Equilibrium speciation dynamics in a model adaptiveradiation of island lizardsDaniel L. Raboskya,b,1 and Richard E. Glorc

aDepartment of Ecology and Evolutionary Biology and Laboratory of Ornithology, Cornell University, Ithaca, NY 14853; bDepartment of Integrative Biologyand Museum of Vertebrate Zoology, University of California, Berkeley, CA 94720; and cDepartment of Biology, University of Rochester, Rochester, NY 14620

Edited* by David B. Wake, University of California, Berkeley, CA, and approved November 5, 2010 (received for review May 30, 2010)

The relative importance of equilibrium and nonequilibrium pro-cesses in shaping patterns of species richness is one of the mostfundamental questions in biodiversity studies. If equilibrium pro-cesses predominate, then ecological interactions presumably limitspecies diversity, potentially through diversity dependence ofimmigration, speciation, and extinction rates. Alternatively, spe-cies richness may be limited by the rate at which diversity arises orby the amount of time available for diversi!cation. These latterexplanations constitute nonequilibrium processes and can applyonly to biotas that are unsaturated or far from diversity equilibria.Recent studies have challenged whether equilibrium models applyto biotas assembled through in situ speciation, as this process maybe too slow to achieve steady-state diversities. Here we demon-strate that speciation rates in replicate Caribbean lizard radiationshave undergone parallel declines to equilibrium conditions onthree of four major islands. Our results suggest that feedbackbetween total island diversity and per-capita speciation ratesscales inversely with island area, with proportionately greaterdeclines occurring on smaller islands. These results are consistentwith strong ecological controls on species richness and suggestthat the iconic adaptive radiation of Caribbean anoles may havereached an endpoint.

island biogeography | macroevolution | species-area relationship |ecological limits | phylogeny

Under MacArthur and Wilson’s equilibrium model of islandbiogeography (1), a positive relationship between an island’s

area and its species diversity arises from a dynamic balance be-tween the rate at which new species colonize an area and the rateat which species are lost due to extinction. For a given degree ofisolation, larger islands should contain more species than smallerislands because they have lower rates of extinction and, poten-tially, increased rates of colonization. Although this model isclearly a simpli!cation of processes in"uencing species richness(2, 3), it has nonetheless retained considerable explanatorypower (2, 4, 5).A number of recent analyses, however, suggest that non-

equilibrium dynamics might prevail when speciation, as opposed toimmigration, is the principal contributor to species richness (6, 7).In some systems, speciation rates may be too low relative to the ageof a given islandor geographic region toachieve equilibrium speciesnumbers (6–8). In other cases, extinction pulses might occur withsuf!cient frequency that diversity never reaches equilibrium (9).Because speciation dominates the assembly of biotas on large is-lands and continents, understanding many patterns of speciesrichness potentially requires a nonequilibrium, evolutionary theoryof diversity. Such a nonequilibriummodel of diversity would entailprimary control of species richness by variation in net diversi!cationrates, clade age, or time within regions (10–14).Alternatively, species richness might be governed by a logistic

growth process (15, 16), such that speciation and extinction ratesreach a balance only when some island- or region-speci!c car-rying capacity has been achieved. These models have been widelyused in paleobiological studies to explain diversity dynamics atthe largest temporal and spatial scales (17, 18), and some recent

studies on dated phylogenetic trees support speciation rate de-cline over time during evolutionary radiations, perhaps due tosaturation of ecological niches with increasing species richness(19, 20). However, the evidence for equilibrium dynamics frommore restricted phylogenetic and spatial scales is generallymixed, particularly for islands (7, 21–23).The species diversity of reptiles and amphibians observed

across theWest Indian archipelago has been used to support bothequilibrium, immigration-based and nonequilibrium, speciation-based explanations for the species–area relationship (1, 7, 24).Here, we test whether equilibrium or nonequilibrium macroevo-lutionary models best characterize patterns of diversi!cation inthe archipelago’s most diverse lizard genus (Anolis). We focus onanole radiations that have occurred on the four large islands of theGreater Antilles (Cuba, Hispaniola, Jamaica, and Puerto Rico),which resulted primarily from in situ speciation (7). Previousanalyses suggested that speciation rates in Caribbean anoles re-"ect far-from-equilibrium dynamics, with relatively constant butisland-speci!c diversi!cation rates through time (7, 25). Theseresults suggest that, at least for anoles, species richness withinislands is limited by the rate at which diversity arises (e.g., thedifference between the speciation rate, !, and the extinction rate, ")and not by ecological limits on diversi!cation or island-speci!ccarrying capacities (14). However, the nonequilibrium model hasnever been tested using methods that explicitly allow for temporalvariation in rates of species diversi!cation through time. If net di-versi!cation rates (!! ") inAnolis follow the equilibriummodel, wepredict that (i) island-speci!c declines in diversi!cation shouldoccur on each of the four major islands of the Greater Antilles and(ii) rates should decline more quickly to an equilibrium on smallerislands, consistent with the hypothesis that small islands have lowercarrying capacities than large islands.

ResultsWe used the state-dependent speciation-extinction (SSE) frame-work that has previously been used to study the relationshipbetween character states and diversi!cation rates (26–28), ex-tended to include dynamic processes of character change, speci-ation, and extinction. The binary-state (BiSSE) model (27)describes the probability that a lineage in state k at some point intime will evolve into a clade identical to the observed clade, givena particular set of speciation (!0, !1), extinction ("0, "1), andcharacter transition (q01, q10) parameters. By assuming that lin-eage dispersal between islands can be modeled as a transitionbetween character states on a phylogenetic tree, we can usea generalization of this model to study the dynamics of diversi!-cation in Caribbean anoles. Let Di(t) be the probability that

Author contributions: D.L.R. and R.E.G. designed research, performed research, contrib-uted new reagents/analytic tools, analyzed data, and wrote the paper.

The authors declare no con!ict of interest.

*This Direct Submission article had a prearranged editor.1To whom correspondence should be addressed. E-mail: drabosky@berkeley.edu.

This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1007606107/-/DCSupplemental.

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a lineage in state i at time t evolves into a clade identical to theobserved clade, and let Ei(t) be the corresponding probability ofclade extinction before the present. For each character state, weobtain a pair of differential equations that describe changes inDi(t) and Ei(t) through time,

dDi

dt! !

!"i;t " !i;t " "

j#i

j!1qij;t

"Di#t$ " "

j#i

j!1qij;tDj#t$ " 2!i;tEi#t$Di#t$

and

dEi

dt! "i;t !

!"i;t " !i;t " "

j#i

j!1qij;t

"Ei#t$ " "

j#i

j!1qij;tEj#t$ " !i;tEi#t$2;

where !i,t and "i,t are the rates of speciation and extinction for theith character state at time t, and where qij,t is the rate of characterchange from state i to state j at time t. For n character states,computing the probability of the observed data given the modeland parameters requires that we solve 2n ordinary differentialequations that jointly describe the dynamics of speciation, ex-tinction, and state change along each branch of a phylogenetictree (SI Materials and Methods). We assume that rates of speci-ation, extinction, and dispersal change linearly through time,such that

r##$ ! maxn0; !r0

#1!

#K

$o;

where r0 is the initial rate at the root node of the complete tree(!i,0, "i,0, or qij,0), # is time measured from the root node, and Kcontrols the rate of change in speciation, extinction, or dispersalthrough time.We applied this framework to a phylogenetic tree for Greater

Antillean Anolis (29) that was 88% complete at the species level(Figs. S1 and S2) and modi!ed initial values for Di and Ei toaccount for incomplete taxon sampling. Implementation of themodel requires an appropriate rate matrix describing possibledispersals between islands (e.g., qij,t = q for a one-rate, time-constant symmetric model). We used maximum likelihood toevaluate 12 alternative time-constant or time-varying dispersalmodels (Materials and Methods, SI Materials and Methods, TableS1, and Fig. S3). Models with temporal declines in the rate ofdispersal between islands !t the data much better than those withtime-invariant dispersal ($AIC = 19.2 in favor of models withtemporal variation in q; Table S1). This result may also beconsistent with the possibility that between-island speciationevents re"ect early vicariance of Antillean proto-islands, ratherthan among-island dispersal (30).We then incorporated this “background” biogeographic model

into a series of diversi!cation models that allowed speciation andextinction dynamics to vary among islands. Our candidate set ofmodels included a model with a common time-invariant specia-tion rate (!) across all islands (model 1: GlobalConstant),a model with island-speci!c but time-invariant ! (model 2:IslandConstant), a model with “global” changes in diversi!cationrate (model 3: GlobalVariable), and two models with island-speci!c linear change in ! through time (model 4: IslandVari-able; and model 5: IslandVariableFull). The IslandVariableFullmodel has separate !0 and K parameters for each island, whereasIslandVariable is a reduced model with a common starting rate!0 at the root node of the tree. For each model of speciationdescribed above, we considered variants with and without ex-tinction (Materials and Methods).The GlobalVariable model describes a scenario where specia-

tion rates across the entire Greater Antillean radiation havechanged with a common underlying dynamic that is independentof the island towhich each lineage belongs. Including thesemodels

enables us to distinguish island-speci!c dynamics fromwell-knownbiases that can lead phylogenetic studies to infer spurious declinesin speciation rates through time (19, 31, 32). If apparent rapidspeciation at the base of a phylogeny is an artifact of tree con-struction, sampling biases, and inadequate models of molecularevolution, we should observe superior !t of the GlobalVariablemodel. This model would also be expected to !t the data well ifdiversi!cation rates have changed during the course of the anoleradiation in response to a common climatic driver.Our results strongly reject the hypothesis that island-speci!c but

time-invariant diversi!cation underlies patterns of anole speciesrichness in the Greater Antilles (Table 1). The conditional prob-ability of the two constant rate models (Materials and Methods) isvery low (P < 0.0001). Rather, our results support the hypothesisthat speciation rates have declined independently on each island(Fig. 1), against a background of low extinction (Table 1). Thebest-!t model speci!ed independent linear declines in the rate ofspeciation on each island (IslandVariable; conditional probability= 0.811), and the second-best model was the IslandVariableFullmodel (P= 0.184). Together, these island-speci!c decline modelsaccount for 0.995 of the total probability of the data explained bythe candidate set of models and do not support the hypothesis thatlineage accumulation patterns in Anolis re"ect global drivers ofdiversi!cation or artifacts of tree construction. If the IslandVar-iableFull model is excluded, the conditional probability of theIslandVariable model is very high (P = 0.994). These results arerobust to phylogenetic uncertainty (Fig. S4); virtually identicalresults are obtained under alternative biogeographic models, in-cluding a simple model with symmetric time-invariant dispersalrates between islands (Table S2). Models without extinction con-sistently !t the data better than the corresponding models withextinction (Table 1).We estimated occupancy probabilities and lineage accumula-

tion curves for each island under the best-!t diversi!cationmodel (Fig. 2); these curves suggest relatively rapid accumula-tion of lineages on Hispaniola, Puerto Rico, and Jamaica. Inconjunction with rate estimates under the best-!t model, theseresults imply equilibrium or near-equilibrium conditions onPuerto Rico, Hispaniola, and Jamaica; speciation rates on eachisland have declined to a small fraction of the inferred initial rate(Fig. 1). Only the largest island, Cuba, appears to have potentialfor substantial species accumulation. Our results further suggestthat the rate of decline in speciation through time is negativelycorrelated with island area: Proportionately more rapid declinesoccur on smaller islands (% = !0.92, P = 0.056; Fig. 3), sug-gesting that per-lineage feedback between speciation rates andtotal species richness is greater on small islands. This negativecorrelation is robust to uncertainty in phylogenetic tree topologyand branch lengths (Fig. S5).We simulated phylogenetic trees and character state data

under maximum-likelihood parameter estimates for Global-Constant, GlobalVariable, IslandConstant, and IslandVariablemodels to assess whether the !tted models could reconstructmajor features of the observed data. Simulated distributions ofspecies richness under the IslandVariable model were closer tothe observed data than alternative models that did not allowisland-speci!c changes in speciation through time (Fig. 4). TheGlobalVariable model underpredicts species richness on Cubarelative to the IslandVariable model and overpredicts richnesson both Jamaica and Puerto Rico (Fig. 4; Table S3). Analyses ofbranch length distributions from simulated trees further suggestthat the IslandVariable model provides a much better match tothe observed data than alternative models specifying globalchanges in speciation rates or constant speciation through time(Fig. S6). Taken together, these results suggest that models withindependent, island-speci!c changes in speciation rates throughtime provide a better absolute !t to the observed data than

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models assuming constant rates through time or global changesin the rate of speciation.

DiscussionThe extent to which biological diversity is regulated by diversity-dependent, equilibriumprocesses relative to diversity-independent,nonequilibrium processes is a fundamental question in evolu-tionary ecology. Our results provide evidence for parallel declinesin speciation rates in radiations ofAnolis lizards on the four majorislands of the Greater Antilles. These results are consistent witha diversity-dependentmodel involving a decline in speciation ratesas species richness and ecological disparity increase (5, 19, 20, 31,33, 34), possibly re"ecting a role for ecological opportunity asa driver of speciation in Caribbean anoles (35, 36). Recent worksuggesting that diversi!cation of phenotypic traits associated withecological specialization also declined through time during theanole radiation further supports this scenario (29, 37).Our results further suggest that three of four islands are at

or near equilibrium diversity and that equilibrium diversity is

a function of island area (Fig. 3). One explanation for the higherdiversity on larger islands involves the presence of multipleecologically similar species occurring in geographic isolation; forexample, both Cuba and Hispaniola harbor multiple species ofmontane twig and trunk-crown ecomorph anoles that are en-demic to isolated mountain ranges (30). Larger islands alsosupport more species specialized for geographically distinctmacrohabitats. Hispaniola, for example, is home to eight spe-cies of allopatrically or parapatrically distributed trunk-groundanoles restricted to distinctly different forest types (e.g., mon-tane, lowland mesic, and lowland xeric). A third aspect of in-creased diversity on larger islands appears to involve !ner-scalepartitioning of habitats available across islands of all sizes (30);sympatric anole assemblages on Cuba and Hispaniola, for ex-ample, may contain more species than the entire island-widefauna of Jamaica (38).Our analyses reject models that posit a shared decline in di-

versi!cation rates across islands in favor of alternative modelswhere speciation dynamics vary among subtrees assigned to dif-

Table 1. Diversi!cation models specifying dynamic or time-invariant rates of speciation (!) and extinction (") !tted to the maximumclade credibility (MCC) tree for the Greater Antillean Anolis radiation

Model Description LogL AIC (np) AIC_EX (np) $i

IslandConstant Rates differ among islands but are constant through time !40.84 93.68 (6) 101.7 (10) 0GlobalConstant Rates are constant through time and among lineages !43.81 93.62 (3) 95.6 (4) 0GlobalVariable Linear change in rates through time; no differences between islands !32.12 72.24 (4) 74.8 (6) 0.005IslandVariableFull Island-speci"c linear change in rates through time !22.36 64.72 (10) 74.08 (18) 0.184IslandVariable Island-speci"c linear change in rates through time; shared r0 (!0, "0) !23.96 61.92 (7) 66.58 (12) 0.811

LogL and AIC give log-likelihoods and AIC scores for models formulated without extinction (" = 0), and AIC_EX gives the corresponding AIC for the modelswith extinction (" $ 0). The number of parameters in each model (np) is given in parentheses after the AIC score. !i: conditional probability of the ith modelgiven the candidate set of models. Models without extinction (" = 0) "t the data better than the corresponding model with extinction in all cases.

Puerto Rico Jamaica Hispaniola Cuba

0.0 0.2 0.4 0.6 0.8 1.0

0

2

4

6

8

Spec

iatio

n ra

te

IslandConstant

A

0.0 0.2 0.4 0.6 0.8 1.0

0

2

4

6

8

Spec

iatio

n ra

te

B

GlobalConstant

0.0 0.2 0.4 0.6 0.8 1.0

0

2

4

6

8

Spec

iatio

n ra

te

C

GlobalVariable

0.0 0.2 0.4 0.6 0.8 1.0

0

2

4

6

8

Spec

iatio

n ra

te

Time

D

IslandVariableFull

0.0 0.2 0.4 0.6 0.8 1.0

0

2

4

6

8

Spec

iatio

n ra

te

Time

E

IslandVariable

0.0 0.2 0.4 0.6 0.8 1.0

0.0

0.5

1.0

1.5

Dis

pers

al ra

te

Time

F

Fig. 1. (A–E) Reconstructed speciation-through-time curves under "ve diversi"cation models "tted to the Anolis phylogeny (Fig. 2, Fig. S1). Green curvesdenote models without state-dependent diversi"cation; other colors describe speciation dynamics on Cuba, Hispaniola, Jamaica, and Puerto Rico. Models aresorted (left to right, top to bottom) from lowest to highest conditional probability (Table 1). Models with island-speci"c changes in speciation (D and E)account for P = 0.995 of the total probability of the data taken across all models. The maximum-likelihood estimate of the dispersal rate between islandsunder the IslandVariable model is shown in F. Rates are shown in relative time units, as the tree was scaled to basal divergence of 1.0.

22180 | www.pnas.org/cgi/doi/10.1073/pnas.1007606107 Rabosky and Glor

ferent islands (Table 1) and add an important dimension to theinterpretation of diversi!cation patterns typically seen in molec-ular phylogenies (19, 20, 39, 40).A criticismof diversity-dependentspeciation, as inferred from molecular phylogenies, is that thispattern might simply be an artifact of phylogeny reconstruction ortaxon sampling. For example, use of inadequate models of mo-

lecular evolution can lead to apparent slowdowns in the rate ofspeciation through time (32), but phylogenies affected by this biasshould not have been favored by models with island-speci!c spe-ciation dynamics. Likewise, if Anolis contains additional crypticspecies diversity that has not been accommodated by our analyses,wewould observe an artifactual slowdown in speciation toward thepresent in the full Anolis phylogeny. However, such incompletesampling would require proportionately greater cryptic diversityon the smallest islands, which have undergone the most severeslowdown in speciation through time (Fig. 3). This pattern ofundersampling is unlikely given the considerable attention re-ceived by Puerto Rican and Jamaican anole faunas relative tothose of Cuba; despite this work, no new species have been de-scribed on either island since the 1960s, whereas new speciescontinue to accumulate on Cuba (30).Elucidating the role of extinction from molecular phylogenies

is notoriously dif!cult (41–44). However, among anole lineagesthat left present-day descendants, extinction appears to have beennegligible, and our results suggest that the decline in net di-versi!cation rates on each island has been mediated by decliningspeciation rates against a background of very low extinction.There is no evidence from explicit modeling of extinction rates(Table 1 and Table S2) or from visual inspection of lineage ac-cumulation plots (Fig. 2) for substantial species turnover duringthe historical occupancy of each island. It is possible that manyspecies have gone extinct, but the dominant signal is of a tendency

A. evermanni

A. distichus

A. rubribarbus

A. placidus

A. semilineatus

A. ricordii

A. vermiculatus

A. argillaceus

A. barbatus

A. chlorocyanus

0.2 0.4 0.6 0.8 1.0

1

5

25

50

300 km

Time

Num

ber

of S

peci

es (l

n)

0.0

A. marcanoi

A. allisoni

Fig. 2. Anolis MCC tree with reconstructed island occupancy probabilities and lineage accumulation curves for Cuba (red), Hispaniola (blue), Jamaica(purple), and Puerto Rico (orange). Occupancy probabilities on internal nodes were estimated under the overall best-"t model (IslandVariable). The MCC treewith all taxon labels is shown in Fig. S1.

2.2 2.3 2.4 2.5

5

6

7

8

9

(Log) Island area

Rat

e de

clin

e pa

ram

eter

Fig. 3. Island-speci"c rate-decline parameters as a function of island area for(from left to right) Puerto Rico, Jamaica, Hispaniola, and Cuba. The rate de-cline parameter is the slope of the relationship between speciation and time(!!0/K). Con"dence intervals re!ect uncertainty in tree reconstruction andrepresent the 0.025 and 0.975 percentiles of the distribution of parameterestimates taken across the posterior distribution of trees sampledwith BEAST.

Rabosky and Glor PNAS | December 21, 2010 | vol. 107 | no. 51 | 22181

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for lineages that arose during the earliest stage of each island’sradiation to persist to the present: Any subsequent extinctionevents have failed to leave a signature that can be inferred frommolecular phylogenies. This result is consistent with previousanalyses that have documented a tendency for major ecologicaltypes to have arisen early during the radiation of anoles on eachisland (29). Such a pattern might be expected if there are strongecological limits on species diversity and if species tend to giverise to ecologically similar species. Even if extinction rates arehigh, comparatively little phylogenetic turnover within islandcommunities would occur once diversity reached saturation, be-cause any particular extinction event would be followed bya speciation event from an ecologically similar member of thesame major lineage.When all Caribbean Anolis communities are considered to-

gether (7), our results imply that communities assembled throughspeciation have proportionately greater equilibrium diversitiesthan are attained when immigration is the sole source of newspecies. This hypothesis follows from the observation that theslope of the species–area curve for Caribbean anoles is greater forislands with appreciable in situ speciation (7) than for immigra-tion-derived island assemblages; qualitatively similar patternsoccur in Caribbean butter"ies (2). This result is not simplyamanifestation of the “small island effect,”whereby demographicstochasticity on smaller islands may eliminate the expected re-lationship between island area and species richness (2); rather,immigration-derived anole communities show a positive species–area relationship (7, 25). Further support for this pattern followsfrom the observation that the slope of the species–area re-lationship for oceanic archipelagoes is positively correlated withmean island endemicity (45). It is unclear why the scaling re-lationship between area and equilibrium diversity might changewhen speciation becomes the dominant contributor to regionaldiversity, but these observations suggest fundamental differencesbetween communities assembled through speciation and immi-gration/dispersal.The variation in species richness among geographic regions,

such as the islands we consider here, potentially results from dif-ferences in rates of species diversi!cation (11, 13, 46) as well as theages of constituent clades (12, 47). With the possible exception ofCuba, our results argue against these nonequilibrium processesand suggest that anole species richness is primarily determined byisland-speci!c limits on total diversi!cation (14). These !ndingshave implications for howwe study the variation in species richnessamong geographic regions: If faunas derived principally from insitu speciation typically reach steady-state diversity, then variationin species richness must result in large part from ecologicalinteractions (3) and not necessarily from variation in clade age andnet rates of species diversi!cation (14, 48–50).

Materials and MethodsPhylogeny Reconstruction. We analyzed ultrametric phylogenetic trees gen-erated by Mahler et al. (29), consisting of 189 species and comprising an%1,500-bp region of mitochondrial DNA extending from the beginning ofthe NADH dehydrogenase subunit 2 (ND2) gene and including "ve tRNAsbefore ending shortly after the start of the cytochrome c oxidase (COI) gene(see SI Materials and Methods for details). We "t all diversi"cation models to400 trees sampled without replacement from the set of pruned trees gen-erated by Mahler et al.’s BEAST analyses.

Diversi!cation Analyses and Biogeographic Model Selection. The modelingframework described here allows for an extremely large candidate set ofmodels and poses a challenging combinatorial problem. Even with simplelinear changes in parameters through time, we must potentially consider 8speciation rates (e.g., initial and "nal rates for each of four islands), 8 ex-tinction rates, and 24 dispersal rates (12 initial rates and 12 "nal rates). Ratherthan consider hundreds of possible biogeographic models, we evaluated 12key models against a diversi"cation background of time-constant but island-speci"c differences in speciation (see SI Materials and Methods for details;Table S1, Fig. S3). These models included a simple 1-parameter symmetricscenario with equal rates between all island pairs, a 2-parameter symmetricmodel with rates changing linearly through time, and a full 12-parameterasymmetric model. The best-"t model from this analysis (Table S1) was se-lected as a background model for all subsequent diversi"cation analyses andallowed only the following transitions: q21, q12, q13, and q24 (Cuba, 1; His-paniola, 2; Jamaica, 3; Puerto Rico, 4). Note that dispersal parameters wereestimated separately for each diversi"cation model shown in Table 1. Vir-tually identical results for diversi"cation were obtained when we consideredsimpler alternative biogeographic models (Table S2). We accounted for in-complete sampling by setting initial states Di(0) and Ei(0) equal to fi and 1 !fi, where fi is the proportion of species on island i that have been sampled(26). For models with extinction, extinction functions through time weremirror images of those used for speciation. For example, GlobalConstantwith extinction had time-invariant rates ! and " for all lineages, andIslandVariable with extinction had a common "0 term and separate K termsfor each island. Additional details are given in SI Materials and Methods.

Model Adequacy and Comparisons. We used Akaike weights to estimate theprobabilityofeachmodel conditionalon theAkaike InformationCriterion (AIC)scoresobservedinthecandidatesetofmodels(51).SeeSIMaterialsandMethodsfor details. To assess model adequacy, we developed a continuous-time phy-logenetic tree simulation program in R to generate trees and character statedata under all SSE models described here. We simulated 2,000 trees undermaximum-likelihood parameter estimates for GlobalConstant, IslandConstant,GlobalVariable, and IslandVariable models and computed a series of summarystatistics to assess the match between the simulated data and the AnolisMCCtree.We tabulated the numbers of species in each character state at the end ofthe simulation, to determine whether simulated patterns of species richnessmatched those observed in theGreaterAntilles (Fig. 4).We then computed twosummary statistics that described the distribution of branch lengths associatedwith particular island states: the mean and coef"cient of variation in terminalbranch lengths associatedwith each character state (SIMaterials andMethods;Fig. S6). The best-"t model (IslandVariable) outperformed the other candidatemodels for all three summary statistics.

0 1 2 3 4 5

Freq

uenc

y

Cuba

log (richness)0 1 2 3 4 5

Hispaniola

log (richness)0 1 2 3 4 5

Jamaica

log (richness)0 1 2 3 4 5

Puerto Rico

log (richness)

GlobalConstant

IslandConstant

GlobalVariable

IslandVariable

Fig. 4. Distribution of species richness for islands of the Greater Antilles predicted under (Top to Bottom) GlobalConstant, IslandConstant, GlobalVariable,and IslandVariable models. Colored lines denote observed species richness on each island; black lines and histograms represent mean values and distributionstabulated from 2,000 datasets simulated under maximum-likelihood parameter estimates for each model. The GlobalVariable model underpredicts speciesrichness on Hispaniola and overpredicts richness on both Jamaica and Puerto Rico relative to the IslandVariable model.

22182 | www.pnas.org/cgi/doi/10.1073/pnas.1007606107 Rabosky and Glor

ACKNOWLEDGMENTS. We thank A. Agrawal, J. Huelsenbeck, I. Lovette,A. McCune, A. Phillimore, R. Ricklefs, K. Wagner, and members of the Glorlab for comments on the manuscript and/or discussion of these topics. Thisresearch was supported by US National Science Foundation Grants DEB-

0814277 and DEB-0920892, by the Fuller Evolutionary Biology Program atthe Cornell Laboratory of Ornithology, by the University of Rochester, andby the Miller Institute for Basic Research in Science at University ofCalifornia, Berkeley.

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Rabosky and Glor PNAS | December 21, 2010 | vol. 107 | no. 51 | 22183

EVOLU

TION

Supporting InformationRabosky and Glor 10.1073/pnas.1007606107SI Materials and MethodsPhylogenetic Methods. Phylogenetic trees were generated byMahler et al. (1). Mahler et al. conducted multiple partitionedanalyses in MrBayes v3.1.2; the consensus tree from theseanalyses was then used as the starting tree for the Bayesian re-laxed clock method implemented in BEAST 1.4.7. All non-Greater Antillean taxa were then pruned from the trees in theposterior distribution of the BEAST analysis.

Diversi!cationAnalyses.Theequationsformodelingstate-dependentdiversi!cation dynamics follow from Maddison et al. (2), and weused simple modi!cations of the original equations. The reader isreferred to the original paper for a clear and detailed explanationof the derivation of the two-state BiSSE model (2). In thisframework, we track—for each character state—two key proba-bilities:Di(t), the probability that a lineage in state i at time t givesrise to a clade like that in the observed data; and Ei(t), the prob-ability that a lineage in state i at time t goes extinct before thepresent (alongwith all of its descendants).Here, t is timemeasuredfrom the present backward in time and !t is an incremental timestep. Let "i,t and #i,t be the speciation and extinction rates fora lineage in state i at time t and qij,t represent the rate of transitionfrom state i to state j at time t. As in Maddison et al. (2) andFitzJohn et al. (3), we assume that only a single event (speciation,extinction, or character change) can happen in the interval!t. Thedifferential equation governing Di(t + !t) is

dDi

dt! !

!#i;t " "i;t " "

j#i

j!1qij;t

"Di#t$ " "

j#i

j!1qij;tDj#t$ " 2"i;tEi#t$Di#t$;

where

!!#i;t " "i;t " "

j#i

j!1qij;t

"

is the rate at which Di(t) decreases due extinction, speciation, orcharacter change (from state i to all other states) in some in-!nitesimal amount of time !t as we move backward down thebranch (toward the root), and

qij;tDj#t$

is the rate at which Di(t) increases due to character change fromstate i to state j [multiplied by the probability that, having un-dergone character change, the lineage will go on to evolve intoa clade like the observed data, Dj(t)]. This term must be summedover all n – 1 character states, hence the summation term. Fi-nally, a lineage at some point in time can undergo a speciationevent and still give rise to the observed data, provided one of thedescendant branches and all of its descendants go extinct beforethe present (thus, we would never observe a speciation event ina reconstructed tree). This process occurs with rate

"i;tEi#t$Di#t$

and it must be multiplied by 2 (as either the left or the rightdescendant branches and all their descendants could go extinct, ifthere is a speciation event on !t).The differential equation governing Ei(t) is

dEi

dt! #i;t !

!#i;t " "i;t " "

j#i

j!1qij;t

"Ei#t$ " "

j#i

j!1qij;tEj#t$ " "i;tEi#t$2

and includes the rate at which lineages go extinct on !t, or #i,t.The equation includes the rate at which lineages undergo noevents on the time interval $t, yet go extinct at some point in thefuture, or

#i;t " "i;t " "j#i

j!1qij;t

plus the rate at which lineages in state i switch states and sub-sequently go extinct, or

qij;tEj#t$;

which must be summed over all n character states. Finally,a lineage might undergo speciation on !t, but for such an eventto occur and yet result in a clade that goes extinct before thepresent, both descendant branches and all their descendantsmust go extinct. These events occur at rate

"i;tEi#t$2:

A total of 2n equations must thus be solved simultaneously todescribe the dynamics of diversi!cation and character changethrough time. The initial conditions, for a tree with completetaxon sampling, are Di(0) = 1 and Ei(0) = 0. The probability thata lineage existing in the present will give rise to the observed data—a single lineage—is necessarily 1, unless we are accounting forincomplete taxon sampling. In this case, the initial state is simplythe probability of sampling the lineage (3). We solved thesesystems of equations by numerically integrating backward alongeach branch using the Fortran LSODA integrator as im-plemented in the R package deSolve (4). At each interior nodein the tree, probabilities Di(t) for right and left descendantbranches were combined as in Maddison et al. (2), and thesecombined values became the initial conditions for integrationbackward down the parent branch. At the root node, we com-bined root-state probabilities using the weighting scheme fromFitzJohn et al. (3). Virtually identical results were obtained usingalternative weighting methods that assumed equal weights to theindividual probabilities D1, D2, . . . , Dn.

Biogeographic Model Selection. A large number of biogeographicscenarios could be considered to model transitions betweencharacter states (e.g., dispersal between islands). Under thesimplest model, dispersal (transition) rates between all islandsmight be identical. This model would specify a symmetric, one-rate transition matrix between states. At the most complex endof the spectrum, each pair of character states might have sepa-rate asymmetric transition rates (qij # qji), and all rates mightvary linearly through time. This model would have a full 24-parameter transition matrix between character states (12 initialrates at the root node and 12 ending rates in the present). Be-tween these scenarios, a very large number of models are pos-sible. We used the state-dependent diversi!cation frameworkdescribed above and subsequent model-!tting analyses to iden-tify an appropriate background model for subsequent diversi-!cation analyses, rather than simply assuming the validity of aone-rate symmetric transition matrix or any other model.

Rabosky and Glor www.pnas.org/cgi/content/short/1007606107 1 of 10

We assumed that all character states (islands) were associatedwith a particular time-constant rate of speciation, with extinctionset to zero. We then used maximum likelihood to !t three bio-geographic models to the Anolis MCC tree: (i) a model withtime-invariant, equal rates between all islands (1 parameter,model qsymm1); (ii) a model with time-varying dispersal be-tween islands, but with a single rate for all islands at any point intime (2 parameters, model qsymm1_TD); and (iii) a model withseparate asymmetric transition rates between all island pairs,with rates constant in time (12 parameters, model qasymm12).Many entries in the 12-parameter transition matrix were esti-mated as zero with a high degree of con!dence, owing to theclear lack of obvious dispersal events between many island pairs(e.g., Jamaica and Puerto Rico).We thus generated a series of secondary “dropped-zero”

transition matrices by dropping all of the estimated zero entriesin the 12-parameter model. Our analyses of the 12-parametermodel recovered two stable solutions that differed in <0.5 log-likelihood units: (i) a model with two-way dispersal betweenCuba and Hispaniola and one-way dispersal from Cuba to Ja-maica and from Hispaniola to Puerto Rico, with all other ratesequal to zero (model suf!x ch/hc/cj/hp); and (ii) an “out ofCuba” model with one-way dispersal from Cuba to all other is-lands, with all other rates equal to zero (model suf!x cuba). Weconsidered a third dropped-zero model by essentially mergingthese two models, thus generating (iii) a model that alloweddispersal from Cuba to all other islands and from Hispaniola toall other islands (model suf!x ch:hc).For all of these secondary dropped-zero models, we considered

the following scenarios: (i) a one-rate constant, time-invariantrate for all nonzero rate entries of the rate matrix (1 parameter),(ii) a k-rate model with separate time-invariant rates between allnonzero entries of the rate matrix (k parameters), and (iii)a model with a single rate that varied through time for all non-zero entries of the matrix (two parameters). All 12 of thesemodels are illustrated in Fig. S3.Of all models we considered, the greatest improvement in

model likelihoods came from simply relaxing the assumption oftime-invariant dispersal between islands (Table S1). For example,the log-likelihood of the 12-parameter time-invariant model(qasymm12) was !48.78, yet a simple 2-parameter model withequal rates between all island pairs at any point in time(qsymm1_TD) had a much higher log-likelihood (!42.68). Theoverall best model was the 2-parameter dropped-zero modelallowing only dispersals between Cuba and Hispaniola and fromCuba to Jamaica and from Hispaniola to Puerto Rico. Resultsusing this model as a biogeographic background model areshown in Table 1.We recognize that our inference about diversi!cation processes

is conditional on the underlying biogeographic model used toaccount for transitions between character states. Ideally, onewould consider all possible biogeographic models—of whichthere are 12, each with 10 diversi!cation models—leading toa minimum of 120 diversi!cation/biogeographic model combi-nations to be considered. Rather than consider all possiblemodels, we !t the 10 diversi!cation models (Table 1) against twosimpler biogeographic models to verify that our results were notsimply a function of choosing the qsmm.ch/hc/cj/hp_TD model(Fig. S3). These results, using the poor-!tting one-rate sym-metric model (qsymm1) and the much better time-varying modelqsymm1_TD provided nearly identical results to those given inTable 1, indicating that our results are not sensitive to the un-derlying biogeographic model used for inference. These resultsare summarized in Tables S2 and S3.

Ancestral State Reconstruction and Lineage Accumulation Curves.Ancestral state (island occupancy) probabilities are essentiallycomputed during the implementation of the model describedabove. At each node in the phylogeny, the probabilities Di(t) foreach descendant branch are combined. By normalizing thesestate probabilities, we obtain an estimate of the probability thata given node k was in any of the N possible character states. Theprobability that node k is in state i is given by

pk;i !Di;k

"N

j!1Dj;k

:

We used these node probabilities to estimate lineage accumu-lation curves for each island (Fig. 2). The approximate number oflineages in state i at time T is then given by

%T;i ! "B

j!1pj;izj;

where pk,i is the probability of state k at node i and z is an in-dicator variable; and zi = 0 if node i is younger than node x (e.g.,t > T) and 1 otherwise (B is the total number of nodes).

Evaluation of Model Adequacy. To assess whether the !tted modelscould recover patterns of species richness and branch lengthsconsistent with those observed for Anolis, we simulated phylo-genetic trees and character state data under maximum-likelihoodparameter estimates for GlobalConstant, IslandConstant,GlobalVariable, and IslandVariable models. We then used threesummary statistics to test whether predictions under the !ttedmodels match patterns in the observed data. We !rst simplytabulated the species richness values for each island at the end ofeach simulation and compared these values to the observed data(Fig. 4 and Table S4).The remaining statistics we computed assessed patterns of

branch length variation in simulated trees. We aremost interestedin how well branch lengths associated with character state imatchbranch lengths associated with character state i in the Anolisdata. Because we do not know with certainty which internalbranch lengths can be assigned to which character state in Anolis,we considered only terminal branch lengths. We thus computedthe mean terminal branch length for all terminals with characterstate i (Fig. S6), as well as the coef!cient of variation in terminalbranch lengths (Fig. S7). These results suggest that the best-!tmodel by likelihood analysis (IslandVariable) consistently !ts theobserved data for all three summary statistics better than thealternative models with time-invariant diversi!cation or globaldeclines in speciation through time.

Model Comparisons. We used Akaike weights to estimate theconditional probability of each model (5). Given the set of AICscores corresponding to the M candidate models, we !rst com-puted the difference (!AICi) between each AIC score and theoverall best (lowest) AIC score. These quantities are then usedto estimate the probability of model i conditional on the AICscores observed in the candidate set. This probability is

!i !exp#! !AICi

2

#

"M

k!1exp

$! !AICk

2

#;

where the term in the numerator is known as the Akaike weight ofthe ith model.

Rabosky and Glor www.pnas.org/cgi/content/short/1007606107 2 of 10

1. Mahler DL, Revell LJ, Glor RE, Losos JB (2010) Ecological opportunity and the rate ofmorphological evolution in the diversi!cation of Greater Antillean anoles. Evolution64:2731–2745.

2. Maddison WP, Midford PE, Otto SP (2007) Estimating a binary character’s effect onspeciation and extinction. Syst Biol 56:701–710.

3. FitzJohn R, Maddison WP, Otto SP (2009) Estimating trait-dependent speciation andextinction rates from incompletely resolved phylogenies. Syst Biol 58:595–611.

4. Soetaert K, Petzoldt T, Setzer RW (2009) deSolve: General solvers for initial valueproblems of ordinary differential equations (ODE), partial differential equations (PDE)and differential algebraic equations (DAE), R package version 1.5Available at http://CRAN.R-project.org/package=deSolve.

5. Burnham KP, Anderson DR (2002) Model Selection and Multimodel Inference—APractical Information-Theoretic Approach (Springer, New York).

Rabosky and Glor www.pnas.org/cgi/content/short/1007606107 3 of 10

Fig. S1. Maximum clade credibility (MCC) tree resulting from BEAST analyses. Posterior probability (pp) values from the MrBayes analyses used to generatethe starting tree for BEAST are indicated by circles above branches (black, pp > 0.95; gray, 0.95 > pp < 0.70; white, pp < 0.70). Island occupancy is indicatedacross the tips of the tree (green, Cuba; blue, Hispaniola; yellow, Puerto Rico; orange, Jamaica).

Rabosky and Glor www.pnas.org/cgi/content/short/1007606107 4 of 10

Bplumifrons Pacutirostris heterodermainderanaeniceforiaeneus

roquetrichardigriseustrinitatusluciae

agassizi casildaemicrotusaqbl sp. nov. 1

frenatuspunctatustransversalisacutusevermannistratuluscookimonensiscristatellusdesechensisernestwilliamsi

scriptusgundlachiponcensiskrugipulchellusbrevirostriscaudalismarronwebsteridistichusbimaculatus

gingivinusferreuslividusmarmoratussabanusnubilusoculatusleachipogusschwartziwattsi ahli

allogusrubribarbusimiasbremeriquadriocellifersagreiophiolepismestreiconfusushomolechis

jubarguafe altaefuscoauratuspandoensis bicaorumlemurinuslimifrons

zeuslionotusoxylophuspoecilopustrachydermatropidogastercarpenterioscelloscapulariscapito tropidonotus

cupreuspolylepishumilispachypusintermediuslaeviventrisortoniiisthmicussericeussminthus

aquaticuswoodibiporcatus bitectuscrassulus nebuloides

quercorumpolyrhachisuniformisutilensisloveridgeipurpurgularis annectens

oncalineatus meridionalisnitensauratusconspersusgrahamigarmaniopalinusvalencienni

lineatopusreconditusalayoniangusticepspaternus placidussheplani

sp. nov. 2allisonismaragdinusbrunneus

longicepsmaynardicarolinensisporcatusaltitudinalis

oporinusisolepis argillaceuscentralispumilisloysiana garridoi

guazumaalfaroimacilentusclivicolacupeyalensiscyanopleurusrejectusvanidicusalutaceus

inexpectatusargenteolusluciusbaleatusbarahonaericordiieugenegrahamichristopheicuvieri barbatuschamaeleonides

guamuhayaporcus armouri

cybotesshreveibreslinihaetianuswhitemanilongitibialisstrahmimarcanoialuminasemilineatusolssonibarbouri

etheridgeifowleriinsolitusalinigersingularischlorocyanuscoelestinusbahorucoensisdolichocephalushendersonimonticola

darlingtonibaracoaenobleismallwoodiequestrisluteogularisbartschivermiculatus occultus

Fig. S2. Consensus tree and branch lengths generated from posterior distribution of MrBayes analysis using the sumt command. This tree includes non-Greater Antillean taxa that were pruned before our analyses. Posterior probability values are indicated by circles above branches (black, pp > 0.95; gray, 0.95 >pp < 0.70; white, pp < 0.70).

Rabosky and Glor www.pnas.org/cgi/content/short/1007606107 5 of 10

C

C

H

H

J

J

P

P

Dispersal from

C

C

H

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P

P

Disp

ersa

l to

Dispersal from

C

H

J

P

C

C

H

H

J

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P

Time

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Disp

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Disp

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l to

Time

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P

Dispersal from

Drop zero rate elements

ch:hcch//hc/cj/hp cuba

qasymm12qsymm1 qsymm_TD

Fig. S3. Biogeographic dispersal models considered for Anolis. We considered 12 possible transition matrices representing dispersals between island states.Colored entries denote rate parameters that were free to vary under the model; white entries denote rate parameters that were set equal to zero. Parameterswith identical colors are constrained to have the same value (e.g., qsymm1, Upper Left, with identical dispersal rates between all islands). The Lower threecolumns of submatrices (ch/hc/cj/hp, cuba, and ch:hc) were formed by eliminating rate parameters from the !tted qasymm12 model if rates under that modelwere estimated as zero (<10!10). Models with time-varying dispersal parameters !tted the datamuch better thanmodels with time-invariant dispersal (Table S1).

Rabosky and Glor www.pnas.org/cgi/content/short/1007606107 6 of 10

0 5 10 15 20 25 30 35 40

Versus GlobalConstant

0 5 10 15 20 25 30 35 40

Versus IslandConstant

0 5 10 15 20 25 30 35 40

Versus GlobalVariable

AIC evidence favoring IslandVariable modelFig. S4. Robustness of results to phylogenetic uncertainty. Histograms show AIC evidence favoring the IslandVariable model (separate linear change inspeciation rates through time on each island) relative to GlobalConstant, IslandConstant, and GlobalVariable models, where all models were !tted to 400 treessampled randomly from the posterior distributions of trees from the BEAST analysis. The IslandVariable model consistently !ts better than GlobalVariable.

-1.0 -0.5 0.0 0.5 1.0

Correlation

Freq

uenc

y

Fig. S5. Pearson correlation between log(island area) and the rate decline parameter (!!0/K) under the best-!t model (IslandVariable) tabulated from 400trees sampled randomly from the posterior distributions of trees from the BEAST analysis. The rate decline parameter is the slope of the relationship betweenthe speciation rate and time. A negative correlation implies that larger islands have slower changes in speciation rates with respect to time.

Rabosky and Glor www.pnas.org/cgi/content/short/1007606107 7 of 10

0.0 0.2 0.4 0.6

Freq

uenc

y

Cuba

BL mean

A

0.0 0.2 0.4 0.6

Hispaniola

BL mean0.0 0.2 0.4 0.6

Jamaica

BL mean

GC

IC

GV

IV

0.0 0.2 0.4 0.6

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BL mean

0.0 0.4 0.8 1.2

Freq

uenc

y

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B

0.0 0.4 0.8 1.2

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BL CV0.0 0.4 0.8 1.2

Jamaica

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0.0 0.4 0.8 1.2

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Fig. S6. Distribution of mean terminal branch lengths (A) and the coef!cient of variation in terminal branch lengths (B) for trees simulated under four !tteddiversi!cation models, partitioned by terminal character state (Cuba, Hispaniola, Jamaica, or Puerto Rico). Models are (Top to Bottom) as follows: GC,GlobalConstant; IC, IslandConstant; GV, GlobalVariable; IV, IslandVariable. Colored lines denote mean values for the Anolis MCC tree; black lines and histo-grams represent mean values and distributions tabulated from 2,000 datasets simulated under maximum-likelihood parameter estimates for each model. TheIslandVariable model provides a much closer match to the observed data than the three alternative models.

Rabosky and Glor www.pnas.org/cgi/content/short/1007606107 8 of 10

Table S1. Biogeographic models evaluated (see Fig. S2 for graphical description)

Model Description np LogL AIC !AIC

qasymm12 Asymmetric transition rates between all island pairs. 16 !48.78 129.56 35.88qsymm1 Single transition rate between all islands. 5 !54.9 119.8 26.12qsymm.ch:hc “Out of Cuba/out of Hispaniola” model. Single rate for all

transitions from Cuba to all other islands and from Hispaniola toother islands (q12, q13, q14, q21, q23, q24); 0 for all others.

5 !53.9 117.8 24.12

qasymm.ch:hc6 Out of Cuba/out of Hispaniola model. Different rates for q12, q13,q14, q21, q23, q24; 0 for all others.

10 !48.78 117.56 23.88

qsymm.cuba “Out of Cuba” model. Single rate for q12, q13, q14; 0 for all others. 5 !52.36 114.72 21.04qasymm.ch/hc/cj/hp.4 Different rates for q12, q21, q13, q24 (between Cuba and Hispaniola

and from Cuba to Jamaica and from Hispaniola to Puerto Rico);0 for all others.

8 !48.8 113.6 19.92

qasymm.cuba3 Out of Cuba, with different rates for q12, q13, q14; 0 for all others. 7 !49.67 113.34 19.66qsymm.ch/hc/cj/hp Single rate for q12, q21, q13, q24; all other rates 0. 5 !51.4 112.8 19.12qsymm.ch:hc_TD Single time-varying transition parameter for all transitions from

Cuba and Hispaniola to all other islands.6 !43.17 98.34 4.66

qsymm1_TD Single time-varying transition parameter between all islands. 6 !42.68 97.36 3.68qsymm.cuba_TD Single time-dependent out of Cuba transition parameter (q12, q13,

q14 > 0); all others = 0.6 !42.67 97.34 3.66

qsymm.ch/hc/cj/hp_TD Shared time-varying parameter for q12, q21, q13, q24. 6 !40.84 93.68 0

All biogeographic scenarios were evaluated against a background diversi!cation model with island-speci!c differences in speciation, but no rate variationthrough time (IslandConstant model). Models with linear time-dependent change in the transition rate (“TD”) !tted the data much better than correspondingmodels without time-dependent transition rates. States 1, 2, 3, and 4 correspond to Cuba, Hispaniola, Jamaica, and Puerto Rico, respectively.

Table S2. Model-!tting results under alternative biogeographic background models (Table S1: qsymm_TD andqsymm)

Diversi!cation model NP (# = 0) LogL (# = 0) !AIC (# = 0) NP (# $ 0) LogL (# $ 0) !AIC (# $ 0) !i

Biogeographic model: Symmetric dispersal between all islands, but rate varies through time (qsymm_TD)IslandConstant 6 !42.68 29.88 10 !42.67 37.86 0GlobalConstant 3 !46.57 31.66 4 !46.56 33.64 0GlobalVariable 4 !34.87 10.26 6 !34.63 13.78 0.006IslandVariableFull 10 !25.97 4.46 18 !22.1 12.72 0.091IslandVariable 7 !26.74 0 12 !24.3 5.12 0.903

Biogeographic model: Symmetric dispersal between all islands, but rate is constant through time (qsymm)IslandConstant 5 !54.91 30.04 9 !54.91 38.04 0GlobalConstant 2 !58.22 30.66 3 !58.19 32.6 0GlobalVariable 3 !46.58 9.38 5 !45.5 11.22 0.004IslandVariableFull 9 !38.11 4.44 17 !27.96 0.14 0.460IslandVariable 6 !38.89 0 11 !35.4 3.02 0.536

All diversi!cation models are identical to those in Table 1. The biogeographic model assumes equal transition rates between allpairs of islands at any point in time, but with (i) a linear change in the rate of transitions through time (Upper row, Center, in Fig. S3),or (ii) identical time-invariant rates through time (Upper row, Left, in Fig. S3). Results are shown for models without (# = 0) and with(# $ 0) extinction. np, number of parameters; !i, conditional probability of each model given the candidate set of models. Modelswithout extinction (# = 0) !t the data better than the corresponding model with extinction in all cases but one (IslandVariableFullunder qsymm). Models specifying island-speci!c changes in " and/or # account for P = 0.994 of the total probability of the data takenacross all models, and the GlobalVariable model !ts much more poorly than the IslandVariable model.

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Table S3. Summary statistics for island species richness indatasets simulated under maximum-likelihood parameters ofGlobalConstant, IslandConstant, GlobalVariable, andIslandVariable models (Table 1)

Model Island Observed Mean Median q25 q75

GlobalConstant Cuba 61 6.93 4 0 10GlobalConstant Hispaniola 40 9.56 6 1 14GlobalConstant Jamaica 6 4.3 0 0 5GlobalConstant Puerto Rico 10 6.8 3 0 10IslandConstant Cuba 61 12.42 7 0 18IslandConstant Hispaniola 40 9.23 6 1 14IslandConstant Jamaica 6 2.3735 0 0 4IslandConstant Puerto Rico 10 2.53 1 0 4GlobalVariable Cuba 61 23.6 15 4 33.25GlobalVariable Hispaniola 40 32.17 23 7 47GlobalVariable Jamaica 6 13.508 4 0 17GlobalVariable Puerto Rico 10 24.284 13 2 35IslandVariable Cuba 61 47.8 30 9 69IslandVariable Hispaniola 40 35.95 26 10 52IslandVariable Jamaica 6 6.5 2 0 8IslandVariable Puerto Rico 10 15 9 2 21.5

Observed denotes observed species richness on each island. q25 and q75

denote 0.25 and 0.75 percentiles of the distribution of richness values undereach simulation model.

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