ISLAND ASSEMBLY THEORY 117Box 5.1 On null models in biogeography
As applied in statistical analysis, a null
hypothesisis the hypothesis of no effect
(in respect of a potential controlling variable), or
of no difference (between two or more
populations). The rejection of the null hypothesis
leads to the inference that there is an effect or a
difference. Null models, on the other hand, are
computer simulations used to analyse patterns in
nature, in an effort to achieve predictability and
falsifiability in ecological biogeography. As
typically applied within island biogeography, the
approach taken is aimed to simulate random
colonization of a set of islands by the members of
a species pool, given particular constraints, such
as how species number per island is constrained
by island area. By repeating the random
simulation a large number of times, it is possible
to determine whether the observed pattern of
species occurrence could have occurred by chance
using a given level of significance.
The use of null models has been the subject of
intense debate virtually wherever they have been
applied within biogeography. Sometimes the
arguments have been technical in nature,
concerning how well the simulations achieve the
intended goal of randomness or how well theymatch the intended constraints. More intractable
is that it is very hard to reach an accord as to the
correct way to set the constraints upon a system,
i.e. which parameters are controlled and which
are allowed to vary. Both sets of problems are
exemplified by the assembly rules controversy
discussed in the text. Here, the aim was to test for
interspecific competition effects by building
models that were neutral in respect of
competition. But is this possible in the real world?
In practice, unlike for simpler forms of
inferential statistics, we can rarely expect
agreement on a single null formulation for use in
biogeographical modelling. It is better to think of
them not as ‘null models’ with the attached
implications of a higher form of objectivity, but
simply as simulation models, each involving a
particular set of assumptions and constraints.
Such models have value in exploring and testing
out ideas, but always leave room for differences
of interpretation.
For further reading and varying perspectives
on the theme see, e.g. Gotelli and Graves
(1996), Grant (1998), Weiher and Keddy (1999),
Moultonet al. (2001), and Duncan and
Blackburn (2002).ocean gaps, and where an otherwise widespread
species is absent from large, ecologically diverse
islands offering a similar range of habitats to those
occupied by the species elsewhere, but which hap-
pen to be occupied by the alternative species, com-
petition is the obvious answer.
Other authors have since joined in the debate.
Stone and Roberts (1990) re-analysed some of the
data employed in Connor and Simberloff’s (1979)
article, but by means of a new form of test that
they termed the C-score, a means of quantifying
the degree of ‘chequerboardedness’. Their analysis
attempted to avoid some of the problems of
Connor and Simberloff’s methods while maintain-
ing the constraints that they assumed. In contrast
to Connor and Simberloff, their re-analyses led to
rejection of random distributions for both the New
Hebrides and the Antilles avifaunas (see also
Roberts and Stone 1990). Thus, they found sup-
port for chequerboard distributions in both fau-
nas, while stopping short of invoking competitive
explanations for their findings. In a further ana-
lysis, Stone and Roberts (1992) examined the
degree of negative and positive relationships
within confamilial species of the New Hebridean
avifauna. In this case they found evidence not for
chequerboard tendencies, but instead for a greater
degree of aggregation than expected by chance,
i.e. confamilial species tended to occur together.
This they interpreted as evidence for similarities
of ecology within a family overriding competition
between confamilial members. However, as they