Supplementary Material
Appendix S1. Estimation of RPIk values.
Let us assume an assemblage of S predator species, in which the diet of predator k (k
= 1, 2, ..., S) is composed by nk  n prey categories (where n is the total number of prey
categories consumed by the whole assemblage), each comprising a proportion pik of
predator diet (i = 1, 2, ...., n). Because model M3 considers all predators as functionally
equivalent, the consumption probability of a given prey category (i) is proportional to its
relative use by the whole assemblage, which in nonrandom cases should be equal to its
relative consumption by each predator. Then, values of i are estimated as the sum, across S
predator species, of the pik values weighted by the relative impact of each predator on prey
populations (RPIk), resulting in the expression in the numerator of eqn 4 (see main text).
The net impact of predator k should be proportional to its abundance in the field and
to the amount of prey needed by an individual predator to survive and reproduce. Then, the
relative impact of each predator on prey populations is estimated as:
A k  DFR k
RPI k  S
 A k  DFR k
eqn S1
k 1
where Ak and DFRk are the abundance and daily food requirement of predator k,
respectively, obtained as follows:
Ak: We have no direct estimation of predator abundance for the entire study period, but we
do so for the last four years (2001 to 2004). The minimum numbers of individuals of F.
sparverius and P. culpaeus at El Cobre ravine come from direct observations. For owls, it is
estimated as the maximum value between the minimum number of individuals sighted and
the minimum number of individuals heard during playback censuses. These estimates and
the numbers of pellets/faeces collected were obtained monthly and averaged for autumn
(April-June), winter (July-September), spring (October-December) and summer (JanuaryMarch). For each predator, these variables (plus the mean number of active scent stations
for P. culpaeus) were included in alternative Structural Equation Models (SEM, Shipley
2000) that considered the actual abundance as its parental latent variable (Fig. S1). The
inclusion of the latter as a latent variable in a SEM yields less biased estimates than using
the minimum abundance in an ordinary multiple regression model (Shipley 2000). To
express this variable in units of minimum number of individuals at the study area (a
measure comparable among species), the coefficient corresponding to the path between that
variable and the minimum abundance (Fig. S1) is fixed at 1 = 1 (Shipley 2000). Models
also include two environmental variables that could affect the abundance of predators
and/or the likelihood of finding pellets or faeces in the field: mean temperature and total
rainfall. These variables improve the estimate of abundance and avoid the structural underidentification of the model due to low ratios between the numbers of manifest variables and
parameters to estimate (Shipley 2000). The alternative SEMs for each predator species
differ in the way that these two environmental variables are hypothesised to affect all the
others mentioned above. They are fitted by means of maximum likelihood methods, and the
best model for each predator species is determined using Akaike’s Information Criterion
(AIC, Richards 2005). Path coefficients of selected SEMs are used to construct equations to
convert the number of collected faeces/pellets into predator abundance for those years with
unavailable direct estimates (see Fig. S1). Analyses are performed using the sem package
for R 2.2.0 (R Development Core Team 2005) and the SEPATH module for Statistica 5.1
(StatSoft Inc. 1997). With the latter software, analyses are conducted on distribution
moments to obtain intercept values for structural equations (StatSoft Inc. 1997). Due to its
sporadic occurrence (range = 1 to 2 individuals), we could not obtain an equation for F.
sparverius, and thus we used the mean number of recorded individuals (1.4) as an estimate
of its abundance whenever detected. Finally, the estimated abundance values for each
predator are averaged for non-breeding (autumn + winter) and breeding (spring + summer)
biological seasons of each year, and transformed into relative abundance.
DFRk: The daily food requirements of predator species are obtained from their expected
field metabolic rate (FMRk) and from published data on the metabolisable energy available
in one gram of food dry-matter (AMEk) and the mean water content of food (WCk), as:
DFR k 
FMR k
AME k  1  WC k 
eqn S2
FMRk values are estimated as recommended by Nagy et al. (1999), using an allometric
relationship of the form: FMR k  a W bk ; where W k is the mean body mass of predator k,
and a and b are scaling coefficients obtained from published data (Jaksic et al. 1996, Nagy
et al. 1999). For birds of prey, we use two different sets of scaling coefficients for nonbreeding and breeding seasons. Because Nagy et al. (1999) found no differences due to
reproductive condition in mammals, we use a single set of scaling coefficients for the fox
P. culpaeus, based on information for canids. Values for all these variables are listed in
Table S1.
Table S1: Information used to estimate the daily food requirement of predators at El Cobre
ravine. The first four columns show data extracted from bibliography, and the latter two
show data estimated here. Headers are: W k : mean body mass; a and b: scaling coefficients
for the allometric equation FMR k  a W bk ; AMEk: mean metabolisable energy available in
one gram of food dry matter; WCk: mean water content in food; FMRk: expected field
metabolic rate; DFRk: expected daily food requirement; gfdm: grams of food dry matter, gw:
grams of water, gf: grams of food. Values without and within parentheses correspond to the
non-breeding and breeding seasons, respectively.
Species
Wk
(g) (a)
a
b
AMEk
(kJ/gfdm)
P. culpaeus
4317
0.25 (b)
0.89 (b)
16.9 (d)
F. sparverius
116 

81 

247 

307 

1227 
G. nanum
A. cunicularia
T. alba
B. magellanicus
(a)
10.5
(c)
(13.8)
0.68
(c)
(0.65)
18 (e)
WCk
(gw/gf)











0.7
(f)
FMRk
(kJ/day)
DFRk
(gf/day)
2970.7
585.9
267.4
49.5
(303.2)
(56.2)
209.4
38.8
(240.1)
(44.5)
447.3
82.8
(495.6)
(91.8)
518.7
96.1
(570.9)
(105.7)
1332.6
246.8
(1404.8)
(260.2)
values from Jaksic et al. (1996)
values calculated from data for canids (n = 6, R2 = 0.99) in Nagy et al. (1999)
(c)
coefficients for birds and values for (d) carnivores, (e) insectivorous birds and reptiles, and (f)
animal prey given by Nagy et al. (1999)
(b)
Fig. S1: Directed graph illustrating the Structural Equation Models used to estimate
predator abundance from the number of pellets/faeces. Boxes are manifest (measured)
variables (MT: mean temperature, RF: mean accumulated rainfall, MN: minimum number
of predators in the study area, PF: number of pellets/faeces collected, SS: number of active
scent stations [only for the fox P. culpaeus]). The actual predator abundance (AB, ellipse)
is a latent (unmeasured) variable. When necessary, AB and MN are log-transformed and PF
is square root-transformed to improve linearity. Similarly, MN and RF are always log- and
square root-transformed, respectively. i, 2 i,  and  i are path coefficients, variances,
correlation coefficients, and error terms, respectively. Symbols in bold indicate fixed
parameters. Segmented box and arrows indicate variables and parameters not included in
all selected models (5 and 6 are never included together). Other direct effects of MT and
RF on MN, PF and SS were also tested, but were not significant for any selected model.
Equations below are: (a) structural equation for the number of pellets/faeces, (b) resulting
equation to estimate AB from PF, after reordering terms in (a).