Table A1. Summary of the variables used/calculated by the model. User: Parameters set by the
user before running the simulations. Model Structure: These variables are set automatically when
the initial species abundances are generated according to the model structure. Simulation: These
variables change constantly during the simulation.
Variable
Number of time steps
Initial number of species
Final number of species
Initial number of basal species
Number of top species
Number of intermediate species
Number of basal species
Number of herbivores species
Number of carnivore species
Number of omnivore species
Number of species presenting cannibalism
Fraction of top species
Fraction of intermediate species
Fraction of basal species
Fraction of herbivore species
Fraction of omnivore species
Fraction of carnivore species
Fraction of caníbal species
Initial Mean Trophic Level
mean trophic level
Standard Deviation of trophic level
maximum trophic level
Links between top and intermediate species
Links between top and basal species
Links between two intermediate species
Links between intermediate and basal species
links per species
Links
Standard Deviation of linkedness
Initial Connectance
Final connectance
clustering coefficient
Standard Deviation of generality
Standard Deviation of vulerability
mean chain length
Standard Deviation of chain length
maximum chain length
Type of Functional Response
Predator Interference
Carrying capacity
Metabolic type
size ratio
mean Amplitude
mean Biomass
mean Standard Deviation
mean Variance
mean CoVariance
Abbreviation
Type
t
S0
S
B0
T
I
B
Herb
Carn
Omn
Can
%T
%I
%B
%Herb
%Omn
%Carn
%Can
TL0
TL
TL.SD
TLmax
links ti
links tb
links ii
links ib
L/S
L
LinkSD
C0
C
Cl
GenSD
VulSD
ChLen
ChSD
ChMax
F
c
K
User
User
Simulation
User
Model Structure
Model Structure
User
Model Structure
Model Structure
Model Structure
Model Structure
Model Structure
Model Structure
User
Model Structure
Model Structure
Model Structure
Model Structure
Model Structure
Simulation
Simulation
Simulation
Model Structure
Model Structure
Model Structure
Model Structure
Model Structure
Simulation
Simulation
User
Simulation
Simulation
Simulation
Simulation
Simulation
Simulation
Simulation
User
User
User
User
User
Simulation
Simulation
Simulation
Simulation
Simulation
Ampli
Biom
StnDv
Var
CoVar
1
Table A2. Pearson correlation and p-value when comparing the response variables (Normalized
Biomass Size-Spectra slope = NBSS slope, and the Pareto Shape Parameter = Pareto’s ) against
the predictor variables not considered in main manuscript. n = 10000
Variable
S
T
I
B
Herb
Omn
Can
%T
%I
%B
%Herb
%Omn
%Can
TL
TL.SD
TLmax
links ti
links tb
links ii
links ib
L/S
L
LinkSD
Cl
GenSD
VulSD
ChLen
ChSD
F
Ampli
Biom
StnDv
Var
CoVar
NBSS slope
Correlation
p-value
-0,2861452
3,20E-121
0,07304625
4,66E-09
-0,2367817
1,67E-82
0,00922782
0,45979028
0,02882955
0,02089839
-0,1624816
3,19E-39
-0,1214539
1,59E-22
0,17046541
4,71E-43
-0,1854501
9,16E-51
0,13165274
3,25E-26
0,12507476
8,44E-24
-0,0990854
1,77E-15
-0,0903862
4,01E-13
-0,1541852
1,91E-35
-0,1772246
1,91E-46
-0,1865681
2,29E-51
-0,0258827
0,03811346
0,10436868
5,15E-17
-0,1582907
2,74E-37
-0,0778394
4,25E-10
-0,1087184
2,45E-18
-0,1493312
2,49E-33
-0,0194655
0,11890246
-0,0637726
3,64E-07
0,014704
0,23883695
0,14991399
1,40E-33
-0,1290439
3,05E-25
0,13738529
2,02E-28
0,11240874
1,67E-19
-0,1635813
9,72E-40
-0,2216094
3,03E-72
-0,1612042
1,26E-38
-0,0674442
6,35E-08
0,11721381
4,44E-21
Pareto’s 
Correlation
p-value
0,24352551
2,64E-87
-0,0313998
0,01187497
0,16929654
1,76E-42
0,03533975
0,00463003
0,01222568
0,32740674
0,10614443
1,51E-17
0,07554268
1,36E-09
-0,1164197
8,17E-21
0,11684958
5,88E-21
-0,0729914
4,78E-09
-0,0713802
1,03E-08
0,04328502
0,00052262
0,04427245
0,00038802
0,09165888
1,87E-13
0,12256121
6,54E-23
0,13824015
9,28E-29
0,02089427
0,09415467
-0,0615421
8,04E-07
0,09582962
1,43E-14
0,06701184
7,71E-08
0,05555651
8,44E-06
0,09655145
9,03E-15
0,03211545
0,01007602
0,01210397
0,33478269
0,00454284
0,71593498
-0,1083106
3,27E-18
0,07132119
1,06E-08
-0,0764029
8,84E-10
-0,098463
2,65E-15
0,10566652
2,10E-17
0,14889402
3,83E-33
0,10384871
7,36E-17
0,04010906
0,00130831
-0,0758892
1,15E-09
2
Figure A1. Tree plot resulting from the Partition analysis performed considering
the slope of the normalized biomass-size spectra (NBSS) as the response variable,
and all the topological network parameters of the food-webs as predictor factors
(only the variables chosen by the analysis are shown). Overall rNBSS2 = 0.594.
3
Figure A2. Tree plot resulting from the Partition analysis performed considering
Pareto’s shape parameter  as the response variable, and all the topological
network parameters of the food-webs as predictor factors (only the variables
chosen by the analysis are shown). Overall rPareto2 = 0.519.
4
Some definitions and formulations related to the
model
The food-web models were built considering virtual allometrically derived species
(VADS), i.e. aggregation of individuals with the same body size, independent of
their taxonomy, and sharing the same set of predators and prey.
A top VADS is a predator that has no predator. An intermediate VADS is a
VADS that is both a predator and a prey. A basal VADS is a prey that has no
prey. The numbers of basal, intermediate, top, and all VADS in a web are denoted
by b, i, t, and S.
Cannibalism (Can) is the act of one individual of a VADS consuming all or part
of another individual of the same VADS as food. Size structured cannibalism, in
which large individuals consume smaller conspecifics, is more common.
Omnivores (Omn) is the fraction of VADS that consume two or more VADS and
have food chains of different lengths (where a food chain is a linked path from a
non-basal to a basal VADS).
Herbivores (Herb) is the fraction of VADS that feed exclusively on basal VADS.
Carnivores (Carn) is the fraction of VADS that feed exclusively on non-basal
species.
The number and proportion of top (t/S), intermediate (i/S), basal (b/S), herbivores
(Herb/S), carnivores (Carn/S), omnivores(Omn/S) and cannibals (Can/S) are
calculated considering that for all the cases the total number of VADS is S.
We calculated a trophic level measure called the mean ‘short-weighted trophic
level’ (TL) (Williams & Martinez 2004). For a particular taxon, short-weighted
5
trophic level is the average of ‘prey-averaged trophic level’ (1 plus the mean
trophic level of all the taxon’s trophic resources) and ‘shortest trophic level’ (1
plus the shortest chain length from the consumer taxon to a basal taxon).
S
TL j  1   lij
i 1
TLi
nj
where nj is the number of prey species in the diet of species j, lij represents the
links between the species i and j in a food web with S species.
A trophic link (hereafter, link) is any reported feeding or trophic relation
between two VADS in a web. For example, a link between a top and an
intermediate VADS is denoted as t-i and a link between two intermediate VADS
as i-i.
Connectance (C) is the proportion of realized links within the food webs,
calculated as the number of actual links (L) divided by the squared number of
VADS (S), which gives the number of possible links within a network.
CL
S2
This is considered a standard measure of food-web trophic interaction richness, as
well as the links per VADS (L/S), which equals the mean number of VADS’
predators plus prey, also referred to as link density.
Other concepts related to the connectance are the Clustering coefficient (Cl), i.e.,
the average fraction of pairs of VADS one link away from a VADS that are also
linked to each other, and the SD linkedness, i.e., the variation of the overall
number of links.
6
The standard deviation of mean generality (GenSD) and vulnerability (VulSD),
quantify the respective variabilities of VADS' normalized prey (Gi) and predator
(Vi) counts (Williams & Martinez 2000).
Gi 
1 s
a ji
L 
j 1
S
Vi 
1 s
aij
L 
j 1
S
Normalizing with L/S makes standard deviations comparable across different
webs by forcing mean Gi and Vi to equal 1.
Functional Response type:
Several function response models have been proposed, all of these models have
deficiencies that affect their utility (Gutierrez 1996). We employ here the Holling
model that considers a (constant) population of N identical individuals which can
engage in only two activities: searching for food and handling a recently found
item (Gurney & Nisbet 1998). It is assumed that while an organism is handling a
food item it cannot continue to search, so the length of time required to process
each item sets an upper limit to the rate at which food can be consumed. Holling
argued that as prey density increases, search becomes trivial, and handling (time
the predator spends pursuing, subduing and consuming each prey item it finds,
and then preparing itself for further search) takes up an increasing proportion of
the predator’s time (Begon, Mortimer & Thompson 1996).
Predator Interference (c) is the degree to which individuals within population i
interfere with one another’s consumption activities, which reduces i’s per capita
consumption if c>0 (Brose et al. 2006). If there are many predators, all
concentrated within profitable patches, they remove prey rapidly thus reducing the
profitability of those patches. Thus, in general, we can expect the apparent
attacking efficiency to decrease as predator density increases (Begon et al. 1996)
7
Carrying capacity: carrying capacity of logistic growth: the population size at
which competition is so great, and net reproductive rate so modified, that the
population replace itself each generation (Begon et al. 1996).
Biological rates: the biological rates of production, R, metabolism, X, and
maximum consumption, Y, follow negative-quarter power–law relationships with
the species’ body masses:
RP = a y M P0.25
X C =a x M −C0. 25
Y C =a y M −C0 . 25
where ar, ax and ay are allometric constants and the subscripts C and P indicate
consumer and producer parameters, respectively (Yodzis and Innes 1992). The
time scale of the system was defined by normalizing all rates according to the
growth rate of the basal population, and the maximum consumption rates were
normalized by the metabolic rates:
r i= 1
X
a M 
xi  C  x  C 
RP
ar  M P 
yi=
0.25
Y C ay
=
X C ax
Inserting these three equations into eqs. 2 and 3 (of Main Document) yields a
population dynamics model with allometrically scaled parameters. The constants
used (yj = 4 for ectotherm vertebrates and yi = 8 for invertebrates; eij = 0.85 for
carnivores and eij = 0.45 for herbivores; K = 1; ar = 1; ax = 0.314 for invertebrates
8
and ax = 0.88 for ectotherm vertebrates) are consistent with prior studies (Brose et
al. 2006; Otto et al. 2007; Rall et al. 2007; Brose 2008).
References
Begon M, Mortimer M, Thompson D (1996) Population Ecology: A Unified Study of Animals and
Plants. 3rd edn. Wiley-Blackwell, UK.
Brose U (2008) Complex food webs prevent competitive exclusion among producer species. Proc
R Soc Lond B Biol Sci 275:2507–2514.
Brose U, Williams RJ, Martinez ND (2006) Allometric scaling enhances stability in complex food
webs. Ecol Lett 9:1228-1236.
Gurney WSC, Nisbet RM (1998) Ecological Dynamics. Oxford University Press, USA.
Gutierrez AP (1996) Applied Population Ecology: A Supply/Demand Approach. John Wiley &
Sons, New York, USA.
Otto SB, Rall BC, Brose U (2007) Allometric degree distributions facilitate food-web stability.
Nature 450:1226–1229.
Rall BC, Guill C, Brose U (2007) Food-web connectance and predator interference dampen the
paradox of enrichment. Oikos 117(2):202–213.
Williams RJ, Martinez ND (2000) Simple rules yield complex food webs. Nature 404:180–183.
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theory and data. Am Nat 163:458-468.
Yodzis P, Innes S (1992) Body size and consumer-resource dynamics. Am Nat 139:1151–1175.
9