Ecological networks, nestedness and sampling effort
ANDER S NIELSEN*† and JORDI B ASCOMPTE‡
†Norwegian University of Life Sciences, Department of Ecology and Natural Resource Management, PO Box 5003,
NO-1432 Ås, Norway, and ‡Estación Biológica de Doñana, CSIC, Apdo. 1056, E-41080 Sevilla, Spain
Summary
1. Ecological networks have been shown to display a nested structure. To be nested, a
network must consist of a core group of generalists all interacting with each other, and
with extreme specialists interacting only with generalist species.
2. Studies on ecological networks are especially prone to sampling effects, as they
involve entire species assemblages. However, we know of no study addressing to what
extent nestedness depends on sampling effort, despite the numerous studies discussing
the ecological and evolutionary implications of nested networks.
3. Here we manipulate sampling effort in time and space and show that nestedness is
less sensitive to sampling effort than number of species and links within the network.
4. That a structural property of an ecological network appears less prone to sampling
bias is encouraging for other studies of ecological networks. This is because it indicates
that the sensitivity of ecological networks properties to effects of sampling effort might
be smaller than previously expected.
Key-words: ecological networks, food webs, mutualistic interactions, nestedness, network structure, pollination, sampling effort
Introduction
Mutualistic networks involving flowering plants and
their mutualistic pollinator or seed disperser animals
can be visualized by a matrix where each column represents an animal species and each row a plant species.
The cells within the matrix are used to indicate whether
there is an interaction between the plant and the animal
species that intersect in the matrix cell (Bascompte
et al. 2003) (Fig. 1). Recent work has described the
structure of both plant-pollinator and other types
of mutualistic networks (Bascompte et al. 2003, 2006;
Jordano et al. 2003; Vázquez 2005; Vázquez et al. 2005;
Fontaine et al. 2006; Ollerton et al. 2007). Specifically,
mutualistic networks are highly nested, i.e. there is a
core group of generalists all interacting with each other,
with extreme specialists interacting only with generalist species (Bascompte et al. 2003) (Fig. 1). Numerous
studies have revealed this nested structure and have
discussed its evolutionary and ecological reasons and
consequences (Bascompte et al. 2003; Dupont et al. 2003;
Ollerton et al. 2003; Memmott et al. 2004; Jordano
et al. 2006; Lewinsohn et al. 2006; Santamaria &
*Author to whom correspondence should be addressed:
Anders Nielsen. Tel. +47 64 96 57 67. Fax +47 64 96 58 01.
E-mail anders.nielsen@umb.no.
Rodríguez-Gironés 2007; Stang et al. 2007). Neither
envisioning plant–pollinator interactions as being
highly specialized, or diffuse, produces highly nested
mutualistic networks. The core of generalist species
may drive the evolution of the whole community, while
specialist species are involved in highly asymmetric
interactions with the generalists. One to one specialist
coevolution is very rare, as seen in the lack of compartments within the networks (Bascompte et al. 2003).
Nestedness has also been shown to increase network
robustness, as nested networks appear less prone to the
detrimental effects of habitat loss (Fortuna & Bascompte
2006) and species extinctions (Memmott et al. 2004).
More recently, nestedness has also been found in
other types of networks, including the defensive interactions between ants and extrafloral nectary-bearing
plants (Guimarães et al. 2006), the network of carcass
visits by scavenger animals (Selva & Fortuna 2007), the
interactions between sea anemones and their associated
fish species (Ollerton et al. 2007), and the interaction
between trees and tree living lichens (A. Nielsen & M. H.
Lie, unpublished data).
Despite the importance of nestedness for network
robustness and coevolution (Thompson 2005), no study
has addressed how sensitive nestedness is to sampling
effort. This is despite the fact that apparent properties
of multispecies systems have been shown repeatedly
Fig. 1. A matrix showing the interactions between plants (rows) and their pollinators (columns). Black squares represent an
interaction occurring between the plant and animal species intersecting in the matrix cell. We used ANINHADO to pack the
matrix (rearranging rows and columns) to achieve maximum nestedness. The line represents the isocline of perfect nestedness
given the matrix size and fill. The core of generalists (both plants and pollinators) occurs in the top left corner of the matrix.
Specialist pollinators tend to interact with plants above the isocline of perfect nestedness (the plant generalists). Specialist plants
tend to interact with pollinators to the left of the isocline of perfect nestedness (the pollinator generalists). The matrix is created
from the Siljan data, and is based on the network created by pooling four plots of clear cut forest (see Fig. 3 and Table 1).
to be prone to the effects of sampling effort (Paine
1988; Cohen et al. 1993; Goldwasser & Roughgarden
1997; Martinez et al. 1999; Winemiller et al. 2001; Bersier
et al. 2002; Banasek-Richter et al. 2004). Numerous
studies have addressed the problem of sampling effort
(e.g. Colwell & Coddington 1994; Mao & Colwell 2005),
including its relation to plant-animal mutualistic
network properties (e.g. Ollerton & Cranmer 2002;
Herrera 2005). A common observation is that the number
of species and links within a network tends to increase
with sampling effort. However, with regard to nestedness, there is currently much debate as to what extent this
nested pattern may be affected by sampling. Vázquez
& Aizen (2006) indicated that relative specialists are
less abundant than generalists, inducing a potential
sampling bias towards the core of generalist species and
thus underestimating the presence of the more specialized
species. Ollerton & Cranmer (2002) suggested that variation in sampling effort might underlie the impression
that tropical plants have more specialized pollination
interactions than temperate plants. As nestedness involves
specialist-generalist linkages, a sparsely sampled
network might be expected to include relatively few
specialist links, and hence appear less nested than a
well-sampled network. Bascompte et al. (2003) showed
that there is a positive relationship between nestedness
and network size and fill, and that there seems to be a
minimum number of species needed for the nested
structure to appear significant. In contrast, RodríguezGironés & Santamaría (2006) found that the nestedness of randomly generated matrices decreased within
the span of network size and fill observed in our study
(less than 50 pollinator species (columns) and less than
30% fill).
While rarefaction curves are primarily used to illustrate how the number of sampled species increases with
the number of individuals or area sampled, they can
also be used to relate other ecological measures to
sampling effort. If the relationship between sampling
effort and, for example, species richness reveals a steadily
increasing curve, we may assume our sampling effort
has been too small, as more extensive sampling would
reveal more species. On the other hand, if the value
appears stable, or levels off and reaches an asymptote,
one can say that there has been sufficient sampling, as
more sampling would not reveal more species. Here we
use rarefaction curves to address whether nestedness is
sensitive to sampling effort compared with number of
species and links within the network. As the significance
level of a nestedness value is related to both the size and
fill of the matrix, we also present relative nestedness
(nestedness corrected for matrix size and fill) as well as
the significance level for the absolute nestedness value
not being obtained from a randomly assembled matrix.
In addition we show the relationship between sampling
effort and network connectance (fill) as connectance is
important for determining the significance of the
nestedness value (Rodríguez-Gironés & Santamaría
2006). Based on previous studies we expect nestedness
to increase with sampling effort towards an asymptote.
Our main question is whether this asymptote is reached
before the entire network (all species and links) is
known. We do this by relating sampling effort, in time
and space, to absolute and relative nestedness, significance level of absolute nestedness, as well as number of
species and links within the network.
Methods
We obtained spatially and temporally structured data on
the plant-pollinator (flower visitor, strictly speaking)
network in a boreal forest landscape near Siljan in
south-east Norway. As the study area is heavily managed (Nielsen et al. 2007), we established 12 20 × 20 m
study sites evenly distributed among forest stands of
three forest maturity categories (clear cuts, young
forest, and old growth forest). The plant-pollinator
network data were collected throughout the summer
of 2004 (3 June to 24 August). To minimize the number
of zero observations, sampling was performed in
fair weather only. Local weather conditions made it
impossible to distribute the sampling days uniformly
throughout the season, so in some weeks 5 days of
sampling were done, while in most weeks between two
and four samplings of each study site were performed.
We sampled each study site an average of 31.33 times
(minimum = 29, maximum = 34). We sampled our
study sites by randomly walking around within them
Table 1. Descriptive measures of the matrices obtained for each of the 12 study sites and the networks created for all four sites
in each forest community category. All data are based on calculations on networks obtained for the entire season. Days are total
number of days of sampling conducted in the particular study site or for the four study sites comprising each forest community.
Visits are the total number of insects recorded in a particular study site. Size equals plants × animals. N equals absolute nestedness
and significance levels are obtained using null model analysis in ANINHADO (see text for details)
Site
Days
Visits
Size (P × A)
Links
Fill (%)
N
Significance
C1
C2
C3
C4
Y1
Y2
Y3
Y4
O1
O2
O3
O4
Clear
Young
Old
30
31
34
33
30
31
33
31
32
29
31
31
128
124
123
269
136
217
172
248
172
192
161
266
49
127
75
794
773
517
7 × 48
8 × 27
7 × 35
9 × 33
8 × 38
8 × 41
8 × 42
5 × 39
8 × 40
3 × 18
6 × 31
3 × 15
12 × 77
11 × 86
10 × 70
72
44
47
60
63
59
62
53
61
19
43
17
154
165
113
21.4
20.0
19.2
20.2
20.7
18.0
18.5
27.2
19.1
35.2
23.1
38
16.7
17.4
16
0.81
0.66
0.72
0.73
0.70
0.80
0.81
0.50
0.80
0.29
0.81
0.35
0.83
0.78
0.80
P
P
P
P
P
P
P
P
P
P
P
P
P
P
P
for 30-min periods, catching all insects seen within
flowers. All insects caught were brought back to the
laboratory for identification and the species of plant it
was caught in was recorded.
To manipulate the temporal sampling effort, we
created plant-pollinator network matrices based on
data obtained from an increasing number of sampling
days. We created plant-pollinator networks for each
level of sampling effort by including data from 4, 6, 8, ...
up to 28 randomly selected sampling days (28 days
were chosen as the maximum sampling effort to ease comparisons among sites, as the lowest temporal sampling
effort was 29 days for a particular site (Table 1)). We
did this for each study site separately. Fifty replicate
matrices were created for each level of sampling effort.
For each of the resulting networks, number of species
and links were counted and absolute nestedness and
connectance were calculated. We also ran null model
analysis for each of the nestedness values and calculated
relative nestedness and the significance level (P-value).
We then plotted all our network measures against the
number of sampling days the network was based on.
For the spatial component of our sampling effort we
used the networks based on sampling throughout the
entire season. To alter the spatial scale we created
networks based on data from single study sites, all combinations of two and three sites, as well as the network
based on data from all four sites within each forest
maturity category. We did not combine networks from
sites of different forest maturity because the spatial
heterogeneity in our system might make us actually
sample more than one network (Paine 1988).
The goal of our sampling protocol was to obtain the
best possible estimate of the ‘real’ plant-pollinator
network within the study area, given a certain amount
of sampling effort applied. To achieve this, we manipulated the temporal and spatial scale independently
= 0.001
> 0.1
> 0.1
= 0.028
> 0.1
= 0.09
= 0.008
> 0.1
= 0.005
> 0.1
= 0.028
> 0.1
< 0.001
< 0.001
< 0.001
of the number and abundance of both plant and pollinator species.
To calculate absolute nestedness, relative nestedness
and significance levels for the nestedness values, we used
the ANINHADO software designed by Guimarães &
Guimarães (2006), which is based on the algorithms
from the Nestedness Temperature Calculator (Atmar
& Patterson 1993). The nestedness calculator has been
criticized for overestimating the nestedness significance,
as it uses a null model based on equal probability for
all interactions to be realized (Cook & Quinn 1998;
Fischer & Lindenmayer 2002). ANINHADO is, in this
sense, a better software package as it allows the possibility to choose from four different null models. Here
we use a null model based on probabilities in each cell
being the arithmetic mean of the connection probabilities of the focal plant and animal species (null
model 2 in Bascompte et al. 2003 and null model Ce in
ANINHADO). This assumes that the probability of an
interaction is proportional to the generalization level
of both species. This null model has been found to
perform better when compared with other models in the
sense of having the smallest type-I errors (RodríguezGironés & Santamaría 2006). ANINHADO gives the
nestedness in temperature or degrees (T ), as an analogy
to physical disorder. As we emphasize nestedness or
order, instead of disorder, we present nestedness, N,
as N = (100 − T/100), with values ranging from 0 to 1
(maximum nestedness). Whether an absolute nestedness value significantly departs from what could be
expected of a random matrix depends on the matrix
size and fill. To allow cross network comparisons we
therefore calculated relative nestedness, a measure that
corrects for variation in species richness and number of
links. Relative nestedness is defined as N* = (N − NR)/
NR, where N is the nestedness of the actual matrix and
NR is the average nestedness of random replicates
generated from null model analysis with ANINHADO
(Bascompte et al. 2003). Details of the matrices obtained
from all 12 study sites and all three forest maturities
are given in Table 1.
The goal of this study is to illustrate whether our
nestedness values are representative for the ‘real’ network under study. However, the question of whether
our networks are significantly nested compared with
random networks with the same number of species
and links does become important as the relationship
between absolute nestedness and significance level
is dependent on the size and fill of the matrix. We therefore report both absolute and relative nestedness as
well as the significance level, and how they relate to
sampling effort in time and space.
Results
As seen in Fig. 2, both number of species and links
increase with temporal sampling effort. Though the
increase does not necessarily follow a linear model, none
of the study sites appear to have reached saturation
levels for these variables within the extent of our sampling
effort. In contrast, the relationship between absolute
nestedness and sampling effort seems much more
stable. For most of the study sites the average absolute
nestedness value does not change markedly with
sampling effort; however, variation around the mean
does decrease. For the study sites with the two smallest
networks (O2 and O4) absolute nestedness decreases
with sampling effort, but seems to level off within our
sampling scale (Fig. 2). As a result of its relationship with
size and fill of the matrix, relative nestedness appears
to be not as stable as the absolute value. For the study
sites exhibiting significant nestedness at higher levels of
sampling effort, relative nestedness does increase with
sampling effort but reaches an asymptotic level well within
the extent of our sampling effort. For the two smallest
networks (O2 and O4) relative nestedness seems quite
stable or even decreasing with sampling effort.
We found similar results for the relationship between
network properties and spatial sampling effort. Both
the number of species and links increase with increasing spatial sampling effort. Nestedness, on the other
hand, seems much more stable. For the clear cut and
young forest study sites, both absolute and relative
nestedness appear quite stable across the extent of our
sampling effort. For the old growth forest, while
average, absolute and relative nestedness increase from
one to two study sites included, these seem to stabilize
as three and four study sites are included. Figure 3
shows the relationship between spatial sampling effort
and the different network properties.
To control for the variation in network size and fill
we calculated relative nestedness and significance levels
for our absolute nestedness values, using null model
analysis. Relative nestedness showed two distinct patterns of relationships with sampling effort, depending
on whether the networks appear to be statistically sig-
nificantly nested at higher levels of sampling effort
(Table 1 and Fig. 2). For the networks not statistically
significantly nested, the relative nestedness value seems
not to change much throughout the extent of our
sampling effort (constantly below zero). The P-value of
these networks stayed high and even increased (O2 and
O4) with sampling effort. The two non-significantly
nested clear cut networks (C2 and C3) had an increase
in relative nestedness and decrease in P-value. Indeed,
we might suspect the nestedness value of these networks
to become statistically significant if we had applied a
higher temporal sampling effort. The relative nestedness of the networks that were statistically significantly
nested increased and stabilized above zero, at high
levels of sampling effort. The P-values of these networks
decreased with sampling effort. These patterns were
also apparent for the increase in spatial sampling effort,
where all three communities were highly significantly
nested at higher levels of sampling effort.
Discussion
As observed in both Figs 2 and 3, our sampling effort
regarding species and links appears to be insufficient.
Our graphs indicate that if we had sampled more days
or more study sites, we would have found more species
and detected more links in our networks. On the other
hand, connectance decreased with sampling effort
towards an asymptotic value and actually stabilized
within the extent of our sampling effort. The main
focus of this study, namely the relationship between
nestedness and sampling effort, did show a quite contrasting pattern. For all but the two smallest networks
(O2 and O4) the absolute nestedness value appeared
stable throughout the entire range of our temporal
sampling effort. The networks that were statistically
significantly nested at high sampling efforts have
slightly increasing absolute nestedness values and do
stabilize at higher values than those that were not
significantly nested. This is in accordance with our
expectations based on previous studies (Bascompte
et al. 2003). Sampling more days or more plots would
probably not significantly affect the estimate of this
network pattern. The absolute value of nestedness is,
however, not meaningful unless considered in relation
to matrix size and fill. Rodríguez-Gironés & Santamaría
(2006) showed that the nestedness temperature of
randomly assembled matrices increased with network
size and attained its maximum value for intermediate
fills. This shows that smaller networks need a lower
temperature (higher nestedness value) to be significantly nested. The sizes of our networks in relation to
temporal sampling effort are all in the range where the
temperature of randomly assembled matrices changes
rapidly (< 50 columns in the matrix). Our matrix fill
decreases with sampling effort, towards a relative stable
value in the range 0.2–0.3. This is within the range where
the nestedness temperature of randomly assembled
matrices attains its maximum value (lowest nestedness
1138
A. Nielsen &
J. Bascompte
Fig. 2. The relationship between number of sampling events (temporal sampling effort) and number of species, number of links, absolute nestedness (N),
relative nestedness, connectance and P-value for the statistical significance of the absolute nestedness value for the 12 study sites. Data are presented for
four replicate study sites in each forest maturity category, and the labels C, Y and O represent study sites in clear cuts, young forest and old growth forests,
respectively. Each point represents the average value for the measure, obtained from 50 random combinations of 4, 6, 8, ... up to 28 sampling days. Error
bars are standard deviation.
© 2007 The Authors
Journal compilation
© 2007 British
Ecological Society,
Journal of Ecology
95, 1134 –1141
1139
Networks,
nestedness and
sampling effort
Fig. 2. continued
value). The two smallest networks (O2 and O4) seem to
have a slightly higher fill, close to 0.4, a value where the
chance that a random matrix will be significantly
nested is smallest (Rodríguez-Gironés & Santamaría
2006). The significance of the absolute nestedness values
for our networks should therefore be most sensitive
to the size of our networks, i.e. the number of species
comprising them.
We acknowledge that our increase in both temporal
and spatial sampling effort is not based on independent
samples. Our spatial scale is based on combinations of
four independent study sites and our temporal scale is
based on between 29 and 34 temporally autocorrelated
days of sampling and, as such, our results must be
interpreted with caution. Despite this, however, we feel
confident that absolute nestedness is less sensitive to
sampling effort in both space and time, compared with
number of species and number of links in our networks.
Previous studies on food webs have shown that number
of links is sensitive to sampling effort, compared with
number of species (Goldwasser & Roughgarden 1997).
Both species and links increase steadily within the
extent of our sampling effort while absolute nestedness
appears much more stable. We take this as an indication
of absolute nestedness being less sensitive to sampling
biases. The exact amount of time and area sampled
before an asymptote is reached is of course dependent
on site-specific properties. However, the point is that
the stability of the absolute nestedness value occurs at
a lower level of sampling effort, in both time and space,
than number of species and number of links, and that
this pattern appears to prevail across study sites. This
study is based on data sampled from 12 study sites situated in forest stands of contrasting maturity. The sites
are indeed very different regarding forest structure
(tree size and age distribution), and there are great
differences in species composition, abundance and diversity among the sites situated in forests of contrasting
maturity (A. Nielsen, unpublished data). We believe
that the heterogeneous outline of the study system
increases the potential applicability of our findings.
With respect to the temporal variation in sampling
effort, the absolute nestedness value, as well as the Pvalue obtained at high sampling effort, varied among
the study sites. That the absolute nestedness seems
not to vary with sampling effort, whether an increase in
sampling effort reveals that the nested pattern is significant or not, also strengthens our confidence that
absolute nestedness values are less prone to arbitrary
effects of sampling effort.
The number of documented ecological networks
displaying a nested structure is increasing (Ollerton
et al. 2003; Lazaro et al. 2005; Vázquez et al. 2005;
Fontaine et al. 2006; Guimarães et al. 2006; Selva &
Fortuna 2007). The nested structure of these networks
has been discussed and interpreted without addressing
the extent to which the absolute nestedness values are
sensitive to sampling effort. Here, we address for the
first time the relationship between sampling effort
and absolute nestedness. We conclude that absolute
nestedness is a relatively robust measure of network
structure, less prone to arbitrary effects of insufficient
1140
A. Nielsen &
J. Bascompte
Fig. 3. The relationship between number of study sites (spatial sampling effort) and number of species, number of links, absolute nestedness (N), relative
nestedness, connectance and P-value for the statistical significance of the nestedness value for the three communities (clear cuts, young forest and old
growth forests). Each point represents the average value for the measure, obtained from single sites (1), and combinations of two (2), three (3) and all four
sites (4). Error bars are standard deviation.
sampling effort than other network descriptors such as
number of species and links.
One potential explanation for the robustness of the
nestedness estimates reported here is related to the
assembly type of a nested matrix. As noted above, nestedness implies a core of generalist plant and animal
species interacting among themselves. Despite imperfect
sampling, these species and links will probably soon be
recorded. The density of links in the core is very high,
so even if some are missed the structure will remain
similar. Rarer, generalist species may not be recorded,
but other, less generalist species will be attached to the
tails of this generalist core. Essentially, nestedness
implies a network assembly similar to Chinese Boxes in
the sense that the pollinators that one plant species
interacts with are included in the larger group of pollinators that a more generalist plant species interacts
with, which, in turn, are contained in the larger group of
pollinators that the most generalist plant species interacts with. There are sets of species within larger sets.
This structure is quite robust in the face of sampling
effort because all layers are built around a central core
containing the most generalist, abundant species. One
could assume that the first species (and layers) going
unnoticed because of imperfect sampling would be the
external ones (containing more specialist species). However, one could still see the global structure of boxes
within larger boxes. If one layer (or box) is removed, the
internal layers still have the same relationship.
Acknowledgements
The Research Council of Norway (project 154442/720)
supported this study (A.N.).
This work was funded by the European Heads of
Research Councils, the European Science Foundation,
and the EC Sixth Framework Programme through
a EURYI (European Young Investigator) award (to
J.B.), and by the Spanish Ministry of Education and
Science (Grant REN2003-04774 to J.B.).
We thank Martin Haugmo and Sverre Lundemo for
field assistance and Frizöe Skoger for letting us use their
forestland for our research. We also thank Jeff Ollerton,
Mary Price and an anonymous reviewer for useful
comments on previous versions of the manuscript.
Tore Randulf Nielsen (Syrphidae), Adrian Pont
(Muscidae), Brad Sinclair (Empididae), Frode Ødegaard
(Coleoptera) and Sigmund Hoggvar (Hemiptera) kindly
identified insects to species level. Fred Midtgaard
determined the less abundant groups of pollinators to
appropriate taxonomic level.
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Received 19 March 2007; accepted 18 May 2007
Handling Editor: Peter Klinkhamer