Download a nearly neutral model of biodiversity

Ecology, 89(1), 2008, pp. 248–258
Ó 2008 by the Ecological Society of America
A NEARLY NEUTRAL MODEL OF BIODIVERSITY
SHU-RONG ZHOU1,2
AND
DA-YONG ZHANG1,3
1
State Key Laboratory of Earth Surface Processes and Resource Ecology, Beijing Normal University,
Beijing 100875, China
2
Laboratory of Arid and Grassland Ecology under the Ministry of Education, School of Life Sciences,
Lanzhou University, Lanzhou 730000, China
Abstract. S. P. Hubbell’s unified neutral theory of biodiversity has stimulated much new
thinking about biodiversity. However, empirical support for the neutral theory is limited, and
several observations are inconsistent with the predictions of the theory, including positive
correlations between traits associated with competitive ability and species abundance and
correlations between species diversity and ecosystem functioning. The neutral theory can be
extended to explain these observations by allowing species to differ slightly in their competitive
ability (fitness). Here, we show that even slight differences in fecundity can greatly reduce the
time to extinction of competitors even when the community size is large and dispersal is
spatially limited. In this case, species richness is dramatically reduced, and a markedly
different species abundance distribution is predicted than under pure neutrality. In the nearly
neutral model, species co-occur in the same community not because of, but in spite of,
ecological differences. The more competitive species with higher fecundity tend to have higher
abundance both in the metacommunity and in local communities. The nearly neutral
perspective provides a theoretical framework that unites the sampling model of the neutral
theory with theory of biodiversity affecting ecosystem function.
Key words: coexistence; competitive asymmetries; dispersal limitation; metacommunity; nearly neutral
model; species diversity.
INTRODUCTION
A perennial challenge in ecology is to explain the
maintenance of species diversity within communities
(e.g., Hutchinson 1959, May 1975, Pacala and Tilman
1993, Chesson 2000). In this context, Hubbell’s (2001)
unified neutral theory of biodiversity provides a simple
and counterintuitive explanation of species diversity
patterns (see also Bell 2000, 2001, 2003). Based on the
hypothesis that all individuals of all species in a
trophically delimited community have identical per
capita probabilities of birth, death, dispersal, and
speciation, Hubbell’s theory predicts that an equilibrium
will be established between stochastic extinction of
species and appearance of new species through immigration or speciation, depending on the spatial scale
considered.
Studies stemming from the neutral theory largely fall
into two categories. One class of studies focuses on
testing the predictions of the neutral models about
species diversity patterns (e.g., Bell 2000, 2003, Hubbell
2001, Chave et al. 2002, Condit et al. 2002, Clark and
McLachlan 2003, Fargione et al. 2003, McGill 2003,
Volkov et al. 2003, McGill et al. 2006). The second line
of research is concerned with the fundamental assumptions of the theory (e.g., Zhang and Lin 1997, Yu et al.
Manuscript received 30 October 2006; revised 17 May 2007;
accepted 21 May 2007. Corresponding Editor: M. Holyoak.
3 Corresponding author. E-mail: [email protected]
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1998, Enquist et al. 2002, Ricklefs 2003, Chave 2004,
Fuentes 2004, Gilbert and Lechowicz 2004, Loreau
2004, Chase 2005, Hubbell 2005, 2006, Leibold and
McPeek 2006, Ricklefs 2006). The hypothesis of
ecological equivalence is the cornerstone of the neutral
theory, albeit rarely tested in empirical studies. In fact,
all species in all trophically defined communities violate
this assumption to some extent, but Hubbell (2001,
2005, 2006) maintains that neutrality provides a good
approximation. Hubbell (2006) also suggests that
ecological equivalence may evolve easily and quickly
and should be especially commonplace in species-rich
communities.
Zhang and Lin (1997) challenged the neutral theory
on the ground that coexistence among functionally
equivalent species is a fragile phenomenon, because even
a slight variation from complete equality of species
would cause a considerable decline in the time to
competitive exclusion. Hubbell (2001) countered by
suggesting that dispersal and recruitment limitations,
which were not considered in Zhang and Lin’s model,
could delay competitive exclusion essentially without
any limit by reducing the effect of competitive asymmetries among the species. Hubbell based his argument on
two theoretical papers by Tilman (1994) and Hurtt and
Pacala (1995), who developed the models in the context
of traditional niche theory. As far as we know, the
quantitative significance of dispersal limitation has not
been fully investigated with reference to neutral or
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A NEARLY NEUTRAL MODEL OF BIODIVERSITY
nearly neutral models (but see Chave et al. 2002 for an
exception).
Our aim here is threefold. First, in response to
Hubbell’s criticism, we extend Zhang and Lin’s (1997)
work by including in the model dispersal limitation. We
show that the dramatic decrease in the time to fixation
(extinction of competitors) caused by very small
differences in per capita fecundity can overwhelm the
effects of dispersal limitation. Second, drawing on an
analogy with the nearly neutral theory in population
genetics (Ohta and Gillespie 1996, Ohta 2002), we
extend Hubbell’s neutral model by introducing slight
differences in species’ competitive ability (per capita
fecundity). Using the nearly neutral model, we are able
to evaluate the importance of competitive asymmetries
among species versus ecological drift in shaping
community structure. We show that adding even very
slight differences in per capita fecundity into Hubbell’s
model will dramatically reduce species richness and
leads to markedly different species abundance distributions. Finally, a positive correlation between a species’
per capita fecundity and relative abundance arises in the
nearly neutral model for the common species at both
metacommunity and local community levels. The latter
prediction is related to recent empirical findings on
grassland communities (Harpole and Tilman 2006).
THE NEARLY NEUTRAL MODEL
We first examine the effect of interspecific differences
in species’ per capita fecundity on the time to
competitive exclusion in a spatially explicit simulation
of an isolated two-species metacommunity of Jm
individuals. We subsume all aspects of offspring
production, offspring survivorship, and offspring establishment into per capita fecundity. Initially, the two
species are equally abundant and the individuals are
randomly distributed on a square lattice of size L 3 L.
The total number of cells in the landscape (L2) equals
the community size Jm. The landscape is assumed to be a
torus, that is, cells on the right edge are neighbors of
those on the left and cells on the bottom are neighbors of
those on the top. This assumption avoids any spurious
edge effects. We assume that the two species are identical
in all respects except per capita fecundity. When an
individual in a cell dies, a new individual will occupy the
cell immediately, according to species’ dispersal kernel
and per capita fecundities (see Appendix A for the
algorithm). There are no empty cells in the landscape,
and the dynamics of the community is a zero-sum game
(Hubbell 2001).
In the simulations, we let L be 16, 32, 64, or 128, with
community size (J m ) of 16 2 , 32 2 , 64 2 , or 128 2 ,
respectively. Parameter w is the per capita fecundity
factor of the focal species relative to the non-focal
species and has the values 1.0 (the neutral case, no
difference in species’ per capita fecundity), 1.01, 1.05,
1.1, 1.2, 1.3, 1.4, and 1.5. Given the values of Jm and w,
the scale of dispersal varies from global dispersal to the
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opposite extreme of nearest neighbor dispersal through
the intermediate cases in which dispersal distance r is
over two or four cells, respectively. Dispersal is uniform
within the distance r.
As in Yu et al. (1998), we use absolute time rather
than relative time, with the former referring to the actual
time interval and the latter to the number of individual
deaths. For example, in a tropical rain forest tree
community, the absolute time may be characterized in
terms of years. Number of deaths in one time interval
(year) is denoted by D, and can be calculated as the
turnover rate times the number of individuals in the
community. In this paper, we use a moderate turnover
rate of 1.7% per year reported for tropical forests
(Swaine et al. 1987). For each parameter set, we run 100
independent simulations and found the median of the
time to fixation (extinction or complete dominance;
MTF) among 100 replicates. The reason for using
median rather than arithmetic mean is that the
distribution of the time to fixation is generally not
normal (cf. Hubbell 2001). The number of times the
species with higher fecundity wins the competition trial
is also recorded.
In the second model, we investigate the influence of
unequal fecundities on species richness and relative
abundances, with dispersal limitation occurring only
from the metacommunity to the local community. We
follow the algorithm described in Hubbell (2001) to
form a metacommunity consisting of Jm ¼ 1 3 105
individuals, with the fundamental biodiversity number h
¼ 100. In contrast to Hubbell’s model, when a new
species enters the metacommunity, we select its per
capita fecundity from the normal distribution N(1, r2),
where r is standard deviation; other distributions
(uniform or exponential) lead to essentially the same
conclusion. A species’ per capita fecundity will fall in the
range (1 3r, 1 þ 3r) with probability 99.7%. We use
values of r ¼ 0, 0.001, 0.002, and 0.003, where r ¼ 0 is
the neutral case. We denote by wi the relative per capita
fecundity of species i.
We first construct the abundance distribution in the
metacommunity. When a randomly selected individual
in the metacommunity is eliminated, one new individual
is recruited. With probability h/(h þ Jm 1), the new
recruit will be a new species, otherwise it will be one of
the existing species. In the latter case, the probability of
birth of species i is wiPi/Rj wjPj, where the sum is taken
over all species in the metacommunity and Pj is the
abundance of species j in the metacommunity. Note that
the recruitment of existing species is biased by their per
capita fecundities. Simulation is continued until the
metacommunity has reached a stochastic equilibrium,
roughly after 10 000 turnovers of the metacommunities.
The distribution of species’ relative abundances is
obtained by averaging over the abundance of the species
with the same rank in different simulations of 100
replicate metacommunities (Jm ¼ 1 3 105 and h ¼ 100).
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SHU-RONG ZHOU AND DA-YONG ZHANG
With the metacommunity constructed as described
here, we investigated the influence of unequal fecundities
on species richness and the distribution of relative
abundances in local communities. For each metacommunity, a local community of size J ¼ 2000 was
randomly sampled. In the local communities, each
species has the same per capita fecundity as in the
corresponding metacommunity.
To model local community dynamics, we eliminate a
randomly selected individual, which is then replaced
either by an immigrant from the metacommunity or by
an offspring of the existing species in the local
community. The rate of dispersal m from the metacommunity is selected to be 0.002, 0.01, 0.05, or 0.25,
respectively. Thus with probability m an individual from
the metacommunity occupies the vacancy, and the
probability that this immigrant is an offspring of existing
species is proportional to each species’ relative abundance in the metacommunity weighted by the species’
per capita fecundity. With probability 1 m, the new
recruit comes from the local community, and with
probability wiNiL/Rj wjNjL the new recruit is an offspring
of species i, where the sum is taken over all species in the
local community and NjL is the local abundance of
species j. The local dynamics are iterated until a
stochastic equilibrium is reached after, again, about
10 000 turnovers of the local community. The distribution of species relative abundances is the average of 100
replicate local communities drawn from the same
metacommunity and assuming the same dispersal rate m.
Additionally, while calculating the distributions of
species’ relative abundances in the metacommunity and
in the local community, we recorded the relationship
between species’ per capita fecundities and their relative
abundances.
RESULTS
The median time to fixation (MTF) decreases by more
than an order of magnitude as the interspecific
difference in per capita fecundity (w) increases, no
matter whether there is any dispersal limitation or not
(Fig. 1). The most dramatic decline in coexistence time
occurs when there is only a slight fecundity difference, w
, 1.1. For example, in a community of 4096 individuals
with nearest neighbor dispersal, MTF is about 272 972
time intervals (years) in the neutral model, but 44 726
time intervals in the case of w ¼ 1.01 (a decrease of 84%)
and only 11 757 time intervals when w ¼ 1.05 (a decrease
of 96%). The decrease in MTF due to a difference in per
capita fecundity becomes more pronounced as the
community size increases (Fig. 1). For example, in the
largest simulated community of 16 384 individuals with
nearest neighbor dispersal, MTF is about 1 145 566 time
intervals (years) in the neutral model, but only 63 420
time intervals in the case of w ¼ 1.01 (a decrease about
96%) and only 14 136 time intervals when w ¼ 1.05 (a
decrease of 99%). The species with a relative fecundity
advantage of w ¼ 1.01 wins 70 times among 100
Ecology, Vol. 89, No. 1
simulation trials when the metacommunity is 16 3 16,
and always wins when w is 1.05 or larger. For larger
metacommunities, i.e., L ¼ 32, 64, and 128 in our
simulation, the superior competitor wins invariably.
These results suggest that competitive exclusion plays a
far more important role than demographic stochasticity,
even when species differ only slightly in competitive
ability.
Hubbell (2001) argued that even with unequal
fecundities in the species, there would be a huge increase
in the time to extinction of competitors in Zhang and
Lin’s model as community size increases to very large
values. However, Fig. 2 shows that dramatic increase in
MTF with community size only occurs in the neutral
case (w ¼ 1.0); even for the small interspecific difference,
w ¼ 1.05, there is no longer a significant increase in MTF
with increasing community size. Similarly, dispersal
limitation does not have as much influence on species
coexistence as implied by Hubbell, and even the extreme
case of nearest neighbor dispersal only doubled MTF in
our simulations. In our simulation, random initial
distribution of the species is assumed. But even when
the species are initially highly clumped the effect of
dispersal limitation is still limited under non-neutral
conditions (Appendix B). In brief, when a slight
difference in species’ per capita fecundity is introduced
into the neutral model, coexistence time will decline
dramatically, significantly weakening the effects of
within-community dispersal limitation and large community size.
Fig. 3 illustrates the influence of interspecific differentiation in per capita fecundity on species richness and
relative abundances in the metacommunity. As expected, the species abundance distribution in the case of very
similar species, r ¼ 0.001, is close to the prediction of the
neutral model. However, even when r becomes a little
bit larger, with r ¼ 0.002 or 0.003, species richness
decreases dramatically and the distribution of relative
abundances deviates far from the patterns predicted by
the neutral theory. At equilibrium, there is a relative
deficiency of species with intermediate abundance and
relatively more of very abundant or rare species.
With a difference in species’ per capita fecundities
included in the model, there is an evident positive
correlation between per capita fecundity and the rank of
the species in abundance for the common species,
whereas the per capita fecundity of intermediate and
rare species fluctuates around 1, the mean of the initial
distribution of species fecundities, with the rarest species
having higher variance (Fig. 4). In other words, those
species that have higher per capita fecundity have an
advantage in competition. The very abundant species
account for only less than 20% of all species in the
metacommunity. Most of the remaining species are
neutral except those very rare species that are new
members of the metacommunity (Fig. 4).
Turning to the structure of local communities, the
influence of fecundity differences among the species is
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251
FIG. 1. The influence of interspecific differences in fecundity (w) and dispersal distance (r) on the median time to fixation (MTF)
in a two-species community. MTF decreases greatly when fecundity (w) and community size increase. L is the number of
contiguous cells in one lattice axis. Note the log scale on the y-axis.
similar to that in the metacommunity, but dispersal
limitation from the metacommunity (m) is also important (Fig. 5). Strong dispersal limitation at the regional
scale results in much fewer species and steeper rank–
abundance distributions in local communities (i.e.,
greater dominance by competitively superior species).
The species abundance distribution will become increasingly similar to that of the corresponding metacommunity as dispersal rate m increases (Fig. 5).
For local communities, there is once again a striking
positive correlation between relative fecundity and
species rank in abundance (Fig. 6). However, this
relationship is somewhat different than in the corresponding metacommunity, as now the fecundity of all
species within a local community is greater at equilib-
rium than the mean. The reason for this difference is
that the rare species in the metacommunity have little
chance to enter the local community, and only species
with high relative fecundity will persist for a long time.
In this case, we may conclude that small competitive
asymmetries among species play a large role in
community structure.
We fitted the neutral model to simulated data from
the nearly neutral local communities with J ¼ 2000, h ¼
100, r ¼ 0.001 or 0.002 under different dispersal rates,
using the method of Etienne (2005). The results are
shown in Appendix C. In the case of low dispersal rates
from the metacommunity (m ¼ 0.002 and m ¼ 0.01), the
neutral model fits to the nearly neutral local communities reasonably well, though not as good as some real
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SHU-RONG ZHOU AND DA-YONG ZHANG
FIG. 2. The influences of community size, dispersal distance
(nearest neighbor vs. global), and interspecific differences in
fecundity on median time to fixation (MTF). MTF increases
proportionally as the community size increases, but a dramatic
increase in MTF with community size occurs only in the neutral
drift case. Increase in MTF due to dispersal limitation is
moderate. Note that w ¼ 1.0 under the neutral model. Note the
log scale on both axes.
communities (Volkov et al. 2003, Hubbell 2006). Under
such situations the dispersal rate (m) tends to be much
overestimated whereas the fundamental biodiversity
number (h) tends to be greatly underestimated. Thus
the failure to reject the null hypothesis based on a
neutral model does not necessarily vindicate the neutral
assumption of ecological equivalence: ‘‘neutral pattern’’
does not imply a neutral process (cf. Purves and Pacala
2005, Walker 2007).
Ecology, Vol. 89, No. 1
neutral theory as a simple extension of the neutral
theory. Relaxing neutrality but without resorting to a
more complex concept of niche differentiation, our
nearly neutral framework effectively removes many of
the inconsistencies between the original neutral model
and empirical data. It also enables us to achieve several
novel insights into species coexistence and community
structure.
Neutral theory clearly does not predict which species
are rare and which are abundant. In contrast, the nearly
neutral theory presented in this paper predicts a positive
correlation between traits associated with competitive
ability and species abundance: the most abundant
species are also the most competitive (see Figs. 4 and
6). We relate this prediction to the recent work of
Harpole and Tilman (2006), who studied grassland
communities at Cedar Creek, Minnesota, USA, where
competition for nitrogen is a key factor structuring
communities. They measured in monoculture the species
trait R*, minimum level of N in the soil for sustainable
growth of the species, and showed that across a variety
of gradients in nitrogen availability (experimental
manipulation, successional, and large scale natural),
species abundance was well predicted by R*, even
though the observed abundance distribution was qualitatively consistent with the neutral theory. Harpole and
Tilman concluded that the pattern they detected
supports some niche mechanism, but we note that their
results are also consistent with the nearly neutral model.
Our examples in Appendix C demonstrate that local
communities of nearly neutral species can often be fitted
by a neutral model, especially when dispersal is highly
limited at the regional scale from the metacommunity to
local communities. According to the nearly neutral
theory, the response of species to environmental change
DISCUSSION
Since the publication of Hubbell’s book in 2001, there
has been much discussion of the neutral theory in
ecology, both pro and con (Whitfield 2002, Norris 2003,
Chave 2004, Gaston and Chown 2005, Alonso et al.
2006, Gewin 2006, Holt 2006, Holyoak et al. 2006, Hu et
al. 2006, Adler et al. 2007). Most ecologists regard the
neutral assumption of all species being equivalent as
highly unrealistic, but Hubbell (2001, 2005, 2006)
contends that differences among the species are small
enough and their dynamics are sufficiently stochastic to
allow the neutral models to capture the essence of the
structuring of ecological communities. Apart from the
strong psychological bias against neutrality felt by most
ecologists, close analyses of several systems have
revealed clearly non-neutral patterns (Adler 2004, Chave
2004, Wootton 2005, Gilbert et al. 2006, Harpole and
Tilman 2006, McGill et al. 2006). Niche differentiation
has been widely considered as the main alternative to
neutrality, but this may not be necessary. As in
molecular evolution (Ohta and Gillespie 1996, Ohta
2002), we can put forward in ecology, too, the nearly
FIG. 3. Metacommunity equilibrium rank–abundance
curves for models with and without differences among the
species in fecundity. Parameter values: metacommunity size, Jm
¼ 1 3 105; fundamental biodiversity number, h ¼ 100; r is the
standard deviation of the normal distribution of the per capita
factor for new species. Note the y-axis log scale.
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253
FIG. 4. The relationship between species’ per capita fecundity and species rank in abundance within the metacommunity. For
definitions of Jm, h, and r, see Fig. 3.
would also be non-neutral, again likely correlated with
species traits.
The generally positive correlation between traits
associated with competitive ability and species abundance supports a strong role for competition in
community assembly. But plant species richness at
Cedar Creek is high despite intense competition for the
limiting soil nutrient. This raises the question of how can
so many species coexist. Interestingly, Harpole and
Tilman (2006) found no evidence for a competition–
colonization tradeoff because seed production of particular species in monocultures was independent of their
R* values. In the light of the nearly neutral community
assembly, superior competitor will not necessarily
exclude all other species, provided that there is a steady
stream of immigrants from the source metacommunity
on the local scale (see also Loreau and Mouquet 1999,
Holt 2004, Zillio and Condit 2007) or through speciation
at the metacommunity scale (Hubbell 2001). In such
circumstances, coexistence occurs in spite of, not
because of, species differences. Here we hasten to
emphasize that the coexistence of nearly neutral species
is not stable (sensu Chesson 2000): most species are in
the process of being driven extinct by interactions with
dominant species. As in the neutral model, diversity is
maintained as a dynamic equilibrium between the
extinction of resident species and the appearance of
new species through immigration or speciation (Loreau
and Mouquet 1999, Fuentes 2004, Zillio and Condit
2007).
Leigh et al. (2004) suggested that tropical tree species
rarely originate by splitting of large populations, but
instead begin with few individuals, essentially in conformity with the point mutation mode of speciation (sensu
Hubbell 2001). If so, Leigh et al. argued, species that are
now common (likely represented by more than 10 million
mature trees) must have spread more quickly than
chance allows; otherwise the species appeared well before
the origin of angiosperms 140 million years ago,
according to the neutral theory. Consequently, Leigh et
al. (2004) concluded that tropical tree species can become
common and widespread only through an advantage
over their competitors. In our nearly neutral model, such
competitive advantages are indeed enjoyed by the most
abundant species within the community (Fig. 6).
Conversely, Ricklefs (2003, 2006; see also Nee 2005)
criticized the neutral theory for its prediction of an
unrealistic long life span of abundant species. This
quandary seems even more serious for the nearly neutral
species, because once some highly fecund species arrived
and became abundant they will be expected to persist for
an even longer time. However, more competitive species
may keep emerging (assuming inheritance in species
traits), and tend to displace the current dominant species.
For some plant communities, there is evidence
suggesting that species diversity promotes productivity
and/or stability (Kinzig et al. 2002, Loreau et al. 2002,
Cardinale et al. 2006), though not everybody agrees with
the interpretation of the data (Hubbell 2006). Complementary resource use via niche differentiation is
commonly invoked to explain these relationships (Kin-
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Ecology, Vol. 89, No. 1
FIG. 5. Local community equilibrium rank–abundance curves of models with and without differences in species’ per capita
fecundities, for different dispersal rates, where m is the rate of immigration from the metacommunity to the local community. Other
parameter values: J ¼ 2000, h ¼ 100. For each panel, the line types from top to bottom in the key correspond to the curves from
right to left.
zig et al. 2002, Loreau et al. 2002). According to the
niche differentiation mechanism, species use resources in
different ways and consequently more of the available
resources are utilized with increasing diversity. Alternatively, a positive diversity effect could represent a
sampling effect, in which diverse communities perform
better due to higher likelihood that they would contain
high yielding species under the particular conditions
(e.g., Huston 1997, Cardinale et al. 2006). While the
neutral theory is incapable of explaining such biodiversity effects, the nearly neutral model does predict a role
for particular species in ecosystem functioning via
sampling processes. The sampling effect has been
suggested to operate merely as a transient phenomenon
(Kinzig et al. 2002, Loreau et al. 2002), but in the nearly
neutral perspective it can exert a lasting impact, as
evidenced by a recent meta-analysis (Cardinale et al.
2006). Most interestingly, Cardinale et al. (2006) find
that, contrary to niche differentiation, the standing
stock of, and resource depletion by, the most speciesrich assemblage tends to be no different from that of the
single most productive species used in an experiment.
We note that this observation can be readily explained
by the nearly neutral theory, provided that there is
further evidence for exclusion of all but the best
competitor. The fact that multiple species continue to
exist in these experiments does not necessarily negate
this interpretation, because experiments may have been
performed at shorter temporal scales or extinction of
inferior competitors may be delayed or even prevented
due to recurrent external immigration (Loreau and
Mouquet 1999, Holt 2004).
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255
FIG. 6. The relationship between species’ per capita fecundity and their rank in abundance in local communities with different
dispersal rates. Other parameter values: J ¼ 2000, h ¼ 100.
So far we have emphasized the similarity and common
ground between the neutral and nearly neutral theories in
general, and between our work and Hubbell’s in
particular. Below we highlight the key differences
between the two models. Hubbell (2001, 2005, 2006)
proposed that dispersal and recruitment limitation would
act as the most important factors to delay competitive
exclusion, which in turn would facilitate evolution and
long-term coexistence of functionally equivalent or nearequivalent species. Hubbell cited the work of Tilman
(1994) and Hurtt and Pacala (1995) as the support to his
view. In particular, Hurtt and Pacala (1995) demonstrated that recruitment limitation could overwhelm the
effects of strong competitive differences between species
on structuring of communities, especially in highly
diverse communities where dispersal and recruitment
limitation is likely to be most pronounced. However,
Hurtt and Pacala modeled only a community of nichedifferentiated species partitioning an environmental axis,
and did not consider the neutral or nearly neutral cases.
We have shown that when the neutral model is modified
to include even slight differences in per capita fecundity,
a significant decrease in coexistence time will follow even
under the strongest dispersal limitation, the nearest
neighbor dispersal. Dispersal limitation can only enhance coexistence to a moderate extent (Fig. 1). Contrary
to Hubbell’s (2001) proposition, we suggest that longterm coexistence of nearly neutral competitors lies more
with large community size than dispersal limitation. As
first noted by Hubbell (2001) himself, relatively small
differences among species in per capita mortality or
fecundity can nevertheless produce large differences in
steady-state relative species abundance, presumably due
to hastened competitive exclusion (Fig. 1). In this sense,
our previous conclusion (Zhang and Lin 1997) holds: the
neutral model of biodiversity is very sensitive to
violations of its fundamental assumption of functional
equivalence of species (see also Fuentes 2004).
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SHU-RONG ZHOU AND DA-YONG ZHANG
An obvious feature of species abundance curves
generated by the nearly neutral model is the reduced
evenness of communities, with excessive dominance of
the common species. In nature, many communities show
this pattern of species abundances, including an old
growth forest in Peru, cited in Hubbell (2001). More
recently, Walker and Cyr (2007) showed that all the
phytoplankton communities they examined did not fit
the neutral model by at least one of three measures used.
Phytoplankton communities deviated from the neutral
toward the nearly neutral model by showing consistent
over-dominance of one or a few most abundant species.
Hubbell (2001) proposed that only a small fraction of
the species in a community tend to show overdominance
under nearly neutral conditions, with the remaining
species being essentially neutral. Our results in Fig. 5
largely confirm this conjecture: less than 20% species are
very abundant and have a discernible advantage in
competitive ability. Most species in the metacommunity
are rare and essentially equal, except some very rare
species that are new members of the metacommunity.
Non-neutral patterns are often regarded as prima
facie evidence for the operation of niche mechanisms, as
if the niche concept were the only alternative to
neutrality. Indeed, it has been customary to invoke
niche differentiation whenever neutrality can be rejected.
To many ecologists, unifying niche and neutral approaches would be an obvious step forward (Chave et al.
2002, Tilman 2004, Volkov et al. 2005, Gewin 2006,
Gravel et al. 2006, Holt 2006, Liebold and McPeek 2006,
Adler et al. 2007, Walker 2007). We do not disagree with
this view, but we also urge ecologists to consider the
merits of the nearly neutral models. It is lack of
stabilizing mechanisms that distinguishes neutral or
nearly neutral models from niche models. We advocate
that competitive asymmetries in the sense analyzed in
this study may be sufficient to provide a parsimonious
general explanation of community structure and biodiversity.
Finally, we wish to acknowledge the limits of our
model in the hope of stimulating further works in this
exciting field. First and foremost, we assume a
stationary, normal, distribution of per capita fecundity
of newly arrived species. This is also the assumption
made in Ohta’s nearly neutral model of molecular
evolution for the fitness effects of new mutant alleles
(Ohta and Gillespie 1996, Ohta 2002). A stationary per
capita fecundity of new species means lack of inheritance
in species traits and no selection toward the species with
highest fitness, which is clearly unrealistic. However, in
the presence of inheritance, one may expect that most of
the new species will have traits similar to the abundant
species. Thus even with the introduction of fitness
inequality, most of the species will tend to be closely
similar, making our approach (stationary distribution of
per capita fecundity, but with very small variance)
perhaps a good operational first approximation. Second,
our nearly neutral model also assumes, as neutral
Ecology, Vol. 89, No. 1
models do, that metacommunities and local communities are in dynamic equilibrium. However, it is possible
that the time to equilibrium in the nearly neutral model
is so long that the equilibrium distribution will rarely be
observed in real ecological communities. Third, our
model is still unable to relate species identity to the
environment and to address species turnover along
environmental gradients, which have been regarded as
the major flaws of the neutral theory so far (e.g., Gilbert
and Lechowicz 2004). Spatial turnover in species
composition is a major determinant of species diversity
at the regional scale. Thus, any attempt to understand
the structure of ecological communities must take into
account the role of species turnover and the factors that
influence it. We still have a long way to go toward a full
understanding of the role of stochastic processes in
community assembly.
ACKNOWLEDGMENTS
We are grateful to I. Hanski and F. He for constructive
criticisms, careful editing, and linguistic help with the manuscript and to M. Holyoak and two anonymous reviewers for
very useful comments. We also thank K. Lin for his help with
computer simulations. This work was supported by the State
Key Basic Research and Development Plan (2007CB106800),
the National Natural Science Foundation of China (30670314
and 30628005), and Beijing Normal University.
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SHU-RONG ZHOU AND DA-YONG ZHANG
Ecology, Vol. 89, No. 1
APPENDIX A
Numerical algorithm used in this paper to investigate the influence of dissimilar fecundities of species on mean time to fixation
(MTF) (Ecological Archives E089-014-A1).
APPENDIX B
A comparison between the time to fixation under random initial distribution and when each species initially occupies one half of
the landscape, the most extreme case of spatial clustering, in a community of 1282 individuals with nearest neighbor dispersal
(Ecological Archives E089-014-A2).
APPENDIX C
Maximum-likelihood estimates of h and m, with J ¼ 2000, h ¼ 100, r ¼ 0.001 or 0.002, and various dispersal rates from the
metacommunity (Ecological Archives E089-014-A3).