S1
Supplementary Methods
Species abundance distributions: neutral models vs. poisson lognormal
In the neutral model 1, a local community is composed of J individuals. These
local communities are nested within a metacommunity, which contains a total of Jm
individuals. Diversity and relative abundance in the metacommunity are determined
by the composite parameter θ, the “fundamental biodiversity number”. θ is a function
of metacommunity size and speciation rate (θ=2νJm, where ν is the probability of
speciation per birth). At each time step, deaths occur at random, with all individuals
equally susceptible to mortality, and empty sites are recolonized by the offspring of a
remaining local community member, or by immigration from the metacommunity,
according to the probability of immigration m. Jointly, m and θ determine the shape of
a local community’s species abundance distribution. The simulations are ran for
50,000 time steps with 1% mortality at each time step (i.e., for 500 turnovers of the
local community), using High Performance Computing facilities at James Cook
University.
To obtain the parameter estimates necessary to generate distributions of
community similarity, we used Hubbell’s procedure (chapter 9 in ref 1) for fitting the
simulation-based neutral model to the species-abundance distributions of our local
community data. In addition to using parameter estimates to predict community
similarities, we also directly compared the neutral model’s fit to the abundance
distributions with that of the poisson lognormal, which has been justified on
biological grounds 2, 3, and is commonly used as a null model for species abundance
in tests of the neutral theory 1, 4-6. Model selection using Akaike’s Information
Criterion (AIC) strongly supports the poisson lognormal as the better model (over
99.99% support for the poisson lognormal vs. less than 0.00% for the simulation
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neutral model; Fig S1). To verify that our results were robust to assumptions specific
to the simulation-based neutral model or its fitting procedure, we also fit an analytical
neutral model 6, 7. This yielded similar results: the two neutral models consistently
underestimate the number of rare species, more dramatically so in the case of the
simulation model, and overestimate the number of species with intermediate
abundances. Consistent with the previous analysis, the poisson lognormal is strongly
supported as the better model (99.68% support for the poisson lognormal vs. 0.32%
support for the analytical neutral model). As for the poisson lognormal 8, the best-fit
parameterisation of the neutral model (with over 99.9% support) is for all local
communities within the same habitat and region to have the same parameters ( and
m). Therefore, we define the metacommunity at this scale for our analyses of
community similarity.
Community similarity under neutral dynamics
Bray-Curtis similarity was calculated for each pair of local communities within
the same metacommunity, for both the empirical and simulated datasets. To verify
that our results were not sensitive to the choice of the Bray-Curtis statistic as a
measure of community similarity, we repeated our analysis using Jaccard statistics,
which use only presence-absence data, and thus contain less information but are more
robust to sampling effects 9. Similar results were obtained with both measures, so only
Bray-Curtis similarities are reported. To test neutral theory predictions against
observed community similarity values, we simulated the dynamics of our 12 local
communities within each of our 15 metacommunities, with J equal to the sample size
for each corresponding local community in the coral dataset, and m and  equal to the
values estimated from our fits to the corresponding coral metacommunity.
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Our comprehensive analysis of community similarities under neutral dynamics
indicates that similarity values are approximately normally distributed. Mean
similarity decreases with increasing diversity (Supplementary Fig. S2 a), because in
species-rich communities there are more species whose abundances can vary among
communities. Isolation decreases mean similarity and increases its variance
(Supplementary Fig. S2 b). However, even moderate rates of immigration (0.1)
generate local communities with very high similarity. In mainland-island neutral
models, the size of the simulated metacommunity (Jm) is usually arbitrary, and not
estimated from data 1. To verify that our results were robust to metacommunity size,
we simulated groups of local communities for fixed θ and m, with Jm varying from
twice the size of the local communities to five orders of magnitude greater. We ran
these simulations using the parameter values estimated for each of the five regions
(Fig. 1). The frequency distribution of community similarity exhibits no trend over
this substantial range of metacommunity sizes for any of the parameter sets
(Spearman’s r, all correlations -0.454 < r < 0.115, P > 0.187, n = 10 for mean
similarity; -0.358 < r< 0.430, P > 0.214, n = 10 for standard deviation of similarity).
Nevertheless, to be conservative, we used the largest metacommunities (five orders of
magnitude greater than local community size) in all our analyses.
There is presently some dispute about the extent to which the community
structure patterns reported for neutral models are stable 10, 11. In particular, analysis of
neutral models over time scales much longer than those used in most neutral model
analyses has shown a trend of increasing variance of abundances and decreasing local
species richness 12. Because this increasing variance could potentially lead to longterm trends in community similarities, we assessed numerically whether our
community similarity distributions had equilibrated by running simulations for a
S4
further 1000 community turnovers. This analysis shows that community structure had
indeed stabilized by 500 turnovers for parameter values above very low migration
rates (m~0.001 or greater), regardless of the value of θ (Supplementary Fig. S3). For
this very broad range of parameter values, the community similarity distributions
produced are markedly different from those exhibited by the data (Fig. 2).
For extremely low migration rates, community structure does not equilibrate,
even after 1500 turnovers (Supplementary Fig. S3 a, b, c). Therefore, the possibility
that distributions of community similarity for these parameter values could resemble
those of our data cannot be ruled out. However, this superficial resemblance should
not be interpreted as evidence for good fit of the neutral model, for several reasons.
Firstly, for these parameter values, local species richness progressively decreased as
communities tended towards mono-dominance (Supplementary Fig. S3 c). This is
clearly not representative of scleractinian coral communities, which have sustained
moderate to high biodiversity for tens of thousands of years. Moreover, the
immigration rates necessary to produce these distributions (m<0.001, or less than one
immigrant to a local community per ten thousand births) differ from the estimated
migration rates from our local community distributions (0.75<m<0.92) by over two
orders of magnitude, and they are also inconsistent with population genetic data,
which indicate moderate to high levels of immigration at spatial scales comparable to
those of our local communities (tens of km) 13, 14.
It is worth note that our finding that very large local communities (10,000
individuals in the simulations used to produce Figs. 2, S2, and S3) exhibit a long-term
trend towards mono-dominance under extreme isolation contradicts earlier claims that
such trends only occur for very small local communities 11. When local communities
with smaller J are used, the neutral theory predictions are nearly identical for high
S5
immigration rates (such as those estimated for our data), and the trend towards monodominance at lower immigration rates becomes even more pronounced.
References
1.
Hubbell, S. P. The Unified Neutral Theory of Biodiversity and Biogeography
(eds. Levin, S. A. & Horn, H. S.) (Princeton University Press, Princeton, 2001).
2.
Engen, S. & Lande, R. Population dynamic models generating the lognormal
species abundance distribution. Mathematical Biosciences 132, 169-183 (1996).
3.
May, R. M. in Ecology and Evolution of Communities (eds. Cody, M. L. &
Diamond, J. M.) 81-120 (Belknap Press of Harvard University Press, Cambridge,
1975).
4.
McGill, B. J. A test of the unified neutral theory of biodiversity. Nature 422,
881-885 (2003).
5.
Olszewski, T. D. & Erwin, D. H. Dynamic response of Permian brachiopod
communities to long-term environmental change. Nature 428, 738-741 (2004).
6.
Volkov, I., Banavar, J. R., Hubbell, S. P. & Maritan, A. Neutral theory and
relative species abundance in ecology. Nature 424, 1035-1037 (2003).
7.
McGill, B., Maurer, B. A. & Weiser, M. D. Empirical evaluation of neutral
theory. Ecology (in press).
8.
Connolly, S. R., Hughes, T. P., Bellwood, D. R. & Karlson, R. H. Community
structure of corals and reef fishes at multiple scales. Science 309, 1363-1365 (2005).
9.
Legendre, P. & Legendre, L. Numerical ecology (Elsevier, Amsterdam; New
York, 1998).
10.
Chisholm, R. A. & Burgman, M. A. The unified neutral theory of biodiversity
and biogeography: Comment. Ecology 85, 3172-3174 (2004).
S6
11.
Hubbell, S. P. & Borda-De-Agua, L. The unified neutral theory of biodiversity
and biogeography: Reply. Ecology 85, 3175-3178 (2004).
12.
Maurer, B. A. & McGill, B. J. Neutral and non-neutral macroecology. Basic
and Applied Ecology 5, 413-422 (2004).
13.
Ayre, D. J. & Hughes, T. P. Genotypic diversity and gene flow in brooding
and spawning corals along the Great Barrier Reef, Australia. Evolution 54, 1590-1605
(2000).
14.
Ayre, D. J., Hughes, T. P. & Standish, R. J. Genetic differentiation,
reproductive mode, and gene flow in the brooding coral Pocillopora damicornis along
the Great Barrier Reef, Australia. Marine Ecology Progress Series 159, 175-187
(1997).