having an individual in a population.
If half of the individuals are consumed each time, it is necessary to use twice
the energy to maintain one individual in the population. In general, it can be
assumed that the amount of energy required for an individual to persist in the
