Islands, Equilibria, and
Speciation
Ricklefs and Bermingham (1) demonstrated
that divergence times of Lesser Antillean avi-
fauna from sister taxa do not follow the expo-
nential distribution predicted with constant
colonization and extinction rates (2). Their ex-
planation for this observation was a lack of
equilibrium due to historical changes in coloni-
zation or extinction rates. However, they mis-
takenly estimated species numbers from the dis-
tribution of divergence time, and they neglected
the possibility that migration and speciation
could have generated the observed pattern.
Ricklefs and Bermingham have con-
founded the measured cumulative distribu-
tions with the time course of colonization
of empty islands. Only the latter has an
asymptote at the equilibrium number of
species. The asymptote of the fitted expo-
nential curve, at 30.8, differs from the total
number of bird lineages on the Lesser An-
tilles not because the model is inadequate,
but because it estimates only the number of
data points, at 37. This ?test? would have
rejected the exponential prediction even if
the data had fit an exponential distribution
perfectly. The fitted constants, even in
more complex models, cannot estimate ab-
solute colonization rates, but only relative
rates (e.g., the ratio of rates in a two-phase
model).
The deviation from an exponential dis-
tribution is, however, supported by other
tests. To explain that deviation, Ricklefs
and Bermingham proposed temporal
changes in extinction or colonization rates.
They did not consider that island popula-
tions may receive migrants from a source
population after colonization and that this
process may cease when a reproductive
barrier arises (speciation) (3). We used
maximum likelihood to fit their data to five
models: (i) the exponential distribution; (ii)
variable extinction rate (two phase); (iii) a
mass extinction event; (iv) migration with
speciation occurring deterministically at a
fixed genetic distance; and (v) migration
with speciation times following an expo-
nential distribution.
The exponential distribution can be re-
jected in favor of any of the other models,
and the speciation and variable-rate models
are all statistically indistinguishable (log
likelihoods differ by much less than two).
The migration-and-speciation models con-
sistently estimate migration rates of about
140 per unit of genetic distance (about two
to three fixations of migrant alleles per
million years) and genetic distances for
speciation in the range of 0.03 to 0.13
(support intervals include significantly
lower values). This viable alternative mod-
el for the deviation from an exponential
distribution deserves further consideration.
Joshua L. Cherry
Department of Organismic
and Evolutionary Biology
Harvard University
Cambridge, MA 02140, USA
E-mail: cherry@oeb.harvard.edu
Frederick R. Adler
Department of Mathematics
and Department of Biology
University of Utah
Salt Lake City, UT 84112, USA
Kevin P. Johnson
Illinois Natural History Survey
607 East Peabody Drive
Champaign, IL 61820, USA
References
1. R. E. Ricklefs, E. Bermingham, Science 294, 1522
(2001).
2. R. H. MacArthur, E. O. Wilson, The Theory of Island
Biogeography (Princeton Univ. Press, Princeton, NJ,
1967).
3. K. P. Johnson, F. R. Adler, J. L. Cherry, Evolution 54,
387 (2000).
14 March 2002; accepted 17 April 2002
Response: Most models of island biogeog-
raphy (1) predict an exponential distribu-
tion of species ages at equilibrium. Accord-
ingly, one can estimate colonization and
extinction rates from the asymptotic accu-
mulation of species with age. This
distribution applies identically to faunal
development of an empty island when col-
onization and extinction are linear with
respect to increasing island diversity. Our
concern was not with estimating the equi-
librium number of species, which is a fea-
ture of the data, but rather with the fit of the
species accumulation curve to an exponen-
tial distribution. Clearly, the fit is not there;
our explanation for the discrepancy in-
volved heterogeneous extinction or coloni-
zation rates, and we concluded that the
system is not in equilibrium (2).
Cherry et al. present an important alter-
native to our analysis, because their model
describes a nonexponential equilibrium
distribution of divergence times under con-
stant conditions. This is accomplished by
creating two classes of island populations
separated by a speciation divide (3). In the
first class, continuing migration of alleles
from continental source populations pre-
vents differentiation until some incompati-
bility mechanism results in species forma-
tion and brings gene flow to a halt. After
that point, a second class of island popula-
tions diverges at a more rapid rate, set, for
example, by mutation and drift in the case
of neutral alleles. Prior to speciation, diver-
gence distances are exponentially distribut-
ed, with a mean asymptotically approach-
ing 1/m (or less when extinction is a factor)
as the time since initial colonization in-
creases. The parameter m is the rate of
fixation of migrant alleles in the island
populations, estimated from our data by
Cherry et al. to be 1.4 per percent mito-
chondrial DNA (mtDNA) sequence diver-
gence. These populations thus accumulate
at low divergence distances, compared with
the larger increments in divergence be-
tween ?speciated? taxa, matching the pat-
tern observed in the Lesser Antillean
avifauna.
The fits of the two models appear to be
indistinguishable statistically, according to
Cherry et al. Whether the two-class specia-
tion model (3) provides a better explana-
tion for the data than our heterogeneous-
colonization-and-extinction model (2) can
be tested by how well it predicts the geo-
graphic structure of genetic variation. Re-
current migration should result in cases in
which divergence (d) from the source pop-
ulation increases with distance in the Less-
er Antilles, with relationships ordered as
[(mainland, nearer island), farther island].
Of 18 nonendemic species in our sample,
only one [d 5 1.2% (farther), 0.4% (near-
er)] showed this pattern. Two others (d 5
0.8%, 0.1%; d 5 0.9%, 0.9%) show multi-
ple colonization of a single island, in one
case from different sources (4 ). Beyond
d 5 1.2%, genetic relationships group is-
land populations within the Lesser Antilles
rather than grouping individual island pop-
ulations with the mainland source. Sympa-
tric species of passerine birds generally
differ by more than 3% mtDNA sequence
divergence (5), which is consistent with the
estimate by Cherry et al. of speciation dis-
tances between 3 and 13% divergence. Giv-
en the interval between migration events of
d 5 1/1.4 5 0.7% estimated by Cherry et
al., one would expect more evidence of
multiple colonization. Along with evidence
of occasional secondary expansion of taxa
within the Lesser Antilles (6 ), observed
phylogeographic patterns suggest that col-
onization from the mainland is episodic,
with transiently high migration rates fol-
lowed quickly by evolutionary indepen-
dence and progressive genetic divergence.
If that is true, the Johnson et al. model (3)
would not predominate in this system. Re-
gardless, additional work on the distribution
of genetic variation in island populations and
their continental sources is needed.
T E C H N I C A L C O M M E N T S
www.sciencemag.org SCIENCE VOL 296 10 MAY 2002 975a
Robert E. Ricklefs
Eldredge Bermingham*
Department of Biology
University of Missouri, St. Louis
St. Louis, MO 63121, USA
E-mail: ricklefs@umsl.edu
*Also Smithsonian Tropical Research Insti-
tute, Box 2072, Balboa, Republic of Panama,
and Department of Biology, McGill Univer-
sity, 1205 Docteur Penfield Avenue, Mon-
treal, Quebec H3A 1B1, Canada.
References
1. R. H. MacArthur, E. O. Wilson, The Theory of Island
Biogeography (Princeton Univ. Press, Princeton, NJ,
1967).
2. R. E. Ricklefs, E. Bermingham, Science 294, 1522 (2001).
3. K. P. Johnson et al., Evolution 54, 387 (2000).
4. N. K. Klein, W. M. Brown, Evolution 48, 1914 (1994).
5. G. C. Johns, J. C. Avise, Mol. Biol. Evol. 15, 1481 (1998).
6. R. E. Ricklefs, E. Bermingham, Ostrich 70, 49 (1999).
10 April 2002; accepted 17 April 2002
T E C H N I C A L C O M M E N T S
10 MAY 2002 VOL 296 SCIENCE www.sciencemag.org975a