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Processes entangling interactions in communities: forbidden

links are more important than abundance in a hummingbird−
plant network
Jeferson Vizentin-Bugoni, Pietro Kiyoshi Maruyama and Marlies Sazima
Proc. R. Soc. B 2014 281, 20132397, published 19 February 2014

Supplementary data "Data Supplement"

http://rspb.royalsocietypublishing.org/content/suppl/2014/02/13/rspb.2013.2397.DC1.h
tml

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Processes entangling interactions in

communities: forbidden links are more
important than abundance in a
rspb.royalsocietypublishing.org
hummingbird – plant network
Jeferson Vizentin-Bugoni1, Pietro Kiyoshi Maruyama1 and Marlies Sazima2
1
Pós-graduação em Ecologia, Instituto de Biologia, and 2Departamento de Biologia Vegetal, Instituto de
Biologia, Universidade Estadual de Campinas, Sao Paulo, Brazil
Research
Understanding the relative importance of multiple processes on structuring
Cite this article: Vizentin-Bugoni J, species interactions within communities is one of the major challenges in ecol-
Maruyama PK, Sazima M. 2014 Processes ogy. Here, we evaluated the relative importance of species abundance and
entangling interactions in communities: forbidden links in structuring a hummingbird–plant interaction network
from the Atlantic rainforest in Brazil. Our results show that models incorpor-
forbidden links are more important than
ating phenological overlapping and morphological matches were more
abundance in a hummingbird – plant network.
accurate in predicting the observed interactions than models considering
Proc. R. Soc. B 281: 20132397. species abundance. This means that forbidden links, by imposing constraints
http://dx.doi.org/10.1098/rspb.2013.2397 on species interactions, play a greater role than species abundance in
structuring the ecological network. We also show that using the frequency
of interaction as a proxy for species abundance and network metrics to
describe the detailed network structure might lead to biased conclusions
Received: 13 September 2013 regarding mechanisms generating network structure. Together, our findings
Accepted: 21 January 2014 suggest that species abundance can be a less important driver of species
interactions in communities than previously thought.

Subject Areas: 1. Introduction

ecology To understand the processes structuring the interactions in ecological communities
remains one of the major challenges in ecology. Considering interacting species as
Keywords: complex networks has revealed some prevalent patterns for key interactions in
communities, such as the skewed distribution of the number of interacting partners,
Atlantic rainforest, morphological match,
nestedness and the asymmetry in the strength of the interactions [1]. These patterns
neutral-based processes, phenological overlap, have important implications for community dynamics [2] and may be driven by
plant – pollinator networks many different, but not mutually exclusive processes. Prevalent patterns in ecologi-
cal networks can be generated by random interaction among species as well as by
phenotypic mismatches influenced by the phylogeny (e.g. morphology, phenology
and spatial distribution), which characterize the forbidden links [1,3–9].
Author for correspondence:
The previous findings on the role of these numerous factors now lead to the
Jeferson Vizentin-Bugoni intense debate on the relative importance of neutral- and niche-based processes
e-mail: jbugoni@yahoo.com.br to the structure of ecological networks [5,10]. In the context of ecological net-
works, neutral-based processes (often treated as neutrality, [9]) presume that
species are ecologically equivalent. This means that individuals interact ran-
domly in the community independently of their traits (specializations), thus
more abundant species interact with more partners and with higher frequency
than rarer species [8–12]. On the other hand, the concept of forbidden links
assumes that niche-based processes constrain the interactions by means of
matches and mismatches on the ecological traits of species [1,3–6,9,10,13].
Previous studies have found that species abundance has a major role in deter-
mining how interactions are structured in different ecological networks, including
Electronic supplementary material is available positive interactions such as plant–pollinators [9,14] and plant–plant facilitation
[15], commensalistic interaction among epiphytes and phorophytes [16] or antag-
at http://dx.doi.org/10.1098/rspb.2013.2397 or
onisms between plant–herbivores and hosts–parasitoids [12,17]. These studies
via http://rspb.royalsocietypublishing.org. also showed that the observed interactions are better predicted by simulations
when other factors are included together with the abundance, such as phenological

& 2014 The Author(s) Published by the Royal Society. All rights reserved.
 Downloaded from rspb.royalsocietypublishing.org on March 26, 2014

overlap [9,11,12], morphological matches among species [14] or the canopy were considered only when their flowers were visible 2
the phylogenetic relationship, which ultimately influences the from the ground. For mass-flowering species with hundreds of
flowers per individual (e.g. Erythrina speciosa), we estimated the

rspb.royalsocietypublishing.org
traits of the species [15]. In this sense, species traits affect the
possibility of interactions by creating forbidden links in the com- mean number of flowers per inflorescence, and then multiplied
this by the number of inflorescences per individual. The total
munity, although their importance seems to be secondary in
number of flowers produced was considered as the abundance
comparison with species abundance.
of each plant species after verifying a strong and linear corre-
Despite the increasing consensus on the major role of species
lation between the total number of flowers produced and the
abundance in structuring different ecological networks, poss- number of individuals for each plant species in our data (see
ible limitations can be highlighted before achieving broader the electronic supplementary material, figure S2).
generalizations. Sampling insufficiency can pose misleading
interpretations, making difficult to discriminate unobserved
interactions owing to undersampling from truly forbidden (c) Phenology and abundance of hummingbirds

Proc. R. Soc. B 281: 20132397

links [13]. The lack of proper estimations of abundance can be We defined hummingbird phenology as the presence of each
another problem, because some studies have used the inter- species during each month of sampling, and abundance as the fre-
action frequency (extracted from the observed network) as a quency of species occurrence in the 60 days spent in the field
proxy for species abundance [8,9,18,19]. This procedure ignores during the study period (approx. 5 days per month). In order to
the intrinsic dependence between the frequency of interactions check whether the frequency of occurrence could be used as an
and the ‘abundance’ generated. Ideally, independent measures adequate measure of abundance, we compared it with the abun-
dance estimated through ‘line transect count’ [27] in 10 fixed
of abundance should be collected directly in the field while the
transects (100 m each) distributed in primary (approx. 47%) and
network data are collected [11]. Overcoming and investigating
secondary forest (approx. 32%), as well riversides (approx. 21%)
the effects of these limitations are then necessary steps towards along our study trails. Every month, we walked each transect
broader generalizations. for 10 min in the early morning, always keeping the same
Hummingbird interactions with their critical food resource, sampling sequence during the study period. To avoid counting
the flowers, are believed to be strongly influenced by the the same hummingbird individual more than once, transects
phenotype of both birds and plants, imposing constraints on were at least 100 m apart from each other, which ensured some
the interactions within communities [20–24] (but see [25] for spatial independence. We counted birds up to 3 h after the sunrise
a different perspective). Nevertheless, studies applying a net- and only during days without rain. The positive and linear
work approach to test the relative importance of abundance relationship between these two estimates (see the electronic
and forbidden links in structuring the interactions among supplementary material, figure S3) suggests that frequency of
occurrence adequately describes species abundance.
hummingbirds and plants are still missing. With this in
mind, we collected data on the interaction among humming-
birds and plants from the Atlantic rainforest in Southeast
Brazil to ask: (i) what are the relative importance of species
(d) Flower and bill morphology
We considered the corolla length as the primary constraint deter-
abundance, morphological match and phenological overlap
mining the ability of a hummingbird to access the nectar in
in predicting the frequency of pairwise interactions among the flower, and measured the effective corolla length [21] for
species in the network? (ii) Are the results obtained using all plant species. For each species, we measured between three
independently collected estimates of abundances the same as and 20 flowers, collected from different individuals.
using ‘abundances’ extracted from species interaction frequen- Hummingbirds’ bill lengths were measured from voucher
cies? (iii) Are abundance, morphology and phenology able to specimens in the zoological museums of the University of
predict network aggregate statistics? São Paulo and the University of Campinas. As hummingbirds
can project their tongues to drink nectar [28], bill measure-
ments that ignore tongue extension can underestimate the
bird’s capacity to access nectar. Because precise measurements
2. Material and methods of tongue length were unavailable for different hummingbird
species, we added one-third to the bill length for each species.
(a) Study area and data collection We consider this correction adequate, because it preserves the
We conducted fieldwork in the Santa Virgı́nia Field Station located proportion by which birds with longer bills also have longer
in Serra do Mar State Park (23817’–23824’ S and 45803’–458 11’ W) tongues [28].
in the state of São Paulo, Brazil (see the electronic supplemen-
tary material, figure S1). The study site has 17 500 ha of Atlantic
rainforest (montane ombrophilous dense forest—sensu [26]),
slope between 248 and 378 and is situated from 850 to 1100 m
(e) Plant –hummingbird interactions
The hummingbird –plant network was constructed from obser-
a.s.l. The region has high precipitation with mean annual rainfall
vations of legitimate visits (when hummingbirds contacted
higher than 2000 mm, always higher than 60 mm per month. We
the flower reproductive structures). For each flowering species,
collected data from September 2011 to August 2012, mostly
we conducted focal plant observations for 12 to 31 h, using
along 12000 m of field trails and dirt roads in the forest borders.
binoculars or video-cameras. Our observations totalled 881 h,
Sampling locations comprised primary forest (approx. 26%), sec-
during which we quantified the interactions between pairs of
ondary forest (approx. 54%) and forest borders, which included
hummingbird and plant species. Observations were conducted
riversides and roadsides (approx. 20%).
in at least two individuals for each plant species, and the use
of video-cameras was restricted to plant species that produced
(b) Flowering phenology and abundance of few flowers per individual in order to prevent any underestima-
tion of the interactions. Finally, we evaluated the sufficiency
hummingbird-pollinated plants of our sampling using individual-based rarefaction analysis
Every month, we counted all hummingbird-pollinated plants [29], applied to links in the network rather than in individual
flowering within 2.5 m of each side of the study trails. Plants in organisms [30].
 Downloaded from rspb.royalsocietypublishing.org on March 26, 2014

(f ) Determinants of the network: constructing (g) Comparing the ability of probability matrices to 3

interaction probability matrices predict observed interactions

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To evaluate the contribution of distinct determinants to the To evaluate whether abundance, phenological overlap and mor-
plant–pollinator network structure, we followed the conceptual phological match can predict detailed structure of the observed
framework developed by Vázquez et al. [9]. To assess whether fre- interaction matrix, we used a likelihood approach. If a probability
quency of interactions can be predicted by species abundance, matrix can predict the observed interactions, then cells with
morphology and phenology, the observed interaction matrix was higher probability in our models (probability matrices A, F, M,
compared with interaction probability matrices. These probability AF, AM, FM, AFM, NULL) would also have a higher number of
matrices were constructed from data on abundance, morphology interactions in the observed matrix (O). We used the Akaike infor-
and phenology of species, or a combination of them. In the follow- mation criteria (AIC) to evaluate the prediction ability of each
ing, we present a brief description of the analyses, detailing some model and DAIC to compare them. DAIC is the value obtained
modifications in relation to Vázquez et al. [9]. by subtracting the AIC of the best-fitting model from the AIC of

Proc. R. Soc. B 281: 20132397

Observed matrix (O): we constructed a quantitative plant– each model. As in Vázquez et al. [9], we assumed that the
pollinator matrix with rows corresponding to plant species (i) probability of interaction between a given plant and pollinator
and columns to pollinators ( j ). Each cell entry represents the followed a multinomial distribution. The likelihood was calculated
number of interactions recorded between a hummingbird and using the function dmultinom in the stats package in R [33].
plant species (oij). The number of parameters used to weight different models’
Probability matrix based on abundance (A): the abundance of complexities was defined as the number of species of each prob-
each plant species was multiplied by the abundance of each ability matrix included in the given model. In this sense, the
hummingbird species to generate a matrix representing the pro- models A, F and M, with nine pollinators and 47 plants, had 56 para-
duct of all plant and pollinator abundances. The cell values in meters (species), and by the same calculation, models AF, AM and
this matrix were normalized by dividing each cell by the FM had 112 (56 for each matrix) parameters. The most complex
matrix sum such that its elements totalled to one, resulting in a model AFM had 168 parameters from three matrices. The simplest
probability matrix A. This matrix can be considered a ‘neutral model ‘NULL’ was assigned with one parameter, because it was
model’ or ‘null model based on abundances’ [31], because by not properly based on a matrix. Using the number of species as a
ignoring phenotypic traits relevant for the interaction among parameter is more conservative than using the number of matrices,
species (e.g. phenology and morphology, which reflect species as done in Vázquez et al. [9], and our decision was intended to avoid
specializations), this matrix considers species to interact random- under-penalization of the most complex models. For the purpose of
ly, irrespective of their ecological differences. One important comparison, we also repeated the analyses using the number of
remark is that abundance is an emerging property at population matrices as parameters, but the results remained consistent (see
level that can be regulated by neutral processes, but also by the electronic supplementary material, figure S5).
species phenotypes and consequently niches [32]. In this sense,
the use of abundance does not mean an evaluation of the role
of purely neutral-based processes in structuring the communities (h) Is model selection biased by abundance measures?
and must be taken as a ‘neutral statistical model’ generator of In order to answer this question, we repeated the abovementioned
patterns, but which does not specify exactly the mechanism analysis considering the observed frequency of interaction as a
behind it [31]. proxy for species abundance, as often assumed in previous studies
Probability matrix based on phenological overlap (F): cell entry in [8,9,19]. The frequency of interaction of each hummingbird (h) was
phenological overlap matrix was expressed by the number of multiplied by the frequency of interaction of each plant species (p)
months in which a plant and a pollinator co-occurred. This producing a matrix hp. This matrix was normalized, resulting in
matrix was also normalized to produce the probability matrix the probability matrix based on frequency of interaction (hp). To
based on phenological overlap (F). verify whether model selection can be biased by h or p indepen-
Probability matrix based on morphological match (M): in this dently, we constructed hybrid models based on the frequency of
matrix, interaction between a given plant and hummingbird interaction (h and p) and independent measures of abundances
was allowed when the length of the hummingbird bill þ tongue (H and P), mentioned before and used to construct the probability
(hereafter ‘bill’ for simplification) was equal to or longer than the matrix A. These combinations resulted in two more models: Hp,
flower corolla length. For interactions considered as possible which combines the abundance for hummingbirds and frequency
based on this morphological match, we assigned 1, and 0 of interaction for plants, and hP, which combines frequency of
otherwise. This matrix was normalized in the same manner as interaction for hummingbirds and abundance for plants. Note
other matrices. It is important to note that three plant species that we did not use an HP model because it would be equal to
had longer corollas than the longest bill (electronic supplementary A. These models were also compared with the observed matrix
material, figure S4). In spite of the apparent bill–corolla mismatch, (O) using a likelihood approach, as in the previous analysis.
these interactions were considered possible in the matrix. In these
three cases, the nectar accumulates in the base of the narrow cor-
olla, allowing the hummingbird with the longest bill to access (i) Analysis of network aggregate statistics
the nectar. We tested how well each of the above-mentioned models predicts
From the matrices A, F and M, we also constructed prob- five frequently used network aggregate statistics (hereafter metrics):
ability matrices with all the possible combinations: AF, AM, nestedness, connectance, interaction evenness, specialization and
FM, AFM, in order to investigate the combined effect of multiple interaction asymmetry (the last was calculated separately for polli-
models. These combined matrices were calculated by Hadamard nators and plants). Nestedness was calculated with WNODF
(or elementwise) product and then also normalized. In this sense, (weighted nestedness metric based on overlap and decreasing
each of the original matrices (A, F and M) had equal impor- fill) [34] implemented as function weighted NODF in the R package
tance in structuring the interactions in the combined matrices. bipartite [33,35]. Specialization was calculated as the H2 index (H2
Additionally, as a benchmark matrix for comparison with other function in bipartite), which measures network-level specialization
probability matrices, we constructed a null matrix (NULL) in quantitative networks [36]. Other network metrics were calcu-
in which all plant and hummingbird species have the same lated as in Vázquez et al. [9]. Using mgen (in bipartite package),
probability of interaction. 1000 randomized networks were created according to eight
 Downloaded from rspb.royalsocietypublishing.org on March 26, 2014

probability matrices (A, F, M, AF, AM, FM, AFM, NULL). The ran- was similar to A (which used an independent measure of 4
domization algorithm generated matrices of the same size as the abundance for both hummingbirds and plants).
observed one and distributed the interactions (1231 in our case)

rspb.royalsocietypublishing.org
In general, abundance, phenology and morphology were
in the cells according to the probability of each interaction. A con- unable to predict nestedness, connectance, specialization, even-
straint was determined such that each species in randomized
ness nor interaction asymmetry (figure 4). Exceptions were
matrices received at least one interaction. The observed metrics
interaction asymmetry for the pollinators, which could be pre-
values (calculated from matrix O) were compared with values
dicted by the complete model, including all matrices (A, F and
from randomized networks and considered as predicted by prob-
abilistic matrices when we found overlap (95% confidence M) and nestedness predicted by the ‘NULL’ model with equal
interval, calculated with function confint in bipartite). probabilities for all interactions (figure 4). Although not accu-
rate for predicting most of the metrics, models including
abundance generated the closest results to the observed ones
for connectance, evenness and asymmetries of interaction.

Proc. R. Soc. B 281: 20132397

3. Results
(a) The plant–hummingbird network
We recorded 47 species of plants pollinated by nine humming- 4. Discussion
birds in the study site (figure 1). Bromeliaceae (20 species) and
(a) Determinants of network structure
Gesneriaceae (seven species) were the most common plant
Contrary to the growing consensus that species abundan-
families. Flowering period was short for most plants, with
ces is a critical factor determining the interaction network
only nine species (19%) flowering for more than three
structure [9–11,15,16], our study shows that morphological
months, and just Fuchsia regia flowering all year around (see
match and phenological overlap are more important than
the electronic supplementary material, figure S6). In general,
abundance for predicting plant –hummingbird interactions.
flower abundance was low and relatively similar for all
The modest importance of abundance in our study can be
plants; 82% of plants produced fewer than 150 flowers in
attributed to several factors, including the low variation in
total, and only four species produced more than 1000 flowers
relative abundances– at least among the three most abundant
(see the electronic supplementary material, figure S7). Flowers’
hummingbird species and many plants. This characteristic of
corollas were generally tubular, with length varying from
the network gives the model based on abundance similar
0.3 cm in Spirotheca rivieri to 5.1 cm in Mannetia chrysoderma
probabilities for most pairwise interactions. At the same
(see the electronic supplementary material, figure S4).
time, morphological and phenological traits varied consider-
From the nine hummingbird species recorded, Phaethornis
ably among species, thus forbidden links generated distinct
eurynome, Thalurania glaucopis and Clytolaema rubricauda were
probabilities for the pairwise interactions even among species
the most abundant (see the electronic supplementary material,
with similar abundances. We believe that both of these factors
figure S8) and recorded in the study area all year round (see
contributed to the modest importance of abundances.
the electronic supplementary material, figure S9). Other species
Abundance clearly did not positively correlate with visi-
were rare, with occasional records. The bill length (þ tongue)
tation for some plant species, such as the abundant but
varied from 1.6 cm in Lophornis chalybeus to 4.5 cm in P. eurynome
scarcely visited Psychotria eriocarpa, which has very small
(see the electronic supplementary material, figure S4).
flowers producing small amounts of nectar, or the less abun-
We recorded 1231 hummingbird visits with 86 distinct
dant, but highly visited Quesnelia sp. with copious nectar
pairwise interactions (figure 1). Rarefaction analysis indicated
production. In this sense, flower abundance seems to be
that our sampling recorded most of the interactions (see the
insufficient to predict the frequency with which a plant will
electronic supplementary material, figure S10). The network
be visited without considering species phenotype and details
was not nested (WNODF ¼ 22.18, null model interval was
of their natural history, such as nectar production or floral
between 16.30 and 25.88), with low connectance (0.20), inter-
display, which affect pollinator activity [37].
mediate value of specialization (H2 ¼ 0.51), high interaction
The striking evidence that phenological overlapping and
evenness (0.83) and mean interaction asymmetry lower for
morphological match are important for network structure can
plants (–0.17) than for hummingbirds (– 0.68; figure 2).
be illustrated by other examples. Most of the plants had short
flowering times and most hummingbirds occurred occasion-
ally. This implies that many species that could potentially
(b) Determinants of the network and their ability to interact because they present a morphological match, do not
predict network metrics overlap in time. This might be the case for the short-billed
The model combining morphological match and phenologi- Leucochloris albicollis, which does not interact with the short cor-
cal overlap (FM—expressing the forbidden links) was the olla flowers of Quesnelia sp. even though this hummingbird
best predictor of the interaction frequency between plants regularly visits other plants with similar flowers. On the other
and hummingbirds, with all models including abundance hand, some species with phenological overlap did not interact
(A) performing poorly (figure 2). This result, however, chan- owing to morphological mismatch. This was the case for
ged when we used the frequency of interaction as a proxy for many long corolla plants such as Vriesea spp. and Nidularium
abundance (figure 3). Among three models using the frequen- spp., species whose flowering overlapped with the presence
cies of interaction, two fitted better to the observed network of short-billed hummingbirds such as Clytolaema rubricauda
than FM and both included p (frequency of interaction as a and Thalurania glaucopis. Our finding is in accordance with pre-
measure of abundance for plants). The model including h vious studies showing the role of morphology and phenology
(frequency of interaction as a measure of abundance for in organizing plant–hummingbird communities [20–24],
hummingbirds) together with an independent measure of pointing to the importance of ecological and evolutionary
abundance for plants exhibited a fit to the observed data that processes in generating the forbidden links.
 Downloaded from rspb.royalsocietypublishing.org on March 26, 2014

Stephanoxis 5
1
lalandi — S.l.
2

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3
4
5
6
7
8
9
10
11
12 1 Alstroemeria inodora — A.i.
13
14 2 Aphelandra colorata — A.c.
Phaethornis 3 Vriesea sp.1 — V.sp1
15
eurynome — P.e. 16 4 Siphocampylus sp. — S.sp
17 5 Nidularium procerum — N.p.
18

Proc. R. Soc. B 281: 20132397

19 6 Nematanthus fritschii — N.fr.
7 Justicia sp.1 — J.sp1
20 8 Centropogon cornutus — C.c.
21 9 Vriesea incurvata — V.i.
22 10 Vriesea erythrodactylon — V.e.
23
24 11 Siphocampylus longipedunculatus — S.l.
25 12 Sinningia glazioviana — S.g.
26 13 Sinningia elatior — S.e.
27
28 14 Sinningia cooperi — S.coop.
29 15 Siphocampylus convolvulaceus — S.conv.
30 16 Nematanthus fluminensis — N.fl.
31 17 Manettia chrysoderma — M.c.
18 Justicia sp.2 — J.sp2
Thalurania 19 Geissomeria sp. — G.sp.
20 Canna paniculata — C.pa.
glaucopis — T.g. 32
21 Vriesea sp.2 — V.sp2
22 Vriesea simplex — V.s.
23 Vriesea carinata — V.c.
33
34 24 Nidularium sp. — N.sp
25 Bilbergia cf. amoena — B.a.
26 Tillandsia stricta — T.s.
27 Aechmea cf. organensis — A.o.
28 Pyrostegia venusta — P.v.
35 29 Edmundoa cf. lindenii — E.l.
Lophornis 30 Besleria longimucronata — B.l.
chalybeus — L.c. 31 Nidularium innocentii — N.i.
Eupetomena 32 Quesnelia sp. — Q.sp
macroura — E.m. 33 Tillandsia sp. — T.sp
36 34 Nematanthus gregarius — N.g.
Amazilia 35 Erythrina speciosa — E.s.
versicolor — A.v. 37
36 Aechmea disticantha — A.d.
38 37 Canistrum perplexum — C.pe.
38 Macrocarpaea rubra — M.r.
39 39 Vriesea cf. philippocoburgii — V.p.
40 Psychotria eriocarpa — P.e.
40 41 Fuchsia regia — F.r.
41
Clytolaema 42 42 Aechmea cf. gamosepala — A.g.
43 43 Spirotheca rivieri — S.r.
rubricauda — C.r.
44 Inga sessilis — I.s.
45 Abutilon sp. — A.sp
46 Nidularium cf. sulphureus — N.s.
47 Psittacanthus dichrous — P.d.
44

Leucochloris
albicollis — L.a. 45
46
Florisuga 47
fusca — F.f.

Figure 1. Hummingbird – plant mutualistic network in the Atlantic rainforest of the Santa Virgı́nia Field Station, Serra do Mar State Park, SE Brazil. Hummingbirds
(right) and plants (left). Grey lines represent species interaction and line thickness indicates frequency of interaction.

If a large proportion of unobserved interactions in the net- metrics of interaction networks [1,7,9,12], studies have only
works with robust sampling is in fact forbidden [13], then recently started to evaluate this limitation [30,38 –40]. Non-
sampling insufficiency might underestimate the importance detection of interactions owing to sampling insufficiency is
of forbidden links in structuring the networks. Although probably a widespread problem in plant –pollinator net-
undersampling potentially influences the structure and works [39], and estimating the sampling sufficiency as done
 Downloaded from rspb.royalsocietypublishing.org on March 26, 2014

6
bp*M
FM

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Bp*M
M
bp

F
Bp*F*M
probabilistic models

NULL Bp

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bp*F*M
AM
Bp*F

A
bp*F

AFM F*M

probabilistic models
M
AF
F
0 1000 2000 3000 4000
DAIC NULL
Figure 2. DAIC values of the probabilistic models ( probabilistic matrices)
resulting from species abundance (A), phenology (F) and morphology (M) bP*M
and all possible combinations among them in relation to the best model
(FM); NULL is the model in which all pairwise interactions have the same bP
probability. Shorter bars indicate better fit of a given model in relation to
the FM model, which presented the best fit to the observed network. A*M

here and in other studies [13,40] seems to be a necessary A

procedure in future studies.
A*F*M

(b) Can frequency of interactions be used as a proxy for bP*F*M

species abundance? A*F

We provide evidence that frequency of interaction is a poor
proxy for abundance, which might drastically change the
bP*F
interpretation of the relative importance of factors structuring
the networks. Abundance was not able to predict the 0 2000 4000 6000 8000
observed network better than forbidden links, but when fre- AIC
quency of interaction was used as proxy for abundance,
models including it performed better than forbidden links. Figure 3. DAIC values of the probabilistic matrices generated from species abun-
The contrast between our findings and some of the previous dance (A), phenology (F) and morphology (M) and all possible combinations. Data
studies that reported higher importance of abundance over were re-analysed considering the frequencies of interaction as an abundance
forbidden links [8,9,18,19] might be due to this difference. measure, which was represented by b for hummingbirds and p for plants; B
This bias might be especially severe when there is no corre- and P represent the ‘real’ abundance measures. Analyses were carried out including
lation between species’ abundances and their frequency of both abundance measures in combination with F and M. NULL is the model in
interactions, as we observed for the plants (see the electronic which all pairwise interactions have the same probability. Shorter bars indicate
supplementary material, figure S11). When there is a better fit of a given model in relation to the observed network. Grey bars show
correlation, as for hummingbirds (see the electronic sup- AIC values calculated using the real abundance measure. Note that when abundance
plementary material, figure S12), the bias seems to be models are constructed using frequencies of interaction (black bars), most of the
minor. However, if there are no data for abundance, this cor- better models (shorter bars) include this ‘abundance’, whereas models constructed
relation cannot be checked. In this rationale, using the using the independent measures of abundance had worse fit (longer grey bars).
frequency of interaction as a proxy for species abundance is
not recommended, because it uses the data to predict itself (c) Prediction of network-aggregated statistics
[11], and might generate misinterpretations by overestimating Although forbidden links better predicted the interaction fre-
the importance of the abundance at the expense of forbidden quency between plants and hummingbirds, they were unable
links in structuring the ecological networks. to reproduce values of network metrics similar to those from
 Downloaded from rspb.royalsocietypublishing.org on March 26, 2014

(a) (b) 7
NULL

rspb.royalsocietypublishing.org
A
F
M
A*F
A*M
F*M
A*F*M
0 0.5 1.0 0 25 50 75 100
connectance weighted NODF
(c) (d)

Proc. R. Soc. B 281: 20132397

NULL
A
F
M
A*F
A*M
F*M
A*F*M
0.50 0.75 1.0 0 0.5 1.0
evenness specialization H2
(e) (f)
NULL
A
F
M
A*F
A*M
F*M
A*F*M

–0.50 0 0.50 –1.0 –0.5 0

asymmetry, plants asymmetry, pollinators
Figure 4. Values of aggregate network statistics (circles, mean; bar, 95% confidence) produced by 1000 randomizations of the eight probabilistic matrices in relation
to the observed values (vertical lines inside the boxes). Black filled circles are models that include the abundance. The eight probabilistic matrices were constructed
based on species abundance (A), phenology (F), morphology (M) or combinations of them. NULL is the model in which all pairwise interactions have the same
probability. Probabilistic models predict a given aggregated network statistic when there is overlap in the observed and expected values.

the observed matrix. Instead, models including abundance frequency of interaction as a proxy for abundance (when
often showed the closest values to observed metrics. This there is no correlation) might overestimate the relative impor-
result contradicts the mechanisms influencing interaction tance of abundance in structuring ecological networks, and
frequencies and the metrics of network structure, which rep- this procedure should be avoided. In addition, even the best
resent distinct attributes of the network. The frequency of predictor models of network structures failed in reproducing
pairwise interactions represents the structure of the network the observed values of network metrics. This might suggest
because it describes each interaction individually, and ulti- that, although useful in capturing some specific properties,
mately this is used for the calculation of the metrics. In this network metrics could be failing in synthesizing the complex-
sense, it seems that although networks metrics are useful for ity of the whole network. In sum, our findings suggest that
investigating patterns on specific network attributes [7,41], species abundance is not always the most important driver
they might be losing some of the data complexity in the process of species interactions in communities.
of synthesizing a single number. Thus, we suggest that net-
work metrics should be chosen carefully when the point is Acknowledgements. We thank ‘Ecological Networks Course’ professors:
to investigate different mechanisms generating the network Diego Vázquez, Luciano Cagnolo and Natasha Chacoff, as well as col-
structure as a whole. leagues, especially Marı́a Soledad Tarantelli and Mónica Nime, for
diverse assistance and suggestions on network analyses. Andrew
In summary, to the best of our knowledge, this study MacDonald, Bo Dalsgaard, Diego Vázquez, Elsa Canard, Jesper Sonne,
reports, for the first time, that forbidden links are of higher Leonardo R. Jorge, Mário Almeida-Neto, Vinicius A. G. Bastazini,
importance than species abundance in structuring an ecologi- Wesley R. Silva and an anonymous reviewer contributed with valuable
cal network. More studies will be required to reveal whether suggestions on the manuscript. We also thank Instituto Florestal and
our result is an exception or not. It would be necessary for Santa Virgı́nia Field Station staff for permission and facilities to carry
out the study and the botanists Maria das Graças L. Wanderley, Cintia
this purpose to investigate different kinds of plant–pollinator Kameyama, Andréa O. Araujo, Silvana Godoy, Milena V. Martins, Mar-
systems and interactions (other than mutualisms) in distinct cela Firens, Maria Fernanda Calió, João Semir and Gustavo Shimizu for
ecosystems. We also provided evidence that using the the help with plant identification.
 Downloaded from rspb.royalsocietypublishing.org on March 26, 2014

Funding statement. Financial support was provided by CNPq through Additional support was provided by CAPES through the Graduate 8
scholarships to J.V.B and P.K.M., and a researcher grant to M.S. programme in Ecology and Faepex-Unicamp.

rspb.royalsocietypublishing.org
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