Ecology, 84(8), 2003, pp. 1945±1956 ᭧ 2003 by the Ecological Society of America

ARE LONG-DISTANCE DISPERSAL EVENTS IN PLANTS USUALLY CAUSED BY NONSTANDARD MEANS OF DISPERSAL?

S. I. HIGGINS,1,4 R. NATHAN,2 AND M. L. CAIN3 1UFZ Umweltforschungszentrum, Leipzig-Halle, Sektion OÈ kosystemanalyse, Permoserstrasse 15, 04318 Leipzig, Germany 2Department of Life Sciences, Ben-Gurion University of the Negev, Beer-Sheva 84105 Israel 3Department of Applied Biology, Rose-Hulman Institute of Technology, Terre Haute, Indiana 47803 USA

Abstract. It has been argued that nonstandard mechanisms of dispersal are often re- sponsible for long-distance dispersal in plants. For example, plant seeds that appear to be adapted for wind dispersal may occasionally be dispersed long distances by birds, or vice versa. In this paper, we explore whether existing data on dispersal distances, colonization rates, and migration rates support the idea that dispersal processes suggested by the mor- phology of the dispersal unit are responsible for long distance dispersal. We conclude that the relationship between morphologically de®ned dispersal syndrome and long-distance dispersal is poor. This relationship is poor because the relationship between the morphology of dispersal units and the multiple processes that move seeds are often complex. We argue that understanding gleaned from the often anecdotal literature on nonstandard and standard means of long distance dispersal is the foundation for both statistical and mechanistic models of long-distance dispersal. Such models hold exciting promise for the development of a quantitative ecology of long-distance dispersal. Key words: island colonization; long-distance dispersal; mechanistic dispersal models; mixture models; morphological dispersal syndrome. pca Feature Special

INTRODUCTION persal unit and dispersal syndrome (e.g., ¯eshy fruits Classical works in ecology and biogeography imply endozoochory), hence dispersal syndrome is typ- stressed the fundamental importance of long-distance ically de®ned by the morphology of the dispersal unit dispersal (LDD) for the distribution and evolution of (e.g., Ellner and Shmida 1981, Hughes et al. 1994). In organisms (e.g., Darwin 1859, Ridley 1930). However, this paper, we refer to these morphological dispersal for much of the last 30 years, research on LDD has syndromes (MDS) as the standard means of dispersal been regarded by some ecologists as irrelevant and an- of a species; if other dispersal agents are involved, they ecdotal (Nathan 2001). Irrelevant, because the advent are considered as nonstandard means of dispersal. Al- of vicariance biogeography meant that disjunct species though the MDS concept provides a useful framework ranges could be explained by vicariance, rather than for describing local dispersal processes (Hughes et al. by LDD. And anecdotal, because the rise of a more 1994), it emphasizes processes that move the majority quantitative approach to ecology meant that dispersal of seeds rather than the rarer processes that move a ecologists focused on local dispersal since it is more small proportion of seeds. The possibility remains that readily quanti®able than LDD. However, the recent these rarer processes may move seeds long distances. work that shows how LDD largely de®nes invasion and There are many de®nitions of LDD, some of which migration rates (Wilkinson 1997, Cain et al. 1998, emphasize the scale of dispersal, others emphasize the Clark 1998, Higgins and Richardson 1999) has resus- shape of the distribution of dispersal distances. In prac- citated ecological interest in LDD. tice, of course, the scale and shape of the distribution Despite the ``rediscovery'' of the importance of are not independent. De®nitions that emphasize scale LDD, we know relatively little about the processes that are more appropriate for investigating the frequency of generate LDD (Cain et al. 2000). It is known that a dispersal events greater than some ecologically mean- great variety of processes can move seeds. These dif- ingful distance (e.g., proportion of seeds moving fur- ferent dispersal processes are often grouped into the ther than the typical distance between patches). Where- ``classic'' syndromes of dispersal, e.g., anemochory, as, shape de®nitions are more appropriate for investi- hydrochory, autochory, ectozoochory, and endozo- gating the magnitude of rare dispersal events (e.g., dis- ochory (van der Pijl 1982). Many investigators rou- tance of the 99th percentile). In this paper, we examine tinely assume a link between the morphology of a dis- a variety of case studies, some of which necessitate scale de®nitions of LDD, some of which necessitate Manuscript received 6 November 2001; revised 1 August shape de®nitions. 2002; accepted 12 August 2002; ®nal version received 30 Sep- tember 2002. Corresponding Editor: R. B. Jackson. For reprints In the ®rst part of the paper, we argue that LDD is of this Special Feature, see footnote 1, p. 1943. poorly related to MDS. It should be noted at the outset 4 E-mail: [email protected] that the lack of a relationship between MDS and LDD 1945 Special Feature ehnsi oesaecniee,wn dispersal of wind models. classes animal-movement±seed-retention considered, Two and models are LDD. of models predictions mechanistic generate to we mod- scarce els mechanistic be using of always potential will the investigate LDD also like events rare on empirical data Because data. dispersal for empirical methods describing statistical demonstrate operate then mechanisms We these routinely. of for many account that argue may ex- and that LDD illustrative mechanisms review dispersal we of a amples LDD the of for guide study To suggestions LDD. The quantitative provides studying LDD. for paper of approach the context quantitative of the part in informative second that means not equally merely it is are LDD; for MDS species capacity all a have that to likely mean however, not, does 1946 omdamt-nlsso h al(distances tail the of meta-analysis a formed aMhn19) hsi sntkonwehrthe whether known not and is be (Chambers it may processes Thus units 1994). other dispersal MacMahon by the the (further) exclude of moved usually some practices that traps Such seed possibility use seeds. or collect conditions re- to controlled typically in dispersal seeds wind lease for mor- be adapted to seem phologically that units dispersal of protocols For studies sampling example, processes. dispersal the additional of excluded explicitly most and Moreover, dispersal local LDD. in¯uences not MDS that mere- showing have may be analysis in- sets the ly hence be data source, the not dispersal at may modes LDDÐmany their mode the the of than dicative greater are dis- dispersal that of in¯u- tances mean MDS the whether Fundamentally, of LDD. question ences the address to studies alge- distribution. the or of (exponential tail shape the the of dispersal to braic) that unrelated shown is is analysis it mode the 1993) of dis- Willson part dispersal and second the (Portnoy the of in tail However, the tribution. in¯uence is does analysis (1993) MDS Willson's that from reaches con- one were The trees. clusion than results distances dispersal mean plants The lower herbaceous had form: growth distances. by in¯uenced dispersal strongly substantially mean had seeds ballisti- lower unassisted while and dispersed dis- species, cally dispersal animal-dispersed MDS: mean than different larger tances with had species seeds mean wind-dispersed of the distances between differences Will- dispersal large sets. found data the (1993) to son ®tted al- were and distributions exponential gebraic negative seed Both comprehen- on most distances. data the dispersal synthesize aware, quantitatively are to we attempts as sive anal- far these as sets; data are, distance yses vs. density seed many of ilo 19)adPrnyadWlsn(93 per- (1993) Willson and Portnoy and (1993) Willson hr r eea motn iiain fuigthese using of limitations important several are There D R ISPERSAL LTOSI BETWEEN ELATIONSHIP ipra itnedistributions distance Dispersal D S NRM AND YNDROME ISPERSAL C APACITY M ORPHOLOGICAL C REAE OF ORRELATES .I IGN TAL. ET HIGGINS I. S. Ͼ mode) aast eeavailable. were sets tree dispersed data her- ballistic and animal-dispersed unassisted few Willson few and and baceous, balanced: Portnoy not the were and addition, (1993) (1993) In Willson analyzed. in and analyses distance collected pro- dispersal were dispersal multiple cesses included that and data if hold MDS would between relationship idadaia D rusddntdfe signi®- differ not did 1A, groups (Fig. MDS MDS the cantly assign of animal to rates and (2001) migration mean wind al. The et species. Bonn to categories and (1988), al. dis- Grime (1930), et wind Ridley ¯oras, or published dispersed taxa used We animal these persed. either of as MDS assigned The (summa- were [1993]). Europe MacDonald and by Kingdom, rized North from United taxa the tree for America, estimates rates published migration used postglacial ob- We of to rates? related migration MDS is served ask: therefore (Wil- We rate 1997). migration to kinson related positively be to capacity n i w uvy losoet dniy56colo- 516 identify to one allows surveys own mainland. his the and from km 7 and The 0.2 1960. 1933± in between 22 are in all and islands islands 1948±1949, in no ®ve islands is 19 surveyed name 1934, its Luther because used). found (the be longer Hayren not by could surveyed island those 19th is- Luther's of 1961). 22 18 (Luther of included 1960 islands ¯ora and the 1933 surveying between by lands followed work Luther Hayren's 1914). on (Hayren up islands ¯oral 19 complete of conducted surveys he Tva 1913, the and in 1907 islands Between on succession op- study started Hayren wonderful to 1900, In in- a colonization. study their provide to portunity Despite islands survive inundation. must these and plants hospitability, winds and low, to typically is exposure is elevation substrate the the rocky, are hospitable: islands particularly New size. not in years that increasing and 7000 are appearing islands still some are existing initiated islands ¯oor, new that sea means ago, Baltic the of up- lift Continuing Finland. southern peninsula, Hanko the iomna a togyi¯ec irto rates migration 1999). Richardson in¯uence and en- strongly (Higgins the of can suitability the vironmental and history life plant been Second, 2001). Lister have and Stewart rates, 1993, migration (Macdonald the tech- questioned reconstruct the of to and assumptions reliability used the niques the as this well First, as why record, convincing. reasons pollen not rate are is migration there in¯uence LDD, result not implication does by MDS and that idea the efre iia nlss letwt mle sam- ( smaller size a ple with albeit who analysis, (1997) similar Wilkinson a with performed agreement in is result This l te hnsbigeul ewudepc LDD expect would we equal, being things other All uhr' 16)mtclu ytei fHayren's of synthesis meticulous (1961) Luthers's Tva Èrminne n ϭ Ðhuad frcyilnssurround islands rocky of .ÐThousands ) lhuhti euti ossetwith consistent is result this Although 8). F ooiainrate Colonization 1,40 irto rate Migration ϭ 0.371, P clg,Vl 4 o 8 No. 84, Vol. Ecology, ϭ 0.543, rin area. Èrminne n ϭ 42). August 2003 LONG-DISTANCE DISPERSAL 1947 pca Feature Special

FIG. 1. Tests of the relationship between correlates of long-distance dispersal (LDD) and morphological dispersal syndrome (MDS). (A) The mean (bars indicate one standard deviation) postglacial migration rates for trees with different MDS's estimated from pollen records in North America and Europe (data are from MacDonald [1993]). (B) The number of colonizing species (bars) and mean colonization frequency per species (circles) recorded on 22 islands in the TvaÈrminne archipelago by MDS (data from Luther [1961]). (C) The number of Tasmanian species (black bars) and number of Tasmanian species also found in New Zealand (white bars) by MDS (data from Jordan [2001]). (D and E) The number of arriving and colonizing species on Surtsey island classi®ed by MDS (white bars) and actual means of dispersal (black bars) (data are from Fridriksson [1975]). The MDS categories are: wind, dispersal units with wings or plumes; attach, dispersal units with hooks, barbs, or other attachment devices; edible, edible (e.g., fruits, nuts) dispersal units; minute, small (Ͻ0.05 mg for TvaÈrminne, Ͻ1mm diameter for New Zealand) dispersal units; water, dispersal units with airspaces; unspec, dispersal units with no apparent morphological features. The edible and attach MDS's are often lumped into an animal MDS. nization events by 163 vascular plant species. We as- nization frequency was not in¯uenced by MDS (Fig. signed these species to six MDS categories (see Fig. 1B, G ϭ 8.651, P ϭ 0.8762). The TvaÈrminne analysis 1B) using the sources described in Migration rate. This therefore suggests that MDS is unrelated to coloniza- procedure probably underestimates the number of spe- tion ability. cies with morphologies suited for ¯otation, since New Zealand.ÐExcluding orchids, there are 187 an- whether a dispersal unit has air spaces within is often giosperm species native to both Tasmania and New not illustrated or not known. Plotting the number of Zealand. A vicariant explanation for these disjunct pop- species that colonize makes it clear that the unspe- ulations would require that allopatric populations re- cialized and wind MDS are the most common colonists. mained in evolutionary stasis for the 80 million years However, this does not mean that species with these that Tasmania and New Zealand have been separated MDSs are the best colonistsÐit may be that these (Jordan 2001). Since stasis for such a long periods is MDSs are the most common in the pool of potential unlikely, it is accepted that these species dispersed source species. Unfortunately, the distribution of the across the 1500±2000 km Tasman Sea more recently MDS in the potential source pool is not known. We (Jordan 2001). Analysis of which of the Tasmanian can, however, ask whether the frequency of coloniza- ¯ora (excluding orchids) colonized New Zealand shows tion per species differs with MDS. A log-likelihood that species with minute seeds (Ͻ1 mm propagule di- ratio for contingency tables (Zar 1999) shows that al- ameter) were more likely to colonize New Zealand though species with MDS for water had, on a per spe- (Fig. 1C, G ϭ 22.82, P ϭ 0.0001, Jordan 2001). Hence, cies basis, higher colonization frequencies, that colo- the evidence from New Zealand suggests that over long Special Feature a emvdb id tahet n neto (Rid- ingestion 1930). and ley attachment, wind, by seeds moved be minute syndromeÐsmall can MDS unspecialized The an colonize. however, to is, likely seeded more small are distances, species dispersal large and scales time 1948 ooiaino hsiln teae a hukfrom shrunk has area (the km The 2.7 island Island. of Heimaey this south of of km southwest colonization km 33 20 lies and Surtsey Iceland 1967. and 1963 between 4% letisgicn ( greater a insigni®cant to albeit col- leads these (44%) MDS of For knowledge 1E). 1972 species, (Fig. onizing and period 1963 this between during colonized arriving observed taxa plant fteerri rdcigteata en fdispersal of means actual the ( predicting reduction in insigni®cant error and the (7%) of small a to leads MDS ␶ ®dteMSa ecie in described as MDS spec- we the dispersal; i®ed of Fridriksson means species, a actual all the with speci®es For confused (1975) genus. been same the have at of could species identi®ed and were level (Fridriksson that genus 1972 taxa the three and excluded 1963 We between 1975). Surtsey on ing data. colonization from of patterns practice common dispersal the inferring with associated as- biases to the us sess allows with comparison arrivals this species colonizations; compare species we knowledge Second, on MDS. based the dis- predicted of of been have means we could (observed) persal First, actual paper. the our whether the in examine of some addressed examine questions to data principal opportunity unusual unique These seeds. a for provide shoreline its the and droppings, island, bird birds, assigned netted were searching seeds regularly of by arrival (Fridriks- of island means re- The the 1975). by sub- on son the plants succession, and of units primary colonization dispersal sequent true of arrival a the both follows cording exceptional it is that study Surtsey in The detail. remarkable in clyaatdfrwtrdsesl(i.1) Goodman (1954) 1D). Kruskal's (Fig. morpholog- and dispersal are water taxa for those adapted of ically quarter one only though dispersal four in 1D). species (Fig. the categories grouped we pli®cation, pce htarv u ontcolonize. not for do than but species arrive colonizing dispersal for that better of species is means MDS actual the its species' that from a seems colo- predict therefore the to It for ability islands. also barren but of ad- ¯otation, nization have for MDS only water not with aptations species that power) sta- insuf®cient tistical arriving with 48 (albeit of suggest suite data These entire species. of the of means In 20% actual species. only and for MDS colonizing dispersal the 10 both the was water of contrast, 50% for means means actual dispersal actual and of MDS the the both predicting was Water in dispersal. of error the of reduction actual Surtsey it-n aao ihrpat eercre arriv- recorded were plants higher of taxa Fifty-one ot(8)pattx rie ysacret,al- currents, sea by arrived taxa plant (78%) Most ϭ 2 n16 o15km 1.5 to 1967 in 0.071; Ðute savlai sadta emerged that island volcanic a is .ÐSurtsey P ϭ .5.Ol 0o h 8higher 48 the of 10 Only 0.35). ␶ hw htkoldeo the of knowledge that shows 2 ␶ n19)hsbe studied been has 1998) in actual irto rate. Migration ϭ 0.438; P .I IGN TAL. ET HIGGINS I. S. o sim- For ϭ 0.32) npoete ftedseslunit dispersal the of Variation properties distance: in dispersal of description Statistical esdsesln itne (see distances ex- wind-dis- long move For seeds might vector. persed updrafts dispersal vertical strong (standard) exceptional ample, or the rare of from behavior result category, events ®rst dispersal the LDD In categories. conceptual birds. exclusive of feet the the on reached mud events Paci®c rafting in rare the transport means: and in nonstandard islands two col- by of that islands species sets the 16 of onized 4±35% that Carlquist concluded example, (1967) For non- 1930). other, (Ridley by means distances also long standard is move it can seeds LDD, that While to clear animals. lead to with can attach adaptations seeds that morphological structures by by other facilitated exempli®ed or be burrs as can adaptations, plants in dispersal LDD mechanisms. of hnohrses(usugradFasn18;see 1987; Franson and (Augspurger seeds farther other considerably travel than to seeds some cause can unit by dispersal see seed 1999; in al. et variation (Hoshizaki interannual rodents in seen as edfrhnrd fkilometers. of disperse may hundreds occasion for longer on seed much hence for and seed h) retain (12±18 can periods bats that indicate al. et Shilton However, distances. short relatively seeds perse huh orti ln ed o hr eid only periods short for seeds plant usually ( are retain bats to fruit, of thought quantities vast Because consume species. they plant small-seeded (1999) of al. dispersal et bat Shilton third of on A work the distances. by long provided is relatively example cause move can to 2000), al. seeds et some (Nathan conditions wind in tion Ͻ alus 16)rahtesm conclusion. same the reach (1967) basis; and Carlquist (1930), regular Ridley (1859), a Darwin on in LDD reviews extensive to lead can mechanisms that these and dispersal of mechanisms nonstandard there of many that are indicates types review brief Our three dispersal. nonstandard of these means on of emphasis special each placing Below, of mechanisms, LDD. examples nonstan- for review a responsible we that is is vector possibility dispersal third dard A dis- responsible events. be the may LDD of mass, for seed property instance a for unit, in persal variability that is possibility o ipra itne ehnsi oesfrlong- wind for by models dispersal Mechanistic distance distance: dispersal for ino ipra itne aito nbhvo fa of behavior vector in dispersal Variation standard distance: dispersal of tion ln ed a oeln itne yarc variety rich a by distances long move can seeds Plant otnosvraini rpryo h dispersal the of property a in variation Continuous vector, dispersal standard a of behavior Exceptional ehnsso D a egopdit he non- three into grouped be can LDD of Mechanisms aiblt ntepoete ftedseslunit dispersal the of properties the in Variability 0mn.Hne asaecmol huh odis- to thought commonly are bats Hence, min). 30 M CAIM OF ECHANISMS aito ntebhvo fastandard a of behavior the in Variation ipra vector dispersal L ONG n nitresnlvaria- interseasonal in and ) .Tescn,btrelated, but second, The ). - DISTANCE .Se characteristics Seed ). clg,Vl 4 o 8 No. 84, Vol. Ecology, ehnsi models Mechanistic ttsia descrip- Statistical D ISPERSAL August 2003 LONG-DISTANCE DISPERSAL 1949 that vary in a discrete manner also can lead to variation nests. Although Ridley (1930) reported this practice, in how far seeds are dispersed. For example, in very more recent studies have reported seed morphologies dry years the desert annual Gymnarrhena micrantha that appear to be designed to attract the attention of produces one to three large ``nondisperser'' seeds in nest building birds (Dean et al. 1990). Hence, the dis- belowground ¯owers (Koller and Roth 1964). In wet persal of seeds as nesting material may be the standard years, the plant continues to produce a small number MDS for some species and a nonstandard means of of nondisperser seeds, but it also produces many small, dispersal for other species. Ridley (1930) also describes wind-dispersed seeds in aboveground ¯owers; these how seed, thought to be ant dispersed, were found at- wind-dispersed seeds have the potential to be dispersed tached to the bodies of Helix asperata snails that had long distances by wind either due to uplifting (see removed (and eaten) the elaiosomes from the seed Mechanistic models for dispersal distance: Mechanis- (elaiosomes are fat- and protein-rich bodies that attract tic models for long-distance dispersal by wind)orby ants). Ridley (1930) argued that these snails could tumbling along the soil surface (see Statistical descrip- move seeds long distances. Similarly, predators often tion of dispersal distance: Nonstandard mechanisms of serve as nonstandard seed dispersal agents when they dispersal). eat fruits (Hickey et al. 1999) or eat herbivores that have previously eaten seed (this and other types of Nonstandard mechanisms of dispersal indirect dispersal are described in the closing paragraph Although it is common to label, based on MDS, one of this section). As discussed by Ridley, Darwin, Ca- mode of dispersal as ``standard'' for a particular spe- rlquist, and others, seemingly novel dispersal mecha- cies, the seed of manyÐperhaps mostÐplant species nisms actually occur on a regular basis, thus providing are dispersed by multiple mechanisms (Ridley 1930, effective means for LDD. Chambers and MacMahon 1994). For a given plant Other nonstandard mechanisms of dispersal can be species, a dispersal mechanism other than its standard thought of as accidental. For instance seed can be trans- one may be a ``classic'' dispersal mechanism (e.g., ported accidentally in the feet of vertebrates, often for pca Feature Special wind, water, animal) that is well described (for instance long distances (Darwin 1859, Ridley 1930). Carlquist by van der Pijl 1982) or it may be a more unusual (1967), for example, estimated that 21.4% of the plant dispersal mechanism that is not commonly reported in species that dispersed to Easter Island (6 of 28 species) the literature. and 21% of the species that dispersed to the Juan Fer- Seeds of many species often are dispersed by com- nandez Islands (21 of 100 species) did so in mud on binations of well-described dispersal mechanisms. For the feet of birds. For small-seeded plant species, large example, apparently wind-dispersed seed frequently herbivores frequently eat seeds by accident as they con- ¯oat and remain viable in rain wash, streams, rivers, sume foliage (Ridley 1930, Janzen 1984). The seed of and even sea currents (Ridley 1930, Carlquist 1967); such plants typically remain viable when passing in such instances, it may be typical that seed are dis- through animal digestive tracts, thus enabling LDD. persed longer distances by water than by wind. In ad- Even more unusually, Fridriksson (1975) found 131 dition, ant-dispersed seed, wind-dispersed seed, and viable seed of ®ve plant species attached to a sample seeds that lack a known dispersal mechanism often of 23 ``mermaids purses'' (the egg casing of the skate, attach easily to the fur or feathers of vertebrates (Ridley Raja batis) on the shores of the volcanic island, Surt- 1930, Bonn and Poschlod 1998). For instance, results sey. The MDS of these ®ve species does not suggest in Berthoud (1892) indicate that buffalo may have been either attachment or ¯otation. effective LDD agents for a wide range of plant species, Finally, nonstandard dispersal vectors can achieve and Kiviniemi and Eriksson (1999) show that seed from LDD of plant seed in an indirect manner. In particular, both wind- and ant-dispersed species attach readily to many different types of predators, including jaguars the hair of cattle and thus could be transported long that eat tapirs, falcons that eat sparrows, and ®sh that distances (up to 120±780 m, depending on the species). eat other ®sh, can serve as regular, indirect, dispersal The ease with which wind-dispersed seed attach to the vectors of plant seeds (Ridley 1930). Indirect seed dis- bodies of vertebrates suggests that nonstandard means persal by predators is especially important in cases of seed dispersal may often be facilitated by the same where the predator is likely to move seeds longer dis- features of the seed that govern the standard mode of tances than does the typical dispersal vector. For ex- dispersal. Finally, humans provide an extremely effec- ample, Nogales et al. (1998) recovered viable plant tive (nonstandard) means of dispersal for many plant seeds from the pellets of shrikes (which disperse rel- species with a wide variety of MDSs (Hodkinson and atively long distances) that had eaten lizards (which Thompson 1997, Bonn and Poschlod 1998). disperse relatively short distances) that had eaten seeds. The additional or nonstandard means of dispersal may also be a dispersal syndrome that is not commonly STATISTICAL DESCRIPTION OF DISPERSAL DISTANCE described in the literature. For example, plant parts (including seed) of wind-dispersed plant species can The implicit argument in the previous section was be transported by birds 3 km or more and used to build that if we understand the multiple dispersal processes Special Feature opnn ouain.I eea,w a represent can of we mixture general, a g is In that populations. population component a from data way ¯exible describe yet to formal, a at- provide they are because distributions tractive Mixture distri- processes. mixture dispersal mul- by tiple that produced dis- data show describe these statistically can we detecting butions Here of sam- capable processes. a is persal design that can we strategy then pling seeds, moving in involved 1950 fvrainices D.The LDD. increase variation of codn othe to according s itr ewe ebl n nexponential an and Weibull a distribution: between we mixture follow that a examples use the In function. density bility ( where itr of mixture a h opnn distributions component The ed Hsiaie l 99.The 1999). al. et (Hoshizaki seeds ipra itne Agpre n rno 97.The 1987). Franson and (Augspurger distances dispersal x F tml)dseslpoescnb obndt il opst ipra itiuin(od18) Pearson's 1988). (Bond distribution dispersal composite a yield to combined be can process dispersal (tumble) ,tepoaiiydniyfnto o distance for function density probability the ), IG h odeso t(oe ausidct etr®t). better a indicate values (lower ®t of goodness the .Saitcl® ftemxuemdl(q )t he ifrn ipra aast lutaighwdfeetsources different how illustrating sets data dispersal different three to 2) (Eq. model mixture the of ®t Statistical 2. . p i stepooto fdsesluista move that units dispersal of proportion the is g ( x k ) opnn este,as densities, component ϭ i hpoaiiydniyfunction, density probability th pf 11 ( x ) ϩ ... eclsturbinata Aesculus f i ( x ahglaversicolor Tachigalia ϩ a eayproba- any be can ) pf kk ( x ) .I IGN TAL. ET HIGGINS I. S. xml hw ewe-ervraini h itnerdnsmoved rodents distance the in variation between-year shows example f rtarepens Protea x i ( (1) x of xml hw htvraini aaams rae ainein variance creates mass samara in variation that shows example ). ofceto aito,9t ecnie n Pearson's and mean, percentiles the ␹ 99th report variation, We of distribution. coef®cient mixture the param- of the estimate eters techniques to likelihood) likelihood Poisson three a maximum next (assuming dis- the use in component we described ®rst subsections, examples the the in In seeds tribution. of proportion the is where ieiodmtos n ign n Richardson and Higgins and methods, maximum using mixtures likelihood ®tting (1999) to guide Ripley practical and a for Venables distributions, overview general mixture a for of (1985) al. et Titterington See 2). ulsml®st h xoeta when exponential the Wei- to that simpli®es (note bull distributions exponential and Weibull 2 agons f® esr)o h te oes(Fig. models ®tted the of measure) ®t of goodness (a xml hw o tnad(id n nonstandard and (wind) standard a how shows example ␣ , ␤ g 1 ( and , x ) ϭ ␤ ϩ p ␣␤ 2 (1 r aaeeso h component the of parameters are ␣␣Ϫ 11 Ϫ␣ Ϫ x p exp ) 1 ␤␤ 1 exp[ 22 Ϫ clg,Vl 4 o 8 No. 84, Vol. Ecology, ΂΃ ( Ϫ x / ␤ x )] ␣ϭ ␣ ␹ )and 1) 2 indicate (2) p August 2003 LONG-DISTANCE DISPERSAL 1951

(1999) for an example of ®tting mixtures of Weibull with the heaviest samaras had a mean dispersal distance distributions to dispersal data. of 17 m, a 99th percentile of 31 m, and a small CV A rationale for using mixture distributions is to com- (34). Fits using data from all populations (assuming an bine sampling techniques that capture the variance in equal proportion of samaras in the ®ve weight cate- the distances that seeds move with statistical tech- gories) generated a mean dispersal distance of 27 m, niques that describe this variance. In the following a 99th percentile of 184 m, and a large CV (119). The three examples we show how mixture distributions can lightest samaras in¯ate the mean dispersal distance and be used to quantify how (1) variation in behavior of a increase the amount of LDD, conversely, sampling a standard dispersal vector, (2) variation in the properties population with heavy samaras would underestimate of the dispersal unit, and (3) additional (nonstandard) the amount of LDD. dispersal processes can in¯uence dispersal distances. Nonstandard mechanisms of dispersal Variation in behavior of a standard dispersal vector Variation in site conditions or temporal variation in Mixture distributions also provide a convenient way conditions, can capture variance in the behavior of the to integrate dispersal data when multiple dispersal standard dispersal vector. For example, Hoshizaki et mechanisms or dispersal vectors move seeds. Obvious al. (1999) examined the dispersal of Aesculus turbi- examples are ¯eshy fruits, most of which fall close to nata, a temperate forest species that is dispersed by the tree canopy, but a small proportion of which are rodents. They monitored dispersal distance by relo- dispersed further by frugivores. We use the slightly cating marked seeds over two years; the between-year more complicated case of secondary dispersal, using variation was staggering. We attempted to ®t a mixture Bond's (1988) data on Protea repens dispersal. Here, of two exponential distributions (Eq. 2, with ␣ϭ1) to primary dispersal is from the canopy to the soil surface each year's data set and to the combined data set. It by wind and secondary dispersal is by tumbling along was only possible to ®t the mixture distribution to the the soil surface. The MDS of Protea repens suggests combined data, a single exponential distribution was that it is adapted for wind and not tumble dispersal. Feature Special ®tted to each year's data. The ®tted models yielded a Bond directly observed primary (wind) and secondary mean dispersal distance of 11 m for the ®rst year, and (tumble) dispersal distances. For wind dispersal, only 59 m for the second year (the CV for the exponential a one-component Weibull distribution could be ®tted: distribution is 100). Combining the data sets yielded the mean dispersal distance was 11 m, the 99th per- an overall mean dispersal distance of 29 m and a CV centile was 24 m, and the CV was only 45, indicating of 177. This mixture distribution predicts that most low variance in dispersal distance. For tumble dis- seeds (87%) move relatively short distances (mean 17 persal, only a one component exponential distribution m) but that a small proportion (13%) move longer dis- could be ®tted: the mean was 12 m and the 99th per- tances (mean 106 m). The 99th percentiles were 51 m centile was 56 m (the CV of the exponential is 100); for the ®rst year, 281 m for the second year, and 275 this exponential provides a conspicuously poor ®t. For m for the combined sample. Hoshizaki et al. (1999) the model combining wind and tumble dispersal pro- could ®nd no obvious reason for the large between- cesses 62% of seeds travel an average of 12 m and 38% year differences. travel an average of 47 m. The overall mean dispersal distance was 26 m, the 99th percentile was 170 m, and Variation in properties of the dispersal unit the CV was 134. A polymorphism, such as the size and color of a vertebrate dispersed ¯eshy fruit or the wing-loading of MECHANISTIC MODELS FOR DISPERSAL DISTANCE a wind-dispersed plume, is another source of variation in dispersal distance. Augspurger and Franson (1987) Statistical models require only data on dispersal dis- investigated variation in seed morphology of wind dis- tances, i.e., they require no information on the under- persed dispersal units by creating arti®cial dispersal lying dispersal processes. While this could be regarded units, modeled on the samaras of Tachigalia versicolor, as an advantage, the disadvantage is that for LDD such of varying mass and area. They explored several kinds data will remain rare. For LDD, mechanistic models of morphological variation, but we concentrate on their are therefore very appealing because they use infor- mass experiment because the variation in samara mass mation on the underlying dispersal processes to inde- investigated was consistent with natural variation. The pendently predict dispersal distances. Of course, mech- samara mass experiment used ®ve arti®cial populations anistic models are not without empirical data require- of increasing mass. Samaras were released in moderate ments: mechanistic models need empirical data for and even winds and the distance that each dispersal model parameterization and validation. The challenge unit moved was directly observed. The ®tting mixtures in developing useful mechanistic models of dispersal, showed that the population with lightest samaras had however, lies in including the appropriate dispersal pro- the highest mean dispersal distance (39 m), 99th per- cesses. In the next two subsections, we examine LDD centile (236 m), and a large CV (118). The population models for wind and animal dispersal. Special Feature u 1952 esn19)adtodfuin(reeadJohnson and (Greene Greene, D. diffusion 1989; two (An- and trajectory perfor- 1991) ¯ight model's dersen existing The to of compared vector. effects was wind mance the the considers on dis- also the topography model of The trajectory units. ¯ight the persal of to simulation vector wind the mea- vertical drive and high-resolution horizontal the using of surements by turbulence model Tackenberg's simulates ¯ight dispersal. seed a of developed model who trajectory (2003) Tackenberg by dressed strong and updrafts needed. is on predict gusts to information However, additional suf- dispersal. is LDD local velocities predict wind to average ®cient the showed (2001) of al. knowledge et Nathan included that instance are For makes model. factors the model which in dispersal in¯uence the will which predictions at scale prop- The scale time erties. integral their ve- and wind structure covariance the their latitudinal), of and longitudinal, statistics (vertical, ®eld temporal factors locity and atmospheric spatial Important the release. are height, release of unit, timing the dispersal and the are of bi- factors velocity or biological terminal atmospheric Important either factors. as ological categorized be can wind 3 )wr esrda h lcwo iiino ueFrs.Tehih frlaei 0m n emnlvlct is velocity terminal and m, 20 is release of height The Forest. Duke (mean of distribution division normal Blackwood a the from at selected measured randomly were m) (33 trahsa lvto rae hnsxtmstecnp height. canopy the times six than greater elevation an reaches it ausrpeetarneo idcniin rmcl id ( winds calm from conditions wind of range a represent values * ABLE as hycpuetetruetsrcueadcoher- and analysis Tackenberg's excursions. structure wind be- vertical turbulent of LDD ency the generated capture models they These cause m). and 150 moving than Tackenberg (seeds more LDD of predicting of models capable were the Greene agricultural only local however, the European at scale: well release relatively of performed models and All typical ®elds. type, conditions unit height dispersal topographic, wind, (m/s)² Notes: h uefrs.Tesmltos(ah1 0 ipra vns eerpae o h different the for repeated were events) dispersal 000 10 (each simulations The forest. Duke the trs( storms h rbe fsmltn prfshsbe ad- been has updrafts simulating of problem The by seeds of dispersal the in¯uence that factors The ieses(omiti oechrnyo h ih trajectory). ¯ight means). the 0.5-h of (2985 coherency days some 65 maintain during (to Forest time-steps Duke of division Blackwood the at canopy h rcinvlct ( velocity friction The ² h uuaiefeunyo idmaueet ihincreasing with measurements wind of frequency cumulative The ³ 2.0 1.0 0.5 0.2 0.1 T ehnsi oesfrln-itnedispersal long-distance for models Mechanistic u for s nulfigeeti eemndi edeeainecescnp egtadrmisaoetecnp tlattwo least at canopy the above remains and height canopy exceeds elevation seed if determined is event uplifting An § * .glabra C. sn h ahne l 20)wn ipra model. dispersal wind (2002) al. et Nathan the using .Saitc fdsesldsacsfor distances dispersal of Statistics 1. u * ttsisaepeetdfrdfeetfito eoiis( velocities friction different for presented are Statistics uuaiefrequency Cumulative observed ϭ .) h etclpol ftela radniy h efae ne 28,adtehih ftecnp top canopy the of height the and (2.8), index area leaf the density, area leaf the of pro®le vertical The 2.0). ormaueet].Ec ipra vn striae ihrwe h edht h rudsraeo after or surface ground the hits seed the when either terminated is event dispersal Each measurements]). [our 99.98 99.89 94.13 57.01 38.12 esnlcommunication personal Յ u ywind by (%)³ * u )sae h etcltase ftehrzna oetm¯ux. momentum horizontal the of transfer vertical the scales *) 83.3 39.4 18.4 al Hickory Maple 6.3 2.8 ein(m) Median 2.5 1.4 0.9 0.4 0.1 oesfor models ) crrubrum Acer .I IGN TAL. ET HIGGINS I. S. Ϯ 9hpretl (m) percentile 99th 314.3 136.0 1 53.1 20.4 10.0 al Hickory Maple SD 0.66 : mpe and (maple) losoe htgnl id hrzna idvelocity wind (horizontal winds gentle that showed also Ͻ ta.20) pitdsesaepeitdt rvllong travel to predicted ( are distances seeds Uplifted (Nathan 2002). forest al. deciduous wind et tall ®ve m for 33 seeds in of species m) dispersed 45 to observed (up the has distribution of description vertical model reliable The a at provide resolutions. to forest temporal shown a each and above of spatial and trajectories ®ne within ¯ight unit the dispersal simulate individual turn in in simulations, which preserved Lagrangian then stochastic are clo- three-dimensional statistics Eulerian These higher-order principles. using above sure by and canopy within mo- forest statistics second velocity the and wind ®rst the di- the of al. data ments computes wind et model observed Nathan this the rectly, by using developed than Rather been (2002). has problem draft LDD. yield not did consequently down- and up- by drafts characterized thermal often with were winds associated strong often drafts; were they as tances itdse omn itntscn mode, second up- distinct a with forming distances, seed dispersal lifted of distribution bimodal ege okd ha-nue prfsdominated. updrafts shear-induced col- and worked, Nathan where updrafts leagues forests thermal the in worked, while dominated, Tackenberg land- where open the tur- in scapes Interestingly, and 1). may strong (Table winds extremely but bulent in conditions, kilometers several wind reach common short rather travel under to expected distances are seeds that shows est, siae for estimated dispersal. ob- (uplifted) a long-distance be and result may uplifted) (not This there short-distance between 2002). dispersal, distinction jective al. wind for et that, (Nathan suggests mode ®rst the from /)wr eta oigdsesluisln dis- long units dispersal moving at best were m/s) 2 u 140.0 oenmrclyavne praht h up- the to approach advanced numerically more A ) h iuain r ae nprmtr siae at estimated parameters on based are simulations The *). Ϯ u h ahne l oe,iiitdwt parameters with initiated model, al. et Nathan The 3.8 2.3 0.9 0.2 * .2msfor m/s 0.12 ϭ u .)t togadtruetwnsascae with associated winds turbulent and strong to 0.1) ,bsdo idmaueet ae ihnthe within taken measurements wind on based *, ay glabra Carya Ͼ 00m;i at h oe rdcsaclear a predicts model the fact, in m); 1000 1371 11 crrubrum Acer 180.0 al Hickory Maple 67.4 24.7 12.4 aiu (m) Maximum .rubrum A. hcoy ipra nt simulated units dispersal (hickory) 646.8 27.1 iprigi eiuu for- deciduous in dispersing 3.2 1.3 0.4 Gen18] 7.84 1980], [Green u ausrcre.These recorded. values * clg,Vl 4 o 8 No. 84, Vol. Ecology, 1.0 0.0 0.0 0.0 0.0 rcinuplifted Fraction al Hickory Maple (%)§ ϳ 0.5 0.0 0.0 0.0 0.0 Ϯ 00m 1000 .3m/ 0.43 August 2003 LONG-DISTANCE DISPERSAL 1953

The former disappear when winds are too strong, the example, Sun et al. (1997) report mean dispersal dis- latter are generated by strong winds; these system-spe- tances of 119±304 m; Yumoto et al. (1999) report mean ci®c effects of strong winds on updrafts explains why dispersal distances of 218±440 m and maximal dis- strong winds inhibit LDD in Tackenberg's study but tances of 288±637 m; Holbrook and Smith (2000) re- facilitate LDD in Nathan et al.'s study. port mean distances of 1127±1947 m and maximal dis- If the Nathan et al. model is run for Carya glabra, tances of 3558±6919 m. which has a 7.8 g nut (the A. rubrum samara is 14 mg) To facilitate comparison among studies, resampling it is shown, as expected, that wind dispersal is limited techniques could be used to generate dispersal distri- (Ͻ3.2 m) under most wind conditions. However, under butions. Such an empirically based approach makes no the wind conditions of the strongest winds recorded assumptions about how the data are distributed, and is during a 65-d period, nuts were uplifted and moved consequently likely to be appropriate in many situa- hundreds of meters (Table 1). Hence, both the A. rub- tions. A resampling algorithm would be (1) Produce rum and C. glabra simulations show that uplift can an empirical distribution of retention times (Fig. 3A). generate LDD, but that uplifting only occurs under ex- (2) Produce many time series of net displacement (Fig. tremely strong and turbulent winds. The implication is 3B shows two time series, 30 were used for the cal- that winds capable of uplifting dispersal units with culations). Note that the net displacement could in- wind MDS may also be capable of uplifting dispersal corporate the three-dimensional movement of the dis- units without wind MDS. However, fundamental dif- persers in relation to the seed source. (3) Sample, with ferences in the wind dispersal potential of these species replacement, a large number (e.g., 10 000) of retention do exist, exempli®ed by the large differences in the times from the empirical distribution of retention times median dispersal distances for all wind conditions (Ta- (Fig. 3A). For each retention time sampled, select a ble 1). Tackenberg (Tackenberg et al. 2003) also used time series (Fig. 3B) and record the net displacement. his ¯ight trajectory model to examine the relationship (4) Summarize the recorded net displacement data us- between MDS and the wind dispersal potential of 335 ing a frequency distribution of dispersal distances (Fig. vascular plant species (mostly European herbs). Al- 3C). Feature Special though Tackenberg's results show that the wind dis- The most dif®cult step of the procedure we propose persal potential (indexed by the proportion of seeds will be to produce the time series of net displacement, dispersed Ͼ100 m) of wind-MDS species was typically as this requires high-resolution movement-path data. higher than non-wind-MDS species, his results also In addition, net displacement data is often highly var- show that many non-wind-MDS species nonetheless iable. However, the popularity and advances in telem- had nontrivial wind-dispersal potentials (Ͼ1% seeds etry mean that such data are now more commonly col- dispersed Ͼ100 m by winds characterized by thermal lected (Turchin 1998). Another option for generating uplift). time series is to use simulation models of animal move- ment to generate net-displacement time series. These Mechanistic model for long-distances dispersal simulation models are useful because they allow the by animals extrapolation from ®ne scale movement observations A second class of mechanistic model combines in- to coarser scale movement patterns (Turchin 1998). formation on animal movement and seed retention to However, such models include many assumptions, yield seed-dispersal distributions. Data on retention some of which may bias estimates of dispersal dis- times in an animal's gut or on an animal's body are tances. This is particularly important when retention relatively easy to obtain. Animal movement data, how- times are longer than the available time series of move- ever, requires more careful treatment. This is because ment data. animal movement is in¯uenced by both habitat and behavioral responses. Moreover, as a computational DISCUSSION convenience, animal-movement studies often use Ideal data sets for testing for a link between LDD movement steps as the currency of analyzing move- and MDS are rare. The analysis of dispersal-distance ment, rather than time steps (Turchin 1998); this ob- data suggests that dispersal capacity is related to MDS viously makes integration with retention time data (Willson 1993). In contrast, the shape of the tail of the problematic. dispersal distribution is not related to MDS (Portnoy Only a handful of studies have combined movement and Willson 1993). Similarly, migration rate data re- data with seed-retention data to generate seed-dispersal veals no relationship between MDS and migration rate distributions. Studies of this type that we reviewed all (MacDonald 1993). involved the dispersal of tropical plant species by fru- Although the studies of Willson (1993), Portnoy and givorous vertebrates, but all used quite different tech- Willson (1993), and MacDonald (1993) are the best niques to generate dispersal distributions. Although data sets of their kind, there are good reasons to be these methodological differences prohibit formal com- skeptical about the value of these results for exploring parison, all these animal-movement±seed-retention relationships between LDD and MDS (see Relationship studies report relatively large dispersal distances. For between morphological dispersal syndrome and cor- Special Feature eae fdseslcapacity dispersal of relates 1954 euei eetdmn ie oyedafeunydistri- simulated. frequency are a data yield The pro- to distances. This this dispersal times distance. of data; many bution dispersal displacement repeated estimated net is an the cedure then from is distance distance time a retention re- this sample (with using then to sampling and time ®rst retention a involves placement) dis- procedure net dis- distance on The dispersal data yield tributions. and to vectors units dispersal dispersal of of placement times retention the on eln rmTsai Jra 01 eeldthat New revealed of colonization 2001) the (Jordan on Tasmania have data from them of The Zealand one-quarter MDS. only water that currents, fact a ocean the by of spite arrived colo- in species and most Surtsey) that Tva of revealed of case case the the (in capacity (in nizations our arrivals improve not predict did to found MDS we of cases, both knowledge In that LDD. to that related evidence poorly is stronger MDS provide 1975) (Fridriksson sey Tva from data onization F IG .A lutaino rcdr o obnn data combining for procedure a of illustration An 3. . rin Lte 91 n Surt- and 1961) (Luther Èrminne rin) h ute data Surtsey The Èrminne). .Hwvr h sadcol- island the However, ). .I IGN TAL. ET HIGGINS I. S. n httemrhlg ftedseslui snot to is (see access unit have mechanisms dispersal seeds which which the of move of informative can morphology necessarily seeds the that ways that many and are they that showed pro- of none. variety for specialized a appear by and colonists. dispersed cesses are frequent species more seed Small were species small-seeded eddsesli lnscnb asdb ohstandard both by caused be can plants in dispersal seed apecniin ile ihretmtso LDD of estimates in variance higher (see included yielded that conditions data Our sample of testing. to analyses hypothesis samples for statistical in power variance statistical reducing increase the of to to mantra contradiction unusual in sampling statistical sample, represent advocating the that in are variance times we increase at effect, or In sites conditions. and at processes different sample by to to moved techniques being developing sam- seeds involves increasing sample of also matter It a effort. merely pro- pling multiple not by is moved This been cesses. have that of units populations detect dispersal need that LDD strategies of sampling seeds. studies design move to empirical that that is processes implication of The diversity the to tention nsi oeswt eddt (see data large mech- ®eld of with the classes models both anistic compare by to predicted distances is dispersal nonstandard challenge and The standard both mechanisms. of to due classes distances dis- non- exceptional both persal predict a Hence review we are dispersal. models animals mechanistic of others means for studies but these standard in MDS animals animal by have moved of Some units animals. quan- dispersal by to the dispersal capacity seed our describe for titatively revolution a seed-attachment represents or data seed-retention with combined Animal-telemetry data movements. animal study made to has easier methods it telemetry their of and availability The factors. track increasing many by to in¯uenced hard are patterns be movement to can dif®cult animals been always because has study, animals second by A dispersal animals. species. Seed by LDD some simulates models for mechanistic of LDD class of means standard ipra ywind by long-distance dispersal for models Mechanistic distance: persal dispersal u eiwo osadr ehnsso dispersal of mechanisms nonstandard of review Our o ipra distance dispersal for htdsesluiswtotMSfrwn a lobe also 1930; can wind (Ridley for uplifted MDS without units dispersal suggest that models wind-dispersal ex- mechanism. new describe dispersal these Furthermore, standard to a way of a distance behavior providing dispersal ceptional thus on simulated, updrafts be of to effects the de- mod- allow dispersal for els wind in approach advances appealing Recent LDD. an scribing provide models nistic u nlssadrve niaeta long-distance that indicate review and analyses Our eas aao D ilawy err,mecha- rare, be always will LDD on data Because ttsia ecito fdsesldistance dispersal of description Statistical .Teproeo h eiwwst rwat- draw to was review the of purpose The ). ,hnewn a lob non- a be also may wind hence ), C ). ONCLUSION ehnsi oesfrdis- for models Mechanistic ehnsso long-distance of Mechanisms clg,Vl 4 o 8 No. 84, Vol. Ecology, ehnsi models Mechanistic ). August 2003 LONG-DISTANCE DISPERSAL 1955 and nonstandard mechanisms of dispersal. Unfortu- Carlquist, S. 1967. The biota of long distance dispersal. V. nately, LDD in plants remains too poorly characterized Plant dispersal to Paci®c islands. Bulletin of the Torrey Botanical Club 94:129±162. to provide a de®nitive answer to the question posed in Chambers, J. C., and J. A. MacMahon. 1994. A day in the the title of this paper. However, given the low predictive life of a seed: movements and fates of seeds and their power of morphological dispersal syndromes and the implications for natural and managed systems. Annual Re- rich variety of nonstandard mechanisms of dispersal, view of Ecology and Systematics 25:263±292. Clark, J. S. 1998. Why trees migrate so fast: confronting we suspect that as additional data become available, theory with dispersal biology and the paleorecord. Amer- the answer will prove to be ``yes.'' ican Naturalist 152:204±224. Some of the processes that cause LDD are amenable Darwin, C. R. 1859. The origin of species. John Murray, to formal investigation (e.g., seeds dispersed as nest London, UK. material, or seeds caught in updrafts), while others Dean, W. R. J., S. J. Milton, and W. R. Siegfried. 1990. Dispersal of seeds as nest material by birds in semiarid seem inherently untractable (e.g., the occasional seed karoo shrubland. Ecology 71:1299±1306. dispersed on an oceanic raft). The multitude of mech- Ellner, S., and A. Shmida. 1981. Why are adaptations for anisms of LDD means that it is dif®cult to exclude the long-range seed dispersal rare in desert plants? Oecologia possibility that a species has access to an undetected 51:133±144. Fridriksson, S. 1975. Surtsey: evolution of life on a volcanic LDD mechanism. However, the fact that the world's island. Butterworths, London, UK. ¯ora is not cosmopolitan reminds us that, although ex- Goodman, L. A., and W. H. Kruskal. 1954. Measures of ceptional dispersal events do occur, not every species association for cross-classi®cation. Journal of the American ends up realizing its potential for the exceptional. Per- Statistical Association 49:732±764. haps more importantly, it reminds us that dispersal is Green, D. S. 1980. The terminal velocity and dispersal of spinning samaras. American Journal of Botany 67:1218± not the only biogeographical barrier. 1224. Can we predict which species will be long distance Greene, D. F., and E. A. Johnson. 1989. A model of wind dispersers? We believe that this question will only be dispersal of winged or plumed seeds. Ecology 70:339±347. resolved once we have better empirical data on the Grime, J. P., J. G. Hodgson, and R. Hunt. 1988. Comparative plant ecology: a functional approach to common British Feature Special phenomena involved in long-distance dispersal. Open- species. Unwin Hyman, London, UK. ing our minds to the possibilities is the ®rst step to- Hayren, E. 1914. Uber die Landvegetation und Flora der wards capturing the data. Meeresfelsen von TvaÈrminne. Acta Societatis pro Fauna et Flora Fennica 39:1±193. ACKNOWLEDGMENTS Hickey, J. R., R. W. Flynn, S. W. Buskirk, K. G. Gerow, and We thank Gabriel Katul for help with the mechanistic wind M. F. Willson. 1999. An evaluation of a mammalian pred- dispersal simulations and Suvi Thomas for help in measuring ator, Martes americana, as a disperser of seeds. Oikos 87: terminal velocities of hickory nuts. Thanks to Oliver Tack- 499±508. enberg for comments on the manuscript and help with mor- Higgins, S. I., and D. M. Richardson. 1999. Predicting plant phological dispersal syndromes. Thanks to Ursula Hertling migration rates in a changing world: the role of long-dis- for help translating German publications. R. Nathan is grate- tance dispersal. American Naturalist 153:464±475. ful for the support of the U.S. National Science Foundation Hodkinson, D. J., and K. Thompson. 1997. Plant dispersal: Grant No. IBN-9981620, the German±Israel Foundation the role of man. Journal of Applied Ecology 34:1481±1496. Grant No. I-2006-1032.12/2000, and the Israeli Science Holbrook, K. M., and T. B. Smith. 2000. Seed dispersal and Foundation Grant No. ISF474/02. movement patterns in two species of Ceratogymna horn- bills in a West African tropical lowland forest. Oecologia LITERATURE CITED 125:249±257. Andersen, M. 1991. Mechanistic models for the seed shadows Hoshizaki, K., W. Suzuki, and T. Nakashizuka. 1999. Eval- of wind-dispersed plants. American Naturalist 137:476± uation of secondary dispersal in a large-seeded tree Aes- 497. culus turbinata: a test of directed dispersal. 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