Ecological Monographs. 68(2), 1998. pp. 213-235 STAGES AND...

Ecological Monographs. 68(2), 1998. pp. 213-235© 1998 by the Ecological Society of America

STAGES AND SPATIAL SCALES OF RECRUITMENT LIMITATION IN

SOUTHERN APPALACHIAN FORESTS

JAMES S. CLARK, ERIC MACKLiN,1 AND LESLIE WOOD

Department of Botany, Duke University, 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 presentan approach that estimates seed production and dispersal under closed canopies and fourlimitations on recruitment: tree density and location, fecundity, seed dispersal, and estab-lishment. Consistent estimates are obtained for 14 canopy species using 5 yr of census datafrom 100 seed traps and several thousand mapped trees and seedlings from five southernAppalachian forest stands that span gradients in elevation and moisture. Fecundity (seedproduction per square centimeter of basal area) ranged over four orders of magnitude, from10° cm2 basal area/yr (Carya, Cornus, Nyssa, Quercus) to >103 cmVyr (Betula). Meandispersal distance ranged from <5 m (Cornus, Nyssa) to >20 m (Acer, Betula, Liriodendron,Tsuga) and was positively correlated with fecundity. Species also differ in the degree ofseed clumping at fine (1 m2) spatial scales. Dispersal patterns can be classed in two groupsbased on dispersal vector: wind-dispersed taxa with high fecundities, long-distance dis-persal, and low clumping vs. animal-dispersal taxa with low fecundities, short-distancedispersal, and a high degree of clumping. "Colonization" limitations caused by sizes andlocations of parent trees, fecundity, and dispersal were quantified as the fraction of sitesreceiving seed relative to that expected under null models that assume dispersal is nonlocal(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 moststands (Acer, Betula, Liriodendron) to ones that leave much of the forest floor withoutseed, despite presence of adults (Carya, Cornus, Nyssa, Oxydendrum). Seedling establish-ment is one of the strongest filters on recruitment in our study area. Taken together, ourresults indicate (1) that fecundity and dispersal can be resolved, even under a closed canopy,and (2) that recruitment of many species is limited by the density and location of source,dispersal patterns, or both.

Key -words: dispersal; establishment; fecundity; forest dynamics; negative binomial; recruitment;seed rain; southern Appalachians.

INTRODUCTION

Field studies and simulation models of forest dy-namics have long assumed that seed is ubiquitous (re-viewed by Clark 1993, Pacala and Hurtt 1993, Ribbenset al. 1994, Clark and Ji 1995, Schupp and Fuentes1995) and, thus, that tree population growth rates arelimited at other life history stages. The assumption thatseed is always available allows one to overlook seedproduction and dispersal and focus instead on micro-sites for seedling establishment, resource limitationson growth, and factors causing mortality. Seed raintends to be ignored, because it is difficult both to quan-tify seed production in closed canopies, where seedshadows from individual crowns overlap (Willson1993), and to track dispersal by wind (Augspurger1986, Matlack 1987, Johnson 1988) and animals (Smithand Follmer 1972, Darley-Hill and Johnson 1981,

Manuscript received 12 February 1997; revised and ac-cepted 1 May 1997.

1 Present address: Harvard University, Harvard UniversityHerbaria, 22 Divinity St., Cambridge, Massachusetts 02138USA.

Schupp 1993, Ribbens et al. 1994). Moreover, mech-anistic models are hard to apply in forest understories,because variable winds, seed release heights, and mi-crotopographic relief are difficult to characterize (e.g.,Greene and Johnson 1989).

Growing realization that seed may often be in shortsupply has led to increased interest in understandinglife history stages where recruitment limitation can oc-cur, including seed arrival at the ground, seed preda-tion, germination, and early seedling survival (Har-combe 1987, Schupp et al. 1989, Nakashizuka et al.1995). Seed arrival depends on: (A) density and dis-persion of adults, (B) adult fecundities, and (C) dis-persal distances of seed. These three constraints on seedarrival are here termed: (A) source-density, (B) source-strength, and (C) dispersal limitations, respectively(Fig. 1). A fourth limitation on recruitment we examinehere, (D) establishment limitation, depends on seed sur-vival and germination and seedling survival. We referto "establishment" as the time from seed arrival at thesoil surface (estimated by seed traps) to the time seed-lings are censused during the first year of growth. Each

213

214 JAMES S. CLARK ET AL. Ecological MonographsVol. 68, No. 2

A. Source densityand dispersion

*£&

Seed densityand dispersion

mean .B. Source strength Total seed production

per adult

Spatial variability

Seedling density

D. Establishment J Fraction of seeds thatbecome seedlings

^^

FIG. 1. The four limitations on recruitment analyzed here (labeled A-D) that link adults to seedlings.

stage may depend on processes operative at severalspatial scales (Schupp 1993, Nakashizuka et al. 1995).At the broadest scale, the distribution of a species alonggeographic or environmental gradients sets limits onthe presence of reproductive individuals (A, sourcedensity). Fine spatial scales describe local densities andcrown areas of seed-bearing trees (A, source density)and dispersal distances (C), which, in turn, determineidentities of neighboring plants and interaction inten-sities. Seedling establishment (D) depends on physical(e.g., light, water, and nutrients) and biotic (e.g., litterdepth, seed and seedling predators, pathogens, andcompetitors) factors that vary at several spatial scales,both "within" and "among" stands (Godman andMattson 1976, Beatty 1984, Streng et al. 1989, Petersonand Pickett 1990, Alvarez-Buylla and Garcia-Barrios1991,Houle 1992a).

Unfortunately, appreciation that recruitment limita-tion can occur does not remove the obstacle that causedmany to ignore it in the first place: lack of character-ization methods. Most efforts to quantify seed produc-tion and dispersal are highly indirect. Seed arrival atthe forest floor is sometimes estimated from seedlingdistributions, a method requiring establishment suc-cess, i.e., that seeds become seedlings. Does absenceof seedlings mean seeds did not arrive or that seedsarrived, but did not germinate? If microrelief or bioticinteractions influence germination success (Godmanand Mattson 1976, Beatty 1984), there may be little(or even a negative) relationship between seed rain andseedlings (Augspurger 1986, Augspurger and Franson1988, Houle 1992a, Nakashizuka et al. 1995, Shibata

and Nakashizuka 1995). Any spatial bias imposed bypost-dispersal processing of seed (e.g., secondary dis-persal by wind (Matlack 1989) or animals (Abbott andQuink 1970, Schupp 1988, Willson and Whelan 1990,Whelan et al. 1991, Willson 1993) alters the relation-ship between seed arrival and seedlings. Moreover, dis-tributions and abundances of seedlings do not neces-sarily give much insight into seed production (fecun-dity) (Willson 1993). Because of these problems pa-rameterizing seed production and dispersal, we areaware of no studies showing how recruitment limita-tions compare among species that co-occur in closedstands.

A way forward is available through models that as-sociate offspring with the spatial pattern and sizes ofpotential parents. Ribbens et al. (1994) used the rela-tionship between seedlings and conspecific trees to es-timate seedling production and dispersal. Their modelpredicts seedling density as the summed contributionof seedlings from all trees on a sample plot. The ap-proach is a significant advance over simple seedlingcounts, because it estimates fecundity and dispersaldistance (of seedlings, rather than seeds) based on thesummed contributions of potential parent trees. A nextstep is the analysis of seed rain to estimate factorsaffecting seed arrival (limitations A, B, and C) vs. es-tablishment (D).

Our objectives are (1) to develop a model to estimateseed production and dispersal under closed forest can-opies, (2) to introduce methods for evaluation of theapproach, and (3) to determine contributions of seedarrival vs. seedling establishment to the distributions

May 1998 RECRUITMENT LIMITATION IN FORESTS 215

TABLE 1. Stand characteristics and basal areas (mVha).

Stand 1 Stand 2 Stand 3 Stand 4 Stand 5Elevation (m)SettingAcer

A. pensylvanicumA. rubrumA. saccharumA. spicatum

Amelanchier arboreaBetula

B. alleghaniensisB. lenta

Carya glabraCastanea dentataComus floridaFagus grandifoliaFraxinus americanaHamamelis virginianaLiriodendron tulipiferaMagnolia

M. acuminataM. fraseri

Nyssa sylvaticaOxydendrum arboreumPinus rigidaQuercus

Q. albaQ. coccineaQ. marilandicaQ. prinusQ. rubraQ. velutinaQ. sp.

Robinia pseudo-acaciaSassafras albidumTilia americanaTsuga canadensis

786xeric ridge

1.960.011.860.000.000.470.030.000.031.330.100.170.010.000.030.030.130.010.120.691.626.358.650.833.560.402.740.101.010.000.770.570.000.00

802mesic cove

4.830.074.500.260.000.032.550.092.463.550.000.610.000.000.069.970.020.000.020.330.150.006.920.000.000.003.351.651.920.000.640.000.590.19

866slope4.690.025.710.000.000.000.700.110.593.860.040.220.000.000.000.710.000.000.002.973.130.00

13.510.000.000.00

10.302.700.460.050.510.090.000.04

1085slope6.581.135.450.000.000.020.020.000.021.350.310.160.001.230.000.030.400.020.382.032.880.00

15.400.000.950.009.834.120.000.510.320.000.000.52

1387slope3.861.150.312.370.060.18

12.768.254.520.340.000.020.591.800.210.000.000.000.000.000.000.008.710.370.000.000.008.330.000.000.000.004.420.00

Note: Rounding results in discrepancies for some totals.

of first-year seedlings in five of the principal standtypes of southern Appalachian forests. We use spatialdistributions of mature trees, seed arrival, and seedlingestablishment to quantify recruitment limitations at twoscales. Model results produce a simple "colonizationindex," the average fraction of 1-m2 plots of soil sur-face expected to receive some seed in any given year.We use the relationship between seed rain and seedlingdistributions as the basis for identifying arrival vs. es-tablishment limitations on recruitment at the stand andat the square-meter scales. Because we expected therelative contributions of seed arrival vs. establishmentlimitation to vary among species and across environ-mental gradients, we analyzed 14 species across fivestands that span gradients in elevation and moisture.

THE STUDY AREA

The study area consists of five stands along an el-evation gradient at Coweeta Hydrologic Laboratory inthe southern Appalachians (35°03' N, 83°27' W). Thewatershed is characterized by high and topographicallyvariable precipitation (177-222 cm/yr). The two prin-cipal vegetation gradients are those discussed by Whit-taker (1956), elevation and moisture. Our five stands

are located to sample these gradients (Table 1). Mesicsites include Cove hardwoods at mid elevation (stand2) and Northern hardwoods at high elevation (stand5)(Table 1). A Pine/oak ridge (stand 1) is the most xericstand. Intermediate in elevation and moisture status areoak-dominated stands (3 and 4). Species restricted tohigh elevation and/or high moisture stands include Acerpensylvanicum, A. saccharum, Betula alleghaniensis,Fraxinus americana, and Tsuga canadensis. Covehardwoods additionally include Liriodendron tulipi-fera. Oak stands (3 and 4) are centers of abundance forAcer rubrum, Nyssa sylvatica, Quercus prinus, and Q.rubra. Xeric stand 1 is dominated by Pinus rigida, Q.alba, Q. coccinea, Q. marilandica, Q. velutina, andSassafras albidum.

METHODS

Data collection was designed to characterize recruit-ment limitations at four stages (Fig. 1) and two spatialscales. Our nested sampling design allowed modelingof seed production and dispersal at the local (within-stand) scale and comparisons of average seed rainamong stands. Within-stand sampling allowed us toestimate fecundity and dispersal of seed by modeling


spatial pattern in seed rain relative to locations andsizes of adult trees. Stand differences in parent treeabundance, seed rain, and seedling establishment dem-onstrated how recruitment limitation varied with can-opy composition across the principal environmentalgradients. The first limitation, (A) source abundance(Fig. 1), was assessed from basal areas. Source strength(B) was estimated (1) at the local scale, from modeledseed rain within stands, and (2) as a stand average,from average seed rain and basal areas. Regressionsbetween stand basal area and seed rain determinedwhether differences in seed rain among stands (i.e.,across environmental gradients) were explained by av-erage basal area of adults. Limitations due to sourcedensity and distribution (A), source strength (B), andseed dispersal (C) were collectively estimated from thefraction of ground surface expected to receive someseed in a given year, based on modeled seed rain withinstands. Establishment limitation (D) was assessed atboth scales. Comparisons of seedling distributionswithin stands with predicted seed rain permitted esti-mation of establishment success at fine spatial scales.Differences in stand averages of seed rain vs. seedlingestablishment were used to identify how establishmentsuccess varied across vegetation types. Together theseresults were used to interpret how different species maybe limited at different stages by factors operating atlocal scales (dispersion of adult trees, dispersal of seed,and microrelief) and at broader scales (gradients inelevation and moisture).

Tree, seed, and seedling data

From each of five stands we (1) mapped all treesgreater than 1 m tall on 60 X 60 m (0.36 ha) plots, (2)collected seed in twenty 0.42 X 0.42 m seed traps, and(3) took a census of seedlings along a 1 X 60 m belttransect. Trees were identified, located using a Topconelectronic Total Station, and diameters measured at aheight of 1.3 m.

Twenty seed traps were established within each ofthe five stands at 5-m intervals along two transectsspaced 20 m apart. We tested several seed trap designs.The design used consists of a plastic basket frame sup-ported 1.5 m above the ground by PVC pipes. Thebasket has drain holes, but seeds falling in the trapremain elevated above the bottom of the basket by 1mm mosquito netting. Elevation of the trap above theground and a layer of wire mesh covering the trapminimized removal of Quercus and Carya seed bysquirrels and other vertebrate seed predators. Concernsthat the wire mesh might cause some seeds to bounceout of traps led us to conduct efficiency trials. We re-leased seeds from sufficient heights to insure terminalvelocities were reached at the trap opening and re-corded numbers of successful trap entries. Trap effi-ciencies were generally high; clear differences amongtaxa could be attributed to size and tendency to bounce.Small Betula seeds never bounced off the covering

mesh. Lowest efficiencies were for Carya (0.86 ± 0.05)and Quercus (0.88 ± 0.03), but even these taxa enteredtraps with high probability. Intermediate were Lirio-dendron (0.98 ± 0.02), Pinus (0.95 ± 0.04), and Acer(0.94 ± 0.04).

Traps were deployed in the field September 1991 andemptied at 2-4 mo intervals through July 1996. Be-cause few species released.seed during summer months,annual averages are based on seed collections betweenJuly of each year. All debris in traps was removed atcollection dates and sorted with the aid of sieves. Seedswere identified to the lowest taxonomic unit possible(Table 2). All seeds collected over the course of thestudy are archived according to trap and collection dateat the Duke University Phytotron.

Seedling transects were established within each ofthe five stands in June 1992 along the lower portion ofsample stands, with location differing somewhat amongstands to avoid areas disturbed by foot traffic. Annualcensuses of newly emerged seedlings were completedin July of 1992, 1993, 1994, 1995, and 1996 to matchthe period for seed rain collection. Newly emergedseedlings were readily distinquished from older seed-lings for all species that occurred within our stands.

Seed dispersal vectors arid taxonomic resolution

Not all seeds and seedlings could be resolved to spe-cies in our study. To permit comparisons among seeds,seedlings, and trees, we used the lowest common tax-onomic group for analysis (Table 2). For example, allAcer seed is treated as a single taxon. Although manycould be confidently identified to species, others (par-ticularly damaged seeds) could not. Because Acer sac-charum trees are abundant only hi stand 5, and Acerpensylvanicum shrubs are short and not close to traps,most seeds on the remaining four plots were probablyAcer rubrum. Acorns were separated as "red" vs."white," and several were identified to species. How-ever, because many could not be separated, and becauseacorns were few, we lumped all Quercus. Carya nutscould not be confidently identified to species, but treeswithin our stands were principally Carya glabra. Forremaining taxa, either seed could be identified to spe-cies or only a single species representative of the taxonoccurred in the study area. Genders of dioecious spe-cies Nyssa sylvatica and, sometimes, Fraxinus ameri-cana, were not determined, so all individuals were in-cluded in the analysis. We did identify seed bearingindividuals of Acer rubrum, so only those individualswere used to estimate fecundity and dispersal. The min-ute seeds of Oxydendrum arboreum were not recoveredin our traps, but we did quantify the dehiscent capsules.

Seeds analyzed include species principally dispersedby wind and animals (Table 2). Our elevated traps char-acterize primarily wind dispersal; seeds "scatter-hoarded" by birds and mammals or dispersed second-arily by wind (e.g., Betula, Matlack 1989, Houle andPayette 1990) are not expected to enter traps.


TABLE 2. Resolution of taxa analyzed in this study and their probable dispersal vectors.

TaxonAcer

AmelanchierBetula

CaryaCornusFraxinusLiriodendronNyssaOxydendrumPinusQuercus

RobiniaTiliaTsuga

TreesA. pensylvanicumA. rubrumA. saccharumA. spicatumA. arboreaB. alleghaniensisB. lento.C. glabraC. floridaF. americanaL. tulipiferaN. sylvaticaO. arboreumP. rigidaQ. albaQ. coccineaQ. marilandicaQ. prinusQ. rubraQ. velutinaR. pseudo-acaciaT. americanaT. canadensis

SeedA. pensylvanicumA. rubrumA. saccharumAcer sp.Amelanchier sp.Betula sp.

Carya sp.C. floridaFraxinus sp.L. tulipiferaN. sylvaticaO. arboreum capsulesPinus sp.Q. rubraQ. velutinaRed oakWhite oak

R. pseudo-acaciaT. americanaT. canadensis

Ist-yrseedlings

A. pensylvanicumA. rubrumA. saccharumAcer sp.A. arboreaBetula sp.

noneC. floridanoneL. tulipiferanonenonenoneQ. prinusQ. rubraQ. velutinaRed oak

nonenonenone

Dispersalvector

wind

birdswind

mammalsbirdswindwindbirdswindwindmammals

windwindwind

Seed production estimation at the stand scale

Fecundity parameters (P) were estimated at two spa-tial scales. An estimate of p among stands is obtainedas the slope of the regression of seed rain against basalarea:

fy = $bk (la)

where bk is the basal area of the Mi stand, and $# isseed arrival at the yth seed trap in the feth stand. Toevaluate constancy of fecundity among stands we alsoestimated p for each stand separately as the ratio ofaverage seed rain and stand basal area:

Pi = T-- (lb)

The following section (Seed production and dispersalmodeling') describes a third estimate of p based on spa-tial patterns of trees and seed rain within stands.

Seed production and dispersal modeling

Our summed seed shadow (SSS) model predicts seedarrival at a location as the summed contribution of seeddispersed from all conspecific trees in the sample area.The method assumes that each tree's contribution toseed rain at a location depends on its size (basal area)and distance. Functions describing how seed rain de-pends on fecundity, tree basal area, and distance areparameterized from an array of seed input data (e.g.,seed traps) and a map of tree locations and sizes (basalareas). The model allows estimation of the seed con-tributions of individual trees. Our SSS model sharessome attributes of that used by Ribbens et al. (1994)to estimate seedling distributions and by Kuuluvainenet al. (1993) to model spatial effects of adult trees.

Clumped distribution of seed.—Distributions of seedarrivals in our stands were "clumped," having highervariance than a Poisson process. This clumped distri-bution was described by a negative binomial distri-bution, generally appropriate for mixtures of randomsources (e.g., Johnson and Kotz 1969). Consider m seedtraps located at various distances from a seed source(a tree). Our likelihood function is based on negativebinomial seed arrival:

•L(S!p,6)w/ " • V> ^-JT Jf/" ,-^

j-f T(SJ + 1)1X6) (s(b, xf, p) -1- 6)^" .

where F(-) is the gamma function, Sj is the observedrate of seed arrival to a given seed trap j, S is the dataset containing m seed traps (the collection of s/s), S (b,xf, p) is the "expected" seed abundance at trap j, and6 is a dimensionless "clumping parameter." The ex-pected seed arrival at trap j is a function s(b, xf, p) thatdepends on distance Xj from a seed source and the size(basal area) b of that source, with fitted parameters p(see Fitting the model, below). The degree of clumpingis determined by the data (6 is a fitted parameter). Val-ues of 0 < 1 imply highly contagious distributions(overdispersed), whereas large values (6 :§> 1) tend toa Poisson process.

The uneven distribution of seed sources.—Now con-sider a stand of many trees, each producing seeds witha source strength that depends on basal area and dis-persing seed some distance. The expectation of the neg-ative binomial distribution at a given location dependson the sizes and distances to all trees in the stand. Herewe derive this expectation as the sum of seed shadowsof individual trees. Tree z's contribution to total seed

218 JAMES S. CLARK EX AL. Ecological MonographsVol. 68, No. 2

arrival at location j is the product of its source strengthQ(b^, a function of its basal area b,:

Q(bt) = p&. (3)

with fitted parameter p (seeds per basal area), and (adensity function of) seeds dispersed to a trap locatedxtj meters away, f(x^). The proportion of a tree's Q(b^)seeds arriving on the area subtended by a trap of di-ameter dx and arc angle dtp is

proportion of seeds falling on the area (x, x + dx, <p)x+dx

- j*

We fitted dispersal functions fix, if) of varying formsand numbers of parameters, including ones that allowfor the "skip" distance that can be associated withdispersion from an elevated source (Sutton 1953, Oku-bo and Levin 1989, Andersen 1991), ones with varyingdegrees of kurtosis, and mixed models. Models with askip distance did not fit the data, because crowns aretoo broad to be regarded as point sources (a boundarycondition assumed in most solutions of Gaussian plumemodels having an elevated source [Okubo and Levin1989]); seeds are broadly dispersed under individualcrowns and then fall off with distance. Models withlarge kurtosis did not fit our data, yielding unstablefecundity estimates. We were unable to obtain conver-gence of mixed models that had some proportion ofseed allocated to a widely dispersed tail due to param-eter redundancy.

The density used is isotropic, i.e., there is no direc-tional bias in the dissemination of seed. It has a modeat the source and adjustable kurtosis:

where a is a dispersion parameter in metres, c is adimensionless shape parameter, and N is a normaliza-tion constant obtained by integrating arc-wise and withdistance:

d<f'dx

= 2<rr2ira2r(2/c)

CO

= I 9J° J

Jm+2\a"T

\ c J

F(2/c)

oJ(3/c)r<2/c>

(4)

and kurtosis that depends only on the shape parameter

F(6/c)r(2/c)T2(4/c) '

This flexible density includes some familiars ones asspecial cases. Exponential densities have c = 1 (John-son 1988, Willson 1993). Our model is Gaussian, hav-ing c = 2. Kurtosis of this arc-wise Gaussian density(i.e., two) is lower than that of a one-dimensionalGaussian density (kurtosis = 3). Ribbens et al. (1994)used a third special case with c = 3 and a lower kur-tosis. Our density then is

exp (5)

with mean displacement from Eq. 4:

aVrrjli _ _^ _ Q.886a.

Arc-wise integration gives the fraction of seed thattravels distance x in all directions, which yields theWeibull density:

Ft(x; c = 2) = — exp

The product of source strength (Eq. 3) and density ofseed arrivals (Eq. 5) is termed the "seed shadow" ofa tree i:

The proper form of N is required to obtain unbiasedparameter estimates (see Fitting the model, below). The;wth moment of this density is

S(b:, xj p) =

Note that for global dispersal the average seed arrivalreduces to Eq. Ib.

Fitting the model.—Assume each tree i dispersesseed to trap /. Seed arrival at trap j is the cumulativecontribution of n conspecific sample trees, each treehaving source strength and seed shadow described byEqs. 3 and 5, respectively:

p) = 2

P ll UGC3v

~ 2 ̂ (6)

giving mean dispersal distance

where p is a vector of fitted parameters [a, p] thatmaximize the likelihood given in Eq. 2, b is a length-n vector of tree basal areas bit and x is the n X m matrixof distances between trees and traps xy. We simulta-neously fit 0; the degree of clumping in the data isestimated together with the seed shadows, s(bt, x:i; p),around individual trees. Bias corrected and accelerated(BCJ confidence intervals for a, p, and 0 were obtainedby 1000 bootstrapped maximum likelihood (ML) es-timates (Efron and Tibshirani 1993). The BC0 intervaldiffers from the standard percentiles in two ways. First,it corrects for the median bias (the difference between


median and mean) in the parameter estimate obtainedfrom the set of bootstrap estimates. Second, it correctsfor the fact that the standard error of the estimate candepend on the parameter value. This correction is ac-complished through an acceleration quantity that es-timates the rate of change in the standard error relativeto the true parameter value. We compared BCa confi-dence intervals with those obtained from standard per-centiles and from a minimum volume ellipse for allparameter estimates. Although BCfl endpoints are moreaccurate than those obtained by other methods (Efronand Tibshirani 1993), we found differences to be smallat the 95% level, the level reported here.

Parameter correlations were determined from thebootstrapped data set, and scatter plots of parameterestimates were examined. Negative correlations in aand p estimates obtained from a simplified version ofthe model demonstrated need for a proper normaliza-tion constant. The normalization constant assures thatnegative correlation between parameters does not dom-inate the fit, an instability we observed for an unnor-malized version of the model that permits a large sourcestrength parameter p to offset a small dispersion pa-rameter a. The normalized model fitted here, however,can have the opposite tendency. Positive correlationoccurs when large dispersion flattens the curve and canbe compensated by large source strength. We obtainedpositive correlations only in a few cases where fits werepoor.

Parameter estimation and evaluation was accom-plished for each species in four steps: (1) estimationof the best (ML) dispersal parameter value a. incor-porating information obtained from all five stands; (2)assessment of consistency of dispersal parameters fromstand to stand; (3) comparison of model performanceagainst a null model of nonlocal dispersal; and (4) ex-amination of potential for bias in parameter estimatesresulting from finite area of mapped stands. One ob-vious source of variance in dispersal among stands isthat associated with different arrangements of trees rel-ative to seed traps. Because there are no conventionalhypothesis tests for such models, we developed several.Our first two steps involve a hypothesis test that dis-persal parameters differ among stands. We computetwo likelihoods of the data. The first likelihood pro-vides parameter estimates that incorporate informationfrom all q (s5) stands having sufficient trees to obtaina fit, yielding the ML of the data for the model with aspecies-specific a parameter:

6)=q stands

(7)

where the parameter set for stand k is p^ = [a, PJ, andP9+i = [<*, Pi, . . . , P,] includes separate fecundity es-timates for each stand and a single dispersal parametera that best predicts seed rain across all stands. Thenumber of stands q included in the likelihood function

varied with species, because trees of all species did notoccur on all plots. In some cases trees did occur, butnumbers were too low to obtain fits. The q + I degreesof freedom for this model are the q + 1 parameters inPq+i, plus one for the clumping parameter 9, minus one.By simultaneously taking advantage of data from allavailable stands, this model provides the best estimateof dispersal distance.

Step 2 requires a ML for the model in which eachstand has a separate a* in order to test whether stand-specific dispersal parameters substantially improve thelikelihood of the data, so much so that we concludethat dispersal distance may differ among stands. Thislikelihood has parameter set p^ = [a l t . . . , a ,̂ p,,...,PJ with 2q degrees of freedom. The likelihood ratiostatistic, or deviance

(8)

is asymptotically distributed as x2 with q — I degreesof freedom, the difference in degrees of freedom (num-ber of parameters) of the individual models. Large de-viance means that dispersal distance differs acrossstands.

For step 3, we viewed an appropriate null model fortesting our results to be one where seed arrival is in-dependent of tree locations, i.e., nonlocal dispersal.This null model is analogous to the conventional re-gression null model of a slope parameter equal to zero,i.e., no relation between variables. Our likelihood ratiotest compares the likelihood obtained with q + 2 MLparameter estimates with the likelihood under the (null)hypothesis that all traps receive, on average, the meanseed rain. The null model has fixed expectation sk inEq. 2 and a single fitted parameter 6. The deviance forthis model,

D= -2 hi (9)

has q degrees of freedom, q + 1 parameters from theML model, minus one parameter for the null model.To safeguard against the event that D was not distrib-uted as x2 we also conducted permutation tests thatinvolved generating a distribution of deviances frompermuted data sets, where S9 in Eq. 9 was replacedwith S^ the Mi random permutation of the data. Theprobability of D calculated from the original data wasdetermined from this distribution of Dk's.

The fourth step of model evaluation was a test forbias in parameter estimates that might arise from finitesize of mapped stands. Contributions of seed from treesoutside the mapped plot might bias fecundity estimatesupward, because the model implicitly assumes that allseeds derive from trees in the plot. Dispersal param-eters might also be sensitive to plot sizes. We fitted themodel beginning at a minimal map area that includedthe central 20 X 40 m to progressively larger map areasout to the full 60 X 60 m.


There is no simple estimate of the variance explainedby the model, but we provide a rough index. The Pear-son correlation coefficient between model and data hasbeen used for such comparisons, but it characterizesthe level of agreement to a best-fitting linear regressionto the model. Thus, high correlations can result evenwhen model predictions are biased (i.e., good fit to alinear model of slope T4 1). We used instead the cor-relation describing the level of agreement betweenmodel and data, i.e., the scatter about the line of slope— 1 •"—" JL .

r= I —

a stands 20 traps"V* ^ /2, 2, ( s j k ~*-i f-i

b; p))2

q stands 20 trapsI 2

(10)

Limited dispersal and clumping of seed reduce theactual colonization rate below that which would occurif dispersal were global, as estimated by C(j). Our es-timate of dispersal limitation makes use of the prob-ability that any given 1-m2 patch j receives some seedgiven the best estimates of local dispersal and clump-ing:

C(Sj) = Pi{Sj > 01 Negative Binomial^, §)}

where sjk is the observed seed rain at trap j in stand k,and sk is the mean seed rain for stand fc. When data arehighly skewed (i.e., 6 <; 1), and the fit weak, this indexhas the limitation that it can be negative (i.e., the meanbetter accounts for seed rain than does the model). Itis a conservative index of variance in the data explainedby the model.

Seed limitation index

Seed limitation at the local scale (1 m2) was esti-mated as the probability that no seed would arrive ina given 1-m2 patch. The 1-m2 scale was chosen for thisindex, because microsites typically analyzed for re-cruitment success are of this order. We considered twosources of limitation: (1) source limitation, the influ-ence of source density, distribution, and fecundity; and(2) dispersal limitation, the influence of the local andclumped nature of seed dispersal. We estimated theselimitations from probabilities calculated using the an-nual predicted seed rain density at each 1 m2 in thecentral 20 X 40 m rectangle of each stand using thetree census maps and parameterized seed dispersalmodels.

Our index of source limitation consists of a com-parison of seed arrival predicted from the fitted modelwith that expected if seed rain was not influenced bylimited dispersal. Assuming uniform distribution ofseed and independent (unclumped) arrivals, the prob-ability of any 1-m2 patch j receiving at least some seedin a given year is

C(s) = 0|Poisson(J)} = 1 - (11)

where

6

The average of these estimates across the m = 800central 1-m2 patches in each sample stand is the col-onization index:

(13)

the expected fraction of patches (at the 1-m2 scale)receiving some seed in a given year. The contributionof dispersal limitation to the colonization index is es-timated as the relative difference between the coloni-zation index that includes only source limitations, C(s),and the colonization index that incorporates dispersaland clumping C:

Dispersal limitation = 1 — -^pr.

is the average seed rain density, and $s is the expectedseed rain to patch j from Eq. 6. Low values of C(5)occur if the total production of seed is low (i.e., in-adequate source density, fecundity, or both), yielding

Source limitation = 1 — C(s). (12)

(14)

Predicted seed rain and observed seedlings

"Establishment limitation," the stage between seeddispersal and establishment as a Ist-yr seedling (Fig.1), was assessed by comparing Ist-yr seedlings withseed rain at stand and local (1-m2) scales. The fractionof seed that produces Ist-yr seedlings was estimatedat the stand scale by comparing average annual seedrain estimated from the 20 traps with average densityof Ist-yr seedlings from ±e belt transects over 5 yr,

Establishment fraction

_ \_ -^ Ist-yr seedling densityy

5 ^Ti seed density^,

To test for establishment limitation at the 1-m2 scale,we compared predicted seed rain to observed Ist-yrseedling density along the belt transects. Parameterizedmodels were used together with the mapped tree dis-tributions to predict seed rain densities at each 1-m2

quadrat of the belt transects in each stand. The spatialscale of coherence between predicted seed rain andannual average Ist-yr seedling densities was assessedby cross-correlation. Significance levels included cor-rection for the autocorrelation within each series byadjusting degrees of freedom according to Clifford etal. (1989).


1000-,Acer

0.011000-1

o

•80>g

Io>IIDD.T3C3U0)

Stand SSS model

FIG. 2. Three estimates of the fecundity parameter £: (1) "within stands," the value fitted by the Summed Seed Shadowmodel, incorporating locations of seed traps relative to individual trees (solid bars); (2) the "stand average," obtained bydividing average seed rain of 20 traps by stand basal area (unshaded bars) (Eq. Ib); and (3) "among stands," obtained byregressing seed rain against basal area across all five stands (hatched bars) (Eq. la). The lower right panel indicates that thedifferent methods show close agreement. For taxa showing poorest agreement, the Summed Seed Shadow model fits appearto be overestimates. Standard errors are bootstrapped (SSS parameter estimates) or from regression.

RESULTSDensity of sources

The most fundamental limitation on recruitment isabsence of parent trees. Some taxa were abundantacross most or all sites (e.g., Acer rubrum, Carya,

Quercus prinus, Q. rubra), whereas others were con-fined to specific stand types (Acer saccharum, Betulaalleghaniensis, B. lenta, Fraxinus, Liriodendron, Pi-nus, Tilia, Table 1). Several taxa were present in moststands, but were nowhere abundant (Cornus, Nyssa,

222 JAMES S. CLARK ET AL.

TABLE 3. Summed seed shadow model parameter estimates, goodness-of-fit, and hypothesis tests.

Ecological MonographsVol. 68, No. 2

TaxonAcer

•Amelanchier

Betula

Carya

Cornus

FraxinusLiriodendron

Nyssa

Oxydendrum

PinusQuercus

RobiniaTilia

Tsuga

Stand<?t

4(1,2,3,4)

2(1,5)

3 (2, 3, 4)

3(1,2,3)

3(1,2,3)

1(5)3 (2, 3, 4)

3(1,3,4)

2(1,3)

1(1)4 (1, 2, 4, 5)

1(1)2 (2, 5)

2(1,4)

Distancea ± 1 SE (m)25.2 ± 2.39

16.9 ± 185

37.1 ± 2.87

.10.8 ± 2.06

3.65 ± 1.52

19.3 ± 5.8433.9 ± 2.56

6.02 ± 4.48

9.23 ± 2.86

15.1 ± 3.2711.8 ± 1.32

14.8 ± 1.3313.0 ± 2.95

19.7 ± 5.04

Fecundity!& ± 1 SE (cm-2-yr-')P, = 69.2 ± 6.82P3 = 37.7 ± 4.00p3 = 23.4 ± 2.58(c)P4 = 32.2 ± 2.84(c)P, = 0.231 ± 450P5 = 4.44 ± 522P2 = 448 ± 62.7(c)|33 = 1470 ± 141p4 = 10200 ± 1040p, = 0.657 ± 0.196P2 = 0.296 ± 0.179P3 = 1.02 ± 0.267P, = 7.68 ± 30.7P2 = 2.28 ± 2.73p3 = 8.87 ± 15.9P3 = 3.40 ± 0.847P2 = 49.8 ± 7.89(c)P3 = 147 ± 15.2(c)P4 = 1590 ± 254P, = 7.30 ± 4.87P3 = 9.12 ± 3.68P4 = 0.151 ± 0.101p, = 24.5 ± 6.26P3 = 0.975 ± 0.484Pi = 2.16 ± 0.558P, = 2.52 ± 0.383P2 = 1.31 ± 0.468P4 = 2.85 ± 0.488Ps = 5.84 ± 1.99p, = 9.57 * 0.454P2 = 22.3 ± 50.5P5 = 12.9 ± 7.57P, = 503 ± 170(c)p4 = 10.6 ± 2.24(c)

ClumpingQ ± 1 SE

10.8 ± 1.95

0.165 ± 3500

5.83 ± 1.22

0.670 ± 1.16

0.447 ±1.15

0.632 ± 0.7575.76 ±1.21

0.528 ±1.12

0.472 ± 0.254

2.01 ± 88.11.30 ± 0.282

65.6 ± 20.60.485 ± 0.374

>100

Explainedvariance§0.714***

0.125

0.681***

0.529***

0.566***

0.379**0.707***

0.554***

0.593***

0.364**0.270***

00.114

0.523***

Note: Maximum likelihood estimates for parameters a. and p include bootstrapped standard errors. BC0 confidence intervalsare included in Fig. 4. Likelihood-ratio statistics (D) and associated r2 values include probability esumates for null modelsdescribed in text.

* P £ 0.05, ** P < 0.01, *** P & 0.001.t The number of stands having sufficient seeds and trees to obtain fits followed by the list of stands in parentheses.$ Estimates with the designation (c) indicate correlations between a and pt exceed 0.60, where k is stand designation.§ The r2 for agreement between data and model (Eq. 10).|| Deviance for the hypothesis test that seed dispersal is nonlocal (Eq. 9) with df = q. Probabilities are from permutation

tests, but x2 probabilities did not differ at the levels in footnotes *, **, or ***.H Deviance for the hypothesis test that dispersion parameters a.k are the same across stands (Eq. 8) with df = q — 1. Blank

cells are for q = 1 and, thus, no degrees of freedom.

Robinia). Unless seed production and dispersal aregreat, recruitment limitation is likely for many taxasimply on the basis of parent tree abundance.

Seed rain at the stand scale

Spatial variability in seed rain affected our ability toestimate fecundity differences among stands. Regres-sions of seed rain against basal areas of the five stands(Eq. la) provide (3 (seeds per basal area) estimatesbased on varying abundances across the landscape("among stands" in Fig. 2). Significant 3 values wereobtained for Acer, Betula, Carya, Cornus, Fraxinus,Liriodendron, Nyssa, Oxydendrum, Pinus, Quercus,Tilia, and Tsuga (Fig. 2). Best fits (r2 > 0.5) wereobtained for taxa having adults distributed rather even-ly across plots, intermediate to large dispersal distanc-

es, and low levels of clumping, including Acer, Betula,Liriodendron, and Tsuga. These factors insure thatseeds are evenly spread at the stand scale and, thus,reflect average tree abundance. Seed rain of taxa withlow dispersal distances, clumped distributions, or high-ly uneven distributions of adults, including Amelan-chier, Carya, Comus, Nyssa, Oxydendrum, Quercus,Robinia, and Tilia, was not well-predicted from basalarea at the stand scale (r2 values <0.25). Intermediatelevels of explained variance were obtained for Fraxinusand Pinus, both of which were abundant in singlestands and had intermediate dispersal distances.

Fecundity parameters |3 estimated from within in-dividual plots varied among stands for some taxa (Fig.2). Betula consistently had the highest fecundities, withlowest values obtained in stand 5, the only stand having


TABLE 3. Extended.

H0: nonlocaldispersal!!

D P

70.4 <0.001

HO: consistentdispersalf

D P

9.55 0.023

3.49

68.4

31.0

79.8

7.1640.7

41.6

11.7

23.069.6

4.3422.3

4.72

0.077

<0.001

<0.001

<0.001

0.016<0.001

0.002

0.003

<0.001<0.001

0.11<0.001

0.053

0.0464 0.829

27.7 0

0.822

3.25

17.5

2.19

3.47

5.47

2.74

0.190

0.663

0.197

0.000157

0.334

0.0626

0.140

0.0981

0.663

substantial B. alleghaniensis (Table 1). Fecundities ofAcer and Liriodendron were consistently high. Acerfecundity was high and especially uniform acrossstands 1-4. Seed came from three species. Acer rubrumaccounted for most seeds in stands 1—4. The few A.rubrum trees in stand 5 were not reproductive. A. sac-charum is dominant at stand 5 (Table 1) and had sub-stantially lower fecundity than A. rubrum. Acer pen-sylvanicum likely contributed some seed in stands 4and 5. Carya and Quercus showed consistently lowvalues across all stands, despite differences in speciescomposition for Quercus. Other taxa with low fecun-dity parameters were Fraxinus americana and Pinusrigida.

Amelanchier, Nyssa, Oxydendrum, Tilia, and Tsugahad variable fecundity estimates. The anomalouslyhigh fecundity for Tsuga in stand 1 is explained by thefact that much seed probably derived from trees outsidethe sample plot. Stand I had only two small Tsugatrees. Variable fecundity estimates of Amelanchier,Nyssa, and Oxydendrum are probably due to 1itnitp.fldispersal.

Several taxa had seed rain on stands where trees wereabsent. Some Pinus seed in the higher elevation stands(i.e., other than stand 1) likely derived from nearby

watersheds dominated by Pinus strobus. Likewise, Tsu-ga seed was encountered in stand 5. Seed of severaltree taxa was rare or absent, including Amelanchierarborea, Robinia pseudo-acacia (Fig. 2), and Sassafrasalbidum (no seed encountered).

Local seed rain

The summed seed shadow (SSS) model providedconsistently good fits for all but a few taxa havingespecially rare seed, few adults, or both. Likelihoodratio tests led to the rejection of the null hypothesis ofuniform dispersal for all but three taxa, two that wererare in the data set (Amelanchier. P = 0.077, Robinia:P = 0.11) and one with the most broadly dispersedseed (Tsuga: P = 0.053). The r2 values from Table 3give a rough guide to the proportion of variance ex-plained by the model. These were >0.35 and highlysignificant for all but Amelanchier, Robinia, and Tilia.Thus, the model leaves much unexplained in the patternof Tilia seed rain, yet it provides a significantly betterexplanation of the pattern than does uniform seed dis-tribution.

Taxa for which good fits were obtained have well-resolved parameter estimates. Standard errors arounddispersion parameters a are generally within 20% ofML estimates for those taxa having significant likeli-hood ratio tests (Table 3). Standard errors on fecundityparameters |3 are also.within this range for wind-dis-persed taxa having large dispersion parameters (a >15 m), with the exception of Tilia and Tsuga, for whichmodel fits are less good. Poorly dispersed types (a <10 m) are those dispersed by animals. These types havelow fecundities, large standard errors on fecundity pa-rameters, and high degrees of clumping (6 < 1). Modelfits for several wind-dispersed types (Acer in stands 3and 4; Betula in stand 2; Liriodendron in stands 2 and3; and Tsuga in stands 1 and 4) have correlations be-tween a and p that exceed 0.6. Tsuga is ill-fitted bythe model due to rare, well-dispersed seed that occurredsporadically in several stands lacking nearby trees. Al-though well-described by the model, overlapping seedshadows for Acer, Betula, and Liriodendron mean thatparameters tended to compensate in some stands (pa-rameter correlation in Table 3). Low taxonomic reso-lution may weaken fits for Quercus.

Parameter estimates are generally consistent amongstands and for different methods. There is variabilityamong stands in 3 estimates for the same species, butdifferences among species exceed variability withinspecies. An exception is Oxydendrum, which has largedifferences in P between stands 1 and 3; these differ-ences also apply to plot-average estimates (Fig. 2). pestimates fitted by the SSS model are in good agree-ment with those obtained from stand average seed rain(Fig. 2, lower right panel). SSS models tend to predicthigher (3 values than do stand averages for the wind-dispersed types, with highest dispersal parameters (a


a) Short to intermediate dispersal b) Long dispersal(a < 25 m) (a > 25 m)

30-,


20-

£ 10-1a.

J5 0-

JU

I 3-3 2-S•55 la:

01-,

_o

IO.SH

80-

^ 0.1-iS 0.01-§ 0.001o: 0.0001-i

0.00001

Fecundity parameterestimates ~

i i i i i

Dispersal parameterestimates

.0

I I I I

3 0 9o n

co o>oj co o in o10 to to CO O)CU CO 0ta o"<o

- ^ !in in

Plot increment (m)

FIG. 3. Effect of increasing sample plot area on bias in parameter estimates. Smallest plot area ("0 m") includes in theparameter estimation only those trees that occur within the central 20 X 40 m of each stand. Plot-increment labels arefollowed by geometric mean plot diameters in parentheses. Progressively larger plot areas (up to "total" with geometricmean diameter of 60 m) show the effect of adding trees that occupy increasing dimensions around this inner 20 X 40 marea. Box plots show median values (thick lines) for all taxa with low (a) and high (b) dispersal estimates, upper and lowerquartiles (75% box edges) and deciles (90% whiskers). Upper panels show the ratio of parameter estimates in reduced plotareas to the ML estimate obtained for the total plot The ratio of 1.0 (i.e., convergence) is indicated by a dashed line. Lowerpanels are correlations (Eq. 10) and correlation probabilities.

> 15 m) and lowest clumping (9 »1), for Acer, Betula,Liriodendron, and Tsuga (Fig. 2).

We failed to reject the null hypothesis of consistentdispersal estimates among stands (i.e., uniform a) forall but three taxa with the highest dispersal estimatesand tendency for parameter correlation: Acer, Betula,and Liriodendron (Table 3). In the case of Acer andLiriodendron, anomalous estimates come from standswith such high densities of trees that seed shadows ofindividual trees cannot be readily discriminated, aproblem most acute for seed that tends to be well-dispersed, but also evident for Quercus in stand 3. Ananomalously high estimate for Betula in stand 4 comes

from a single tree. Consistent estimates from remainingtaxa and straightforward interpretations for anomalousfits for these few well-dispersed taxa indicate that dis-persal is generally consistent from stand to stand.

By changing the area of mapped plots we found thatparameter estimates converged to stable values at plotdimensions smaller than those used in this study (Fig.3). Fecundity parameters are consistently overestimat-ed when sample plot areas are inadequate, because themodel assumes all seed is contributed by mapped trees.Dispersal parameters are also overestimated for un-dersized plots, because poor fits inevitably tend to con-verge on broad (nonlocal) dispersal; the model is un-


a) Parameter confidence intervals

£.

aT

%

IQ.

e

40-i

10-

H H-

f 1

-51T

t-1

1

"t

1

imt

*

1

+ * <I

V *)

ft

—

n Acer

A /tore/

V l

T <

It <

tefu/

Ja/yi

lOiTI

0.1

O Frax'nus

A Uriodendron

Q Oxydendrum

B Pinus

• Quercus

• Robinia

X TWa

^« Tsuga

100 1000 10000

Fecundity parameter (seeds/cm2 basal area)

b) Seed shadows200 n

Uriodendron05

AcerOxydendrum

Pinus, Fraxinus0 Ca/ya-

50 0Distance (m)

0 50

Animal-dispersed —

50

FIG. 4. (a) BCa 95% confidence intervals for fecundity parameter (3 and mean displacement of seed from the parent tree|x, derived from dispersal parameter a (Eq. 4). The fitted model is Eq. 7, having q estimates of fj and a species-specific aestimate, (b) Fitted seed shadows are for a 50 cm diameter tree. Note that animal-dispersed taxa (shaded symbols) have lowfecundity and dispersal estimates (a), which results in localized seed dispersal (b) (see log-scale insert).

able to identify the pattern of seed rain based OE treeswithin the map. Fortunately, biases in parameter esti-mates associated with undersized plots are not hidden;they are flagged by poor model fits. The biased param-eter estimates of small plot areas are attended by lowcorrelation between data and model and unacceptablyhigh P values (Fig. 3a, b). The stabilization of param-

eter estimates that is achieved with increasing plot areaoccurs as median correlations rise to >0.6 and medianP values fall to <0.001. Overcoming parameter biasrequires larger mapped plots for better dispersed seedtypes (Fig. 3b). Parameter estimates for short to inter-mediate dispersed types converged to stable valueswithin 10 m of the of the interior 20 X 40 m plot (Fig.


Comus stand 2 Nyssa stand 3


x + + x +

0. P)

X X Xs,

Oxydendrum stand 1 Pinus stand 1

Acer rubrum stand 1 LJriodendron stand 2

FIG. 5. Maps of trees, seed rain, and fitted seed shadows in mapped stands. Trees are indicated by ffi scaled to indicaterelative sizes of trees. Seed traps that received no seed are indicated by +. Seed traps receiving at least one seed over thesample interval are indicated by X within a box, the size of which is proportionally scaled to seed density. Contour intervalsindicate seed rain (m"2-yr~') predicted by the model for fitted parameters in Table 3. Taxa are arranged from poorly dispersed(upper left) to well dispersed (lower right).

3a). Plots this size have geometric mean diameters of50 m, well above the mean seed displacement distancesof taxa having a < 25 m. Well-dispersed types (Betula,Liriodendron, Tsuga), however, require at least 15 m(Fig. 3b), and these types are still not well-fitted bythe model in all stands.

Seed rain modeling revealed large interspecific dif-ferences in fecundities and dispersal distances (Fig. 4a)and, thus, in seed-shadow shapes (Fig. 4b). The most

obvious differences are among taxa having differentdispersal modes. High fecundity/well-dispersed taxa(Betula, Liriodendron, and Tsuga), contrast with lowfecundity/poorly-dispersed taxa (Amelanchier, Carya,Cornus, Nyssa, Quercus, and Robinia) that mostly relyon animal vectors for dispersal. Wind-dispersed taxawith intermediate fecundities (Acer, Fraxinus, Pinus,and Tilia) also have intermediate dispersal distances.The dehiscent capsules of Oxydendrum have restricted

May 1998 RECRUITMENT UMTTATION IN FORESTS

Carya stand 3 Quercus stand 5

227

Fraxinus stand 5 T7//8 stand 5

Betula stand 2 Tsuga stand 4

FIG 5. Continued.

dispersal, likely because they lack specialized dispersalstructures.

Comparisons of parameterized SSS models with ob-served seed rain (Fig. 5) demonstrate how nonunifonndistributions of trees and restricted dispersal limit seedarrival. Highly restricted dispersal for taxa havingmean displacement distance JJL, < 10 m (e.g., Cornus,Nyssa, Carya, and Quercus) leaves much of the groundsurface uncolonized by seed, despite abundant adulttrees. Thus, seed recovered from these typically ani-mal-dispersed taxa was largely restricted to below thecrown area. This restricted dispersal exaggerates dif-

ferences in seed rain among nearby traps. Although notanimal-dispersed, Oxydendrum capsules also remainclose to adult trees. Intermediate dispersal distanceswere observed for Pinus, Fraxinus, Tilia, and Acer(Fig. 5). High seed production of Acer rubrum in stand1 contributed to well-resolved patterns in seed rain.

Maps for Liriodendron, Tsuga, and Betula illustratepotential problems resolving individual seed shadowsfor well-dispersed taxa (Fig. 5). When seed is evenlydispersed over broad areas, the likelihood surface (Eq.2) flattens, and parameter resolution is difficult. Despitethese limitations, good fits were obtained for both Lir-


iodendron and Betula on plots where adults were nottoo dense (Table 3). Maps show that the ground surfacebecomes saturated with seed in these stands. AlthoughTsuga has relatively high fecundity, our stands con-tained only small individuals, and seed rain was lowand sporadic. We did not capture cones in our traps.

Additional sources of spatial variability in seed rainthat are weakly related or unrelated to distributions ofadults and dispersal distances cause clumping, de-scribed by parameter 9. Clumping is greatest for animaldispersed taxa (6 < 1) (Table 3). Once the variabilityin seed rain contributed by tree location and dispersaldistance is taken into account, the residual variation inwell-dispersed types is indistinguishable from a Pois-son process (6 » 1). There remains, however, muchunexplained variation in animal-dispersed seed distri-butions.

Sources of variability in colonization

The sources of variation that determine the proba-bility of leaving sites unoccupied included densitiesand fecundities of trees (A and B in Fig. 1), arrange-ment of trees in stands (A in Fig. 1), dispersal distances(summarized by a), and clumping (summarized by 6),i.e., the dispersion of seed about the mean seed shadow(C in Fig. 1). In the absence of variability conferredby dispersal, differences among stands in colonizationindices C(S) (the odds of at least some seed arrivalgiven that the mean seed arrival s is everywhere thesame) would depend only on densities and fecunditiesof adults. C(s) thus serves as a baseline against whichwe evaluate colonization limitation that results fromrestricted dispersal. The dispersal limitation index (Eq.14) contrasts the odds of seed arrival given the truearrangement of trees and estimated seed shadows C(Eq. 13) against that predicted for uniform seed arrivalC(5). This ratio is near unity if seeds blanket much ofthe ground surface (neither source limitation nor dis-persal limitation) or if seeds are well-dispersed but ev-erywhere rare (source limitation only).

The effect of dispersal on colonization in our standsis illustrated with two distributions. The contributionof the mean seed shadow (the contours in Fig. 5) isextracted in Fig. 6 to show how the spread about thismean seed shadow controls C. The seed shadows forAcer, Cornus, and Tsuga are each the means of (neg-ative binomial) distributions § that decrease with dis-tance (right-hand side of Fig. 6). In the absence of anyspread about the mean, the distribution of seed arrivalsacross the stand would be g(§) (thick line on left-handside of Fig. 6). The spread about S in Fig. 6 contributesvariance to seed arrivals, described by a probabilitydistribution of seeds:

(15)

where p(s \ S, §) is a negative binomial distribution de-scribing the conditional probability of s seeds given

expectation £ and clumping 9. Note that C = 1 — p(0).Thus, in the case of Acer (Figs. 5, 6a, all 1-m2 patchesin stand 1 are predicted to receive, on average, >1seed-nr2-yr-' (distribution g(s)), yet the additionalvariability about mean seed shadows (Fig. 6a) meanssubstantial probability for seed densities lower than thisvalue (p(s)). Two other examples in Fig. 6 include con-trasting dispersal types Cornus (Fig. 6b) and Tsuga(Fig. 6c). Poor dispersal for Cornus means that most1-m2 patches receive, on average, no seed, and highclumping serves to further reduce colonization (i.e., itincreases p(0)). Tsuga is relatively rare in stand 4, yetso well-dispersed, that all patches are expected to re-ceive two to three seeds each year (g(£) in Fig. 6c).Despite minimal clumping, however (9 »• 1 in Table3), the spread about the mean seed shadow is stillenough to yield measurable probability of no seed ar-rival p(0).

Dispersal and source limitations (Fig. 7) are corre-lated with dispersal distance and fecundity, and theydepend on spatial pattern of trees. The odds of 1-m2

patches receiving at least some seed are high for fecundand well-dispersed Acer, Betula, Liriodendron, andTsuga in all stands where trees are present, and, thus,colonization is as successful as it would be with un-limited dispersal (dispersal limitation near zero in Fig.7). Tsuga is the only well-dispersed taxon having con-sistently low colonization indices (Fig. 7), due to fewadults. Colonization indices are high for some poorlydispersed taxa Quercus, Nyssa, and Oxydendrum instands where parent trees were abundant. Restricteddispersal especially limits poorly dispersed and lessabundant Amelanchier, Carya, Cornus, and Robinia(Fig. 7). Restricted and clumped dispersal explain lowCarya and Comus indices, while source limitation(rather than restricted dispersal) is the primary causefor low colonization indices in other taxa in particularstands, including Nyssa, Quercus, Tilia, and well-dis-persed Tsuga.

Establishment relative to other limitations at thestand scale

Over the five years of seedling censuses, total seed-lings and, especially, newly emerged seedlings wererare. Ist-yr seedlings were sufficiently rare that wewere able to estimate establishment fractions (Ist-yrseedlings divided by seed rain) for a limited subset ofspecies present in the overstory. Establishment frac-tions were highest for Acer, ranging from 0.019 (stand4) to 0.87 in stand 2 (Fig. 8a). Seedlings in stand 5were mostly Acer pensylvanicum, and they were abun-dant in only one of the five sample years.

Limitations on Acer rubrum recruitment vary acrossthe five stands. Seedling recruitment appears limitedby source density (basal area) on low elevation stands1 and 2; seed rain is proportional to basal area (Fig.2), implying that increased basal area would result inincreased seed density. Establishment does not limit


Distributions of seed rain densities

a) Acer, stand 1

r\—C (chances of no seed)

1-

^0.8-

|0.6-|"0.4-

b) Comus, stand 2

c) Tsuga, stand 41-

0.8-

0.6-0.4-

°-2:j

||— t>g(s) (effect of|| mean seed shadow)

J| & p(s) (clumping spreads%£ the distribution)

0 20Seed density (seeds -m"2- yr"1)

Seed shadows(50 cm diameter tree) and 90 percentiles

100-i

fiOJ

100-

p(s|s,l) (negativebinomial distribution)

Distance (m)

FIG. 6. Distributions of seed arrival rates for selected taxa mapped in Fig. 5. The effect of the mean seed shadow andof clumping (right side) on the distribution of seed arrivals is demonstrated by the comparison of distributions at the left.The distributions are described by Eq. 15.

D Acer

A Amelanchier

+ Betula

V Carya

tt Comus

O Fraxinus

A LJriodendron

+ Nyssa

O Oxydendrum

H Pinus

• Ouercus

• Robinia

X Tilia

• Tsuga

0.2 0.4 0.6 0.8 1Source limitation

FIG. 7. Dispersal vs. source limitations on recruitment derived from colonization indices. Source limitation (1 —where C(S) is given by Eq. 11, is the probability of seed arrival if seed were evenly spread across stands, without the constraintof limited dispersal. Dispersal limitation is the degree to which probability of seed arrival is reduced by the limited dispersaland clumping of seed (Eq. 14). Contours are colonization indices C (Eq. 13), the fraction of patches expected to receivesome seed.


a) Acer

20-CO

B. Source strengthA. Source density , _, , 2.. , > 20-i3 (seeds/cnr basal area) ^

(basal area) 20-i r~| to

b) Betula

i i i

Seed density500-,

to

inn ln1 1 1 1 1

0-.-4HU.V I l I

C. Dispersal(colonization index),j

1000-,

CM

g 0-

Seedlingdensity

0.05-,D. Establishment fraction «f

(seedlings/seed)uououy ej_ (seedling

J..JT 0]JC.-.i i i i i u i i ^ i n

CM

c) LJriodendron d) Quercus

i i i i > i1 2 3 4 5

StandFIG. 8. The four limitations on recruitment summarized in Fig. 1 for four taxa having at least some seedlings across the

five stands. Solid bars indicate densities of individuals at three stages (adults, seeds, and seedlings). Unshaded bars indicatethree limitations that determine transition rates from one stage to the next.

recruitment in the cove hardwoods stand 2, where>80% of seeds become Ist-yr seedlings, but establish-ment is a strong limitation on all other stands, es-pecially at higher elevations (stands 3, 4, and 5). Acersaccharum has a source of seed only at stand 5. Lim-itations in seed production and in establishment bothappear important here.

Betula is limited in all stands by establishment suc-cess (Fig. 8b). High fecundity and long dispersal blan-ket all stands with seed. Even stand 1, which includesonly three small trees, has higher Betula seed rain thanof most other taxa. First-year seedlings are absent from

all stands but 4, and there establishment fractions areless than one seedling in 1000 seeds.

Liriodendron limitation varies substantially amongstands. Source trees and establishment are importantlimitations in xeric (stand 1) and upper elevation(stands 4 and 5) stands (Fig. 8c). Both source densityand establishment fraction are high in the cove hard-wood stand 2, indicating conditions amenable for Lir-iodendron seedlings and adults. The low colonizationindex in stand 1 results from lack of source trees, ratherthan short dispersal.

Establishment and dispersal are principal limitations


on Quercus recruitment Adult trees are everywhereabundant, insuring moderate seed rain across all stands.Poor dispersal of that seed, however, means that muchof the stand area receives little or no seed. Establish-ment fraction is highest in stand 4 (0.0054) and nearlynonexistent elsewhere. The 5-yr average fraction usedhere yields low fecundity estimates that belie high seedproduction in most years (years one and five of thisanalysis).

Despite lack of seedlings, colonization indices forother taxa permit interpretation of how density ofsource trees, dispersal, and clumping contribute to re-cruitment limitation. Low colonization indices forAmelanchier, Carya, Comus, Nyssa, Oxydendrum, andRobinia suggest that even if suitable microsites wereavailable, these taxa would fail to colonize due to lackof seed.

Establishment limitation at the local scale

Analysis of the relationship between seed rain andseedling recruitment at the local scale was hindered bythe low density of seedlings found at our site. OnlyAcer seedlings were sufficiently abundant to permitcomparisons between predicted seed rain and Ist-yrseedling density at the 1-m2 scale. For this genus, noconsistent relationship is apparent between seed rainand seedlings, with cross correlations between seedsand seedlings at lags <10 m being weak or absent inall stands (Fig. 9). With the high fecundity and inter-mediate dispersal of Acer, few safe sites would likelybe left uncolonized (Fig. 7). If Ist-yr seedling patternmerely reflects the distribution of safe sites, little re-lationship between seed rain and Ist-yr seedling densitywould be expected.

Local regression (Cleveland and Devlin 1988) be-tween predicted seed rain and Ist-yr seedlings takenacross all stands suggests a weak positive associationbetween seeds and seedlings at low seed density (Fig.10). This suggests that colonization of safe sites isproportional to seed density when the flux of seeds islow, but that density-dependent seed predation or seed-ling mortality may limit Ist-yr recruitment when seeddensity is high and/or seeds and seedlings are close toconspecific adults.

DISCUSSION

In contrast with the growing tendency to treat treepopulation dynamics as though seeds are always avail-able, we found that all tree populations in our studyarea face substantial recruitment limitation. Thestage(s) at which limitation occurs varies considerably.We found that limitations from source density, sourcestrength, dispersal, and establishment vary among spe-cies, within species across environmental gradients,and across different scales of measurement. Few of thetree populations in our study area are capable of sat-urating the forest floor with seed. Only a small fractionof that seed germinates and survives to be censused in

10CH

c\r

coen

m0)CO

ro

TJCD

w

0 10 20 30 40 50 60Distance (m)

FIG. 9. The relationship between Acer seed rain predictedby the parameterized model and seedlings across the fourstands (smooth curve) compared with seedlings in 1-m2 con-tiguous census plots (bars).

the first year. Distributions of seedlings in our studysite provided little indication of which stages were re-sponsible for poor recruitment. Before considering themagnitudes of these limitations, we first discuss theadvantages and limitations of this method for identi-fying stages that limit reproduction in tree populations.

How to fit seed shadows in closed stands

Tracking dispersal of falling seeds as the basis forinterpreting how seed arrival controls recruitment in-volves several obstacles. The statistical estimation offecundities and dispersal from trees having overlappingcrowns is complicated by high temporal and spatial


20-

10-

COI•aa>

1-

t 0.2-

0 Stand 1

O Stand 2

A Stand 3

* Stand 4

T Stands

10 100 200

Predicted seed rain (seeds • m'2- yr"1}

FIG. 10. Locally weighted (LOWESS) regression for combined data in Fig. 9.

variability contributed by factors other than dispersal.Our results provide some guidance for handling statis-tical challenges pertaining to sampling and analysis.Lack of conventional models for parameter estimationand hypothesis testing led us to introduce evaluationprocedures for bias in estimates, comparison with al-ternative models, and parameter consistency thatshould simplify recruitment analysis in future studies.

The data: how much and -where to sample?—Equipped with little more than vague notions of seedproduction and dispersal distances and with knowledgethat seed shadows must strongly overlap, the first prob-lem we encountered concerned sampling, i.e., numbersof seed traps and how to distribute them within andamong stands. Intervals of 5 m between traps distrib-uted over areas of 103 m2 worked reasonably well, giv-ing good parameter estimates for both poor- and well-dispersed taxa. Mapped plot areas of trees with meandiameters twice as large as the mean seed-displacementdistances may be a rule-of-thumb minimal plot area(Fig. 3). This limit is approached by our best dispersedtaxa; they are the only taxa tending toward parametercorrelation and inconsistent dispersal estimates (Table3). The inclusion of multiple stands proved invaluablefor our model parameterization, for it afforded differentdensities and arrangements of trees. Multiple standswere the basis for both of the hypothesis tests.

What sort of a spatial process is seed dispersal?—Inability of a Poisson model to descibe the clumpedpattern of seed arrival led us to implement (and, now,recommend) a negative binomial (Eq. 2). A model in-cluding the many sources of variation responsible forclumping would require a far greater number of pa-rameters than could be fitted with realistic data sets.We simply acknowledged that many sources are prob-ably operative, which led us to the negative binomial.We obtained much lower error on fecundity and dis-persal parameters using the negative binomial (Fig. 4)than with alternative distributions. The model also per-mitted comparison of clumping differences among taxa

(Table 3). For animal dispersed taxa clumping has alarge influence on colonization rates.

How to sort out the overlapping crowns?—The so-lution to the overlapping crown problem, indepen-dently derived by Ribbens et al. (1994), is to add themtogether (Eq. 6). By estimating contributions of indi-vidual trees to any location on the forest floor, the meth-od is, thus far, the sole broadly applicable approach foranalyzing the link between recruitment and the popu-lation of adults responsible for producing those re-cruits. Dispersion patterns of seeds or seedlings aroundisolated adults provide valuable insights (Sharpe andFields 1982, Johnson 1988, Guevara and Laborde1993), but dispersal distances in open fields differ fromthose in closed canopies (Willson 1993), and the ap-proach cannot be applied where seed shadows of con-specific trees overlap. Nevertheless, the conceptualsimplicity of the model and small number of parametersbelie some statistical challenges.

Model evaluation: defining some conventions.—Be-cause conventional methods provide little guide tomodel evaluation, our approach was to stay close toconvention by way of analogy. The r2 between modeland data (Table 3) is a rough guide to explained vari-ation. Tests of hypotheses that local dispersal betterexplains pattern than does evenly distributed seed, andthat dispersion parameters are consistent among sites,provide a basis for model evaluation. These tests con-tributed to our conclusion that sample plots were nearthe minimum size needed to parameterize seed shadowsof the best dispersed taxa. For example, Betula showedexcellent agreement between model and data (r2 -0.68***), was clearly identified as local dispersal (P< 0.001), yet produced inconsistent dispersal param-eter estimates across sites (P = 0). Together, these re-sults suggest the fit might be improved with largermapped plots for Betula. Tilia was not well-describedby the model (r2 = 0.11, NS), yet the model was clearlya better description of seed rain than was the alternativethat seed rain is independent of trees (P < 0.001), and


50-.

s>to8"3.0)

10-

Befu/a\ _

>-7<

^Liriodendron

-TsugaAcer

Quercus

0.1 1Fall velocity (m/s)

10

FIG. 11. Mean displacement of wind-dispersed seed taxaand fall velocities measured in studies cited in text and (forCarya and Quercus) from J. HilleRisLambers (personal com-munication). A Gaussian plume model predicts that modaldispersal distance is roughly proportional to the inverse offall velocity (Okubo and Levin 1989).

dispersal estimates were consistent among stands (P =0.0981). These results suggest the fit for Tilia wouldbe improved with a larger data set, e.g., more trapsand/or longer collection period. In remaining cases, theagreement between indices (acceptable explained vari-ance, local dispersal, and consistent dispersal esti-mates) indicate that the model provides a good de-scription of seed shadows.

How good are the estimates?—Although parameterswere well-resolved by the model and generally con-sistent across stands (OL'S in Table 3) and scales O's inFig. 2), we find further support from evidence externalto our data sets. Our dispersion estimates generallyagree with measured fall velocities from other studies,and they match the prediction of Gaussian plume mod-els that modal distance is roughly proportional to theinverse of fall velocity (Fig. 11). Rolling samaras ofFraxinus have higher fall velocities than nonrollingAcer (Green 1980), in agreement with the relationshipwe found between a. values. Heavy Tilia clusters at-tached to large bracts have higher fall velocities thanAcer (Matlack 1987), consistent with estimated low otvalues for Tilia. High dispersal for Betula agrees withits low measured fall velocities. Our low-dispersal es-timates for animal-dispersal taxa (Fig. 4) are consistentwith lack of specialized structures for wind dispersal.The high-dispersal estimates we obtained for Lirio-dendron contrast with relatively rapid descent for theserolling samaras (Green 1980). Liriodendron trees tend-ed to be taller than other species of similar diameter.Dispersal distance is expected to increase with releaseheight (Okubo and Levin 1989, Willson 1993). Becausemodels like ours consider only diameter, and not height,long dispersal for Liriodendron might reflect allometry.

limits recruitment?

Summed seed shadow models demonstrated sub-stantial differences among species within differentstands in limitations due to source density (parent treeabundance), source strength (fecundity), dispersal, andestablishment limitation.

Source density: number, sizes, and dispersion ofadults.—Absence of parent trees was a limitation onseed arrival for the many taxa that are rare in our stands(Table 1). The importance of a nearby source obviouslydepends on dispersal distance (Figs. 4, 5). Becauseadults were often clumped within stands, source densitylimited seed availability not only for poorly dispersedtaxa, but also for some taxa with well-developed struc-tures for wind dispersal. Low adult density, clumpingof adults, or both, meant that seed did not reach muchof the ground surface for Carya, Cornus, Fraxinus,Liriodendron, Nyssa, Quercus, Pinus, Tilia, and Tsugain some or all stands (Figs. 5, 7); only Acer and Betulaseed consistently blanketed the forest floor in sufficientdensity to insure high colonization indices (Fig. 7). Theparameterized model demonstrates that the abundanceand contagion of adults combined with local dispersalis the cause of this limitation.

Source strength: rates of seed production.—Ordersof magnitude differences among taxa in their fecund-ities tended to compound limitations produced by lim-ited dispersal. Correlation between fecundity and dis-persal (Fig. 4) means that taxa producing few seedsdispersed seed short distances. Little tendency for pos-itive parameter correlations (Table 3) means that suchcorrelation is not by chance. And the agreement be-tween fecundity estimates at two scales (Fig. 2) sug-gests that the correlation is not spurious but resultsfrom a tendency for seed number to trade off with seedsize (Smith and Fretwell 1974, Salisbury 1976, Geritz1995). This is a likely explanation for the differencesbetween animal- and wind-dispersed taxa. Althoughempirical evidence for this relationship within thesetwo dispersal modes is not strong (Greene and Johnson1986, Primack 1987), there is a clear tendency for thewind-dispersed taxa with low dispersal to also havelower seed production in our study (Fig. 4). We didnot estimate seed viability, but low viabilities of manytaxa would reduce fecundity estimates. These can beless than 5% for Acer rubrum and Tsuga canadensisin New Hampshire (Graber and Leak 1992) and Tiliaamericana in Wisconsin (Godman and Mattson 1976)and range from 5-70% for Acer pensylvanicum, A. sac-charum, and Betula alleghaniensis (Houle and Payette1990, Graber and Leak 1992, Houle 1992b). Animal-dispersed seed can also have low germination rates(Smith 1975).

Dispersal.—Dispersal limitation was taxon-specificand explained by seed morphologies that increase dragand (for spinning samaras) generate lift (Green 1980,Augspurger 1986, Matlack 1987) or that attract animal


vectors (Howe and Smallwood 1982, Willson et al.1990, Martinez-Ramos and Soto-Castro 1993). Our re-sults imply that recruitment of Carya, Comus, Nyssa,and Quercus is limited by dispersal throughout ourstudy area. High frequency of adult trees did not resultin seed arrival to much of the forest floor (Fig. 8d).Animal vectors are the sole means for moving seedoutside the perimeters of tree crowns for some taxa.Like Masaki et al. (1994), we found the bulk of seeddirectly below crowns and scattered arrivals elsewhere.

Establishment.—Establishment limitation is amongthe strongest filters on recruitment for many taxa ondifferent parts of the Coweeta watershed. Few taxa hadIst-yr seedlings achieving densities as high as 5 seed-lings/m2 (Fig. 8). The only one that did so consistently(Acer rubrurri) (Fig. 8a) had seedlings poorly correlatedwith seed shadows (Fig. 9b,c). Environmental gradientsappear to have governed establishment limitations atseveral scales. Fine-scale variability within sampleplots appears responsible for altering seedling distri-butions after seed arrival (Fig. 9). This difference be-tween seed rain and seedling distributions is expectedif germination (for Ist-yr seedlings) or seedling sur-vival (for older seedlings) depends on suitable micro-sites that are poorly correlated with the distribution ofparent trees (e.g., Nakashizuka 1989, Houle and Pay-ette 1990, Houle 1992a, Shibata and Nakashizuka1995). Even for late-successional Acer saccharum andBetula alleghaniensis, our germination percentageswere far lower than viabilities estimated in New Hamp-shire (Graber and Leak 1992). Although we only con-sidered here Ist-yr seedlings, survival rates of theseseedlings were low for a combination of reasons nowunder investigation.

Implications for forest communities

Our analysis supports the argument that conventionalassumptions concerning recruitment limitation (or lackthereof) in forests are overly simplistic (Clark 1993,Pacala and Hurtt 1993, Schupp 1993). Factors con-trolling seed arrival, including distribution and abun-dances of adults, fecundities, and dispersal distances,all vary substantially among species. While previousstudies demonstrate large species-specific differencesfor primarily animal-dispersed taxa in tropical forests,we show this also to be the case in temperate forestscontaining mostly wind-dispersed taxa having overlap-ping crowns. The relatively high densities of canopyindividuals in relatively low-diversity forests (com-pared to the tropics) does not necessarily mean thatseed reaches much of the soil surface. Establishmentlimitation varied considerably among species, and therelative importance of all limitations varied across en-vironmental gradients. These differences mean that thelimitations imposed by the recruitment process are like-ly to be an important factor affecting diversity in for-ests, patterns of species composition within stands, anddistributions of species across environmental gradients.

ACKNOWLEDGMENTSWe thank Merlise Clyde and David Higdon for statistical

advise and Bob Wilber for assistance with seedling identifi-cations. Field assistance and comments on the manuscriptwere provided by Brian Beckage, Phil Camill, Charlie Can-ham, Brenda Cleveland, Bruce Raines, Janneke HilleRis-Lambers, Pete Wyckoff, and two anonymous reviewers. Thisresearch was supported by NSF grant BSR-9444146.

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