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Why network analysis is often disconnected from community ecology: A critique and an ecologist's guide

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Abstract

Network analyses of mutualistic or antagonistic interactions between species are very popular, but their biological interpretations are often unclear and incautious. Here I propose to distinguish two possible implications of network patterns in conjunction with solutions to avoid misinterpretations. Interpretations can be either(1)niche-based, describing specialisation, trait (mis-)matching between species, niche breadth and niche overlap and their relationship to interspecific competition and species coexistence, or(2)impact-based, focusing on frequencies of interactions between species such as predation or infection rates and mutualistic services, aiming to quantify each species’ relative contribution to an ecological effect.For niche-based implications, it is crucial to acknowledge the sampling limitations of a network and thus control for the number of observations of each species. This is particularly important for those kinds of networks that summarise observed interactions in communities (e.g. bipartite host–parasitoid or plant–animal networks), rather than compile information from different sources or experiments (as in many food webs). Variation in total observation frequencies may alone explain network patterns that have often been interpreted as ‘specialisation asymmetries’ (nestedness, dependence asymmetries). I show analytically that ‘dependence asymmetries’ between two species (or two guilds) only reflect variation in their total observation frequencies. To depict true asymmetries in niche breadth, independent data are required for both species.Moreover, simulated co-extinction scenarios assume that each species ‘depends’ on its associated partners in the network (again niche-based), but species that appear most endangered are simply those with one or very few observations and are not necessarily specialised. Distinguishing niche-based and impact-based interpretations may help to bridge terminological and conceptual gaps between network pattern analyses and traditional community ecology.ZusammenfassungMutualistische oder antagonistische Beziehungen zwischen Arten einer Gemeinschaft werden derzeit häufig mit Hilfe von Netzwerkanalysen beschrieben. Da die biologische Deutung solcher Analysen oft missverständlich ist, wird in diesem Artikel vorgeschlagen, zwei Interpretationsarten zu unterscheiden:(1)Ökologische Nische, z.B. Spezialisierung, Nischenbreite und überlappung, sowie Kompatibilität von Merkmalen zwischen Arten.(2)Interaktionseffekte, die von der relativen Häufigkeit der Wechselwirkungen abhängig sind, z.B. Prädations- und Infektionsraten oder mutualistische Funktionen.Bei nischenbezogenen Deutungen von Netzwerken, die auf beobachteten Interaktionen basieren, muss jedoch berücksichtigt werden, dass die Gesamtzahl der Beobachtungen pro Art limitiert ist und sich zwischen Arten stark unterscheidet. Allein diese Variation kann viele Netzwerkmuster erklären, beispielsweise “Nestedness”, was oft als asymmetrische Spezialisierung missverstanden wurde. Hier wird analytisch bewiesen, dass eine mutmaßliche “Spezialisierungs-Asymmetrie” zwischen zwei Arten allein auf deren unterschiedliche Beobachtungshäufigkeit zurückgeführt werden kann. Unhabhängig erhobene Daten für beide Arten sind notwendig, um diesen Trugschluss zu vermeiden.Das Aussterben von Arten durch Verlust des Assoziationspartners (Koextinktion) wurde in mehreren publizierten Studien modelliert. Solche Simulationen basieren auf der Annahme, dass jede Art von seinen beobachteten Assoziationspartnern abhängig ist (nischenbasierte Deutung). Hier kann jedoch gezeigt werden, dass vor allem solche Arten scheinbar gefährdet sind, die nur ein- oder wenige Male beobachtet wurden, also nicht notwendigerweise Spezialisten darstellen. Die explizite Unterscheidung zwischen nischen- und effektbasierter Interpretation könnte demnach eine hilfreiche konzeptionelle Brücke darstellen, um Netzwerkanalysen und klassische Gemeinschaftsökologie zusammenzuführen.
Basic and Applied Ecology 11 (2010) 185–195
INVITED VIEWS IN BASIC AND APPLIED ECOLOGY
Why network analysis is often disconnected from community ecology:
A critique and an ecologist’s guide
Nico Blu¨thgen
Department of Animal Ecology and Tropical Biology, University of Wu
¨rzburg, Biozentrum, Am Hubland, 97074 Wu
¨rzburg,
Germany
Received 19 September 2009; accepted 19 January 2010
Abstract
Network analyses of mutualistic or antagonistic interactions between species are very popular, but their biological
interpretations are often unclear and incautious. Here I propose to distinguish two possible implications of network
patterns in conjunction with solutions to avoid misinterpretations. Interpretations can be either
(1) niche-based, describing specialisation, trait (mis-)matching between species, niche breadth and niche overlap and
their relationship to interspecific competition and species coexistence, or
(2) impact-based, focusing on frequencies of interactions between species such as predation or infection rates and
mutualistic services, aiming to quantify each species’ relative contribution to an ecological effect.
For niche-based implications, it is crucial to acknowledge the sampling limitations of a network and thus control for
the number of observations of each species. This is particularly important for those kinds of networks that summarise
observed interactions in communities (e.g. bipartite host–parasitoid or plant–animal networks), rather than compile
information from different sources or experiments (as in many food webs). Variation in total observation frequencies
may alone explain network patterns that have often been interpreted as ‘specialisation asymmetries’ (nestedness,
dependence asymmetries). I show analytically that ‘dependence asymmetries’ between two species (or two guilds) only
reflect variation in their total observation frequencies. To depict true asymmetries in niche breadth, independent data
are required for both species.
ARTICLE IN PRESS
www.elsevier.de/baae
Nico Blu¨ thgen
1439-1791/$ - see front matter &2010 Gesellschaft fu¨rO
¨kologie. Published by Elsevier GmbH. All rights reserved.
doi:10.1016/j.baae.2010.01.001
Tel.: þ49 931 318 4370; fax: þ49 931 888 4352.
E-mail address: bluethgen@biozentrum.uni-wuerzburg.de
Moreover, simulated co-extinction scenarios assume that each species ‘depends’ on its associated partners in the
network (again niche-based), but species that appear most endangered are simply those with one or very few
observations and are not necessarily specialised. Distinguishing niche-based and impact-based interpretations may
help to bridge terminological and conceptual gaps between network pattern analyses and traditional community
ecology.
&2010 Gesellschaft fu¨ rO
¨kologie. Published by Elsevier GmbH. All rights reserved.
Zusammenfassung
Mutualistische oder antagonistische Beziehungen zwischen Arten einer Gemeinschaft werden derzeit ha¨ufig mit Hilfe
von Netzwerkanalysen beschrieben. Da die biologische Deutung solcher Analysen oft missversta¨ndlich ist, wird in
diesem Artikel vorgeschlagen, zwei Interpretationsarten zu unterscheiden:
(1) O
¨kologische Nische, z.B. Spezialisierung, Nischenbreite und u¨ berlappung, sowie Kompatibilita¨t von Merkmalen
zwischen Arten.
(2) Interaktionseffekte, die von der relativen Ha¨ufigkeit der Wechselwirkungen abha¨ngig sind, z.B. Pra¨dations- und
Infektionsraten oder mutualistische Funktionen.
Bei nischenbezogenen Deutungen von Netzwerken, die auf beobachteten Interaktionen basieren, muss jedoch
beru¨cksichtigt werden, dass die Gesamtzahl der Beobachtungen pro Art limitiert ist und sich zwischen Arten stark
unterscheidet. Allein diese Variation kann viele Netzwerkmuster erkla¨ren, beispielsweise ‘‘Nestedness’’, was oft als
asymmetrische Spezialisierung missverstanden wurde. Hier wird analytisch bewiesen, dass eine mutmaßliche
‘‘Spezialisierungs-Asymmetrie’’ zwischen zwei Arten allein auf deren unterschiedliche Beobachtungsha¨ufigkeit zuru¨ ckge-
fu¨hrt werden kann. Unhabha¨ngig erhobene Daten fu¨ r beide Arten sind notwendig, um diesen Trugschluss zu
vermeiden.
Das Aussterben von Arten durch Verlust des Assoziationspartners (Koextinktion) wurde in mehreren publizierten
Studien modelliert. Solche Simulationen basieren auf der Annahme, dass jede Art von seinen beobachteten
Assoziationspartnern abha¨ ngig ist (nischenbasierte Deutung). Hier kann jedoch gezeigt werden, dass vor allem solche
Arten scheinbar gefa¨hrdet sind, die nur ein- oder wenige Male beobachtet wurden, also nicht notwendigerweise
Spezialisten darstellen. Die explizite Unterscheidung zwischen nischen- und effektbasierter Interpretation ko¨nnte
demnach eine hilfreiche konzeptionelle Bru¨ cke darstellen, um Netzwerkanalysen und klassische Gemeinschaftso¨ko-
logie zusammenzufu¨ hren.
&2010 Gesellschaft fu¨ rO
¨kologie. Published by Elsevier GmbH. All rights reserved.
Keywords: Ecological networks; Ecological niche; Nestedness; Mutualism; Sampling effects; Specialisation asymmetry; Species
extinctions; Parasitism
Introduction
Analyses of ecological networks are highly fashion-
able, and have recently stimulated a revival of ‘descrip-
tive’ observations of interactions in the context of
natural communities. This may provide valuable in-
sights that cannot be achieved when species are studied
in isolation. In contrast to food webs, bipartite
ecological networks comprise mutualistic or antagonis-
tic interactions between two defined parties, e.g. plant
and animal communities. Since the seminal work by
Jordano (1987) and subsequent work (particularly
Bascompte, Jordano, Melian, & Olesen, 2003;Olesen
& Jordano, 2002), a large number of studies charac-
terised the structure of bipartite networks (see reviews
by Bascompte & Jordano, 2007;Ings et al., 2008;
Va´ zquez, Blu¨thgen, Cagnolo, & Chacoff, 2009).
More generally, networks describe ‘nodes’ (or ‘ver-
tices’), which are connected by ‘edges’ (or ‘links’, as it
will be adopted for this paper) (Newman, 2003). Most
ecological networks drawn so far comprise species as
nodes and a particular kind of interaction between two
species as links, e.g. feeding interactions, mutualistic
associations or parasitism (Bascompte & Jordano,
2007). Network analysis is then typically concerned
with describing the ‘degree distribution’ of the number
of links (whether it reflects a scale-invariant power law
function), small world properties or the density of links
(‘connectance’). The distribution of the links is often
described with regard to ‘nestedness’ (Box 1).
Do network tools and metrics help to understand
community ecology? First, I will sketch some niche-
based and impact-based questions raised in community
ecology, before I highlight one general and two specific
ARTICLE IN PRESS
N. Blu¨thgen / Basic and Applied Ecology 11 (2010) 185–195186
ARTICLE IN PRESS
Box 1.Ecological implications derived from network metrics.
A simple hypothetical example network comprises three plant
and six flower visitor species and shows many typical features of
real ecological networks such as the fact that several species are
observed only once or few times. Cell entries (link weights)
provide the interaction frequencies between two species, i.e. how
many individual visitors were observed on a particular plant.
Species are sorted by observation totals (S). For definitions of
each metric and additional information, see Bersier et al. (2002),
Blu
¨thgen et al. (2006, 2008) and Dormann et al. (2009).
Descriptor of network
topology
Ecological interpretation
Connectance (C)is
C=9/18=0.5, i.e. 9 of the
18 potential links are
zeros.
Often interpreted as specialisation level of the network (high
connectance=high generalisation), this metric is in fact a mixture of
niche and sampling property. Note that most species are entered with
very few observations, so that many zeros will be due to limited
sampling. Sampling limitations usually increase in larger networks
with more rarely observed species. Connectance only distinguishes
whether links are present or absent (unweighted, binary links), hence
information about interaction frequencies is lost.
Nestedness (N) is high:
N=69.71.
Both metrics are commonly interpreted as niche property: ‘specialists
interact with generalists’ (asymmetric specialisation), e.g. suggesting
that beetle species D is highly specialised and thus depends on flower
species G (b
DG
=1/1=1.0), but G not reciprocally on D (b
GD
=1/17=0.06).
However, note that most species such as D have only few total
observations (here: 1) and thus inevitably few links with high
‘dependence’ values. Even if all species interacted randomly and were
thus entirely unspecialised, the expected level of nestedness
(unweighted links) and dependence asymmetries (weighted links)
would be similar as in the example network. Rather than asymmetric
specialisation (niche property), these metrics may simply reflect a
‘frequency asymmetry’ (impact or sampling property). Before niche-
based conclusions can be drawn, the limitation by observation totals
needs to be carefully controlled.
Interaction strengths
(b
ij
) between species i
and j(‘dependencies’)
are asymmetric;b
ij
gives the number of
interactions between i
and jas a proportion of
the total observations
for i,b
ji
of the total for
j, hence many b
ij
ab
ji
.
The average
interaction strength
asymmetry is
ASij ¼0:24.
The degree
distribution follows a
power law function.
P(k)=k
g
(r
2
=1.0)
Some species have many links, while many species have few links.
Except in highly specialised systems, the degree distribution is an
inevitable consequence of the distribution of total observations per
species (or the underlying species abundances), which is typically
described by a log normal distribution. Like the indices above, it
shows a mixture of niche and sampling properties.
Interaction diversity
and evenness.
Some links are strong (i.e., high interaction frequencies), many others
are weak (low frequencies), suggesting variation in ecological
impacts. Low interaction evenness (E
2
) depicts a high variation in
N. Blu¨thgen / Basic and Applied Ecology 11 (2010) 185–195 187
pitfalls in network interpretation, followed by sugges-
tions how to overcome these problems.
Some basic questions in ecology
Among the most important topics tackled by commu-
nity ecologists is the interplay between interspecific
competition and the ecological niche (Begon, Townsend,
&Harper,2006). Competition is commonly linked to
niche breadth (specialisation versus generalisation) and
niche partitioning, and in cases of niche overlap,
competition may drive shifts from fundamental to realised
niches. A narrow fundamental niche may also suggest a
higher vulnerability of a species to disturbance, e.g.
specialised consumers may suffer from declines of their
food sources (Kleijn & Raemakers, 2008). Multiple other
research areas in community ecology exist, but many can
be boiled down to competition and niche. For instance, to
reveal whether biodiversity is important for maintaining
ecosystem functioning, knowledge about (functional)
niche complementarity is crucial (Rosenfeld, 2002). If
each species fulfils only a specialised function (narrow
niche), the coexistence of several species with comple-
mentary functions is required to provide the full breadth
of functions in a community. In turn, the insurance
hypothesis assumes that different species are functionally
ARTICLE IN PRESS
e
H
2
¼6.7
E
2
¼0.66
interaction frequencies between different species pairs. This may
translate into relative contributions to ecological functions,
particularly when the recorded interactions are representative for the
community. The quantitative heterogeneity of links (E
2
) reflects the
ecological connectivity between the interacting parties. Given that
links are weighted, E
2
may better reflect this connectivity than the
connectance index using unweighted links. Moreover, the interaction
diversity (e
H
2
) may provide a measure of the complexity of the
associations in the selected system. Comparisons of e
H
2
across
networks should consider whether they are based on comparable
boundaries and decisions which species to include or exclude from
analysis.
Complementary
specialisation
For the given number of observations per species, both indices (H
2
0on
the network-, d
i
0on the species-level) describe the deviation from a
completely neutral configuration of associations. Hence, these metrics
remove the bias due to total observation frequencies on network
patterns in order to describe a niche property that is independent from
variation in observations between species. H
2
0describes the
complementarity (or exclusiveness) of interactions: when species are
specialised on different association partners (high niche
differentiation), d
i
0of these species and consequently H
2
0of the entire
network increases. For the network shown above, H
2
0is low and not
significantly different from neutrality (p=0.46). Overall, species in this
network are relatively conform, suggesting a high level of niche
overlap or redundancy of interactions for the given limitation of
observations.
(H
2
0and d
i
0).
H
2
0¼0.22
e.g.
d
A
0¼0.00
d
D
0¼0.00
d
F
0¼1.00
d
G
0¼0.12
d
I
0¼0.44
H
2
0is closely related to the weighted mean d
i
0across all species (with
each species weighted by its observation totals). For each species, d
i
0
is large for species that are found on otherwise rarely visited
associates (d
F
0=1 for species F) and small if predicted by neutrality
(species D: d
D
0=0). In contrast, species D and F are assigned a
‘dependence’ of b
DG
=b
FI
=1.0 (see above) irrespective of their particular
association being likely or unlikely. Hence, d
i
0represents an indicator
of the exclusiveness of a species’ niche that may be used to predict its
fragility to co-extinction.
When a relatively rarely observed species (e.g. D) is truly specialised
on a commonly visited partner, such asymmetric specialisations may
go undetected in d
i
0and H
2
0, being indistinguishable from neutrality.
N. Blu¨thgen / Basic and Applied Ecology 11 (2010) 185–195188
redundant (Hooper et al., 2005). Moreover, for a
mechanistic and evolutionary understanding of interac-
tions in communities, a closer examination of species or
individual traits plays an important role. Such traits
include adaptations such as attractive signals to mutualists
or defences against antagonists.
Apart from niche-based questions, the ecological
impact (or interaction strength) among species within
a community and ecosystem is a typical focus of
ecological studies (Wootton & Emmerson, 2005) includ-
ing food web analyses (Berlow et al., 2004). Ecological
impacts involve predation and parasitism rates, various
kinds of mutualistic services or facilitation effects
among many other kinds of multispecies interactions.
These studies usually focus on the magnitude of effects,
e.g. the extent of herbivory on plants, the contribution
of different pollinators to reproduction, or mortality
risks due to predation and parasitism. For assessing
relative impacts of different species on a target organ-
ism, their relative interaction frequencies are often
crucial (Va´ zquez, Morris, & Jordano, 2005) besides
variation in species-specific or per-capita effect sizes.
Although niche and impact can be related, the
interpretation of ecological data benefits from a clear
distinction between them, as we shall see.
Pitfalls in ecological interpretations of network
patterns
Network patterns are often implicitly assumed to
represent unbiased ecological niche properties, e.g. when
drawing conclusions about specialisation or dependencies
on certain association partners. However, when interac-
tions are recorded in natural communities, only a small
subset of the realised interactions is usually observed. This
suggests that while some ‘zero’ entries in the network may
truly mirror absent links, many ‘zeros’ rather reflect limited
observations. The precision differs between species within a
network and between networks. Therefore, comparisons of
niche properties between different species should account
for the fact that many, if not most of the species in a
community are only rarely observed and thus provide only
limited information compared to the common ones. In
biodiversity studies, a meaningful comparison between
habitat A and B calls for an appropriate control for the
total number of observations (individuals) in each habitat
(see Gotelli & Colwell, 2001) – in network studies, an
interpretation that species A has a broader spectrum of
associated partners than species B is often proposed
without such control. Conclusions from network studies
often ignore that the number of links, the magnitude of
‘interaction strengths’ and other network metrics strictly
depend on the number of observations per species (Box 1).
This represents a strong bias for assigning niche properties,
although not necessarily for impact-based interpretations
to which I will come back in the final section.
The skewness in the number of observations per species
(often reflecting an underlying log-normal abundance
distribution), combined with a limited overall sampling
intensity, may alone explain a high level of nestedness and
‘dependence’ asymmetries, power-law degree distributions
and the variation in connectance and other commonly
applied metrics (Blu¨ thgen, Fru¨ nd, Va´zquez, & Menzel,
2008;Dormann, Fru¨ nd, Blu¨ thgen, & Gruber, 2009). The
problem is particularly apparent in metrics that only
account for the presence or absence of unweighted links
(Banasˇek-Richter, Cattin, & Bersier, 2004;Dormann
et al., 2009). For instance, when the connectance of two
networks is compared, but one of them has been sampled
less intensively than the other, it should not be surprising
that they differ in this metric (Blu¨thgen et al., 2008;
Goldwasser & Roughgarden, 1997).
A number of nearly universal trends were found in
network analyses. For instance, when species with few
‘links’ (low ‘species degree’) are translated as ‘specialists’,
(1) rare or rarely observed species appear more ‘specia-
lised’ (Va´zquez & Aizen, 2004),
(2) larger, more species-rich interaction networks (Ole-
sen & Jordano, 2002) or food webs (Rejma´ nek &
Stary
´, 1979)have a lower connectance,
(3) more ‘specialised’ species appear to preferentially
associate with ‘generalised’ partners (Bascompte
et al., 2003), and
(4) ‘specialists’ appear to be more vulnerable to
simulated losses of their associated hosts or partners
(Dunne, Williams, & Martinez, 2002;Memmott,
Waser, & Price, 2004).
However, all these trends may largely or even solely
reflect a sampling bias for drawing conclusions about niche
breadth: for rarely observed species, only few links can be
recorded – an inevitable consequence of limited informa-
tion. An analysis of 51 mutualistic networks that controlled
for the number of observations of each species found
contrasting results to the above‘rules:(1)thedegreeof
specialisation of a species is independent of its frequency,
and (2) the seemingly higher specialisation in larger
networks disappears (Blu¨thgen, Menzel, Hovestadt, Fiala,
&Blu¨thgen, 2007). For the other two conclusions (3–4), I
will examine the pitfalls of observation limitation in more
detail in the following two paragraphs.
Do specialisation asymmetries exist and
promote community stability?
Several studies on mutualistic networks have claimed a
high prevalence of specialisation asymmetries (e.g. Bas-
compte et al., 2003;Bascompte, Jordano, & Olesen, 2006;
Guimara˜es,Rico-Gray,dosReis,&Thompson,2006;
ARTICLE IN PRESS
N. Blu¨thgen / Basic and Applied Ecology 11 (2010) 185–195 189
Va´zquez & Aizen, 2004) which were then also reported
from non-mutualistic networks (e.g. Burns, 2007). Spe-
cialisation asymmetries have been proposed to generate a
more stable association between mutualistic communities
(Bascompte et al., 2006;Bastolla et al., 2009). It has been
argued that for a specialised species A, it may be beneficial
to specialise on a partner B that is a generalised mutualist
(asymmetry). If instead B would be reciprocally specialised
on A (symmetry), both may be more vulnerable to co-
extinction after one of the partners becomes less reliable,
e.g. due to a declining population (Ashworth, Aguilar,
Galetto, & Aizen, 2004). However, it can also be argued
that true specialisation asymmetries may lead to higher
interspecific competition when the associations represent
limited resources or services. On a generalised resource B,
a specialised consumer A may then experience stronger
interspecific competition with other consumers than on a
resource with a narrow consumer spectrum. Competition
may be avoided by interacting with more exclusive
partners (i.e. symmetric or reciprocal specialisation), since
niche partitioning should decrease interspecific competi-
tion. Interestingly, recent findings of network modelling
challenge this view (Bastolla et al., 2009), showing a
decreased interspecific competition for the scenario with
highest niche overlap (nested or fully connected net-
works). However, these authors did not incorporate the
dynamics of competition for mutualism in their model,
thus conflicting with niche theory where mutualistic
benefits are viewed as a limited resource.
The question of whether specialisation is symmetric or
asymmetric may hold important insights for ecology and
conservation, but also for understanding co-evolutionary
ARTICLE IN PRESS
Box 2.Proof that interaction strength asymmetries reflect the ratio of observation totals.
Let a
ij
represent the observed interaction frequency between animal species iand plant species j. The
total observation frequency of the animal species is referred as A
i
¼S
J
a
ij
, the total number of
observations on the plant species A
j
¼S
I
a
ij
, with Iand Jbeing the total number of animals and plants,
respectively. The interaction strength (Va
´zquez et al., 2007) or ‘dependence’ (Bascompte et al. 2006)of
animal ion plant jcan then be defined as
bij ¼aij
Ai
:
In turn, the interaction strength jconfers on iis defined as
bji ¼aij
Aj
:
In cases where b
ij
Eb
ji
, one would regard interaction strengths as being symmetric or reciprocal,
otherwise they are termed asymmetric. Bascompte et al. (2006) defined their ‘dependence asymmetry’ as
ASij ¼jbij bji j
maxðbij ;bji Þfor all realised links ðaij 40Þ:
To maintain information on the direction of the asymmetry, this approach can be modified as
AS0
ij ¼bij bji
bij þbji
for all realised links ðaij 40Þ:
Accordingly, AS
ij
0
varies between 1 and þ1.
However, resetting this equation shows that AS
ij
0
is completely independent of the interactions
between a species pair and solely depends on the ratio of their observation frequency totals:
ASij
0¼bij bji
bij þbji
¼
aij
Aiaij
Aj
aij
Aiþaij
Aj
¼
aij 1
Ai1
Aj

aij 1
Aiþ1
Aj

¼
AjAi
AiAj

AjþAi
AiAj

¼AjAi
AiþAj
:
This also holds for the original AS
ij
which becomes
ASij ¼jAjAij
maxðAj;AiÞ:
N. Blu¨thgen / Basic and Applied Ecology 11 (2010) 185–195190
trajectories (Thompson, 2005). Unfortunately, a single
count of the interactions between two species from a single
network cannot be used to estimate specialisation of both
species independently. In fact, the ‘dependence’ asymmetry
between species A and B, discussed as stabilizing property
of mutualism (Bascompte et al., 2006), simply reflects the
ratio of total observations of A versus B – a mathematical
consequence of its definition (see Box 2 for proof). When
species A is observed five times, species B ten times, their
dependence asymmetry (AS’
ij
) is 0.33, no matter how often
they interact. Consequently, the average ‘dependence’
asymmetry for the whole network is simply given by the
ratio of species numbers (Box 2). In other words, when
there are three times as many pollinator species as plant
species, the average pollinator ‘dependence’ on plants is
twice as high as that of plants on pollinators, resulting in an
average asymmetry of 0.5. This is acceptable and may be
desired for impact-based hypotheses where relative
frequencies are part of the interpretation (e.g. Va´zquez,
Blu¨thgen et al., 2009;Va´zquez, Chacoff, &Cagnolo, 2009;
Va´zquez et al., 2007). Hence, the pattern describes an
interaction frequency asymmetry of associated partners, or
abundance asymmetry when based on abundance data that
are independent of the network (Va´zquez et al., 2007).
However, the constraints by observation frequency are an
artefact if one intends to assign specialisation and thus
‘dependence’. Most networks include numerous species
with a single or very few observations, and the interactions
of these species account for the majority of high
asymmetries reported by Bascompte et al. (2006).Note
that completely randomised interactions even yield the
highest degree of interaction strength asymmetries
(Blu¨thgen et al., 2008), although randomised associations
are, by definition, the opposite of specialisation.
When the effect of variation in observation totals
is removed (Blu¨ thgen, Menzel, & Blu¨ thgen, 2006),
specialisation in most networks indeed appears
more symmetric than expected by chance (Blu¨ thgen
et al., 2007, 2008). This does not imply that specialisation
asymmetries do not exist. The null model of randomised
interactions may contain true specialisation asymmetries,
but these simply cannot be distinguished from frequency
asymmetries when a single network is analysed. As a
solution to disentangle specialisation and frequency
asymmetry, one could use external information on
specialisation for one of the two guilds (e.g. pollinators)
from data sources other than the network itself, or from
experimental evidence. Alternatively, one could perform a
comparison across different networks with varying
partner availabilities. For instance, when the abundance
of resource species is changed between different experi-
mental treatments, a comparison of the consumers’
preferences may help to clarify whether they are more
likely to utilise the most common resource species or the
most generalised ones.
Can we predict co-extinctions based on network
patterns?
Specialised consumers depend on their specific resources
and are thus more vulnerable to population declines or
even local extinction if such resources become less available
or disappear entirely. A higher level of generalisation in a
ARTICLE IN PRESS
For each species, the mean interaction strength of each species iacross all Jpotential links is simply
bij ¼1
JX
J
j¼1
bij ¼1
J;since X
J
j¼1
bij ¼1:
For each species jacross all Ilinks, this becomes
bji ¼1
IX
I
i¼1
bij ¼1
I;since X
I
i¼1
bji ¼1:
Consequently, the mean AS
ij
0
(analogously AS
ij
) across all interactions is approximately determined
by the balance between the species richness of animals (I) and plants (J)as
ASij
0bij bji
bij þbji
¼IJ
IþJ;
which corresponds to simulations of randomised networks (Blu
¨thgen et al. 2007). This argument
shows that external network parameters (observation totals, species richness) directly determine the
interaction strength (or ‘dependence’) asymmetries, irrespective whether the two species interact
frequently or not. Rather than specialisation asymmetries, AS
ij
0
describes asymmetries of species total
frequencies.
N. Blu¨thgen / Basic and Applied Ecology 11 (2010) 185–195 191
community may thus function as a buffer against such co-
extinctions and represent a stabilising mechanism. How-
ever, when specialisation is inferred from a network as the
number of ‘links’, there are two substantial errors that
inflate the impression of instability:
(1) Rarely observed species have fewer links and thus
seem more vulnerable irrespective of their real level
of specialisation.
(2) Assuming that a ‘zero’ link in a network is ‘forbidden’
and cannot be realised may underestimate the dyna-
mics of interactions in a community.
The first problem represents a bias in the estimation of
specialisation and can be circumvented by quantitative
metrics with appropriate corrections for the number of
observations (see ‘proposed guide’ below). Solving the
second problem may require comparing the behaviour of
the same species across different networks to examine the
dynamics of interactions under variable conditions.
Several studies simulated extinction scenarios based on
networks (Dunne et al., 2002;Memmott et al., 2004).
Usually, species of one party (e.g. plants) are removed from
a dataset to examine the putative impact to the other party
(e.g. pollinators). This nicely illustrates the stability of
networks, if the network pattern represents the niche
breadth of each species and their constraints, i.e. ‘zeros’
mirror ‘forbidden’ links rather than insufficient sampling.
However,thisisclearlynotthecaseforthedatasets
currently used. I will outline this problem for a network
used to predict the consequences of climate change
(Memmott, Craze, Waser, & Price, 2007), although it is a
pervasive feature of such analyses in general. The
simulation was based on an empirical binary flower-visitor
‘network’ recorded by Robertson (1928) in North America.
The authors predicted that most animal species that may
go extinct – due to a simulated phenological mismatch with
flowers – are those recorded only on a single plant (link). A
closer look at the taxonomic affinities of the single-link
visitor species in Robertson’s data (Fig. 1) suggests that
many of them are occasional flower visitors, which may
only visit flowers opportunistically, but do not depend on a
single flower species. Oligolectic bees represent one of the
few taxa that are known to depend on one or few closely
related plants, but they represent only ten (2.6%) of the
single-link visitor species (Fig. 1). Moreover, only 17% of
the total 1420 visitor species were recorded more than 5
times by Robertson. This sampling limitation is particularly
severe for the single-link visitors, of which 95% had been
observed only 1–5 times. As a result, the percentage of
visitors that would go extinct might be overestimated in the
simulations.
Analyses based on binary data (number of links) may not
only overestimate specialisation, but also fail to distinguish
the proportional distribution of different species. When an
insect visits a single flower species most of the time, but
occasionally other flowers, the number of links alone would
underestimate its true ‘specialisation’. Binary network
metrics may thus be inadequate to estimate the dependence
of consumers on specific resources. Quantitative approaches
use weighted links, e.g. by counting interaction frequencies.
However, even the quantitative ‘dependence’ metric
(Bascompte et al., 2006;Jordano, 1987) becomes inevitably
1.0 (maximum dependence) for those species with a single
record, thus suffering from the same bias as the number of
links when interpreted as niche breadth (Box 1).
A proposed guide to ecologists
When network patterns are translated into niche proper-
ties such as specialisation, trait matching, dependencies or
secondary extinction risks, we need to test whether diff-
erences between species or between networks do not merely
reflect differences in observation frequencies. Observation
limitation is ubiquitous in community-wide ecological data-
sets and represents a familiar problem in biodiversity stud-
ies, e.g. when different habitats are compared (Gotelli &
ARTICLE IN PRESS
Fig. 1. So-called ‘specialised’ flower visitors assumed to depend
on a single flowering plant species in co-extinction simulations.
The diagram shows proportions of different insect taxa among
the 382 identified visitors with a single link in Robertson’s
(1928) dataset from Illinois, USA. Numbers of species are based
on a database compiled by John Hilty, who incorporated
taxonomic updates, but also provided additional biological
information about the interactions recorded by Robertson and
other ecologists (see http://www.flowervisitors.info/). Note that
many of these taxa are parasitoids, predators and other guilds
that may represent facultative consumers of floral resources and
clearly do not ‘depend’ on single flower species. Three under-
lined taxa (bees, hoverflies and butterflies) are known to include
some flower specialists (e.g. ‘oligolectic’ bees), but represent
relatively small proportions.
N. Blu¨thgen / Basic and Applied Ecology 11 (2010) 185–195192
Colwell, 2001). There are several non-exclusive ways to deal
with this bias: (1) Rarefaction analysis holds appropriate
tools to examine the effects of observation frequency. This
can be performed on the network level to reveal overall
trends (Banasˇek-Richter et al., 2004).Rarefactiononthe
species-level (Herrera, 2005)isneededtoallowafair
comparison of species’ niche breadths. (2) Null models can
be applied based on the given number of observations per
species or their abundance (Blu¨thgen et al., 2007;Dormann
et al., 2009;Va´zquez & Aizen, 2004;Va´zquez, Chacoff et al.,
2009;Va´zquez et al., 2007). Alternative solutions, although
only partly reducing the bias, may include (3) to intensify
the sampling effort (Martinez, Hawkins, Dawah, & Feifa-
rek, 1999), (4) to exclude rarely observed species from the
analysis, or (5) to use additional information sources as evi-
dence which links may exist but have gone undetected in a
network sample (e.g. Bosch, Gonza´lez, Rodrigo, &
Navarro, 2009).
Quantitative network metrics that use interaction
frequencies as link weight are more robust against variation
in sampling effort and often more meaningful than metrics
that only assign links as present or absent (Banasˇek-Richter
et al., 2004;Bersier, Banasek-Richter, & Cattin, 2002;
Blu¨thgen et al., 2008;Kay & Schemske, 2004;Va´zquez,
Chacoffetal.,2009). Focusing on the residual deviation of
network patterns from a null model that accounts for
observation frequencies alone, may help to explore niche-
based specialisation (Blu¨thgen et al., 2007, 2008)andtrait
matching (Stang, Klinkhamer, Waser, Stang, & van der
Meijden, 2009;Va´zquez, Chacoff et al., 2009).
To describe niche properties of the network and of
each species, only the information-theoretical metrics H
2
0
and d
i
0(Box 1) are not systematically biased by the species’
total observation frequencies. They can be used directly to
compare different species within a network or make
comparisons across networks despite variation in total
frequencies. Their interpretation is arguably not as straight-
forward as e.g. counting the number of links, as they
describe the degree of complementary specialisation
(or exclusiveness of species interactions). This makes them
partly insensitive to detect ‘specialisation’ on a niche that is
shared with common species, because such a configuration
would also be expected under neutrality (Box 1). Given that
high complementarity or exclusiveness requires high
specialisation, H
2
0and d
i
0can thus be viewed as a
(conservative) measure of specialisation. Other measures
of niche breadth and overlap are available (Krebs, 1999,see
Blu¨thgen et al., 2006), and useful alternatives include
quantifying the residuals from neutrality based on species
abundances rather than interaction totals (Va´zquez, Chac-
off et al., 2009). However, species degree, nestedness and
interaction strength or dependence are not independent
from observation frequencies and should not be directly
interpreted as niche properties (Box 1).
When impact-based interpretations are the scope of a
study, e.g. describing variation in interaction frequencies
(e.g. Bersier et al., 2002;Tylianakis, Tscharntke, & Lewis,
2007), a ‘correction’ for total number of observations may
be inadequate. Relative abundances or interaction frequen-
cies of species are often the most important part of their
ecological effect, e.g. when the contribution of different
pollinator species to the pollination success of a plant is
examined (Va´zquez et al., 2005). The heterogeneity of
interaction frequencies among different species can then be
described by quantitative interaction diversity metrics.
Interaction diversity (such as e
H
2
) and evenness (E
2
)canbe
computed on the network level or for each species (termed
‘generality’ or ‘vulnerability’, Bersier et al., 2002). On the
network level, e
H
2
expresses a measure of the complexity of
the interactions, E
2
the ‘connectivity’ between the two parties
(Box 1). Comparisons between species or networks are most
meaningful when the observed focal links are representative
for the realised ones, and when the species’ observation
totals are not biased by the sampling protocol.
Finally, networks compiled from heterogenous areas or
different seasons may contain numerous species pairs that
cannot interact because of non-overlapping ranges,
habitats and/or activity periods – resulting in erroneously
high specialisation estimates. For instance, the observation
catalogue compiled by Robertson (1928) covered a large
area and contained many different natural and urban
habitats and, hence, flowers that only occurred in habitats
where some of the recorded pollinator species were absent
andviceversa.Focusingonsmaller units facilitates an
ecological interpretation of a network, where the absence
of a link may indicate a meaningful mismatch in species
traits, which prevents its realisation (for example, the
proboscis of a nectar feeding insect can be too short to
access the nectar at the base of the flower tube; Stang et al.,
2009), if it is not just due to limited sampling.
Network approaches hold useful tools to
explore different ecological and evolutionary processes
that may shape complex interaction patterns in local
communities. However, this promising avenue requires a
clear translation of network language to established
concepts of community ecology, and an awareness of
the pitfalls.
Acknowledgements
I am grateful to John Hilty (see legend of Fig. 1)for
fruitful discussions on Robertson’s data and their inter-
pretability, and for making them available in his database.
I further thank Diego Va´zquez, Carsten Dormann,
Martina Stang, Gita Benadi, Robert Junker, Florian
Menzel and three anonymous reviewers for helpful
comments on an earlier draft, Teja Tscharntke for his
kind invitation to submit this view, and Klaus Ho¨vemeyer
for improving its style. Our research is funded by the
Deutsche Forschungsgemeinschaft, DFG (Biodiversity
Exploratories, SFB 554 and BL 960/1-1).
ARTICLE IN PRESS
N. Blu¨thgen / Basic and Applied Ecology 11 (2010) 185–195 193
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... We estimated the importance of nyala individuals in each network considered for all nyalas in each reserve using three indices, namely, index of individual nyala specialization (d'), individual host strength (IHS), and centrality (C). Individual nyala (host) specialization (d') describes the deviation from a neutral configuration of associations (Blüthgen et al. 2006, Blüthgen 2010. In other words, it compares the frequency distribution of interactions with a null distribution when interactions between host individuals and parasites are proportional to their observed total Content courtesy of Springer Nature, terms of use apply. ...
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... Specialization and generalization are defined by the number of interactions established by the nodes (visitor ID/blueberry cultivars) in relation to all possible interactions in the system. Because H 2 0 is mathematically independent of the total frequency of observations, it allows comparisons of networks differing in size and sampling effort(Blüthgen, 2010;Blüthgen et al., 2006); (c) Modularity, the tendency of the network to have compartments interacting with visitors and blueberry cultivars. ...
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