152 Stephen P. Hubbell
Third, fitting issues aside, I have more fun-
damental problems with the lognormal hypoth-
esis. First of all, the lognormal is essentially a
generic statistical distribution whose parameters
are not derived from population biological pro-
cesses, whereas every parameter of neutral theory
has a straightforward biological interpretation.
Although there have been several attempts to
construct theories of community organization
that result in lognormal-like distributions, such
as the sequential broken stick model (Sugihara
1980) or the nested niche hierarchy model (Sug-
iharaet al.2003), the evidence marshaled to
support these models is not ecologically or evo-
lutionarily compelling, in my opinion, and once
again, the parameters do not have straightforward
connections to population biology. Proponents
of the lognormal have not adequately addressed
two really serious problems with the distribu-
tion. The first problem is the assumption of
a fixed variance, or spread, between the com-
monest and rarest species in a community, the
so-called canonical hypothesis (Preston 1962).
The canonical hypothesis means that, for exam-
ple, with a doubling in sample size, each species
should increase in logarithmic proportion, so that
the variance in log abundances remains con-
stant even as mean species abundance doubles.
The only way this can happen is if the abun-
dances of the rarest species also increase in
logarithmic lockste pwith the common s pecies.
But this is never observed in real samples. In
reality the rarest species in a sample are almost
always singletons, regardless of sample size, so as
the common species increase in abundance, the
variance in relative abundances also increases.
There is no such canonical assumption in neutral
theory. The second problem is that the lognor-
mal fails as a dynamical model of communities;
it can be fit only to static relative abundance
data (Hubbell and Borda de Água 2004). This
limitation does not apply to neutral theory, as we
will see below.
Another critique of neutral theory was made
by Dornelaset al.(2006), who analyzed rel-
ative abundance patterns in a geographically
large collection of reef communities (the “reef
metacommunity”). They found that the meta-
community had a relative abundance distribution
with an interior mode, resembling a lognormal
distribution, whereas local reefs had a Fisher
logseries-like distribution, just the opposite to
the prediction in my book (Hubbell 2001). They
asserted that this observation “refutes” neutral
theory.Of coursetheydidnothingof thesort–any
more than one can “refute” the Hardy–Weinberg
equilibrium – because both are mathematical the-
orems. What one can legitimately say, however, is
this case does not fit neutral theory as presented
in my book. In doing good science, there should
be regular feedback between empirical work and
theory development. When a theory fails in a par-
ticular case, the next thing to do is to figure out
why it happened. We began a quest for possi-
ble causal factors that might invert the pattern
of relative species abundance. After considering
the biogeographic differences between the coral
reef and rainforest systems, we realized that two
contrasting theoretical scenarios of metacommu-
nity structure would lead to inverted patterns of
relative abundance on local and regional scales
(Volkovet al. 2007). On the one hand, one could
have relatively small, partially isolated local com-
munities surrounded by a very large metacom-
munity acting as a source of immigrants, which
is the structure I envisioned in my book for tropi-
cal rainforests (Hubbell 2001). On the other hand,
one could have spatially very isolated island com-
munities whose assemblage in aggregate acts as
the metacommunity, as in coral reefs. In the tropi-
cal forest scenario, the time for species turnover
in the metacommunity is extremely long rela-
tive to turnover in local communities, so that the
relative abundance distribution in the metacom-
munity is essentially fixed or “frozen” as a source
of immigrants compared with the fast dynam-
ics of the local community. This is very different
from the coral reef scenario. In the latter case,
each local community receives immigration from
all the surrounding, isolated island communities,
in each of which relative species abundances are
not frozen. This means that the effect of disper-
sal limitation emerges only on metacommunity
scales, not on local scales. As a consequence,
one can prove that logseries-like distributions will
be found in local reef communities, but not on
regional scales (Volkovet al.2007). So the new
insight is that the relative abundance pattern you