stages and spatial scales of recruitment limitation in southern appalachian forests

23 Pages·1999·0.33 MB·English

EcologicalMonographs,68(2),1998,pp.213–235
(cid:113)1998bytheEcologicalSocietyofAmerica
STAGES AND SPATIAL SCALES OF RECRUITMENT LIMITATION IN
SOUTHERN APPALACHIAN FORESTS
JAMES S. CLARK, ERIC MACKLIN,1 AND LESLIE WOOD
Departmentof Botany,DukeUniversity,Durham,North Carolina 27708 USA
Abstract. Recruitment limitation of tree population dynamics is poorly understood,
because fecundity and dispersal are difficult to characterize in closed stands. We present
an approach that estimates seed production and dispersal under closed canopies and four
limitations on recruitment: tree density and location, fecundity, seed dispersal, and estab-
lishment.Consistentestimatesareobtainedfor14canopyspeciesusing5yrofcensusdata
from 100 seed traps and several thousand mapped trees and seedlings from five southern
Appalachian forest stands that span gradients in elevation and moisture. Fecundity (seed
productionpersquarecentimeterofbasalarea)rangedoverfourordersofmagnitude,from
100 cm2 basal area/yr (Carya, Cornus, Nyssa, Quercus) to (cid:46)103 cm2/yr (Betula). Mean
dispersaldistancerangedfrom(cid:44)5m(Cornus,Nyssa)to(cid:46)20m(Acer,Betula,Liriodendron,
Tsuga) and was positively correlated with fecundity. Species also differ in the degree of
seedclumpingatfine(1m2)spatialscales.Dispersalpatternscanbeclassedintwogroups
based on dispersal vector: wind-dispersed taxa with high fecundities, long-distance dis-
persal, and low clumping vs. animal-dispersal taxa with low fecundities, short-distance
dispersal, and a high degree of clumping. ‘‘Colonization’’ limitations caused by sizes and
locations of parent trees, fecundity, and dispersal were quantified as the fraction of sites
receivingseedrelativetothatexpectedundernullmodelsthatassumedispersalisnonlocal
(i.e., long-distance) and not clumped (i.e., Poisson). Difference among species in coloni-
zation levels ranged from those capable of saturating the forest floor with seed in most
stands (Acer, Betula, Liriodendron) to ones that leave much of the forest floor without
seed, despite presence of adults (Carya, Cornus, Nyssa, Oxydendrum).Seedlingestablish-
ment is one of the strongest filters on recruitment in our study area. Taken together, our
resultsindicate(1)thatfecundityanddispersalcanberesolved,evenunderaclosedcanopy,
and (2) that recruitment of many species is limited by the density and location of source,
dispersal patterns, or both.
Keywords: dispersal;establishment;fecundity;forestdynamics;negativebinomial;recruitment;
seed rain; southern Appalachians.
INTRODUCTION Schupp 1993, Ribbens et al. 1994). Moreover, mech-
anisticmodelsarehardtoapplyinforestunderstories,
Field studies and simulation models of forest dy-
because variable winds, seed release heights, and mi-
namics have long assumed that seed is ubiquitous (re-
viewedbyClark1993,PacalaandHurtt1993,Ribbens crotopographicreliefaredifficulttocharacterize(e.g.,
et al. 1994, Clark and Ji 1995, Schupp and Fuentes Greene and Johnson 1989).
1995) and, thus, that tree population growth rates are Growing realization that seed may often be in short
limitedatotherlifehistorystages.Theassumptionthat supply has led to increased interest in understanding
seed is always available allows one to overlook seed lifehistorystageswhererecruitmentlimitationcanoc-
production and dispersal and focus instead on micro- cur, including seed arrival at the ground, seed preda-
sites for seedling establishment, resource limitations tion, germination, and early seedling survival (Har-
on growth, and factors causing mortality. Seed rain combe 1987, Schupp et al. 1989, Nakashizuka et al.
tendstobeignored,becauseitisdifficultbothtoquan- 1995). Seed arrival depends on: (A) density and dis-
tify seed production in closed canopies, where seed persion of adults, (B) adult fecundities, and (C) dis-
shadows from individual crowns overlap (Willson persaldistancesofseed.Thesethreeconstraintsonseed
1993), and to track dispersal by wind (Augspurger arrivalareheretermed:(A)source-density,(B)source-
1986,Matlack1987,Johnson1988)andanimals(Smith strength, and (C) dispersal limitations, respectively
and Follmer 1972, Darley-Hill and Johnson 1981, (Fig.1).Afourthlimitationonrecruitmentweexamine
here,(D)establishmentlimitation,dependsonseedsur-
Manuscript received 12 February 1997; revised and ac- vival and germination and seedling survival. We refer
cepted1 May 1997.
to‘‘establishment’’asthetimefromseedarrivalatthe
1Presentaddress:HarvardUniversity,HarvardUniversity
soilsurface(estimatedbyseedtraps)tothetimeseed-
Herbaria, 22 Divinity St., Cambridge, Massachusetts02138
USA. lingsarecensusedduringthefirstyearofgrowth.Each
213
214 JAMESS.CLARKET AL. EcologicalMonographs
Vol.68,No.2
FIG. 1. Thefourlimitationson recruitmentanalyzedhere(labeledA–D)thatlink adultsto seedlings.
stage may depend on processes operative at several and Nakashizuka 1995). Any spatial bias imposed by
spatialscales(Schupp1993,Nakashizukaetal.1995). post-dispersal processing of seed (e.g., secondary dis-
Atthebroadestscale,thedistributionofaspeciesalong persalbywind(Matlack1989)oranimals(Abbottand
geographic or environmental gradients sets limits on Quink 1970, Schupp 1988, Willson and Whelan1990,
the presence of reproductive individuals (A, source Whelan et al. 1991, Willson 1993) alters the relation-
density).Finespatialscalesdescribelocaldensitiesand shipbetweenseedarrivalandseedlings.Moreover,dis-
crown areas of seed-bearing trees (A, source density) tributions and abundances of seedlings do not neces-
and dispersal distances (C), which, in turn, determine sarily give much insight into seed production (fecun-
identities of neighboring plants and interaction inten- dity) (Willson 1993). Because of these problems pa-
sities.Seedlingestablishment(D)dependsonphysical rameterizing seed production and dispersal, we are
(e.g., light, water, and nutrients) and biotic (e.g.,litter aware of no studies showing how recruitment limita-
depth, seed and seedling predators, pathogens, and tions compare among species that co-occur in closed
competitors)factors thatvaryatseveralspatialscales, stands.
both ‘‘within’’ and ‘‘among’’ stands (Godman and A way forward is available through models that as-
Mattson1976,Beatty1984,Strengetal.1989,Peterson sociate offspring with the spatial pattern and sizes of
and Pickett 1990, Alvarez-Buylla and Garc´ıa-Barrios potential parents. Ribbens et al. (1994) used the rela-
1991, Houle 1992a). tionshipbetweenseedlingsandconspecifictreestoes-
Unfortunately, appreciation that recruitment limita- timate seedling production and dispersal. Their model
tioncanoccurdoesnotremovetheobstaclethatcaused predicts seedling density as the summed contribution
many to ignore it in the first place: lack of character- of seedlings from all trees on a sample plot. The ap-
izationmethods.Mosteffortstoquantifyseedproduc- proach is a significant advance over simple seedling
tion and dispersal are highly indirect. Seed arrival at counts, because it estimates fecundity and dispersal
the forest floor is sometimes estimated from seedling distance (of seedlings, rather than seeds) based on the
distributions, a method requiring establishment suc- summedcontributionsofpotentialparenttrees.Anext
cess, i.e., that seeds become seedlings. Does absence step is the analysis of seed rain to estimate factors
of seedlings mean seeds did not arrive or that seeds affecting seed arrival (limitations A, B, and C) vs. es-
arrived, but did not germinate? If microrelieforbiotic tablishment (D).
interactions influence germination success (Godman Ourobjectivesare(1)todevelopamodeltoestimate
and Mattson 1976, Beatty 1984), there may be little seed production and dispersalunderclosedforestcan-
(orevenanegative)relationshipbetweenseedrainand opies, (2) to introduce methods for evaluation of the
seedlings (Augspurger 1986, Augspurger and Franson approach, and (3) to determine contributions of seed
1988, Houle 1992a, Nakashizuka et al. 1995, Shibata arrival vs. seedling establishment to the distributions
May1998 RECRUITMENTLIMITATIONIN FORESTS 215
TABLE 1. Standcharacteristicsand basalareas(m2/ha).
Stand 1 Stand 2 Stand 3 Stand 4 Stand 5
Elevation(m) 786 802 866 1085 1387
Setting xericridge mesiccove slope slope slope
Acer 1.96 4.83 4.69 6.58 3.86
A. pensylvanicum 0.01 0.07 0.02 1.13 1.15
A. rubrum 1.86 4.50 5.71 5.45 0.31
A. saccharum 0.00 0.26 0.00 0.00 2.37
A. spicatum 0.00 0.00 0.00 0.00 0.06
Amelanchierarborea 0.47 0.03 0.00 0.02 0.18
Betula 0.03 2.55 0.70 0.02 12.76
B. alleghaniensis 0.00 0.09 0.11 0.00 8.25
B. lenta 0.03 2.46 0.59 0.02 4.52
Carya glabra 1.33 3.55 3.86 1.35 0.34
Castanea dentata 0.10 0.00 0.04 0.31 0.00
Cornus florida 0.17 0.61 0.22 0.16 0.02
Fagus grandifolia 0.01 0.00 0.00 0.00 0.59
Fraxinus americana 0.00 0.00 0.00 1.23 1.80
Hamamelisvirginiana 0.03 0.06 0.00 0.00 0.21
Liriodendron tulipifera 0.03 9.97 0.71 0.03 0.00
Magnolia 0.13 0.02 0.00 0.40 0.00
M. acuminata 0.01 0.00 0.00 0.02 0.00
M. fraseri 0.12 0.02 0.00 0.38 0.00
Nyssa sylvatica 0.69 0.33 2.97 2.03 0.00
Oxydendrumarboreum 1.62 0.15 3.13 2.88 0.00
Pinus rigida 6.35 0.00 0.00 0.00 0.00
Quercus 8.65 6.92 13.51 15.40 8.71
Q. alba 0.83 0.00 0.00 0.00 0.37
Q. coccinea 3.56 0.00 0.00 0.95 0.00
Q. marilandica 0.40 0.00 0.00 0.00 0.00
Q. prinus 2.74 3.35 10.30 9.83 0.00
Q. rubra 0.10 1.65 2.70 4.12 8.33
Q. velutina 1.01 1.92 0.46 0.00 0.00
Q.sp. 0.00 0.00 0.05 0.51 0.00
Robinia pseudo-acacia 0.77 0.64 0.51 0.32 0.00
Sassafras albidum 0.57 0.00 0.09 0.00 0.00
Tilia americana 0.00 0.59 0.00 0.00 4.42
Tsuga canadensis 0.00 0.19 0.04 0.52 0.00
Note:Rounding resultsin discrepanciesforsometotals.
of first-year seedlings in five of the principal stand are located to sample these gradients (Table 1).Mesic
types of southern Appalachian forests. We use spatial sites include Cove hardwoods at mid elevation (stand
distributionsofmaturetrees,seedarrival,andseedling 2) and Northern hardwoods at high elevation (stand
establishmenttoquantifyrecruitmentlimitationsattwo 5)(Table1).APine/oakridge(stand1)isthemostxeric
scales. Model results produce a simple ‘‘colonization stand.Intermediateinelevationandmoisturestatusare
index,’’ the average fraction of 1-m2 plots of soil sur- oak-dominated stands (3 and 4). Species restricted to
face expected to receive some seed in any given year. highelevationand/orhighmoisturestandsincludeAcer
Weusetherelationshipbetweenseedrainandseedling pensylvanicum, A. saccharum, Betula alleghaniensis,
distributions as the basis for identifying arrivalvs.es- Fraxinus americana, and Tsuga canadensis. Cove
tablishmentlimitationsonrecruitmentatthestandand hardwoods additionally include Liriodendron tulipi-
at the square-meter scales. Because we expected the fera.Oakstands(3and4)arecentersofabundancefor
relative contributions of seed arrivalvs.establishment Acer rubrum, Nyssa sylvatica, Quercusprinus,andQ.
limitation to vary among species and across environ- rubra. Xeric stand 1 is dominated by Pinus rigida, Q.
mental gradients, we analyzed 14 species across five alba, Q. coccinea, Q. marilandica, Q. velutina, and
stands that span gradients in elevation and moisture. Sassafras albidum.
THE STUDY AREA METHODS
The study area consists of five stands along an el- Datacollectionwasdesignedtocharacterizerecruit-
evation gradient at CoweetaHydrologicLaboratoryin mentlimitationsatfourstages(Fig.1)andtwospatial
the southern Appalachians (35(cid:56)03(cid:57) N, 83(cid:56)27(cid:57) W). The scales. Our nested sampling design allowed modeling
watershedischaracterizedbyhighandtopographically of seed production and dispersal at the local (within-
variable precipitation (177–222 cm/yr). The two prin- stand) scale and comparisons of average seed rain
cipalvegetationgradientsarethosediscussedbyWhit- among stands. Within-stand sampling allowed us to
taker (1956), elevation and moisture. Our five stands estimate fecundity and dispersal of seed by modeling
216 JAMESS.CLARKET AL. EcologicalMonographs
Vol.68,No.2
spatial pattern in seed rain relative to locations and mesh.LowestefficiencieswereforCarya(0.86(cid:54)0.05)
sizes of adult trees. Stand differences in parent tree andQuercus(0.88(cid:54)0.03),buteventhesetaxaentered
abundance,seedrain,andseedlingestablishmentdem- traps with high probability. Intermediate were Lirio-
onstrated how recruitment limitation varied with can- dendron(0.98 (cid:54) 0.02), Pinus(0.95 (cid:54) 0.04), andAcer
opy composition across the principal environmental (0.94 (cid:54) 0.04).
gradients. The first limitation, (A) source abundance TrapsweredeployedinthefieldSeptember1991and
(Fig.1),wasassessedfrombasalareas.Sourcestrength emptied at 2–4 mo intervals through July 1996. Be-
(B) was estimated(1)atthelocalscale,frommodeled causefewspeciesreleasedseedduringsummermonths,
seed rain within stands, and (2) as a stand average, annualaveragesarebasedonseedcollectionsbetween
from average seed rain and basal areas. Regressions July of each year. All debris in traps was removed at
between stand basal area and seed rain determined collectiondatesandsortedwiththeaidofsieves.Seeds
whether differences in seed rain among stands (i.e., were identified to the lowest taxonomic unit possible
acrossenvironmentalgradients)wereexplainedbyav- (Table 2). All seeds collected over the course of the
erage basal area of adults. Limitations due to source studyarearchivedaccordingtotrapandcollectiondate
density and distribution (A), source strength (B), and at the Duke University Phytotron.
seeddispersal(C)werecollectivelyestimatedfromthe Seedling transects were established within each of
fraction of ground surface expected to receive some thefivestandsinJune1992alongthelowerportionof
seedinagivenyear,basedonmodeledseedrainwithin samplestands,withlocationdifferingsomewhatamong
stands. Establishment limitation (D) was assessed at stands to avoid areas disturbed by foot traffic.Annual
both scales. Comparisons of seedling distributions censuses of newly emerged seedlings were completed
within stands with predicted seed rain permitted esti- in July of 1992, 1993, 1994, 1995, and 1996 to match
mation of establishment success at fine spatial scales. the period for seed rain collection. Newly emerged
Differencesinstandaveragesofseedrainvs.seedling seedlings were readily distinquished from older seed-
establishmentwereusedtoidentifyhowestablishment lings for all species that occurred within our stands.
success varied across vegetation types. Togetherthese
Seed dispersal vectors and taxonomic resolution
resultswereusedtointerprethowdifferentspeciesmay
be limited at different stages by factors operating at Notallseedsandseedlingscouldberesolvedtospe-
localscales(dispersionofadulttrees,dispersalofseed, ciesinourstudy.Topermitcomparisonsamongseeds,
and microrelief) and at broader scales (gradients in seedlings, and trees, we used the lowest common tax-
elevation and moisture). onomic group for analysis (Table 2). For example, all
Acer seed is treated as a single taxon. Although many
Tree, seed, and seedling data
could be confidently identified to species, others (par-
From each of five stands we (1) mapped all trees ticularlydamagedseeds)couldnot.BecauseAcersac-
greaterthan1mtallon60(cid:51)60m(0.36ha)plots,(2) charum trees are abundant only in stand 5, and Acer
collectedseedintwenty0.42(cid:51)0.42mseedtraps,and pensylvanicum shrubs are short and not close to traps,
(3) took a census of seedlings along a 1 (cid:51) 60 m belt most seeds on the remaining four plots were probably
transect. Trees wereidentified,locatedusingaTopcon Acer rubrum. Acorns were separated as ‘‘red’’ vs.
electronic Total Station, and diameters measured at a ‘‘white,’’ and several were identified to species.How-
height of 1.3 m. ever,becausemanycouldnotbeseparated,andbecause
Twenty seed traps were established within each of acorns were few, we lumped all Quercus. Carya nuts
the five stands at 5-m intervals along two transects couldnotbeconfidentlyidentifiedtospecies,buttrees
spaced20mapart.Wetestedseveralseedtrapdesigns. within our stands were principally Carya glabra. For
Thedesignusedconsistsofaplasticbasketframesup- remaining taxa, either seed could be identified to spe-
ported 1.5 m above the ground by PVC pipes. The ciesoronlyasinglespeciesrepresentativeofthetaxon
basket has drain holes, but seeds falling in the trap occurred in the study area. Genders of dioecious spe-
remain elevated above the bottom of the basket by 1 cies Nyssa sylvatica and, sometimes, Fraxinus ameri-
mm mosquito netting. Elevation of the trap above the cana, were not determined, so all individuals werein-
ground and a layer of wire mesh covering the trap cluded in the analysis. We did identify seed bearing
minimized removal of Quercus and Carya seed by individuals of Acer rubrum, so only those individuals
squirrelsandothervertebrateseedpredators.Concerns wereusedtoestimatefecundityanddispersal.Themin-
that the wire mesh might cause some seeds to bounce uteseedsofOxydendrumarboreumwerenotrecovered
out of traps led us to conduct efficiency trials. We re- inourtraps,butwedidquantifythedehiscentcapsules.
leased seeds from sufficient heights to insure terminal Seedsanalyzedincludespeciesprincipallydispersed
velocities were reached at the trap opening and re- bywindandanimals(Table2).Ourelevatedtrapschar-
corded numbers of successful trap entries. Trap effi- acterize primarily wind dispersal; seeds ‘‘scatter-
ciencies were generally high; clear differences among hoarded’’ by birds and mammals or dispersedsecond-
taxacouldbeattributedtosizeandtendencytobounce. arily by wind (e.g., Betula, Matlack 1989, Houle and
Small Betula seeds never bounced off the covering Payette 1990) are not expected to enter traps.
May1998 RECRUITMENTLIMITATIONIN FORESTS 217
TABLE 2. Resolutionof taxaanalyzedin thisstudy and theirprobabledispersalvectors.
1st-yr Dispersal
Taxon Trees Seed seedlings vector
Acer A. pensylvanicum A. pensylvanicum A. pensylvanicum wind
A. rubrum A. rubrum A. rubrum
A. saccharum A. saccharum A. saccharum
A. spicatum Acersp. Acersp.
Amelanchier A. arborea Amelanchiersp. A. arborea birds
Betula B. alleghaniensis Betulasp. Betulasp. wind
B. lenta
Carya C. glabra Caryasp. none mammals
Cornus C. florida C. florida C. florida birds
Fraxinus F. americana Fraxinussp. none wind
Liriodendron L. tulipifera L. tulipifera L. tulipifera wind
Nyssa N. sylvatica N. sylvatica none birds
Oxydendrum O. arboreum O. arboreumcapsules none wind
Pinus P. rigida Pinussp. none wind
Quercus Q. alba Q. rubra Q. prinus mammals
Q. coccinea Q. velutina Q. rubra
Q. marilandica Red oak Q. velutina
Q. prinus Whiteoak Red oak
Q. rubra
Q. velutina
Robinia R. pseudo-acacia R. pseudo-acacia none wind
Tilia T. americana T. americana none wind
Tsuga T. canadensis T. canadensis none wind
Seed production estimation at the stand scale Clumpeddistributionofseed.—Distributionsofseed
Fecundityparameters((cid:98))wereestimatedattwospa- arrivals in our stands were ‘‘clumped,’’ having higher
tial scales. An estimate of (cid:98) among stands is obtained variance than a Poisson process. This clumped distri-
bution was described by a negative binomial distri-
astheslopeoftheregressionofseedrainagainstbasal
bution, generally appropriate for mixtures of random
area:
sources(e.g.,JohnsonandKotz1969).Considermseed
s (cid:53) (cid:98)b (1a) traps located at various distances from a seed source
jk k
(a tree). Our likelihood function is based on negative
where b is the basal area of the kth stand, and s is
k jk binomial seed arrival:
seed arrival at the jth seed trap in the kth stand. To
evaluate constancy of fecundity among standswealso L(S|p, (cid:117))
estimated (cid:98) for each stand separately as the ratio of (cid:80)
average seed rain and stand basal area: (cid:53) mtraps (cid:71)(sj (cid:49) (cid:117)) sˆsj(b, xj; p)(cid:117)(cid:117) (2)
j(cid:53)1 (cid:71)(sj (cid:49) 1)(cid:71)((cid:117))(sˆ(b, xj; p) (cid:49) (cid:117))sj(cid:49)(cid:117)
s
(cid:98) (cid:53) k. (1b) where (cid:71)(·) is the gamma function, s is the observed
k b j
k rate of seed arrival to a given seed trap j,Sisthedata
The following section (Seed production and dispersal set containing mseedtraps(thecollectionofs’s),sˆ(b,
j
modeling)describesathirdestimateof(cid:98)basedonspa- x; p) is the ‘‘expected’’ seed abundance at trap j, and
j
tial patterns of trees and seed rain within stands. (cid:117) is a dimensionless ‘‘clumping parameter.’’ The ex-
pectedseedarrivalattrapjisafunctionsˆ(b,x;p)that
Seed production and dispersal modeling j
dependsondistancex fromaseedsourceandthesize
j
Oursummedseedshadow(SSS)modelpredictsseed (basal area) b of that source, with fitted parameters p
arrivalatalocationasthesummedcontributionofseed (seeFittingthemodel,below).Thedegreeofclumping
dispersedfromallconspecifictreesinthesamplearea. isdeterminedbythedata((cid:117)isafittedparameter).Val-
The method assumes that each tree’s contribution to ues of (cid:117) (cid:44) 1 imply highly contagious distributions
seed rain at a location depends on its size (basal area) (overdispersed), whereas large values ((cid:117) (cid:107) 1) tend to
and distance. Functions describing how seed rain de- a Poisson process.
pends on fecundity, tree basal area, and distance are Theunevendistributionofseedsources.—Nowcon-
parameterized from an array of seed input data (e.g., siderastandofmanytrees,eachproducingseedswith
seedtraps)andamapoftreelocationsandsizes(basal a source strength that depends on basal area and dis-
areas). The model allows estimation of the seed con- persingseedsomedistance.Theexpectationoftheneg-
tributions of individual trees. Our SSS model shares ativebinomialdistributionatagivenlocationdepends
some attributes of that used by Ribbens et al. (1994) onthesizesanddistancestoalltreesinthestand.Here
to estimate seedling distributions and by Kuuluvainen wederivethisexpectationasthesumofseedshadows
et al. (1993) to model spatial effects of adult trees. of individual trees. Tree i’s contribution to total seed
218 JAMESS.CLARKET AL. EcologicalMonographs
Vol.68,No.2
arrivalatlocationjistheproductofitssourcestrength (cid:97)(cid:71)(3/c)
(cid:109) (cid:53) (4)
Q(b), a function of its basal area b: 1 (cid:71)(2/c)
i i
Q(b) (cid:53) (cid:98)b (3) and kurtosis that dependsonlyontheshapeparameter
i i
with fitted parameter (cid:98) (seeds per basal area), and (a (cid:71)(6/c)(cid:71)(2/c)
.
density function of) seeds dispersed to a trap located (cid:71)2(4/c)
x meters away, f(x ). The proportion of a tree’s Q(b)
ij ij i
seeds arriving on the area subtended by a trap of di- This flexible density includes some familiars ones as
ameter dx and arc angle d(cid:119) is specialcases. Exponential densitieshave c(cid:53)1(John-
son1988,Willson1993).OurmodelisGaussian,hav-
proportion of seeds falling on the area (x, x (cid:49) dx, (cid:119)) ing c (cid:53) 2. Kurtosis of this arc-wise Gaussian density
(cid:69) (cid:82)
x(cid:49)dx (i.e., two) is lower than that of a one-dimensional
(cid:53) f(x(cid:57), (cid:119)(cid:57)) d(cid:119)(cid:57) dx(cid:57) (cid:248) (cid:119)xf(x)dx. Gaussian density (kurtosis (cid:53) 3). Ribbens et al.(1994)
x (cid:119) used a third special case with c (cid:53) 3 and a lower kur-
tosis. Our density then is
We fitted dispersal functions f(x, (cid:119)) of varying forms [ ]
and numbers of parameters, including ones that allow f(x ; c (cid:53) 2) (cid:53) 1 exp (cid:50)(cid:49)xij(cid:50)2 (5)
for the ‘‘skip’’ distance that can be associated with ij (cid:112)(cid:97)2 (cid:97)
dispersionfromanelevatedsource(Sutton1953,Oku-
with mean displacement from Eq. 4:
boandLevin1989,Andersen1991),oneswithvarying
degrees of kurtosis, and mixed models. Models witha (cid:97)(cid:207)(cid:112)
(cid:109) (cid:53) (cid:53) 0.886(cid:97).
skip distance did not fit the data, because crowns are 1 2
too broad to be regarded as point sources (aboundary
Arc-wise integration gives the fraction of seed that
conditionassumedinmostsolutionsofGaussianplume
travels distance x in all directions, which yields the
models having an elevated source [Okubo and Levin
Weibull density:
1989]); seeds are broadly dispersed under individual
[ ]
crowns and then fall off with distance. Models with 2x (cid:49)x(cid:50)2
large kurtosis did not fit our data, yielding unstable F(cid:117)(x; c (cid:53) 2) (cid:53) (cid:97)2 exp (cid:50) (cid:97) .
fecundity estimates. We wereunabletoobtainconver-
gence of mixed models that had some proportion of The product of source strength (Eq. 3) and density of
seedallocatedtoawidelydispersedtailduetoparam- seed arrivals (Eq. 5) is termed the ‘‘seed shadow’’ of
eter redundancy. a tree i:
The density used is isotropic, i.e., there is no direc- sˆ(b, x ; p) (cid:53) Q(b)f(x ).
i ij i ij
tional bias in the dissemination of seed. It has a mode
Note that for global dispersal the average seed arrival
at the source and adjustable kurtosis:
[ ] reduces to Eq. 1b.
f(x ) (cid:53) 1 exp (cid:50)(cid:49)xij(cid:50)c Fitting the model.—Assume each tree i disperses
ij N (cid:97) seed to trap j. Seed arrival at trap j is the cumulative
where (cid:97) is a dispersion parameter in metres, c is a contribution of n conspecific sample trees, each tree
having source strength and seed shadow described by
dimensionless shape parameter, and N is a normaliza-
Eqs. 3 and 5, respectively:
tionconstantobtainedbyintegratingarc-wiseandwith
(cid:79)
distance: ntrees
(cid:69) (cid:82) sˆ(b, x; p) (cid:53) Q(b)f(x )
(cid:96) [ ] j i ij
N (cid:53) 0 (cid:69)2(cid:96)(cid:112)exp (cid:50)[(cid:49)(cid:97)x(cid:50)c d](cid:119)(cid:57) dx (cid:53) (cid:112)i(cid:53)(cid:98)(cid:97)12 n(cid:79)it(cid:53)re1es bi exp[(cid:50)(cid:49)x(cid:97)ij(cid:50)2] (6)
(cid:49)x(cid:50)c 2(cid:112)(cid:97)2(cid:71)(2/c) where p is a vector of fitted parameters [(cid:97), (cid:98)] that
(cid:53) 2(cid:112) x exp (cid:50) dx (cid:53) .
0 (cid:97) c maximize the likelihood given in Eq. 2, b is a length-
nvectoroftreebasalareasb,andxisthen(cid:51)mmatrix
The proper form of N is required to obtain unbiased i
of distances between trees and traps x . We simulta-
parameterestimates(seeFittingthemodel,below).The neously fit (cid:117); the degree of clumpingijin the data is
mth moment of this density is
estimated together with the seed shadows, sˆ(b, x ; p),
i ij
(cid:49)m(cid:49)2(cid:50) aroundindividualtrees.Biascorrectedandaccelerated
(cid:69)(cid:96) (cid:82) (cid:97)m(cid:71) (BCa)confidenceintervalsfor(cid:97),(cid:98),and(cid:117)wereobtained
c by 1000 bootstrapped maximum likelihood (ML) es-
(cid:109)m (cid:53) 0 2(cid:112) (x(cid:57))mf(x(cid:57), (cid:119)(cid:57)) d(cid:119)(cid:57) dx(cid:57) (cid:53) (cid:71)(2/c) tdiimffaetressfr(oEmfrothneasntdanTdiabrsdhpirearncie1n9ti9le3s).inTthweoBwCaayisn.tFerirvsatl,
giving mean dispersal distance it corrects for the median bias (thedifferencebetween
May1998 RECRUITMENTLIMITATIONIN FORESTS 219
median and mean) in the parameter estimate obtained variedwithspecies,becausetreesofallspeciesdidnot
fromthesetofbootstrapestimates.Second,itcorrects occur on all plots. In some cases trees did occur, but
for the fact that the standard error of the estimate can numbersweretoolowtoobtainfits.Theq(cid:49)1degrees
depend on the parameter value. This correction is ac- of freedom for this model are the q (cid:49) 1 parametersin
complished through an acceleration quantity that es- p ,plusonefortheclumpingparameter(cid:117),minusone.
q(cid:49)1
timatestherateofchangeinthestandarderrorrelative By simultaneously taking advantage of data from all
to the true parameter value. We compared BC confi- avaliable stands, this modelprovidesthebestestimate
a
denceintervalswiththoseobtainedfromstandardper- of dispersal distance.
centiles and from a minimum volume ellipse for all Step 2 requires a ML for the model in which each
parameterestimates.AlthoughBC endpointsaremore stand has a separate (cid:97) in order to test whether stand-
a k
accurate than those obtained by other methods (Efron specificdispersalparameterssubstantiallyimprovethe
andTibshirani1993),wefounddifferencestobesmall likelihood of the data, so much so that we conclude
at the 95% level, the level reported here. that dispersal distance may differ among stands. This
Parameter correlations were determined from the likelihoodhasparametersetp (cid:53)[(cid:97) ,...,(cid:97) ,(cid:98) ,...,
2q 1 q 1
bootstrapped data set, and scatter plots of parameter (cid:98) ] with 2q degrees of freedom. The likelihood ratio
q
estimates were examined. Negative correlations in (cid:97) statistic, or deviance
and (cid:98) estimates obtained from a simplified version of [L(S |p , (cid:117))]
the model demonstrated need for a proper normaliza- D (cid:53) (cid:50)2 ln q 2q (8)
L(S |p , (cid:117))
tion constant. The normalization constant assures that q q(cid:49)1
negativecorrelationbetweenparametersdoesnotdom- is asymptotically distributed as (cid:120)2 with q (cid:50) 1 degrees
inate the fit, an instability we observed for an unnor- offreedom,thedifferenceindegreesoffreedom(num-
malizedversionofthemodelthatpermitsalargesource berof parameters)oftheindividualmodels.Largede-
strength parameter (cid:98) to offset a small dispersion pa- viance means that dispersal distance differs across
rameter(cid:97).Thenormalizedmodelfittedhere,however, stands.
can have the opposite tendency. Positive correlation Forstep3,weviewedanappropriatenullmodelfor
occurswhenlargedispersionflattensthecurveandcan testing our results to be one where seed arrival is in-
be compensatedbylargesourcestrength.Weobtained dependent of tree locations, i.e., nonlocal dispersal.
positivecorrelationsonlyinafewcaseswherefitswere This null model is analogous to the conventional re-
poor. gressionnullmodelofaslopeparameterequaltozero,
Parameter estimation and evaluation was accom- i.e.,norelationbetweenvariables.Ourlikelihoodratio
plished for each species in four steps: (1) estimation test compares the likelihood obtained with q (cid:49) 2 ML
of the best (ML) dispersal parameter value (cid:97) incor- parameterestimateswiththelikelihoodunderthe(null)
porating information obtained from allfivestands;(2) hypothesis that all traps receive,onaverage,themean
assessmentofconsistencyofdispersalparametersfrom seed rain. The null model has fixed expectation s in
k
stand to stand; (3) comparison of model performance Eq.2andasinglefittedparameter(cid:117).Thedeviancefor
against a null model ofnonlocal dispersal;and(4)ex- this model,
[ ]
amination of potential for bias in parameter estimates L (S |p , (cid:117))
resulting from finite area of mapped stands. One ob- D (cid:53) (cid:50)2 ln ML q q(cid:49)1 (9)
L (S |(cid:117))
vious source of variance in dispersal among stands is null q
thatassociatedwithdifferentarrangementsoftreesrel- has q degrees of freedom, q (cid:49) 1 parameters from the
ative to seed traps. Because there are no conventional ML model, minus one parameter for the null model.
hypothesistestsforsuchmodels,wedevelopedseveral. To safeguard against the event that D was not distrib-
Our first two steps involve a hypothesis test that dis- uted as (cid:120)2 we also conducted permutation tests that
persal parameters differ among stands. We compute involved generating a distribution of deviances from
two likelihoods of the data. The first likelihood pro- permuted data sets, where S in Eq. 9 was replaced
q
videsparameterestimatesthatincorporateinformation with S , the kth random permutation of the data. The
q,k
fromallq((cid:35)5)standshavingsufficienttreestoobtain probability of D calculated from the original data was
a fit, yielding the ML of the data for the model witha determined from this distribution of D’s.
k
species-specific (cid:97) parameter: The fourth step of model evaluation was a test for
biasinparameterestimatesthatmightarisefromfinite
(cid:80)
qstands sizeofmappedstands.Contributionsofseedfromtrees
L(S |p , (cid:117)) (cid:53) L(S |p , (cid:117)) (7)
q q(cid:49)1 k k outsidethemappedplotmightbiasfecundityestimates
k(cid:53)1
upward, because the model implicitly assumes thatall
wheretheparametersetforstandkisp (cid:53)[(cid:97),(cid:98)],and seeds derive from trees in the plot. Dispersal param-
k k
p (cid:53) [(cid:97), (cid:98) , ..., (cid:98) ] includes separatefecundityes- etersmightalsobesensitivetoplotsizes.Wefittedthe
q(cid:49)1 1 q
timatesforeachstandandasingledispersalparameter model beginning at a minimal map area that included
(cid:97) that best predicts seed rain across all stands. The thecentral20(cid:51)40mtoprogressivelylargermapareas
numberofstandsqincludedinthelikelihoodfunction out to the full 60 (cid:51) 60 m.
220 JAMESS.CLARKET AL. EcologicalMonographs
Vol.68,No.2
Thereisnosimpleestimateofthevarianceexplained Limited dispersal and clumping of seed reduce the
bythemodel,butweprovidearoughindex.ThePear- actual colonization ratebelowthat whichwouldoccur
soncorrelationcoefficientbetweenmodelanddatahas if dispersal were global, as estimated by C(s). Oures-
been used for such comparisons, but it characterizes timate of dispersal limitation makes use of the prob-
thelevelofagreementtoabest-fittinglinearregression ability that any given 1-m2patch j receives some seed
to the model. Thus, high correlations can result even given the best estimates of local dispersal and clump-
when model predictions are biased (i.e., good fit to a ing:
linear model of slope (cid:177) 1). We used instead the cor-
relation describing the level of agreement between C(sˆ) (cid:53) Pr{sˆ (cid:46) 0|Negative Binomial(sˆ, (cid:117)ˆ)}
j j j
modeland data, i.e.,thescatteraboutthelineofslope
(cid:53) 1: (cid:53) 1 (cid:50) (cid:49) (cid:117)ˆ (cid:50)(cid:117)ˆ.
(cid:79) (cid:79) sˆ (cid:49) (cid:117)ˆ
qstands 20traps j
(s (cid:50) sˆ (x, b; p))2
r2 (cid:53) 1 (cid:50) k(cid:53)1 (cid:79)j(cid:53)1 (cid:79)jk jk (10) The average of these estimates across the m (cid:53) 800
qstands 20traps central 1-m2 patches in each sample stand is the col-
(s (cid:50) s )2
jk k onization index:
k(cid:53)1 j(cid:53)1
(cid:79)
where s is the observed seed rain at trap j in stand k, 1 m
jk C (cid:53) C(sˆ) (13)
andskisthemeanseedrainforstandk.Whendataare m j(cid:53)1 j
highlyskewed(i.e.,(cid:117)(cid:75)1),andthefitweak,thisindex
hasthelimitationthatitcanbenegative(i.e.,themean the expected fraction of patches (at the 1-m2 scale)
better accounts for seed rain than does the model). It receiving some seed in a given year. The contribution
isaconservativeindexofvarianceinthedataexplained of dispersal limitation to the colonization index is es-
by the model. timated as the relative difference between the coloni-
zationindexthatincludesonlysourcelimitations,C(s),
Seed limitation index
and the colonization index that incorporates dispersal
Seed limitation at the local scale (1 m2) was esti- and clumping C:
mated as the probability that no seed would arrive in
agiven1-m2patch.The1-m2scalewaschosenforthis Dispersal limitation(cid:53) 1 (cid:50) C . (14)
index, because microsites typically analyzed for re- C(s)
cruitmentsuccessareofthisorder.Weconsideredtwo
sources of limitation: (1) source limitation, the influ-
Predicted seed rain and observed seedlings
enceofsourcedensity,distribution,andfecundity;and
(2) dispersal limitation, the influence of the local and ‘‘Establishment limitation,’’ the stage between seed
clumped nature of seed dispersal. We estimated these dispersal and establishment as a 1st-yr seedling (Fig.
limitations from probabilities calculated using the an- 1), was assessed by comparing 1st-yr seedlings with
nual predicted seed rain density at each 1 m2 in the seedrainatstandandlocal(1-m2)scales.Thefraction
central 20 (cid:51) 40 m rectangle of each stand using the of seed that produces 1st-yr seedlings was estimated
tree census maps and parameterized seed dispersal at the stand scale by comparing average annual seed
models. rain estimated from the 20 traps with average density
Our index of source limitation consists of a com- of 1st-yr seedlings from the belt transects over 5 yr,
parison of seed arrival predicted fromthefittedmodel
with that expected if seed rain was not influenced by Establishment fraction
limited dispersal. Assuming uniform distribution of (cid:79)
1 5 1st-yr seedling density
seed and independent (unclumped) arrivals, the prob- (cid:53) y.
5 seed density
abilityofany1-m2patchjreceivingatleastsomeseed y(cid:53)1 y
in a given year is
Totestforestablishmentlimitationatthe1-m2scale,
C(s) (cid:53) Pr{sˆ (cid:46) 0(cid:122)Poisson(s)} (cid:53) 1 (cid:50) e(cid:50)s (11) we compared predicted seed rain to observed 1st-yr
j
seedlingdensityalongthebelttransects.Parameterized
where
models were used together with the mapped tree dis-
(cid:79)
1 m tributions to predict seed rain densities at each 1-m2
s (cid:53) sˆ
m j quadrat of the belt transects in each stand. The spatial
j(cid:53)1
scale of coherence between predicted seed rain and
is the average seed rain density, and sˆ is the expected
j annual average 1st-yr seedling densities was assessed
seed rain to patch j from Eq. 6. Low values of C(s)
by cross-correlation. Significance levels included cor-
occur if the total production of seed is low (i.e., in-
rection for the autocorrelation within each series by
adequate source density, fecundity, or both), yielding
adjusting degrees of freedom according to Clifford et
Source limitation (cid:53) 1 (cid:50) C(s). (12) al. (1989).
May1998 RECRUITMENTLIMITATIONIN FORESTS 221
FIG.2. Threeestimatesofthefecundityparameter(cid:98):(1)‘‘withinstands,’’thevaluefittedbytheSummedSeedShadow
model, incorporating locations of seed traps relative to individual trees (solid bars); (2) the ‘‘stand average,’’ obtained by
dividing average seed rain of 20 traps by stand basal area (unshaded bars) (Eq. 1b); and (3) ‘‘among stands,’’obtainedby
regressingseedrainagainstbasalareaacrossallfivestands(hatchedbars)(Eq.1a).Thelowerrightpanelindicatesthatthe
differentmethodsshowcloseagreement.Fortaxashowingpoorestagreement,theSummedSeedShadowmodelfitsappear
to be overestimates.Standarderrorsarebootstrapped(SSSparameterestimates)or fromregression.
RESULTS Quercus prinus, Q. rubra), whereas others were con-
Density of sources fined to specific stand types (Acer saccharum, Betula
The most fundamental limitation on recruitment is alleghaniensis, B. lenta, Fraxinus, Liriodendron, Pi-
absence of parent trees. Some taxa were abundant nus, Tilia, Table 1). Several taxa were presentinmost
across most or all sites (e.g., Acer rubrum, Carya, stands, but were nowhere abundant (Cornus, Nyssa,
222 JAMESS.CLARKET AL. EcologicalMonographs
Vol.68,No.2
TABLE 3. Summedseed shadow modelparameterestimates,goodness-of-fit,and hypothesistests.
Stand Distance Fecundity‡ Clumping Explained
Taxon q† (cid:97)(cid:54) 1 SE (m) (cid:98)k(cid:54) 1 SE (cm(cid:50)2·yr(cid:50)1) (cid:117)(cid:54) 1 SE variance§
Acer 4(1,2,3,4) 25.2 (cid:54) 2.39 (cid:98) (cid:53) 69.2 (cid:54) 6.82 10.8 (cid:54) 1.95 0.714***
(cid:98)1(cid:53) 37.7 (cid:54) 4.00
(cid:98)3(cid:53) 23.4 (cid:54) 2.58(c)
(cid:98)3(cid:53) 32.2 (cid:54) 2.84(c)
Amelanchier 2(1,5) 16.9 (cid:54) 185 (cid:98)4(cid:53) 0.231 (cid:54) 450 0.165 (cid:54) 3500 0.125
(cid:98)1(cid:53) 4.44 (cid:54) 522
Betula 3(2,3,4) 37.1 (cid:54) 2.87 (cid:98)5(cid:53) 448 (cid:54) 62.7(c) 5.83 (cid:54) 1.22 0.681***
(cid:98)2(cid:53) 1470 (cid:54) 141
(cid:98)3(cid:53) 10200 (cid:54) 1040
Carya 3(1,2,3) 10.8 (cid:54) 2.06 (cid:98)4(cid:53) 0.657 (cid:54) 0.196 0.670 (cid:54) 1.16 0.529***
(cid:98)1(cid:53) 0.296 (cid:54) 0.179
(cid:98)2(cid:53) 1.02 (cid:54) 0.267
Cornus 3(1,2,3) 3.65 (cid:54) 1.52 (cid:98)3(cid:53) 7.68 (cid:54) 30.7 0.447 (cid:54) 1.15 0.566***
(cid:98)1(cid:53) 2.28 (cid:54) 2.73
(cid:98)2(cid:53) 8.87 (cid:54) 15.9
Fraxinus 1(5) 19.3 (cid:54) 5.84 (cid:98)3(cid:53) 3.40 (cid:54) 0.847 0.632 (cid:54) 0.757 0.379**
Liriodendron 3(2,3,4) 33.9 (cid:54) 2.56 (cid:98)5(cid:53) 49.8 (cid:54) 7.89(c) 5.76 (cid:54) 1.21 0.707***
(cid:98)2(cid:53) 147 (cid:54) 15.2(c)
(cid:98)3(cid:53) 1590 (cid:54) 254
Nyssa 3(1,3,4) 6.02 (cid:54) 4.48 (cid:98)4(cid:53) 7.30 (cid:54) 4.87 0.528 (cid:54) 1.12 0.554***
(cid:98)1(cid:53) 9.12 (cid:54) 3.68
(cid:98)3(cid:53) 0.151 (cid:54) 0.101
Oxydendrum 2(1,3) 9.23 (cid:54) 2.86 (cid:98)4(cid:53) 24.5 (cid:54) 6.26 0.472 (cid:54) 0.254 0.593***
(cid:98)1(cid:53) 0.975 (cid:54) 0.484
Pinus 1(1) 15.1 (cid:54) 3.27 (cid:98)3(cid:53) 2.16 (cid:54) 0.558 2.01 (cid:54) 88.1 0.364**
Quercus 4(1,2,4,5) 11.8 (cid:54) 1.32 (cid:98)1(cid:53) 2.52 (cid:54) 0.383 1.30 (cid:54) 0.282 0.270***
(cid:98)1(cid:53) 1.31 (cid:54) 0.468
(cid:98)2(cid:53) 2.85 (cid:54) 0.488
(cid:98)4(cid:53) 5.84 (cid:54) 1.99
Robinia 1(1) 14.8 (cid:54) 1.33 (cid:98)5(cid:53) 9.57 (cid:54) 0.454 65.6 (cid:54) 20.6 0
Tilia 2(2,5) 13.0 (cid:54) 2.95 (cid:98)1(cid:53) 22.3 (cid:54) 50.5 0.485 (cid:54) 0.374 0.114
(cid:98)2(cid:53) 12.9 (cid:54) 7.57
Tsuga 2(1,4) 19.7 (cid:54) 5.04 (cid:98)5(cid:53) 503 (cid:54) 170(c) (cid:46)100 0.523***
(cid:98)1(cid:53) 10.6 (cid:54) 2.24(c)
4
Note:Maximumlikelihoodestimatesforparameters(cid:97)and(cid:98)includebootstrappedstandarderrors.BC confidenceintervals
a
are included in Fig. 4. Likelihood-ratio statistics (D) and associated r2values includeprobabilityestimatesfornullmodels
describedin text.
*P(cid:35) 0.05, **P(cid:35) 0.01, ***P(cid:35) 0.001.
†The numberof standshaving sufficientseeds and treesto obtainfits followedby the listof standsin parentheses.
‡Estimateswiththe designation(c)indicatecorrelationsbetween(cid:97) and (cid:98) exceed0.60, wherekis standdesignation.
k
§The r2foragreementbetweendataand model(Eq. 10).
(cid:92)Deviance for the hypothesis test that seed dispersal is nonlocal (Eq. 9) with df (cid:53) q. Probabilities arefrompermutation
tests,but (cid:120)2probabilitiesdid not differatthe levelsin footnotes*, **, or ***.
¶Devianceforthehypothesistestthatdispersionparameters(cid:97) arethesameacrossstands(Eq.8)withdf(cid:53)q(cid:50)1.Blank
cellsareforq(cid:53) 1 and, thus, no degreesof freedom. k
Robinia). Unless seed production and dispersal are es,andlowlevelsofclumping,includingAcer,Betula,
great, recruitment limitation is likely for many taxa Liriodendron, and Tsuga. These factors insure that
simply on the basis of parent tree abundance. seeds are evenly spread at the stand scale and, thus,
reflect average tree abundance. Seed rain of taxa with
Seed rain at the stand scale
lowdispersaldistances,clumpeddistributions,orhigh-
Spatialvariabilityinseedrainaffectedourabilityto ly uneven distributions of adults, including Amelan-
estimate fecundity differences among stands. Regres- chier, Carya, Cornus, Nyssa, Oxydendrum, Quercus,
sionsofseedrainagainstbasalareasofthefivestands Robinia, and Tilia, was not well-predicted from basal
(Eq. 1a) provide (cid:98) (seeds per basal area) estimates area at the stand scale (r2values (cid:44)0.25). Intermediate
based on varying abundances across the landscape levelsofexplainedvariancewereobtainedforFraxinus
(‘‘among stands’’ in Fig. 2). Significant (cid:98)valueswere and Pinus, both of which were abundant in single
obtained for Acer, Betula, Carya, Cornus, Fraxinus, stands and had intermediate dispersal distances.
Liriodendron, Nyssa, Oxydendrum, Pinus, Quercus, Fecundity parameters (cid:98) estimated from within in-
Tilia, and Tsuga (Fig. 2). Best fits (r2 (cid:46) 0.5) were dividualplotsvariedamongstandsforsometaxa(Fig.
obtainedfortaxahavingadultsdistributedrathereven- 2).Betulaconsistentlyhadthehighestfecundities,with
lyacrossplots,intermediatetolargedispersaldistanc- lowestvaluesobtainedinstand5,theonlystandhaving