Can Neutral Theory Predict the Responses of Amazonian Tree Communities to Forest ...

14 Pages·2006·0.83 MB·English

vol. 168, no. 3 the american naturalist september 2006 (cid:1)
Can Neutral Theory Predict the Responses of Amazonian Tree
Communities to Forest Fragmentation?*
Benjamin Gilbert,1,† William F. Laurance,2,3,‡ Egbert Giles Leigh Jr.,2,§ and Henrique E. M. Nascimento3,k
1.DepartmentofBotany,UniversityofBritishColumbia, Keywords:edgeeffects,extinction,forestdynamics,habitatfragmen-
Vancouver,BritishColumbia,Canada; tation,rainforest,treecommunities.
2.SmithsonianTropicalResearchInstitute,Apartado0843-03092,
Balboa,RepublicofPanama;
3.BiologicalDynamicsofForestFragmentsProject,National Treesprovidethearchitecturalbasisforforestecosystems,
InstituteforAmazonianResearch(INPA),C.P.478,Manaus, generate most of their primary productivity, and provide
Amazonas69011-970,Brazil
the foundation for much of their biodiversity. In Ama-
zonian forests, tree diversity can exceed 280 species (≥10
SubmittedNovember12,2005;AcceptedApril26,2006;
cm diameter at breast height [dbh]) per hectare (Gentry
ElectronicallypublishedAugust7,2006
1988; Oliveira and Mori 1999), among the highestvalues
Onlineenhancements:appendixes,figures,tables. seen anywhere on earth.
Unfortunately,Amazonianforestsarebeingclearedand
fragmentedatanalarming—andaccelerating—rate(Laur-
ance et al. 2001a, 2004). To learn how habitat fragmen-
tation affects forest ecosystems, the Biological Dynamics
abstract: We use Hubbell’s neutral theoryto predicttheimpact
of Forest Fragments Project (BDFFP) was established in
ofhabitatfragmentationonAmazoniantreecommunities.Forforest
1979 near Manaus, Brazil, in forest as diverse as any in
fragments isolatedforabouttwodecades,wegenerateneutralpre-
dictionsforlocalspeciesextinction,changesinspeciescomposition Amazonia(Lovejoyetal.1983,1986;Lauranceetal.2002).
withinfragments,andincreasesintheprobabilitythatanytwotrees To study tree communities, permanent 1-ha plots were
withinafragmentareconspecific.Wetestedthesepredictionsusing established between 1980 and 1990 in areas soon to be-
fragment and intact forest data from the Biological Dynamics of come fragments and in nearby intact forest. These plots
ForestFragmentsProjectincentralAmazonia.Tosimulatecomplete have been regularly censused since. They show that frag-
demographic isolation, we excluded immigrants—species absent
mentation has a large impact on the mortality, recruit-
fromafragmentorintactforestplotintheinitialcensusbutpresent
ment,biomass,andcommunitycompositionofrainforest
initslastcensus—fromourtests.Theneutraltheorycorrectlypre-
trees(e.g.,Lauranceetal.1997,1998a,1998b,2000,2001b,
dictedtherateofspeciesextinctionfromdifferentplotsasafunction
2006; D’Angelo et al. 2004; Nascimento and Laurance
of the diversity and mortality rate of trees in each plot. However,
the rate of change in species composition was much faster than 2004; Nascimento et al. 2006).
predictedinfragments,indicatingthatdifferenttreespeciesrespond Here, we use Hubbell’s (2001) neutral theory of forest
differentlytoenvironmentalchanges.Thisviolatesthekeyassump- dynamicsanddiversityasanullhypothesisforpredicting
tionofneutraltheory.Whenimmigrantswereincludedinourcal- theimpactoffragmentationondiverseAmazonianforest.
culations, they increased the disparity between predicted and ob- Neutral theory uses simplifying assumptions to develop
served changes in fragments. Overall, neutral theory accurately precise, far-reaching predictions that bring a wealth of
predictedthepaceoflocalextinctionsinfragmentsbutconsistently
seemingly unrelated phenomena within the scope of a
underestimatedchangesinspeciescomposition.
commontheoreticalframework.Itisconstructedinstrict
parallel with the neutral theory of population genetics
* Thefirstthreeauthorscontributedequallytothiswork. (Leigh et al. 2004a), which is based on the assumption
† E-mail:[email protected]. that the alleles in a population are selectively equivalent
‡ Correspondingauthor;e-mail:[email protected]. (Kimura 1983). By assuming that all mature trees, re-
§ E-mail:[email protected]. gardlessoftheirspecies,arecompetitiveequivalents,Hub-
k E-mail:[email protected]. bell’s theory makes plausible predictions about species-
Am.Nat.2006.Vol.168,pp.304–317.(cid:1)2006byTheUniversityofChicago. area curves (Durrett and Levin 1996), the relative
0003-0147/2006/16803-41429$15.00.Allrightsreserved. abundanceoftreespeciesonplotsofdifferentsizes(Bram-
Neutral Theory and Forest Fragmentation 305
son et al. 1996; Hubbell 2001), and the rate of species composition are being assessed in the BDFFP study area,
turnover in space (Chave and Leigh 2002; Condit et al. usinganetworkof1-hapermanentplotsinwhichalltrees
2002). Hubbell (2001) emphasizes the potentialrelevance (≥10 cm dbh) are being monitored. Our study is based
of neutral theory for predicting community responses to ondatafrom30plots,17ofwhicharearrayedacrossnine
habitat fragmentation, but to date there have been very forest fragments (four of 1 ha, three of 10 ha, two of 100
few empirical tests of such predictions (e.g., Leigh et al. ha),withtheremaining13inintactforest(table1).These
1993). plots, a subset of a larger plot network, were selected to
In this study, we use Hubbell’s (2001) neutral theory representdifferentdistancesfromtheforestedgeforeach
to generate predictions about the impact of forest frag- fragment and to minimize pseudoreplication. Multiple
mentation on the species diversity, species composition, plotswithinasinglefragmentwerecombinedforanalyses.
andrateoflocalextinctionsofmature(≥10cmdbh)trees. All plots were first censused between 1980 and 1990,
Wederivethesepredictionsusingtheapproachembodied
then recensused three to five times, with the most recent
inMoran’s(1958,1962)neutralmodelofgeneticdriftand
recensuscompletedinJune1999.Duringtheinitialcensus,
comparethemwithobservationsfromexperimentalforest
treesineachplotweremarkedwithnumberedaluminum
fragmentsandintactforest(control)plotsincentralAma- tags and mapped. During recensuses, all new trees (≥10
zonia.Althoughwefocusonhowwellneutraltheorypre-
cm dbh) were mapped and marked, and all dead and
dicts the initial effects of fragmentation, some of our re-
damaged trees were recorded. On average, 95.4% of all
sultsbearontheapplicabilityofneutraltheorytotropical
trees in each plot were identified to species or morpho-
forest ecology as a whole.
specieslevel,usingsterileorfertilematerialcollectedfrom
eachtree.Voucherspecimensforeachtreearemaintained
Study Area and Methods in the BDFFP Plant Collection, Manaus, Brazil. At the
BDFFP,individual1-haplotsaverageover250treespecies
This BDFFP study area spans about 1,000 km2 and is lo-
cated 80 km north of Manaus, Brazil (2(cid:2)30(cid:1)S, 60(cid:2)W), at (table 1), anda 9-ha squarehad702speciesamong5,271
identified trees.
50–100 m elevation. The topography consists of flat or
undulating plateaus interspersed by many steeply eroded
gullies. Rain forests in the area are not seasonally inun-
dated. Annual rainfall varies from 1,900 to 3,500 mm,
Table 1: Numbers of identified trees (≥10 cm dbh) during the
averaging 2,600 mm. There is a pronounced dry season
firstandlastcensuses(N andN),thenumberofspeciesamong
from June to October (Laurance 2001), with the driest 1 2
them(S andS),theintervalbetweenthefirstandlastcensuses
quarter of the year averaging 346 mm of rain. The forest 1 2
(T) in months, and the annual mortality rate (m) for a repre-
canopy is 30–37 m tall, with emergents to 55 m. The
sentative subset of forest fragments and intact forest plots in
dominant soils in the study area are xanthic ferralsols, central Amazonia
whichareheavilyweathered,acidic,andverypoorinnu-
Plot N S N S T m
trients such as P, Ca, and K (Chauvel et al. 1987). Rates 1 1 2 2
1-ha fragment1104.1 580 276 556 269 209 1.0844
of natural tree mortality in these nutrient-starved forests
1-ha fragment2107.1 694 284 739 285 183 2.6623
arelowrelativetomostforestselsewhereintheNeotropics,
1-ha fragment2108.1 646 253 768 266 183 3.8313
averaging about 1.2%/year (Laurance 2001).
1-ha fragment3114.1 587 251 586 258 181 3.0557
The study area is surrounded by large expanses (1200 1 ha in 10-hafrag-
km) of continuous forest to the west, north, and east. In ment 1202.3 558 243 519 231 208 1.9664
the early 1980s, a series of forest fragments were isolated 3 ha in 10-hafrag-
(bydistancesof70–1,000m)fromthesurroundingforest ment 2206a 1,997 494 2,099 507 183 2.3650
byclearingtheinterveningvegetationtoestablishpastures 4 ha in 100-hafrag-
in three large (∼5,000 ha) cattle ranches. Fragmentswere ment 3304a 2,647 550 2,571 556 170 1.3377
Intact forest ha 1101.1 548 254 515 246 218 1.1792
fenced to prevent encroachment by cattle. Reservesrang-
Intact forest ha 1105.1 617 245 614 251 204 1.2328
ing from 1 to 1,000 ha in area were delineated in nearby
Intact forest ha 1109.1 556 231 511 224 204 1.6179
continuous forest to serve as experimentalcontrols.Parts
Intact forest ha 1201.3 616 224 535 208 215 1.6864
of the three ranches were later abandoned; Cecropia-
Intact forest ha 1301.4 583 267 566 265 164 .6846
dominatedregrowthprevailsinareasthatwereclearedbut
Intact forest ha 3402.7 550 258 569 271 156 .6063
not burned, and Vismia-dominated regrowth prevails in
Note:SeeappendixDintheonlineeditionoftheAmericanNaturalistfor
pastures that were repeatedly burned (Mesquita et al.
thecompletedataset.
2001).
a Numbersoftreesandspeciesforeachfragmentarepooledfromoneto
Long-term changes in tree community dynamics and fourplots,treatingthedataasasinglelargeplot.
306 The American Naturalist
Generating Neutral Theory Predictions species cannot change by more than one individual per
for Forest Fragments time step. This model assumes that each mature tree will
be pollinated, no matter how isolated it may be. In ad-
The fundamental premise of Hubbell’s neutral theory of dition, in testing the theory, we count a tree as being
forestdynamicsanddiversityisthattheprospectsofdeath mature when it attains 10 cm dbh—which in reality can
or reproduction for a tree are never influenced by the take several decades after its seed germinates—even
speciestowhichitoritsneighborsbelong.Theformalism thoughthetheoryassumesthatthistreematuresinstantly
used to derive predictions is that of the neutral theoryof when its predecessor dies.
allelefrequencychangeatamultialleliclocusinahaploid All neutral predictions derived below were confirmed
population. This formalism employs four specific as- withsimulationsusingtheinitialcensusesfromtheBDFFP
sumptions. First, all mature trees are fundamentally the fragment and control plots. All simulations were run
same; that is, each mature tree has identical prospects of 10,000 times at three timeintervalsthatencompassedthe
dying or reproducing. Second, the overall density of ma- time elapsed (in tree generations) between the first and
turetreesinanycommunityisconstant.Therefore,ifone last censuses of these plots. When converted to tree gen-
speciesincreases,atleastoneothermustdecrease(azero- erations (by dividing the total number of tree deaths by
sum game). To be specific, if atreedies,itisimmediately theinitialnumberoftreesineachplot),theelapsednum-
replaced by the instantly maturing offspring of a living ber of tree generations in our plots ranged from 0.15 to
treeinthecommunity.Third,theenvironmentisuniform 0.58. To ensure that our predictions were accurate over
(or, at the least, temporal or spatial variation in environ- this range of values, we ran separatesimulationsfor0.33,
mental conditions does not favor some species over 0.5, and 1.0 tree generations.
others). Fourth, each new tree has the same tiny proba-
bility v of being a new species.
Neutral Prediction 1: Extinction Rates
Althoughtheseassumptionsareunrealistic(e.g.,Harms
etal.2000,2001;Hubbelletal.2001;ClarkandMcLachlan To calculate the rate of extinction of tree species from a
2003;GilbertandLechowicz2004;Willsetal.2006),neu- fragment, first consider the probabilitythataspeciesrep-
tral theory provides a valuable null hypothesis by which resented in an isolated fragment by one mature tree at
to test for effects of differences among species (Leigh et time 0 is extinct by time t. If t is small enough that the
al. 2004a, 2004b). Here, we derive testable predictions of number of mature trees of this species at time t is likely
rates of local extinction, the decline of tree diversity, to be a small proportion of the total number of mature
andthechangeinspeciescompositioninrecentlyisolated treesinthefragment,wemayusethemethodofbranching
forest fragments. We use the neutral theory to probe processes(Harris1963)tocalculatetheprobabilitythatit
whether environmental conditions in fragments favor isextinctbytimet.Thismethodassumesthattreesofthis
sometreespeciesoverothersoralteraspectsofthewhole species die and reproduce independently of each other.
community. Letatreealiveattimethaveprobabilitydtofdyingby
We model the neutral theory of tree diversity using time t(cid:1)dt and probability dt of bearing one instantly
Moran’s (1958) neutral model of genetic drift for a mul- maturing young by this time, where time is measured in
tiallelic locus in a haploid population in which each new tree generations. We use the method of generating func-
mutationgivesrisetoanentirelynewallele(Ewens2004). tions (see app. A in the online edition of the American
IntheMoranmodel,eachhaploidindividualhasonegene Naturalist) to calculate the probability E(t)thataspecies
1
at this locus, so we equate genes with individual trees, represented in the fragment by one mature tree at time0
alleles with species, and new mutations with new tree is extinct by time t. We find thatE (t)pt/(1(cid:1)t). As the
1
species. deathandreproductionofdifferenttreesareindependent
Weapplythismodeltoanisolatedforestfragmentwith events, the probability E(t) that a species represented in
j
Ntrees.Weassumethatthefragmentissmallenoughthat thefragmentbyjmaturetreesattime0isextinctbytime
we can ignore dispersal limitation so that any tree in the t is E(t)ptj/(1(cid:1)t)j.
j
fragment is equally likely to be the parent of a new tree If we know how many species are represented in the
(Hubbell 2001). Let successive time steps be separatedby fragmentbyjmaturetreesapieceforallj(thedistribution
1/Nofatreegeneration,whereatreegenerationisdefined ofmaturetreesoverspecies)andtheprobabilityE(t)that
j
as the time required for N trees to die in this fragment. a species with j mature trees in the fragment at time 0 is
At each time step, let a tree be chosen at random to die, extinctfromitbytimet,wecancalculatethetotalnumber
and let another (which could be the same tree) be inde- of species dying out from the fragment within t treegen-
pendently chosen to be the seed parent of the dead tree’s erations. If there are S(j) species with j trees apiece atthe
replacement. Thus, the number of trees in a particular initial census (time 0), and if eachof these specieshasan
Neutral Theory and Forest Fragmentation 307
independent probability E(t) of dying out by time t, we Table 2: Fisher’s a, x p N/(N (cid:1) a), and the predicted and
j 1 1
may calculate confidence intervals (CIs) for the number observednumbersoftreespeciesrepresentedbyone(S[1]),two
of these species dying out by time t if we remember that (S[2]), and three (S[3]) trees ≥10 cm dbh apiece, in four 1-ha
fragmentsand a single1-haplot in a 10-ha fragment
the probability p(j) that N(j) of these species die out by
time t is given by the binomial distribution Plota
1104.1 2107.1 2108.1 3114.1 1202.3
Area (ha) 1 1 1 1 10
{ }
S(j)!
p(j)p [E(t)]N(j)[1(cid:2)E(t)]S(j)(cid:2)N(j). a 210 180 155 169 169
N(j)![S(j)(cid:2)N(j)]! j j x .7365 .7951 .8085 .7781 .7671
S(1) pre 155 143 125 132 130
S(1) obs 159 162 135 156 133
In 1-ha tropical forest plots of Abraham et al. (1996)
S(2) pre 57 57 51 51 50
and Leigh (1999), and in 1-ha plots of the BDFFP, the S(2) obs 58 50 57 47 44
distributionoftrees≥10cmdbhoverspeciesapproximates S(3) pre 28 30 27 27 26
a log series, especially for species with few trees (table2). S(3) obs 23 27 27 21 24
In the log series, the number S(j) of species with j trees
Note:Thesuffixes“pre”and“obs”indicatethenumberpredictedbythe
apiece is axj/j, where a is Fisher’s a (Fisher et al. 1943). logseriesandthenumberobserved.
Thedynamicsinaplotofspecieswithfewtreesthere,like a PredictedvaluesofS(1),S(2),andS(3)are,respectively,ax,ax2/2,and
the dynamics of very rare alleles (Fisher 1930; Gillespie ax3/3,thevaluesexpectedfromthelogseries.N isthenumberoftrees≥10
1
1991), is dominated by chance. The log series applies to cmdbhrecordedintheinitialcensus.
(cid:1)
rare species in a plot because migration into the plot of
(cid:3) xjpj 1
species previously absent, and dispersal outside the plot a paln
ofyoungoftreesinit,crudelyapproximatetheroleplayed jp1 j 1(cid:2)px
bymutationingeneticsmodelsandbyspeciationinHub- N(cid:1)a
bell’s (2001) metapopulation (E. G. Leigh, unpublished paln . (1)
N(1(cid:2)p)(cid:1)a
manuscript). Approximate log series in these small plots
neither imply nor deny the wider validity of the neutral
This formula applies to small plots and fragments in our
theory. studyareabecauset!0.5andS(j)E(t)≈0forj13,while
If S(j)paxj/j, the total number S of species on the the log series applies for j≤3. j
plot or fragment is
To summarize, neutral theory predicts that the rate at
whichtreespecieswillbecomelocallyextinctinafragment
( ) (the number of species lost per generation) increasesina
ax2 ax3 1
Spax(cid:1) (cid:1) (cid:1) … paln . predictablewaywiththemortalityrateoftrees.Inaneutral
2 3 1(cid:2)x
world, species are lost only via random death and re-
cruitment. According to the neutral theory, no species is
Moreover, if S(j)paxj/j, the number N(j) of trees in inherently favored by fragmentation, so abundantspecies
species with j trees apiece is jS(j)paxj, and the frag- usually disappear far less quickly than rare ones.
ment’s total number N of trees is
Neutral Prediction 2: Changes in Species Composition
ax
Npax(cid:1)ax2(cid:1)ax3(cid:1) … p . Consideraspeciesrepresentedattime0byjmaturetrees
1(cid:2)x
in an isolated fragment that has N(0) mature treesatthis
time,wherejKN(0).Withprobabilityj/N(0),oneofthese
Therefore, xpN/(N(cid:1)a), and Spaln[(N(cid:1)a)/a]. treesdiesatthenexttimestep,and,withequalprobability,
InafragmentwithNmaturetreesattime0,theneutral onewillproduceasingle,instantlymaturingyoungatthis
theory predicts that if tKN, then E(t), the probability time.AsthereareN(0)timestepspertreegeneration,the
j
that a species represented in the fragment by j trees at species undergoes an average of 2j instances of death or
time 0 dies out from that fragment by time t, is pj,where reproduction per tree generation, an average of 2jt in t
ppE (t)pt/(1(cid:1)t).Ifthedistributionoftreesoverspe- tree generations. Each instance has an equal probability
1
cies follows the log series, then the total number E(t) of of being a birth or a death, nearly independently of all
tree species lost by the fragment within t treegenerations theotherinstances(ifthereisaconstantnumberofmature
is S(1)E (t)(cid:1)S(2)E (t)(cid:1)S(3)E (t)(cid:1) …. If S(j)paxj/j, treesinthefragment,thereisaslightnegativecorrelation
1 2 3
then E(t) is among these instances in whether a birth occurs). Just as
308 The American Naturalist
themeansquaredifferencebetweenthenumbersofheads meansquarepopulationchangeinaspecieswithonetree
and tails in 2jt tosses of a fair coin is 2jt, so the mean at time 0 increases by 2/N per time step. If the fates of
square change ina fragmentduringtimetinthenumber different trees are independent, the mean square popu-
of trees of a species represented by j trees at time 0 is 2jt. lation in a species with j trees at time 0 increases by 2j/N
The expected value of the sum of the meansquaredpop- per time step, and S increases by 2 per time step. Thus,
ulation changes of all tree species in the fragment during according to neutral theory, species composition changes
time t is thus 2N(0)t. progressively because nothing stabilizes it (Pandolfi1996;
To determine confidence limitsaboutthesumSofthe Clark and McLachlan 2003).
mean square changes in the populations in the fragment,
we begin by calculating the variance in this quantity. If
Neutral Prediction 3: Decay of Diversity
we assume that each tree in the fragment at time t has a
probability dt of dying by timet(cid:1)dt and an equalprob- Inaforestfragmenttoosmallforspeciationtoberelevant
abilityofproducingasingle,instantlymaturingyoungby overafewtreegenerations,newspeciesneverappear,but
thattime,independentlyofalltheothers,thenthevariance chance fluctuations in population size cause species to
inthesquareofthechangeinthenumberoftreesduring disappear, so diversity declines. How fast is this decline?
timetinaspecieswithjtreesattime0,thefourthmoment To find out, set speciation rate vp0. Let diversity be
about the mean change minus the square of the variance measured by the quantity H(t), the probability that two
(Feller1971,p.48),is2jt(cid:1)8j2t2(cid:1)24jt3 (app.A).Ifspe- trees sampled atrandomwithreplacementfromthefrag-
ciesnhasj treesattime0,thenthevarianceinSshould ment at time t are of different species. Then H(t)p1(cid:2)
n
be nearly the sum of the corresponding quantityforeach F(t),whereF(t),therelativedominance(Leighetal.1993)
species, or in the fragment at time t, is the probabilitythattwotrees
(cid:1) sampled at random with replacement from the fragment
S
are of the same species. The quantity H(t) is Simpson’s
2N(0)(t(cid:1)12t3)(cid:1)8t2 j2
n index of diversity (Simpson 1949), which is commonly
np1
usedinecology.Lettheproportionoftreesinthisfragment
p2N(0)(t(cid:1)12t3)(cid:1)8[tN(0)]2F(0), (2)
at time t that belong to species i be x(t). Then
(cid:1) i
whereSisthenumberofspeciesinthefragmentandF(0) F(t)p x2(t). (5)
is the relative dominance in the fragment at the initial ip1 i
census (eq. [5]).
SimulatingpopulationchangesusingtheMoranmodel The expected change in the relative dominance during
shows that S is distributed according to a lognormal(see one time step is the expected value of F(t(cid:1)1/N)(cid:2)F(t),
app. B in the online edition of the American Naturalist) where N is the total number of trees on the fragment.By
with mean Sp1.97N(0)t and variance definition, a time step includes one death and one re-
cruitment. We therefore calculate the expected change in
j2p1.97N(0)t(cid:1)1.97[2N(0)t]2F(0). (3) relative dominance caused by a single such death and re-
placement. If we assume that a newly dead tree is likely
ThemeanMandvarianceS2ofln(S)arerelatedtoM(S) to be replaced by any other tree on the fragment, that is,
and j2 by the equations if dispersal limitation can be ignored on a fragment this
small, we find (see app. C in the online edition of the
( S2) American Naturalist) that
M(S)pexp M(cid:1) ,
2
( ) ( )
1 1
j2pexp(2M(cid:1)S2)(expS2(cid:2)1) F t(cid:1) (cid:2)F(t)pH(t)(cid:2)Ht(cid:1)
N N
(Moran 1968, p. 317). Thus, ln(S) has a 95% chance of 2H(t)
falling within the limits M(cid:3)2S, which is equivalent to p . (6)
N2
exp(cid:2)2(cid:2)ln[1(cid:1)(j/m)2] exp2(cid:2)ln[1(cid:1)(j/m)2]
Thisassumptionofpanmicticdispersalisacceptedbyneu-
(cid:2)1(cid:1)j2/m2 !S! (cid:2)1(cid:1)j2/m2 . (4) traltheorists:Hubbell(2001,p.86)assumesthatifanewly
dead tree on a 50-ha plot is not replaced bythe youngof
In sum, if a tree has probability 1/N of dying and an a tree outside the plot, then every tree in the plot has an
equal probability of reproducing at each time step, the equal chance of providing the young that replaces it.
Neutral Theory and Forest Fragmentation 309
Theprobabilitythatanytwotreesinthesamefragment means that our neutral predictions should overestimate
areconspecificincreasesovertimebecauseifonedies,the changes in fragments and intact forest plots.
probability is 1/N that it will be replaced by the youngof Neutral theory measures time in tree generations, im-
the other tree. Therefore, after Ns time steps (s tree gen- plying that the rate of change in a fragment is paced by
erations), the mortality rate of its trees. To test our neutral predic-
tions,weequatedthenumberoftreegenerationsbetween
( ) the first and last censuses of a plot or fragment to the
Ns
Ht(cid:1) pH(t(cid:1)s) numberofyearsbetweenthesecensuses,multipliedbythe
N
average annual mortality rate of its trees.
( )Ns Ourtestsassessthesignificanceofdeviationsfromneu-
2
pH(t)1(cid:2) (7) tral expectation for individual fragments or control plots
N2 inintactforest.Foreachofourthreepredictions,wealso
pooledobservationsfromallfragmentstotestwhether,as
( )
≈H(t)exp(cid:2)2s. agroup,fragments(orcontrolplots)deviatefromneutral
N predictions. Because the distributions of the variates we
generatedwerenotnormal,weusednonparametricMann-
The mean change M(s) in F from time 0 to generation s Whitney U-tests to evaluate the significance of these de-
is roughly 2[1(cid:2)F(0)]s/N if sKN. The variance V(1/N) viations.Findingsforselectedfragmentsandcontrolplots
in the change of F over one time step, whichis themean arediscussedbelow,withcompleteresultsforallsitespro-
square change in F minus the square of the meanchange videdinappendixDintheonlineeditionoftheAmerican
during one time step, is (app. C) Naturalist (tables D1–D5).
(cid:1)
8( ip1xi3(cid:2)F2)(cid:1)4F(1(cid:2)F). (8) Local Extinctions
N2 N4
First, we compare the proportions of species represented
Ifs!1,thevarianceV(s)inthechangeofFoverNstime in a fragment or intact forest plot by one, two, and three
trees (≥10 cm dbh) that die out by the final census with
steps (s tree generations) is Ns times the variance from a
theneutralpredictionthataspeciesrepresentedbyktrees
single time step. Simulations show that the change DF(s)
at time 0 has probability E (t)ppk of becoming extinct
in F over Ns time steps is close to normally distributed k
fromittgenerationslater;pistheprobabilitythataspecies
(app. B), so that the change in F has 95% probability of
falling within the limits DF(s)(cid:3)2[V(s)]1/2. represented by a single tree at time 0 is extinct at time t,
where ppt/(1(cid:1)t). If E(t) consistently exceeds its pre-
To summarize, in a neutral world, tree diversity in an k
dictedvaluefork11,butnotforkp1,wemayconclude
isolated fragment declines because the distribution of
that the fates of conspecific trees in a fragment or intact
stems among species becomes less even with the passage
forest site are correlated, contrary to the assumptions of
oftime,leavingmoreandmorespecieswithnorepresen-
neutral theory. We thentesttheneutraltheoryprediction
tatives at all.
thatthetotalnumberofextinctionsonaplotorfragment
with N trees (eq. [1]) is
Testing Predictions of Neutral Theory
[ N(cid:1)a ]
Wetestedthesethreepredictionsarisingfromneutralthe- aln .
ory using our data for forest fragments and intact forest N(1(cid:2)p)(cid:1)a
plots in central Amazonia. Because our predictions were
generatedbyassumingthatthefragmentsarefullyisolated,
we tested predictions 2 and 3 after excluding immigrant
Changes in Species Composition
species (defined as those present in the final but not the
initialcensusofasite)fromourdata.Wecannot,however, For our second test, we calculate S for each fragment or
j
excludeimmigrantsofspeciesalreadypresentontheplot. intact forest plot j by summing the squared changes in
Anexchangeofmigrants,especiallyofcommonerspecies, numbers of trees (≥10 cm dbh)betweenthefirstandlast
between a plot and its surroundings should stabilize spe- censuses for each of its species,excludingimmigrantsab-
cies composition, just as it stabilizes genetic composition sent from the first census, and compare this calculatedS
j
intheneutraltheoryofpopulationgenetics(Wright1931). withthepredictedvalue1.97N(t),whereN(0)isthenum-
j j
Our inability to exclude immigrants of common species ber of trees in the fragment or plot j at the initialcensus.
310 The American Naturalist
WetestforthesignificanceofthedeviationofS fromthe predictedinsevenof13controlplotsandinthreeofnine
j
predictedvaluebyaskingwhetherS fallsoutsidethecon- fragments—significantlylowerthanexpectedinonefrag-
j
fidence limits given by equation (4). ment, and never significantly higher than expected (table
D2).Similarly,amongdoubletons,therewasonlyonesig-
nificant deviation from the predicted number of extinc-
Changes in Tree Diversity
tions: one control plot lost too many.
Forourlasttest,weconsidertherelationshipbetweenthe Mortality rates differed markedly among the various
relative dominance F of each forest fragment or control plots and fragments, and extinction rate varied with tree
plot j in its first and final censuses. Equation (7) implies mortality rate in remarkable accord with neutral theory
thatF(t)p1(cid:2)H(t)is1(cid:2)H(0)exp((cid:2)2t/N),whichmay predictions (fig. 3A; tableD2),suggestingthatweapplied
j j j j
also be expressed as 1(cid:2)[1(cid:2)F(0)]exp((cid:2)2t/N), where N the neutral theory correctly and appropriately.
j j j
is the number of trees (≥10 cm dbh) in the fragment at Predictions of extinctions from different control plots
the first census, and t is the number of tree generations andfragments,basedonalog-seriesapproximation,were
between the first and last censuses. In each fragment, we usually somewhat less accurate (table D3). Predictions
compare the observed with the predicted values of F(t) were exact (within rounding error) for one fragmentand
j
for the last census. Equation (8) predicts that when tp three control plots, but they were underestimated for six
Ns, the standard deviation in the value of H(t)p of the remaining eight fragments and nine of the 10 re-
j
H(Ns) is very nearly maining control plots.
j
(cid:2)
[ (cid:1) ] Changes in Species Composition
(cid:2)V(t)p Ns 8( kp1xj3k(cid:2)F2)(cid:1)4F(1(cid:2)F) , When immigrants were excluded, the observedchangein
N2 N4
species composition was within a factor of two of the
neutral theory prediction in 12 of 13 controlplotsandin
where x is the proportion of trees in fragment j at time
jk sixofninefragments(tableD4).Changewasusuallyfaster
0 that belong to species k, and F pF(0). We assess the
j j on plots with higher mortality, as neutral theory predicts
significance of the divergence of the observed from the
(fig. 3B).
predicted value of F(t) by asking whether thisdivergence
j Therewas,however,aclearcontrastbetweenfragments
exceeds 2[V(t)]1/2. Here again, we calculated this change
and control plots. Change was slower than predicted in
excluding species that were present in the last census but
10 of 13 controlplots(perhapsfromthestabilizinginflu-
not in the first census.
enceofthegainandlossofmigrantsofspeciesalreadyin
the plot), whereas it was faster than predictedinsevenof
ninefragments,andsignificantlysoinfive.Theprevalence
Results
ofsuchrapidchangesevenwithoutimmigrants(tableD4)
Tree mortality rates were much higher in fragments than suggests that fragmentation favors a species composition
control plots (tp4.20, dfp10, P!.001), causing large that is different from that in intact forest, implying that
differencesinneutralpredictionsforfragmentsrelativeto differenttreespeciesresponddifferentlytoenvironmental
control plots (fig. 1; app. D). New immigrants (species change.
presentatthelastcensusbutabsentfromthefirst)arrived The rate of change in species composition varied far
at a significantly faster rate in fragments than in control more among control plots than predicted by neutral the-
plots (Fp35.31, dfp1,19, P!.0001; fig. 2A), which ory:thischangewassignificantlyslowerthanpredictedin
caused much larger changes in fragments than in control six control plots, and significantly faster in two. The sig-
plots (fig. 2B; app. D). The elevated immigration rate in nificance of this result is enhanced if the exchangeofmi-
fragments was largely the result of many pioneer species grantsofcommonerspeciesstabilizesspeciescomposition.
colonizing the fragments (table 3). When immigrants were included, the rate of changein
species composition in control plots never deviated from
the neutral prediction by more than a factor of two, but
Local Extinctions
it changed over six times faster than predictedinthreeof
Neutral theory accurately predicted the number of local ninefragmentsandovertwicethatpredictedinthreeoth-
extinctions of species initially represented by one (single- ers. Although the neutral theory prediction is not mean-
ton)ortwo(doubleton)trees≥10cmdbhincontrolplots ingful if immigrants are included, this contrast is useful.
or the censused portions of fragments. The number of Immigration accelerated changes in species composition
singletons dying out by the final census was lower than farmoreinfragmentsthancontrolplots(fig.2B),inflating
Figure1:Effectofmortalityratesonneutralpredictions.Eachpointrepresentsafragment(filledcircles)orcontrolplot(opencircles),andtheline
is1:1,whichisexpectedifthereisnodifferencebetweenmeasures.A,Time(tpmortalityrate#time betweenfirstandlastcensusdates)used
inneutralpredictionscalculatedwithaveragemortalityratesfromundisturbedforestandwiththemortalityrateofthefragmentorcontrolplot.
B,Neutralpredictionsforthetotalnumberoflocalextinctions.Predictionswerecalculatedusingaveragemortalityratesandmortalityratesfrom
individualfragmentsorcontrolplots.
312 The American Naturalist
Figure 2: Effect of immigrationonfragments(filledcircles)andcontrolplots(opencircles).A,Numberofimmigrantsasafunctionoftime(t).
Fragmentsandcontrolplotshavesignificantlydifferentslopes(P!.0001).B,Effectofimmigrantsonthechangeinspeciescomposition(S).When
immigrantsareincluded,Sincreasesonaverageby23incontrolplotsandby3,333onfragments.
change 20-fold in a 10-ha fragment (no. 3209; table D4), prediction in any fragment, whereas diversity declined
partly as a result of immigration of many pioneers (table more than predicted in 10 of 13 control plots, and sig-
D3). nificantly so in two (table D5). Neutral theory predicts
that,byincreasingthedistancetoneighboringforest,iso-
Decay of Diversity lating a fragment reduces immigration to it, leading to a
Whenimmigrantswereexcludedfromthelastcensus,the decline in its diversity. Nonetheless, when we included
declineindiversitydidnotdiffersignificantlyfromneutral immigrants in our calculations, we found that diversity
Neutral Theory and Forest Fragmentation 313
Table 3: Pioneer species that invaded or increased in ratesandthepaceofchangeinspeciescomposition.When
three 1-hafragments weusedtheactualmortalityrateforeachfragment(rather
Fragmentand tree thanthetypicalrateinintactforest)togenerateourneutral
mortality(%/year) predictions,wefoundthatthetheoryaccuratelypredicted
2107.1 2108.1 3114.1 the numbers of rare species (singletons and doubletons)
Species (2.66) (3.83) (3.06) that disappeared in the initial 1–2 decades afterfragmen-
Guatteriaolivacea tation (fig. 3; table D2). The theory also predicted, albeit
(Annonaceae) 0 r 13 0 r 1 less accurately, the total numberoflocalextinctionsfrom
Cecropiasciadophylla each fragment or control plot, given its Fisher’s a, total
(Moraceae) 0 r 1 0 r 39 0 r 29 number of trees, mortality rate, and time since theinitial
Pouroumaguianense census (table D3). Thus, when modified to incorporate
(Moraceae) 1 r 10 actual mortality rates, neutral theory was reasonably ef-
Pouroumatomentosum
fective in predicting the pace of species loss.
(Moraceae) 1 r 11 2 r 7
In contrast, species composition often changed signif-
Pouroumavelutina
icantlymorerapidlyinforestfragmentsthanpredictedby
(Moraceae) 0 r 6
neutral theory (fig. 3; table D4), even when predictions
Crotonlanjourensis
(Euphorb) 1 r 24 were based on the actual, elevatedmortalityratesinfrag-
Mabea angularis ments. Habitat fragmentation alters the ecology of Ama-
(Euphorbiaceae) 1 r 10 0 r 15 zonianforestsinmanyways,especiallyviaincreasedlight,
Inga heterophylla desiccationstress,canopydisturbance,andbioticchanges
(Leguminosae) 0 r 8 1 r 12 associated with the abrupt, artificial boundaries of forest
Inga paraense 3 r 12 fragments (Laurance et al. 2002). Different tree species
Inga pezizifera 0 r 2 0 r 10 varygreatlyintheircapacitytotoleratesuchchanges(e.g.,
Belluciadichotoma 1 r 20 0 r 1
Metzger 2000; Wright et al. 2003), and the net result is
Miconiaburchellii 0 r 13 0 r 27 0 r 1
rapid shifts in tree community composition, with light-
Note:Arrowsindicatethechangeindensity(no./ha)ofeach loving pioneers often increasing dramatically at the ex-
speciesbetweenthefirst(prefragmentation)andfinalcensuses. pense of old-growth tree species (Laurance et al. 1998a,
2006).Hence,afundamentaltenetofneutraltheory—that
increased in four of our nine fragments (table D5). If
speciesareequivalentecologically—isclearlyviolated,and
immigrants are included, diversity should increase in
the efficacy of the theory for predicting compositional
about half of the control plots; in fact, diversity declined
changes in fragments appears limited.
in 10 of the 13 control plots and significantly so in one.
A second way that our study area departed from the
conditionshypothesizedbyHubbell(2001)forfragmented
systemsisthat,despitebeingphysicallyisolatedfromother
Discussion
primary forest, our fragments were probably not entirely
In a neutral world such as that envisioned by Hubbell isolated functionally. Seed dispersers and pollinators of
(2001), species richness in isolated communities should some rain forest trees, such as certain birds, bats, and
gradually erode over time, with rare species disappearing insects,cantraversethematrixofcattlepasturesandyoung
via random demographic processes, much as rare alleles regrowth that surrounds our fragments (Gascon et al.
are lost stochastically in isolated populations via genetic 1999; Laurance et al. 2002) and may thereby move prop-
drift.Theexpectedrateofspecieslossinahabitatfragment agules and pollen among sites. A subset of tropical tree
is a function of the population sizes of its constituent species may be dispersed among fragments by wind (cf.
species and their mortality rate, which is assumed to be Baclesetal.2006).Forestfragmentsalsoprobablyreceived
constantamongspeciesandinallplaces.Overtime,most a substantial seed rain from pioneer and generalist trees
forest fragments should become increasingly dominated thatoftenproliferateinthesurroundingmatrix(Laurance
bythespeciesthatwereoriginallymostabundant(Hubbell etal.2006;Nascimentoetal.2006).Thenetresultisthat,
2001). for a portion of all tree species, populations infragments
In applying neutral theory to fragmented tree com- are not fully isolated demographically or genetically (Al-
munities in Amazonia, we encountered two obvious de- drich and Hamrick 1998; Dick et al. 2003; Bacles et al.
parturesfromtheidealizedconditionspostulatedbyHub- 2006).
bell. First, tree mortality rates are not constant but are When we excluded species that had immigrated into
sharplyelevatedinfragments(Lauranceetal.1997,1998b, our plots, species composition in control plots usually
2000).Thisacceleratedmortalityincreasedlocalextinction changedmoreslowlythanpredictedbyneutraltheoryand