TURNOVER 101of small islets within a Swedish lake. Even with con-
sistent survey techniques, they achieved at best only
79% efficiency per survey. As different species are
missed on different occasions, a significant propor-
tion of the recorded turnover could be attributed to
pseudoturnover. Having assessed the rate of
pseudoturnover, they were then able to calculate a
best estimate of real turnover. However, such proce-
dures cannot be applied with any confidence to
surveys by different teams many years apart, wherein
the expertise, experience, special taxonomic interests
or biases, methods, and time spent in surveying are
scarcely known or quantifiable. If the islands in ques-
tion are large or otherwise difficult to survey, the prob-
lems are multiplied. It follows that larger, richer
islands will have greater rates of apparent turnover
because the degree of error in surveying them is liable
to be at least as great as for small islands, and will
therefore involve larger numbers of species. In
circumstances of this sort, resort has to be made to
special pleading in order to justify rate estimates and
theory verification (e.g. Rosenzweig 1995, pp. 250–8).
Such data may tell interesting ecological stories, but
scarcely allow unequivocal tests of the EMIB to be
made (Whittaker et al. 1989; 2000)
In his 1980 review, Gilbert argued vigorously that
turnover at equilibrium, a key postulate of the
EMIB, and one that set it aside from other compet-
ing theories, had not been convincingly demon-
strated; the best empirical evidence coming from
Simberloff and Wilson’s mangrove arthropod
experiments (below). Simberloff (1976) had
acknowledged the same point in an earlier article,
and in the terms demanded by Lynch and Johnson
(1974) one is hard pressed to find convincing evi-
dence of stochastic, equilibrial turnover to this day.
One paper that comes close is Manne et al.’s (1998)
analyses of immigration and extinction rates for
bird species on 13 small islands of the British Isles.
They use a maximum likelihood method to test if
immigration rate declines with increasing distance,
and extinction rate declines with island size (both
should be concave functions, as Fig 4.1). Although
the relationships were found to be in the predicted
direction, the analyses failed to support the conclu-
sions statistically.
When is an island in equilibrium?
MacArthur and Wilson (1967) understood that
measuring the real rates of IandEin the field is
exceptionally difficult. They therefore suggested a
means of testing turnover using the variance–mean
ratio. They argued that if a series of islands of simi-
lar area and isolation were to be selected, it is rea-
sonable to suppose that the variance of the number
of species on different islands will vary with the
number of species present, i.e. variance should be
a function of the degree of saturation. At the earliest
stages of colonization the variance should be close
to 1, declining to about 0.5 as islands become
saturated. This provides an approach to assessing
whether a series of similar islands (i.e. similar in iso-
lation, area, etc.) might be viewed as equilibrial (e.g.
Brown and Dinsmore 1988), but does not constitute
a particularly precise tool.
Simberloff (1983) argued that for equilibrium
status to be judged it is necessary for researchers
to spell out how much temporal variation they
will accept as consistent with an equilibrium
condition. Only by adopting a specific coloniza-
tion model, and then testing it against the data,
can the equilibrium hypothesis be considered
falsifiable. He undertook a study using a simple
Markov model, in which extinction and immigra-
tion probabilities were estimated independently
for passerine birds of Skokholm island, land birds
of the Farne Islands, and birds of Eastern Wood (a
habitat island in southern England). By compari-
son of the simulations with the observed data
series of between 25 and 35 years, he found a poor
fit with the equilibrium model. The data did not
show the regulatory tendencies expected if
species interactions cause species richness to be
continuously adjusted towards equilibrium. For
an alternative statistical analysis of these and
other data sets, reaching a similar conclusion of
non-equilibrium dynamics, see Golinski and
Boecklen (2006).
As defined by MacArthur and Wilson (1967) in
their glossary (Box 4.3), I, E, and Trates concern
change per unit time, and take no account of the size
of source pools (although they do elsewhere in that