25 JULY 2014 • VOL 345 ISSUE 6195 383 SCIENCE
structure of 23 communities, Rohr et al.
show that more nested mutualistic networks
permit multispecies coexistence for a wider
range of species growth rates: They are more
structurally stable (see the figure).
Rohr et al.’s results imply that if a community can explore a full range of species
growth rates during assembly, nestedness is
the configuration most likely to be observed
because of the structural stability that it imparts. This is an important step toward reconciling previous results based on Lyapunov
stability. However, it remains to be shown
how maximization of structural stability affects Lyapunov stability. Insights may come
from studies that allow ecological networks
to assemble through a stochastic exploration
of species growth rate combinations (8–10).
These studies have found that as communities assemble, they become more resistant
to invasions by new species, likely because
they have come close to the center of the
coexistence domain of growth rates (see the
figure). At the same time, these communities
tend to be less resilient (that is, they return
more slowly to equilibrium after perturbations). This fragility may explain previous
results showing that nestedness undermines
resilience to perturbations (4, 11).
Future work must take two critical factors into account. First, Rohr et al. study
variations in growth rates independently of
interspecific and intraspecific interaction
parameters. Yet, these three sets of parameters are not independent and will covary,
because they all depend on the metabolic
rates of individuals. For example, both interaction and growth rates scale with body size
(12, 13). Second, the methods and the results
of Rohr et al. cannot directly be applied to
consumer-resource systems and only to certain classes of competitive systems. This is
a crucial limitation that future work must
strive to overcome, because mutualistic
systems are typically embedded in a larger,
more complex network of interactions that
also include competitive and consumer-resource interactions. ■
1. R. M. May, Stability and Complexity in Model Ecosystems
(Princeton Univ. Press, Princeton, NJ, 1974).
2. R. P. Rohr, S. Saavedra, J. Bascompte, Science 345,
3. S.Allesina,S. Tang, Nature 483,205(2012).
4. U.Bastolla et al., Nature
5. S. Suweis et al., Nature 500, 449 (2013).
6. A.I.Dell etal.,
7. A. James et al ., Nature 487, 227 (2012).
8. S. Pawar, J. Theor. Biol. 259, 601 (2009).
9. T. Fukami, Popul. Ecol. 46, 137 (2004).
10. R. Law, R. D. Morton, Ecology 77, 762 (1996).
11. P.P.A.Staniczenko,J.C.Kopp, S.Allesina,
4, 1391 (2013).
12. S. Pawar etal .,Nature 486, 485 (2012).
13. S. Tang, S. Pawar, S. Allesina, Ecol. Lett. 10.1111/ele.12312
Mutualistic communities maximize their structural stability
Department of Life Sciences, Imperial College
London, Silwood Park, Ascot, Berkshire SL5 7PY,
U K. E-mail: email@example.com
Why are plant-pollinator
Interactions between species in a com- munitymay be mutuallybeneficial, com- petitive, or exploitative. The resulting ecological networks strongly influence the population dynamics of species (1). Nonrandom features of such networks
may reflect organizing processes. For example, mutualistic networks such as plant-pollinator communities are “nested.” Specialist
pollinator species visit plant species that are
subsets of those visited by more generalist
pollinators (see the figure). But what drives
the emergence of nestedness? On page 416
of this issue, Rohr et al. (2) provide theoretical and empirical evidence for the decade-old idea that nestedness prevails because it
stabilizes mutualistic networks.
Different studies have produced conflicting results about the consequences of nestedness at the community level (3–5). Rohr
et al. argue that these conflicts
arise because most studies have
focused on how nestedness affects Lyapunov stability. This type
of stability analysis is concerned
with whether, for a given community, population trajectories will
return to an equilibrium point
after they are perturbed from it
(say, due to sudden reduction in
the population densities of one
or more species). Instead, Rohr
et al. study whether nestedness
improves structural stability. In
ecological communities, structural
stability analyses aim to determine
whether a network feature (such
as nestedness) widens or constricts
the feasible region for multispecies coexistence when biological
parameters are varied (1) (see the
This shift from Lyapunov sta-
bility to structural stability, origi-
nally suggested in 1974 (1), has
profound implications. Any equi-
librium of a community cannot be
permanent because real commu-
nities are not static: Individual species may
undergo changes, e.g., in their growth rate,
and the species composition of the commu-
nity may change, e.g., when phenotypically
different individuals immigrate or emigrate.
Such changes are even more likely when
individuals respond to changes in environ-
mental conditions such as temperature (6).
This is why it is necessary to ask whether a
system will be structurally stable to changes
in biological parameters.
Rohr et al. investigate how structurally
stable mutualistic networks are to changes
in the intrinsic growth rates of species. Intrinsic growth rate is a fundamental biological parameter that determines the absolute
fitness of species’ populations and varies
with the metabolic rate (rate of energy use)
of individuals. The intrinsic growth rate has
typically been treated as a fixed parameter
across all species in a community (4, 5, 7).
Combining theory and data on the network
By Samraat Pawar
Pollinator growth rates
Pollinator growth rates
Less nested network = low structural stability
Highly nested network = high structural stability
Nestedness and structural stability. According to Rohr et al. ( 1),
a highly nested network (top, fully nested in this case) has a high
structural stability. This means that species can coexist over larger
ranges of species’ growth rates (gray shaded coexistence domain).
A less nested network (bottom) will have lower structural stability
(a smaller coexistence domain). Thus, perturbations to plant or
pollinator growth rates can more easily displace an equilibrium point
of the community out of the coexistence domain, resulting in one or
more populations going extinct.