Using exactly the same network configuration
as in the experiments, we show that we obtain
the same results when we change the node where
the perturbation occurs (21) (fig. S19).
We then examined the effects of the perturbation at greater distances from the targeted patch.
For that, we used simulated networks with the
same degree distribution as the experimental
networks but with a thousand nodes and with
variable modularity and perturbation intensities
(21) (fig. S21). With this approach, we first go
back to the observed result of buffering being
greater at a distance of two links, as opposed to
one link, from the perturbation. Our simulations
indicate a nonlinear increasing relationship between network modularity and the average buffering effect (fig. S22), and this effect increases
markedly with distance from the perturbed node.
This result confirms our experimental finding
and extends it across a range of network sizes.
Modularity is therefore a major determinant of
the spread of a perturbation in these metapopulation networks.
Next, we used our simulations to assess the
extent to which the observed beneficial role of
modularity in containing perturbations is medi-
ated by the intensity of perturbations. Although
we did not observe population extinctions, small
population sizes are correlated with high extinc-
tion risk (22). Populations within a module where
a perturbation originates are expected to have a
greater risk of extinction. Modularity constrains
dispersal within the module, hindering network-
wide dispersal. This may reduce total metapop-
ulation size in comparison with a configuration
in which dispersal occurs at the scale of the entire
network, allowing individuals to easily disperse to
any other node (23). It is unclear, therefore,
whether a trade-off exists between modularity-
driven population persistence and overall network
population size, as well as whether perturbations
favor modular networks. To explore this trade-
off, we simulated metapopulations with the same
number of nodes and subject to the same per-
turbation as those of the experiments but with
different modularity values—achieved by increas-
ingly randomizing the original network while
keeping constant the degree of each node (24).
The results of these simulations corroborate our
experimental result. We find that increasing
modularity leads to a stronger buffering effect
against perturbations (21) (fig. S23). We find a
positive correlation between overall network
metapopulation size and the degree of modu-
larity, and this correlation strengthens with
increasing link distance from the perturbation.
The positive correlation between modularity and
metapopulation size occurs only in the presence
of perturbations, and this correlation increases
asymptotically as perturbation intensity increases
(Fig. 4). However, in unperturbed networks, total
network population size decreases as modularity
increases. Therefore, modularity comes at a cost
to network metapopulation size in unperturbed
systems. However, when a perturbation occurs,
even when it is small and localized to a single
node, modularity permits a larger overall meta-
population size. Therefore, the dynamical impli-
cations of modularity have to be assessed in light
of the likelihood and intensity of the pertur-
bations the system has to face.
Human-dominated landscapes are increasing-
ly fragmented into habitat networks of varying
spatial complexity and connectivity (25). Pop-
ulation extinction can occur as habitat is lost
and perturbations spread through networks of
habitat fragments. We have shown that spatial
modularity is a crucial aspect of habitat network
connectivity that affects the likelihood of popu-
lation persistence despite unpredictable pertur-
bations. Our findings suggest that network-based
approaches to conservation should be considered
when restoring connectivity in heavily fragmented
landscapes (26, 27), when designing protected
areas (28), or when limiting the expansion of a
disease outbreak (29). In all of these scenarios,
spatial modularity can be managed in habitat
networks to reduce the cascading impacts of
perturbations that may drive extinction and threat-
en biodiversity. Our demonstration of the buffer-
ing effect offered by a modular structure during
perturbation also has implications for other
fields in which networks are good descriptors of
the system’s structure. One such field is finance,
where the recent global crisis has led to the
suggestion that managing network modularity
may reduce systemic risk (1, 30, 31). The inter-
play between experimental and simulated networks
used here confirmed the value of understand-
ing how network structure limits the impact of
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We thank H. McIntosh, G. L’Heureux, Y. Yan, and J. Yang for help
with the experiment; J. Bustamante for making the link with the
microelectronics institute; and M. A. Fortuna and D. Wechsler for
comments on a previous draft. We also thank Z. Lindo, C. Albert,
R. Maupetit, C. Atomei, K. O’Kane, and M. F. Martínez for advice
and help in the lab. Research was funded by the European
Research Council through an Advanced Grant (to J.B.), the Spanish
Ministry of Education through a Formación Personal Universitario
Ph.D. fellowship (to L.J.G.), the Natural Sciences and Engineering
and Research Council (NSERC) of Canada through a postdoctoral
fellowship (to B.R.), and a Discovery Grant (to A.G.). A.G. is
supported by NSERC, the Quebec Centre for Biodiversity Science,
the Canada Research Chair program, the Liber Ero Chair in
Conservation Biology, and a Killam Fellowship. All experimental
data are presented in table S1.
Materials and Methods
Figs. S1 to S25
15 November 2016; resubmitted 2 May 2017
Accepted 16 June 2017
Fig. 4. Perturbation intensity mediates the
overall effect of modularity. The simulations
show that modularity has a positive effect on total
metapopulation size only in the presence of
perturbations. Perturbation intensity is measured
as the fraction of individuals removed from node
5—we perturbed this node to recreate in silico
the experimental setting. The relationship between network modularity and the total number
of individuals inhabiting the metapopulation is
measured as Spearman correlation coefficients.
Solid symbols are statistically significant
Spearman correlation coefficients (P < 0.05),
whereas open symbols are not statistically
significant (P > 0.05). The dashed line is a visual aid
to differentiate between negative and positive
correlation coefficients. To estimate the standard
deviation (error bars) for the correlation values, we
subsampled pairs of values of correlation
magnitude and perturbation intensity. We created
100 subsamples without replacement of half
the length of the original set of values.