THE DEVELOPMENT OF THE EQUILIBRIUM THEORY 81densities would have little chance of persisting
and should frequently go locally extinct. And, the
further they had to travel from the mainland, the
less frequently they would recolonize. Hence the
ISARs should vary in relation to isolation, as a
function of varying rates of immigration to and
extinction from the islands: producing predictable
patterns of richness and turnover. There should
also be systematic variation in SADs accompany-
ing the pattern in ISARs; although sampling
problems in detecting the form of the tail of SADs
(and analytical problems in comparing them)
make this harder to assess.
It has been noted that K.W. Dammerman (1948),
in his monograph on Krakatau, had described sev-
eral of the key elements of the eventual equilibrium
theory, although he had failed to put them into a
mathematical framework (Thornton 1992). Another
biologist, Eugene Munroe, went one better than
Dammerman. In his studies of the butterflies of the
West Indies, Munroe presented a formulaic version
of the equilibrium model, similar to that independ-
ently developed by MacArthur and Wilson in their
1963 paper (Brown and Lomolino 1989). Munroe’s
formula appeared only in his doctoral thesis (1948)
and in the abstract of a conference paper published
in 1953. Neither Dammerman nor Munroe went on
to develop the ideas beyond a fairly rudimentary
form.
In the following sections we explore, in a little
more depth, the components MacArthur and
Wilson brought together in their theory.
Island species–area relationships (ISARs)
Building on previous work, MacArthur and Wilson
(1963, 1967), concluded that for a particular taxon
and within any given region of relatively uniform
climate, the ISAR (Box 4.2) can often be approxi-
mated by the power function model:
S=cAzwhere Sis the number of species of a given taxon
on an island, Ais the area, and candzare constants
determined empirically from the data, which thus
vary from system to system.
MacArthur and Wilson, like others before and
since, were interested in determining species–area
relationships in the most tractable fashion for fur-
ther analysis, which is to find the best transforma-
tion that linearizes the relationship. Following
Arrhenius (e.g. 1921) they favoured logarithmic
transformations of both axes (sometimes termed
Arrhenius plots). The equation thus becomes:
logSlogczlogA
which enables the parameters candzto be deter-
mined using simple least squares (linear) regres-
sion. In this equation, zdescribes the slope of the
log–log relationship and log cdescribes its inter-
cept. Thus, a low zvalue (slope) means that there is
less sensitivity to island area than for a system of
highzvalue, while cvalues reflect the overall
biotic richness of the study system, and thus vary
with taxon, climate and biogeographical region.
Values of zare easy to compare between study sys-
tems, but the parameter cchanges with different
scales of measurement used (e.g. km^2 versus
miles^2 ), requiring conversion of data to a common
measurement scale before they can be analysed for
comparative purposes.
From the data at their disposal, MacArthur and
Wilson (1967) found that in most cases zfalls
between 0.20 and 0.35 for islands, but that if you
take non-isolated sample areas on continents (or
within large islands), z values tend to vary
between 0.12 and 0.17. Thus, the slope of the
log–log plot of the species–area curve appeared to
be steeper for islands, or, in the simplest terms,
any reduction in island area lowers the diversity
more than a similar reduction of sample area
from a contiguous mainland habitat.
Wilson’s (1961) own data for Melanesian ants
(Fig. 4.2) was one of the data sets used in this
analysis, although there is a problem in the
construction of this and other such comparisons,
as we explain later.
Although it is possible to find many examples
that broadly support this island–mainland distinc-
tion (e.g. Begon et al. 1986, Table 20.1; Rosenzweig
1995), there are also exceptions. Williamson (1988)
reviews surveys providing the following slope