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m
i
100
Species-averaged PPMR is lower
80
n
i
60
40
r
i
20
0
12345
6789 0
100
Individual-predator PPMR is lower
80
60
40
20
0
1
2345
Individual identity
i
6789 0
Figure 3
Example distributions of body mass m
i
, prey count n
i
, and PPMR r
i
of
predator individuals within a species when the inequality
(4)
is (upper) satisfied and
(lower) not. Solid, dashed, and grey lines indicate m
i
, n
i
, and r
i
, respectively. We
randomly assigned values between 10 and 100 to the parameters of 10 predator
individuals, with the assumptions that larger individuals have more prey in the guts
and that larger values of PPMR (i.e. m
i
1
m
i
, n
i
1
n
i
, and r
i
1
r
i
).
relationship between individual body mass m
i
and PPMR r
i
(e.g. random),
individual-predator PPMR may be lower than the species-averaged PPMR.
We may easily identify these counter-examples through numerical experi-
ments (
Figure 3
).Next, let us consider the comparison of individual-preda-
tor and species-averaged PPMRs at the community level. Suppose that
predator species j has individual-predator PPMR
R
j
and consists of
N
j
individuals, and that S predator species are included in the data (i.e. j
r
¼
1
to S). The species-averaged and individual-predator PPMRs of the com-
munity are calculated, respectively, as
¼
