96 SPECIES NUMBERS GAMES: THE MACROECOLOGY OF ISLAND BIOTAS
models against empirical data sets rather than
setting out to find the best straight-line fit through
the data.
Lomolino (2000c) has also questioned the
approach of using data transformation in search of
the best linear fit. He argues that there may be good
ecological reasons to posit more complex scale-
dependent relationships, and that untransformed
SPARs should exhibit a sigmoidal form, with a
phase across low values of area, where species
numbers scarcely increase, followed by a rapid
increase with area and a subsequent flattening as
the number of species approaches the richness of
the species pool (Fig. 4.6).
At the left-hand end of the plot, the existence of
a ‘small island’ effect appears well established
(Lomolino 2000c, 2002; Lomolino and Weiser 2001)
although this is not to say it occurs in all data sets
(below). Lomolino and Weiser (2001) provide a
formal analysis of a large sample of ISARs, com-
paring the results of conventional regression
analyses with those obtained from breakpoint
regression. These analyses show that the small-
island effect is comparatively common in island
data sets. The threshold area tended to be highest
for species groups with relatively high resource
requirements and low dispersal abilities, and also
to be comparatively high for more isolated archi-
pelagoes. But with regard to the right-hand end,
Williamson et al. (2001, 2002) contend that there is
no evidence of the upper asymptote whereby the
log–log ISAR flattens off across the largest islands.
As Williamson and colleagues note, just as the
species pool from which isolated biotas are
derived contains a finite number of species, so too
does the area, i.e. any particular ocean system con-
tains a largest island. The shape of the ISAR as it
approaches maximum area might be of a variety
of forms, but they contend, empirically fails
to show departure from a straight line relationship
at the right hand end when plotted in log–log
space. Recent analyses by Gentile and Argano
(2005) of sets of terrestrial isopod data from
Mediterranean islands in which sigmoid models
were evaluated against linear, semi-logarithmic,
and logarithmic models tend to support this view.
Despite the occurrence of a small-island effect, a
sigmoid model failed to provide the best
representation of the data. This suggests that
the evolutionary effect posited by Lomolino
on large islands in practice has an indistiguish-
able impact on the form of ISARs, which is
essentially as suggested by MacArthur and Wilson
(1967).
It is noteworthy that the form and biological
meaning of ISARS and other forms of species–
area plots remain the subject of so much debate
and confusion. One important reason is that
empirical data sets each have their own unique
combination of variation in contributory environ-
mental variables, of area, elevation, climate,
habitat type, isolation, disturbance histories, etc.
This introduces both structure (e.g. Kalmar and
Currie 2006) and some noise into ISARs, which
after all merely consider one independent vari-
able: area. Comparison of published regression
models, in which richness has been analysed
against an array of independent variables, not
surprisingly shows a diversity of answers as to
which factors enter the models in which order,
and with what particular relationship to richness.
Each of these variables has relevance, but does
not necessarily have significance over all scales
within the empirical data gathered. Perhaps
unsurprisingly, few analyses have attempted to
tackle the possibility of threshold responses in
respect of the complex array of potentially impor-
tant, interacting variables: even for area, formal
testing for threshold effects and more complex
models of the form of the relationship has been
only a recent and fairly controversial develop-
ment. What we can say with respect to simple
data transformations, is that conventional analy-
ses have shown that sometimes semi-log and
sometimes log-log plots of ISAR data provide the
best fit. The generally preferred approach of
log–log plotting of ISAR data typically provides a
good fit over most of the range in area, with most
evidence for systematic divergence being of the
form of the small-island effect.