© 1999 Macmillan Magazines Ltd
14 OCTOBER 1999
letters to nature
Determinants of biodiversity
regulate compositional stability
Mahesh Sankaran & S. J. McNaughton
Biological Research Laboratories, Syracuse University, Syracuse,
New York 13210-1244, USA
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The world is witnessing a decline in biodiversity which may be
greater in magnitude than even previous mass-extinction
events1–3. This has rekindled interest in the relationships between
biodiversity and the stability of community and ecosystem
processes4that have been reported in some empirical studies5–7.
Diversity has been linked with community and ecosystem pro-
cesses8–14, but disputes remain over whether it is diversity, envir-
onmental factors or the variety of functional groups in a
community that drive these patterns15– 21. Furthermore, it remains
unclear whether variation in diversity resulting from species loss
within communities has similar effects on stability as natural
variation in diversity associated with gradients in factors that
regulate diversity. We believe that, across larger ecological scales,
extrinsic determinants of biodiversity such as disturbance
regimes and site history may be the primary determinants of
certain measures of community stability. Here we use controlled
ﬁeld experiments in savanna grasslands in southern India to
demonstrate and explain how low-diversity plant communities
can show greater compositional stability when subject to experi-
mental perturbations characteristic of their native environments.
These results are best explained by the ecological history and
species characteristics of communities rather than by species
diversity in itself.
We studied the responses of natural savanna-grassland commu-
nities to disturbance within the Kalakad-Mundanthurai Tiger
Reserve (KMTR, 778159–778409E, 88259–88559N), along the
southern section of India’s Western Ghats Mountains. The stability
of species composition of three low-elevation grassland types
(200 m above sea level)—representing different positions along a
productivity, diversity and disturbance gradient (see Methods)—
were measured in 72 plots (each 4 m 34 m) during 1997 –98
following experimental perturbations in the form of ﬁres, herbivore
exclusion and simulated high-intensity grazing. The stability of
species composition was characterized with two indices: (1) resis-
tance to compositional change, R
, measured as the change in the
relative contribution of different species to the canopy between pre-
and post-disturbance states22; and (2) resistance to species turnover,
, calculated as the proportion of species common to pre- and
Across all communities, compositional stability as measured by
was negatively correlated with diversity (Fig. 1a, using arcsin
:r¼20:304, P¼0:009), and low-diversity communities
were more compositionally stable than high-diversity ones. In
contrast, more diverse communities were more stable as measured
by resistance to species turnover R
(Fig. 1b, using arcsin (R
is inﬂuenced both by patterns of species colonization and
by loss from plots, each of these processes was analysed separately
(Fig. 2a and b). The number of new species recorded in plots
following the start of the experiment decreased as a function of
initial diversity (Fig. 2a; r¼20:482, P,0:001), while those lost
from plots increased with diversity (Fig. 2b; r¼0:617, P,0:001).
In most cases, the number of colonizing species outweighed those
lost from plots, resulting in the observed positive correlation
between diversity and R
(Fig. 1b). For communities that share a
common species pool, as was the case here, a negative relationship
between diversity and colonization can result, even in the absence of
speciﬁc ecological interactions, simply because fewer species remain
in the pool to colonize species-rich plots. A positive correlation
between species loss and diversity can result if high-diversity plots
contain a greater number of rare species, which are likely to be lost
due to purely stochastic processes. Across all plots, the number of
rare species (cover ,1%) initially present was positively correlated
with diversity (r¼0:387, P,0:05). Irrespective of whether these
observed trends were a consequence of an underlying ecological
mechanism or a statistical phenomenon23,24, low-diversity plots in
this study had a greater turnover of species than high-diversity plots.
Unlike the relationships that appear so evident when data are
pooled across communities, no consistent patterns were observed
between diversity and either measure of stability within individual
communities (arcsin (R
P.0:05; Aristida setacea:r¼20:44, P,0:05; mixture:
r¼20:20, P.0:05; arcsin (R
P,0:05; A. setacea:r¼20:14, P.0:05; mixture: r¼0:29,
P.0:05). These results do not constitute evidence for lack of
signiﬁcant effects of species diversity on the functioning of individ-
ual communities, as diversity was not speciﬁcally manipulated in
these experiments. However, when coupled with the contrasting
patterns observed between diversity and R
0.0 0.5 1.0 1.5 2.0 2.5 3.0
Initial species diversity, H'
0.0 0.5 1.0 1.5 2.0 2.5 3.0
Figure 1 Compositional stability of communities as related to species diversity.
a, Resistance to compositional change (arcsinð
9þ0:813) and b,
resistance to species turnover (arcsinð
9þ0:585), both plotted against
initial species diversity (
9) of 72 experimental plots. Symbols identify communities
(open circles) and mixtures (dots).
© 1999 Macmillan Magazines Ltd
communities (Fig. 1a and b), it does question the validity of
absolute measures of species diversity, in and of themselves, as
predictors of ‘stability’ in natural communities.
Species diversity in nature is an emergent property which results
from historic, biotic and abiotic interactions among different
constituent elements25,26. Consequently, we may expect diversity
in nature to co-vary with factors that regulate the distribution and
abundance of species, such as disturbances, site productivity or site
history (segregation of communities along the diversity axis in
Fig. 1a and b). These factors inﬂuence the identities of potential
member species in a community and can, therefore, affect its
stability properties. To determine how much of the observed
relationships in R
were attributable to species and dis-
turbance characteristics rather than diversity in itself, a multiple
regression analysis was used on arcsin-transformed R
separate effects of community type, diversity, disturbance type and
proneness to disturbance (see Methods). These variables cumula-
tively explained 42% of the observed variation in R
R2¼0:424; P,0:001), but only community type and proneness
to disturbance had signiﬁcant effects (P,0:001). On the other
hand, 53% of the variation in R
was explained by variables
included in the regression (multiple R2¼0:529; P,0:01), but
only diversity was signiﬁcant in this case (H9:P,0:001).
Greater species turnover in low-diversity communities in this
study did not translate into lowered stability as measured by R
most species that colonized (or were lost from) plots were rare and
did not contribute signiﬁcantly to total cover. Compositional
stability as measured by R
depends on the sum total of shifts in
relative cover of individual species. Dominant species are likely to
have disproportionate effects on R
as they are capable of larger
absolute shifts in cover compared to rare species. Low-diversity
systems dominated by one or a few species can therefore show a
large range of variation in compositional stability, depending on the
response of the dominant species (triangular scatter of data points
in Fig. 1a). Similar patterns of greater variation in community
properties such as CO
ﬂux13, biomass and density14 at lower
diversities have also been reported for synthesized microbial com-
munities. Even though low-diversity communities may show
greater variation in levels of stability, they may be more stable
than some higher-diversity communities when the dominant
species responds ‘favourably’ to the disturbances in question.
Given the role that disturbances play in structuring natural com-
munities, such patterns may be more common in nature than is
Previous studies investigating the biodiversity– stability relation-
ship have focused on aggregate community properties such as
biomass, productivity and nutrient cycling, while the relationship
between diversity and constancy of species composition has
received less attention22. Greater stability of aggregate community
properties with increasing diversity has been argued to result from
the increased probability of species or functional groups being
present that can adequately compensate for those harmed by the
disturbance4,6–8,11,14,27. However, compensation, by deﬁnition,
implies compositional change. As our data show, species and
dominance characteristics (collectively identiﬁed by community
type in this study) and disturbance history (as indexed by proneness
to disturbance) may better explain compositional stability patterns
across different community types.
These results have several implications for community, restora-
tion and conservation biologists. First, it is critical that different
aspects of the biodiversity– stability relationship arising from dif-
ferent choices of spatial and temporal scales not be confused.
Evidence for a negative effect of lowered species diversity on stability
resulting from species loss in a community in ecological time does
not imply that species-poor communities in nature, which have
evolved over evolutionary time, are necessarily less stable than
species-rich ones. Second, as our data indicate, and as has been
noted previously28, patterns of community stability vary depending
on the speciﬁc process measured. Third, disturbance regimes, site
productivity and other environmental factors that are currently
being modiﬁed can alter the stability properties of communities. In
situ declines in species diversity due to local extinctions can further
modify these patterns. Last, evidence for stability of aggregate
community properties such as nutrient cycling or above-ground
biomass does not preclude compositional shifts in communities6,7.
Communities and ecosystems are more than the biomass that
they support or the nutrients that they cycle. Even though
biomass or rates of nutrient cycling may remain unchanged, altered
abundance of food or host plants can change, and potentially
destabilize, herbivore and dependent predator populations.
Although high biodiversity may in some cases be associated with
‘desirable’ responses such as stability of nutrient cycling or produc-
tivity, we warn against concluding that species-rich ecosystems will
necessarily ‘cope’ better than species-poor ones in the face of
Responses of three different community-types to disturbances were studied at KMTR
during 1997– 98. Communities dominated by C. ﬂexuosus were the most productive, but
had low species richness and sustained low levels of herbivory. A. setacea-dominated
communities were the least productive, had intermediate species richness and suffered
highest levels of herbivory. Communities that had both species present were intermediate
in productivity and levels of herbivory sustained, and had the highest species richness.
Communities also differed in ﬁre-proneness, with C. ﬂexuosus communities the most ﬁre-
prone, and A. setacea communities the least. The contribution of grass species to the
letters to nature
14 OCTOBER 1999
Number of new species recorded
Initial species diversity, H'
Number of species lost
Figure 2 Patterns of species colonization and loss from plots. a, The number of new
species that colonized plots (NEW ¼24:123
9þ23:58) and b, the number of species
that were lost from plots (LOST ¼3:856
9þ3:692) after 1 year, both plotted against
initial species diversity (
9) of experimental plots. Symbols as in Fig. 1.
© 1999 Macmillan Magazines Ltd
understory canopy varied from 85% in C. ﬂexuosus communities, to 70% in A. setacea
communities, and 60% in mixture communities.
The experimental design was a 2 33 factorial experiment with two burning treatments
(burned and unburned) and three grazing treatments (natural levels of grazing, ungrazed
and experimentally clipped). All experimental plots were 4 m 34 m, located within an
area of ,1km
, subject to similar climate conditions and potentially shared a common
species pool. Overall, there were nine replicates for each unburned treatment and 18 for
treatment combinations involving burning (three and six in each of three community
types, respectively). Plots not experimentally manipulated (unburned, naturally grazed
treatments) were excluded from the analysis. At each sampling session, species richness
and cover was enumerated in eight and four 1-m
sub-plots, respectively, using a stratiﬁed
sampling scheme. Species cover in sub-plots was estimated using a 1m 31 m grid frame
subdivided into 100 units of 0.01 m
each. Data reported here are for one year following
experimental manipulations, and are therefore devoid of any seasonal biases. Where
necessary, they were transformed to ﬁt the assumptions of normality.
Rc¼Sminimum ðpii;pofÞ, where p
represent the relative cover of the ith species
in pre-disturbance and 1 year post-disturbance plots, respectively22.Rst ¼Ncom=Ntot,
represents the total number of distinct species recorded in pre-disturbance and
1 year post-disturbance plots, and N
represents the number of species common to pre-
disturbance and 1 year post-disturbance plots. Diversity was calculated using the
Shannon– Weiner index29 as H9¼SpilnðpiÞ, where p
represents the proportional con-
tribution of the ith species to the canopy. Proneness of communities to different
disturbance combinations was calculated as Pbg ¼PbþPg, where the subscripts b and g
represent the speciﬁc burning and grazing treatments. Proneness to burning was
determined on the basis of the cover of C. ﬂexuosus present initially in the plot (P
treatments were assigned the value P
whereas unburned treatments were assigned a value
of (1 2Pc) for this index. We believe that this is a valid index because C. ﬂexuosus
individuals are characteristic of the ﬁre-prone environments, and also promote ﬁres
because of the extent of litter and standing dead biomass they produce. For the grazing
treatments, grazed and clipped plots were assigned the value P
and ungrazed plots
(1 2Pg), where P
represents the fraction of species initially grazed in plots.
Received 27 July; accepted 16 August 1999.
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We thank the Tamil Nadu Forest Department for granting permission to work at KMTR,
and J. Ratnam for support and comments. Wealso thank L. L. Wolf, D.Frank, T. R. Shankar
Raman and D. Barua for comments; R. Ali, V. Vinatha, K. Kar Gupta, M. Katti,
D. Mudappa, N. M. Ishwar, K. Vasudevan and K. S. Gopi for their help; and C. Sankaran,
P. Kumar and C. Jayseelan for ﬁeld assistance. This work was supported by the Wildlife
Conservation Society (India), NSF and the Sophie Danforth Conservation Biology Fund.
Correspondence and requests for materials should be addressed to M.S.
letters to nature
14 OCTOBER 1999
Symmetry in locomotor central
pattern generators and animal gaits
Martin Golubitsky*, Ian Stewart†, Pietro-Luciano Buono‡& J. J. Collins§
*Mathematics Department, University of Houston, Houston,
Texas 77204-3476, USA
†Mathematics Institute, University of Warwick, Coventry CV4 7AL, UK
‡Mathematics Institute, University of Warwick, Coventry CV4 7AL, UK
§Department of Biomedical Engineering, Center for BioDynamics,
Boston University, 44 Cummington Street, Boston, Massachusetts 02215, USA
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Animal locomotion is controlled, in part, by a central pattern
generator (CPG), which is an intraspinal network of neurons
capable of generating a rhythmic output1–4. The spatio-temporal
symmetries of the quadrupedal gaits walk, trot and pace5–8 lead
to plausible assumptions about the symmetries of locomotor
CPGs9–11. These assumptions imply that the CPG of a quadruped
should consist of eight nominally identical subcircuits, arranged
in an essentially unique matter. Here we apply analogous argu-
ments to myriapod CPGs. Analyses based on symmetry applied
to these networks lead to testable predictions, including a dis-
tinction between primary and secondary gaits, the existence of a
new primary gait called ‘jump’, and the occurrence of half-integer
wave numbers in myriapod gaits. For bipeds, our analysis also
predicts two gaits with the out-of-phase symmetry of the walk and
two gaits with the in-phase symmetry of the hop. We present data
that support each of these predictions. This work suggests that
symmetry can be used to infer a plausible class of CPG network
architectures from observed patterns of animal gaits.
The architecture of CPGs is seldom observable in vivo. Aspects of
CPG structure are therefore usually inferred from observable gait
features such as the phase of the gait cycle at which a given limb hits
the ground, and the ‘duty factor’—the proportion of the gait cycle
that a limb is in contact with the ground. It is usual to model CPGs
as networks of nominally identical systems of differential equations,
variously described9–17 as ‘units’, ‘oscillators’ or ‘cells’. We use the
Here we discuss a schematic CPG network10 (Fig. 1) that has twice
as many cells as the animal has legs. For expository purpose we
assume that cells 1, …,2ndetermine the timing of leg movements,
and refer to the remaining cells as ‘hidden’.
The structure of the CPG network for a quadruped shown in
Fig. 1b can be deduced from six assumptions: (1) the abstract CPG
network is composed of identical cells, and the signal from each
cell goes to one leg; (2) different gaits are generated by the same