1
Predator-prey mass ratio
2
Predator-prey mass ratio (PPMR) is a key parameter in size-based food-web
3
studies (e.g., Brose et al. 2006; Maury et al. 2007; Blanchard et al. 2009; Hartvig et al.
4
2011). Here we explain in detail how to evaluate PPMR for the three definitions (i.e.,
5
species-averaged, link-averaged, and individual-link. First, species-averaged PPMR is
6
measured by using the mean body mass values of the predator and prey species:
7
species  averaged PPMR 
Mean mass of predator individual s of a species
Mean mass of the prey individual s of the predator species
8
Link-averaged PPMR also uses the mean body mass values of multiple individuals
9
within a species, but differs from species-averaged PPMR in that it uses the individual
10
body masses of predators and prey that actually consume or are consumed by the
11
interacting species:
12
13
14
link  averaged PPMR 
Mean mass of predator individual s that consumed a prey species
Mean mass of the prey individual s that were consumed by the predator species
Finally, individual-link PPMR considers each predation event and is defined as follows:
individual  link PPMR 
Mass of an indivudual predator t hat consumed a prey individual
Mass of the prey individual that was consumed by the predator individual
15
To take an example, suppose the following simple situation where three
16
individuals of one predator species feed on three individuals of two prey species, A and
17
B, (Fig S1). Dark and light grey circles indicate individual and species identity,
18
respectively. Arrows represent individual feeding links. Mi and mi denote individual
19
body masses of predator and prey, respectively. In this system, species-averaged PPMR
20
is calculated as
M1  M 2  M 3  / 3
m1  m 2  / 2
M1  M 2  M 3  / 3
and
m3
1
for two interspecific
M1  M 2  / 2
m1  m 2  / 2
21
interactions, respectively. Link-averaged-PPMR is calculated as
and
22
M3
for two interspecific interactions, respectively. Finally, individual-link PPMR is
m3
23
calculated as
M3
M1 M 2
,
, and
for three inter-individual interactions, respectively.
m1 m 2
m3
24
25
References
26
Blanchard, J. L., Jennings, S., Law, R., Castle, M. D., McCloghrie, P., Rochet, M.-J., &
27
Benoît, E. 2009 How does abundance scale with body size in coupled size-structured
28
food webs? J. Anim. Ecol. 78, 270-280. (DOI 10.1111/j.1365-2656.2008.01466.x)
29
Brose, U., Williams, R. J., & Martinez, N. D. 2006 Allometric scaling enhances stability
30
in
31
10.1111/j.1461-0248.2006.00978.x)
32
complex
food
webs.
Ecol.
Lett.
9,
1228-1236.
(DOI
Hartvig, M., Andersen, K. H., & Beyer, J. E. 2011 Food web framework for
33
size-structured
populations.
34
10.1016/j.jtbi.2010.12.006)
J.
Theor.
Biol.
272,
113-122.
(DOI
35
Maury, O., Faugeras, B., Shin Y.-J., Poggiale, J.-C., Ari, T.B., & Marsa, F. 2007
36
Modeling environmental effects on the size-structured energy flow through marine
37
ecosystems.
38
10.1016/j.pocean.2007.05.002)
part
1:
the
model.
Progr.
39
2
Oceanogr.
74,
479-499.
(DOI
40
Figure S1
Predator
M1
m1
41
M2
M3
m2
Prey species A
m3
Prey species B
3