Nonequilibrium Diversity
Dynamics of the Lesser
Antillean Avifauna
Robert E. Ricklefs1* and Eldredge Bermingham1,2,3
MacArthur and Wilson?s model of island diversity predicts an increase in the
number of species until colonization and extinction are balanced at a long-term
steady state. We appraise this model on an evolutionary time scale by molecular
phylogenetic analysis of the colonization of the Lesser Antilles by small land
birds. The pattern of accumulation of species with time, estimated by genetic
divergence between island and source lineages, rejects a homogeneous model
of colonization and extinction. Rather, our results suggest an abrupt, roughly
10-fold increase in colonization rate or a 90% mass extinction event 0.55 to
0.75 million years ago.
MacArthur and Wilson?s (1) equilibrium the-
ory of biogeography explains the number of
species on islands as representing a balance
between colonization and extinction. Accord-
ingly, the biota of an island reaches a steady
state at which the appearance of new species
equals the disappearance of residents. Lack
(2) argued instead that colonization was not
limiting and that the ecological space on is-
lands was filled with established populations
that resisted replacement by new colonists.
Both theories hold that the number of species
on an island should be stable over long peri-
ods, but they differ with respect to the rate of
accumulation of species and the prediction of
species turnover.
Some aspects of the equilibrium theory of
biogeography have been supported (3?7).
However, most studies to date have ad-
dressed dynamics on ecological time scales
(typically ,100 years). Evolutionary time
scales (. ;104 years), which are applicable
to the biotas of large islands and archipela-
goes (8?12), have been inaccessible because
of the absence of detailed fossil records from
islands.
Here, we use a molecular phylogenetic
approach based on mitochondrial DNA
(mtDNA) sequences to estimate relative col-
onization times of the avifauna of the Lesser
Antilles. Many of these species are endemic
(13), indicating that patterns of avian distri-
bution and diversity in the archipelago are
established over evolutionary time. We con-
structed phylogenetic hypotheses on the basis
of mtDNA sequences (14) for island popula-
tions and continental sister populations or
sister taxa representing 39 lineages observed
in 37 of the 65 species of land birds in the
Lesser Antilles, including 30 of 38 passerine
species (Passeriformes) (15). The relative
time of colonization of each lineage was de-
termined by the average genetic divergence
(dA) between Lesser Antillean populations
and the closest sister population or sister
species in Trinidad or Venezuela to the south
or in the Greater Antilles to the north (Fig. 1).
We characterized the temporal pattern of
colonization of the contemporary avifauna of
the Lesser Antilles by plotting the cumulative
number of species as a function of dA be-
tween island and continental or Greater An-
tillean populations (Fig. 2). The resulting cu-
mulative divergence curve shows a distinct
change in slope at about 1 to 2% genetic
divergence.
The simplest model for the gain and loss
of taxa from an archipelago features constant
colonization and extinction rates (6). Accord-
ingly, lineages would become established in
the Lesser Antilles at rate C, which is inde-
pendent of the number of lineages in the
archipelago, and they would become extinct
at rate M, which is independent of lineage age
in the archipelago. The survival of Lesser
Antillean lineages would be an exponentially
declining function of time (x) since their ar-
rival. Thus, the density distribution of extant
lineages (L) with respect to time x since
initial colonization of the archipelago would
be
dL
dx
5 Ce 2 Mx (1)
For this model, the cumulative number of
lineages at time t is the integral of the density
function from x 5 0 to t, that is
L~t! 5
E
x 5 0
t
Ce 2 Mx 5
C
M S
12e 2 Mt
D
(2)
This function is exponentially asymptotic to
L 5 C/M, which represents the equilibrium
number of lineages within the system (16).
The cumulative lineages function was fit-
ted to the data in Fig. 2 (17) by nonlinear
curve fitting (18), which estimated C 5
1701 6 132 SE and M 5 55.2 6 5.0 SE (Fig.
3A). Thus, the estimated equilibrium number
of lineages (C/M) would be 30.8, i.e., consid-
erably fewer than the number of extant lin-
eages of land birds in the Lesser Antilles.
Using the error mean square (MSE) as a
goodness-of-fit criterion, we determined that
this model fits the observed data poorly (P 5
0.995) (19). The apparent lack of homogene-
ity in colonization and extinction rates of
Lesser Antillean birds prompted us to explore
heterogeneous models incorporating an
abrupt change in these rates or an extinction
event at some time in the past superimposed
on homogeneous ?background? rates of col-
onization and extinction.
A stepwise change in either colonization
1Department of Biology, University of Missouri?St.
Louis, St. Louis, MO 63121, USA. 2Smithsonian Trop-
ical Research Institute, Box 2072, Balboa, Republic of
Panama. 3Department of Biology, McGill University,
1205 Docteur Penfield Avenue, Montreal, Quebec
H3A 1B1, Canada.
*To whom correspondence should be addressed. E-
mail: ricklefs@umsl.edu
Fig. 1. Approximate phylogeographic
relationships of populations of six spe-
cies of passerine birds in the Lesser An-
tilles. The vertical scale of relative age is
the mtDNA sequence divergence (dA)
between island populations and sister
populations in external source areas
[solid rectangles, Puerto Rico (PR) and
Trinidad (TR)]. Major Lesser Antillean
islands (solid circles), from north to
south, are Antigua/Barbuda (BU), Mont-
serrat (MO), Guadeloupe (GU), Do-
minica (DO), Martinique (MA), St. Lucia
(SL), St. Vincent (SV ), and Grenada
(GR).
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16 NOVEMBER 2001 VOL 294 SCIENCE www.sciencemag.org1522
or extinction rates would imply a similarly
dramatic change in ecological conditions
within the Caribbean Basin. Application of a
molecular clock indicates that the change in
slope of the lineage accumulation curve cor-
responds approximately to the onset of major
Pleistocene glaciation, suggesting that cli-
mate and associated habitat change might
have been a causative factor. An increase in
arid, open habitat, possibly associated with
drier climates during glacial periods (20) and
combined with lowered sea levels and greater
extent of exposed land, might have led to
higher colonization rates. Climate fluctua-
tions during the latter part of the Pleistocene
could have resulted in higher extinction rates.
We constructed a model with different
colonization and extinction rates before and
after a break point (B) corresponding approx-
imately to the inflection of the lineage accu-
mulation curve in Fig. 2 (21). Comparably
good fits were obtained for break-point val-
ues of genetic divergence (dB) between 0.02
and 0.04; however, the estimated extinction
rate before the break point [M(.dB)] did not
differ significantly from 0. We then estimated
the value of M(,dB) associated with an un-
changing colonization rate and M(.dB) 5 0.
The error mean square was minimized when
dB was 0.026, at which point the estimated
colonization rate (C) was 2433 6 56 and
M(,dB) was 110 6 2, or more than 100% per
1% sequence divergence (Fig. 3B). At such a
high rate of archipelago-wide extinction one
would expect frequent extinction of individ-
ual island populations. However, none of the
younger lineages in the Lesser Antilles have
gaps in their distributions indicative of ex-
tinct island populations. Thus, we feel that
elevated archipelago-wide extinction is
unlikely.
We also fitted a model with constant ex-
tinction rate and a change in colonization rate
between C(.dB) and C(,dB) at break point
B. The best fit occurred at dB 5 0.011, for
which the estimate of M (3.8 6 2.4) did not
differ significantly from 0. With background
extinction removed from the model, dB 5
0.011 continued to provide the best fit, for
which C(,dB) 5 1618 6 35 and C(.dB) 5
151 6 6 (Fig. 3C).
As an alternative to a stepwise change in
the colonization rate, we included a transient
extinction event in an otherwise homoge-
neous colonization and extinction model. Po-
tential causes would include a tsunami pro-
duced by a marine landslide (22) or deep-
water bolide impact (23), which rarely leave
superficial geological evidence (24). Hurri-
canes and volcanic eruptions are probably too
localized to cause widespread extinction (25,
26), but loss of habitat following abrupt cli-
mate change might have a regional impact.
To model an extinction event, we supposed
that proportion S of existing lineages sur-
vived an event at time E. The best fit of this
model to the data occurred at dE 5 0.011, for
which C 5 1616 6 36, M 5 3.8 6 2.5 (not
significantly different from 0), and S 5
0.120 6 0.020. When background extinction
was deleted from the model (M 5 0), C 5
1618 6 35 and S 5 0.093 6 0.005. The fit is
identical to the model of step-wise increase in
colonization rate (Fig. 3C) because the ex-
tinction of 1 ? S lineages is equivalent to
reducing the colonization rate to proportion S
of its previous value.
Deleting background extinction (M) from
the model of lineage dynamics eliminates the
curvature in the lineage accumulation relation
(Fig. 3B), which provided a better fit to the
data for recent colonization events [i.e., dA ,
dB; compare Fig. 3B (MSE 5 0.88) with Fig.
3C (MSE 5 1.74)]. However, this curvature
can be produced in the absence of back-
ground extinction by the stochasticity of nu-
cleotide substitution combined with a change
in colonization rates or a mass extinction
event (Fig. 4). For a particular time of colo-
nization (A), the number of nucleotide chang-
es between a colonist and its source popula-
tion is binomially distributed with mean knA,
where k is the rate of nucleotide substitution
and n is the number of nucleotides (842 for
ATPase 6 and 8). We simulated the genetic
divergence of 37 lineages colonizing the ar-
chipelago between the present and a point in
the past equivalent to a genetic divergence
(dA 5 kA) of 0.15. In the model, the coloni-
zation rate increases in stepwise fashion by
factor R at break point B. This is equivalent to
a mass extinction event at time B with pro-
portion 1/R of lineages surviving (27). The
best fit of this stochastic substitution model
was obtained for B 5 0.011 and R 5 13 (or
S 5 0.077) (28). For these parameters, 51%
of the colonization events occurred during the
more recent period (A , B) and the apparent
colonization rates were 1705 (A , B) and 131
(A . B). As shown by the close fit to the data
Fig. 2. Cumulative number of lineages of Lesser
Antillean birds with increasing relative coloni-
zation time (genetic distance, dA). The open
symbols indicate two species for which dA is
probably overestimated owing to inadequate
sampling of potential continental sister taxa.
These are not included in the present analyses.
Fig. 3. (A) Best fit of a homogeneous rates
model to the observed lineage accumulation
curve. (B) Heterogeneous extinction rates mod-
el with a breakpoint at dA 5 0.026. (C) Heter-
ogeneous colonization model or homogeneous
colonization model with an extinction event
(S 5 0.094) at dA 5 0.011.
Fig. 4. Model of lineage accumulation with
relative age in which genetic distance is esti-
mated by a stochastic model of nucleotide
substitution with a change in the colonization
rate at B 5 0.011. The apparent colonization
rates are 1705 (A , B) and 131 (A . B). The
genetic distance scale extends only to 0.08 to
emphasize the fit to the more recent accumu-
lation of lineages.
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www.sciencemag.org SCIENCE VOL 294 16 NOVEMBER 2001 1523
in Fig. 4, this model does not require back-
ground extinction within the archipelago.
Regardless of the cause of temporal hetero-
geneity, it is clear that Lesser Antillean avian
biogeography has been dominated by nonequi-
librium dynamics and that the number of spe-
cies in the avifauna of the Lesser Antilles is, at
present, far from equilibrium. The earliest ex-
tant colonists to the archipelago have dA values
on the order of 0.15, which because of the
absence of significant background extinction
may represent the beginning of the present avi-
faunal build up. Estimated times of subsequent
colonization are consistent with two contrasting
scenarios. One has a homogeneous colonization
rate of about 1700 per unit sequence divergence
(17 per 1% sequence divergence) and a tran-
sient extinction event involving more than
90% of all lineages at a relative time about dA
5 0.011 in the past. The other postulates a
change in colonization rate from about 130 to
1700 per unit sequence divergence at about
the same time. Calibrations for avian mito-
chondrial molecular clocks [;1.5 to 2% se-
quence divergence per million years (My)]
(8, 29) place the origin of the contemporary
avifauna at 7.5 to 10 million years ago (Ma)
and the change in colonization rates or mass
extinction event at 0.55 to 0.75 Ma. A colo-
nization rate of 1700 is equivalent to only 26
to 34 new arrivals per My, or an average
interval between arrivals of 29 to 39 thousand
years.
Because there is no statistically detectable
background extinction, the number of lineag-
es in the Lesser Antilles apparently is not
currently regulated by extinction around a
stable number. The pool of potential colonists
ultimately must limit the number of lineages
in the archipelago; however, such an effect
has not yet left a strong imprint on the ob-
served lineage accumulation curve. When the
number of lineages on an island approaches
that of the pool of colonists in a linear model,
new lineages should appear infrequently be-
cause most have already colonized the island
and the lineage accumulation curve should
decelerate and approach an asymptote (30). It
does not. This suggests that the long-term
pool of potential colonists is larger than the
number of suitable taxa in the source area at
any given time.
Dramatic events, possibly including mass
extinction or the opening of a region to ac-
celerated colonization, have kept the contem-
porary avifauna of the Lesser Antilles far
from a steady state. History has left an en-
during imprint on this system. MacArthur
and Wilson?s (1) emphasis on extinction and
turnover appears not to apply to Lesser An-
tillean birds on an archipelago-wide basis,
although extinction may be a prominent fea-
ture of individual island populations. In this
case, the paucity of pre-human extinction
among small land birds in the Lesser Antilles
as a whole may be due to occasional coloni-
zation phases of endemic taxa that re-estab-
lish individual island populations from within
the archipelago, referred to as the taxon cycle
(31, 32). Lack?s idea of ecological limitation
(2) also must be re-evaluated because the
number of lineages in the Lesser Antillean
avifauna appears to be limited by the rate of
colonization and the archipelago is not close
to saturation.
Clearly, one must exercise caution in ap-
plying equilibrium theories of homogeneous
colonization and extinction to the numbers of
species in island archipelagoes. Beyond the
possible mass extinction event detected in the
Lesser Antilles, there is little evidence for a
?background? level of extinction. Moreover,
the islands of the Lesser Antilles were no-
where near ecologically saturated with bird
species (33) even before the arrival of human
populations. Human-caused extinctions of
birds and other animals have decimated is-
land biotas in many parts of the world, in-
cluding the West Indies (34). However, it is
evident that the pre-human biotas of some of
these islands were shaped by natural environ-
mental changes or catastrophes of an even
greater magnitude (35).
References and Notes
1. R. H. MacArthur, E. O. Wilson, The Theory of Island
Biogeography (Princeton Univ. Press, Princeton, NJ,
1967).
2. D. Lack, Island Biology Illustrated by the Land Birds of
Jamaica (Univ. of California Press, Berkeley, CA,
1976).
3. B. A. Wilcox, Science 199, 996 (1978).
4. D. Simberloff, E. O. Wilson, Ecology 50, 278 (1969).
5. G. J. Russell, J. M. Diamond, S. L. Pimm, T. M. Reed, J.
Anim. Ecol. 64, 628 (1995).
6. J. M. Diamond, Proc. Natl. Acad. Sci. U.S.A. 69, 3199
(1972).
7. R. J. Whittaker, Global Ecol. Biogeogr. 9, 75 (2000).
8. R. C. Fleischer, C. E. McIntosh, C. E. Tarr, Mol. Ecol. 7,
533 (1998).
9. P. R. Grant, Oikos 92, 385 (2001).
10. L. R. Heaney, Global Ecol. Biogeogr. 9, 59 (2000).
11. K. P. Johnson, F. R. Adler, J. L. Cherry, Evolution 54,
387 (2000).
12. J. B. Losos, in New Uses for New Phylogenies, P. H.
Harvey, A. J. L. Brown, J. M. Smith, S. Nee, Eds.
(Oxford Univ. Press, Oxford, 1996) pp. 308?321.
13. J. Bond, Checklist of Birds of the West Indies (Acade-
my of Natural Sciences, Philadelphia, 1956).
14. Phylogenetic reconstructions were based on 842 base
pairs (bp) of the partially overlapping mitochondrial
ATPase 6 and ATPase 8 protein-coding genes. Rela-
tive time of colonization is estimated by Tamura-Nei
genetic distances. Altogether, the analysis is based on
295 sequences from 161 island populations of 37
species of Lesser Antillean birds plus 82 sequences of
Greater Antillean or continental sister taxa. For de-
tails, see Science Online at www.sciencemag.org/cgi/
content/full/294/5546/1522/DC1.
15. Species and lineages do not match exactly because
two radiations have occurred within the Lesser Anti-
lles and several species include multiple colonization
events. For additional information, see Science On-
line at www.sciencemag.org/cgi/content/full/294/
5546/1522/DC1.
16. The cumulative number of lineages with progressive-
ly older colonization times is identical to the build up
of lineages over time. Thus, looking back through
time, dL/dx 5 C ? ML, which can be rearranged and
integrated to give L(t ) 5 C[1 ? exp(?Mt)]/M.
17. Continental sampling for the two oldest coloniza-
tions was poor and these lineages were, therefore,
deleted from analyses. Including these did not change
results qualitatively. For details, see Science Online at
www.sciencemag.org/cgi/content/full/294/5546/
1522/DC1.
18. Proc NLIN (nonlinear regression) of the Statistical
Analysis System (SAS), version 6.12 (SAS Institute,
Cary, NC).
19. We generated data by simulating the homogeneous
rates model with C 5 1701 and M 5 55.2. For each
simulated data set, we produced 37 extant lineages
by drawing colonization times at random from a
uniform probability distribution between 0 and 0.15
genetic distance, followed by exponentially declining
probability of survival to the present. This was re-
peated 1000 times. The MSE of the cumulative spe-
cies-distance curve fitted to the observed data (8.0)
exceeded 995 of the 1000 simulated values (mean,
2.2; median, 1.8).
20. E. Bonatti, S. Gartner Jr., Nature 244, 563 (1973).
21. We modified the homogeneous model to the follow-
ing expression (primed variables refer to dA . dB):
cumulative number of lineages L(dA) 5 C[1 2
exp(2MdA)]/M for dA , dB, and L(dA) 5 C[1 2
exp(?MdB)]/M 1 exp(?MdB)C9{1 ? exp[M(dA2dB)]}/
M9 for dA . dB. Models were fitted for values of dB in
0.001 increments. For constant colonization and
M(.dB) 5 0, the second expression becomes L(dA) 5
i[1 2 exp(?MdB)]/M 1 exp(?MdB)C(dA ? dB).
22. S. Krastel et al., J. Geophys. Res. 106, 3977 (2001).
23. F. Tsikalas, S. T. Gudlaugsson, J. I. Faleide, J. Geophys.
Res. 103, 30469 (1998).
24. R. Gersonde et al., Nature 390, 357 (1997).
25. J. W. Wiley, J. M. Wunderle Jr., Bird Conserv. Int. 3,
319 (1993).
26. W. J. Arendt, D. W. Gibbons, G. Gray, Bird Conserv.
Int. 9, 351 (1999).
27. Colonists were apportioned to the older (A . B) and
more recent (A , B) time intervals in proportion to the
product of the colonization rate and the length of the
time interval. Colonization times were first randomly
distributed between time intervals and then were ran-
domly distributed within each time interval. For each
colonization time (A), genetic divergence was deter-
mined at random from the binomial distribution
P(x ? p) 5
S x
n
D
px~1 2 p!n 2 x
where x is the number of nucleotide substitutions
and p is equal to the expected proportion of substi-
tutions, kA. The value of P was drawn at random from
a uniform 0-1 distribution, and the equation solved
for x using the RANBIN function of SAS, version 6.12
(SAS Institute, Inc., Cary, NC). The 37 divergence
values were rank-ordered, and the simulation was
repeated 1000 times and averaged to estimate the
lineage accumulation curve with respect to genetic
divergence. Goodness-of-fit (f) was calculated as the
square root of the sum of the squared differences
between observed and predicted divergence values.
28. The goodness-of-fit (f) was 0.0201 for these param-
eters. Fits to the model were only slightly less good
for parameter combinations (R, B, f): 10, 0.014,
0.0224; 11, 0.013, 0.0222; 12, 0.012, 0.0209; 14,
0.010, 0.0205; and 15, 0.009, 0.0216.
29. C. Krajewski, D. G. King, Mol. Biol. Evol. 13, 21 (1996).
30. Constant colonization is unrealistic but there is no
indication that the external species pool limits colo-
nization rate. For further details see Science Online at
www.sciencemag.org/cgi/content/full/294/5546/
1522/DC1.
31. E. O. Wilson, Am. Nat. 95, 169 (1961).
32. R. E. Ricklefs, G. W. Cox, Am. Nat. 106, 195 (1972).
33. G. W. Cox, R. E. Ricklefs, Oikos 29, 60 (1977).
34. G. K. Pregill, D. W. Steadman, D. R. Watters, Bull.
Carnegie Mus. Nat. Hist. 30, 1 (1994).
35. Supported in part by grants from the National Sci-
ence Foundation, the National Geographic Society,
and the Smithsonian Institution. We are grateful to
R. J. Whittaker and two anonymous reviewers for
helpful comments.
2 August 2001; accepted 9 October 2001
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