848
Ecology, 86(4), 2005, pp. 848?860
q 2005 by the Ecological Society of America
ANNUAL AND SPATIAL VARIATION IN SEEDFALL AND SEEDLING
RECRUITMENT IN A NEOTROPICAL FOREST
S. JOSEPH WRIGHT,1,3 HELENE C. MULLER-LANDAU,2,4 OSVALDO CALDERO? N1 AND ANDRE? S HERNANDE? Z1
1Smithsonian Tropical Research Institute, Apartado 2072, Balboa, Anco?n, Republic of Panama
2National Center for Ecological Analysis and Synthesis, Santa Barbara, California 93101-5504 USA
Abstract. An economy of scale may lead to selection to increase interannual variation
in seed production when the per seed probability of seedling establishment increases with
seed production. Variable annual seedfall will, however, reduce this probability when post-
dispersal seed fate is negatively density dependent on the local density of seeds, and seed
dispersal and density dependence act identically across years. Intuitively, more variable
annual seedfall causes the representative seed to experience a greater density of conspecific
seeds and suffer greater density-dependent effects. This handicap must be overcome for
the per seed probability of recruitment to be greater in years with greater seed production.
We quantified spatial and annual variation in seedfall and seedling recruitment, evaluated
density dependence and economies of scale during the seed-to-seedling transition, and
investigated the synergistic consequences of density dependence and variable annual seed-
fall for seedling recruitment on Barro Colorado Island (BCI), Panama. Weekly censuses of
200 0.5-m2 seed traps documented seedfall for 15 years and 108 plant species. Annual
censuses of 600 1-m2 seedling plots documented recruitment for nine years and 32 species.
The density of seedling recruits tended to increase with the density of seeds; however, the
per seed probability of recruitment invariably decreased with seedfall density. Negative
density dependence characterized the seed-to-seedling transition. Observed levels of spatial
and interannual variation in seedfall density would reduce long-term recruitment by up to
28% if negatively density-dependent survival acted identically across years; however, the
strength of negative density dependence varied significantly among years for 12 of 32
species. Negative density dependence occurred in all years for these species but was sig-
nificantly weaker during the one or two years of greatest seedfall than during the remaining
years of lower seedfall. The per seed probability of recruitment increased significantly with
annual seedfall for eight of these species. These eight species realized postdispersal econ-
omies of scale despite the reduction in long-term recruitment expected from the synergism
between variable annual seed production and negatively density-dependent seed fate.
Key words: Barro Colorado Island; density dependence; lianas; masting; Panama; pest satiation;
seedling recruitment; seed production; tropical trees.
INTRODUCTION
Population-level seed production varies widely
among years in many plant species and is relatively
constant in many others (Kelly and Sork 2002). This
interannual variation has important implications for
population, community, and ecosystem dynamics; for
example, it can drive large population fluctuations of
seed and fruit consumers and species with which they
interact (Jones 1998, Wright et al. 1999). Current un-
derstanding of the causes of observed levels of inter-
annual variation centers on three classes of hypotheses
(Kelly 1994). Seed production may track or match var-
iation in a limiting resource (the resource-matching hy-
Manuscript received 10 November 2003; revised 29 July
2004; accepted 9 August 2004; final version received 17 Septem-
ber 2004. Corresponding Editor S. Lavorel.
3 E-mail: wrightj@si.edu
4 Present address: Department of Ecology, Evolution and
Behavior, University of Minnesota, St. Paul, Minnesota
55108 USA.
pothesis). Alternatively, natural selection may act to
increase or decrease interannual variation. Natural se-
lection may favor variable seed production when large
seed crops are timed to anticipate future environmental
conditions that favor reproductive success (the resource
prediction hypothesis), or when large seed crops them-
selves cause disproportionately large increases in re-
productive success (the economy of scale hypothesis).
In either case, enhanced recruitment following large
reproductive efforts must offset opportunities for re-
cruitment lost in years when the reproductive effort is
curtailed, in order for natural selection to favor variable
seed production or to increase interannual variation
(Waller 1979).
Much attention has focused on the economy of scale
hypothesis (Silvertown 1980, Herrera et al. 1998, Kelly
and Sork 2002). Possible mechanisms that might lead
to an economy of scale include the facilitation of wind
pollination, the attraction of animal mutualists leading
to increased pollination or seed dispersal, and the sa-
April 2005 849SEEDFALL AND SEEDLING RECRUITMENT
TABLE 1. Studies of interannual variation in seed production and predation.
Predation timing/
plant part
Principal
predator
Economy
of scale? Source
Predispersal predation
Developing seed insect yes Crawley and Long (1995)
insect yes DeSteven 1982 (1983)
insect yes Gardner (1977)
insect yes? Kelly and Sullivan (1996)
insect yes McQuilkin and Musbach (1977)
insect yes Nilsson and Wa?stljung (1987)
insect yes Shibata et al. (1998)
insect yes Shibata et al. (2002)
insect yes Spere (1997)
rodent opposite DeSteven (1982)
Postdispersal predation
Dispersed seed small mammals opposite Gardner (1977)
vertebrates yes Nilsson and Wa?stljung (1987)
rodent null Schupp (1990)
rodent null Shibata et al. (2002)
rodent yes Wolff (1996)
Seedling recruitment rabbit yes Crawley and Long (1995)
Saplings rodent yes Jensen (1985)
none identified null Hett (1971)
Notes: Economies of scale, in which larger seed crops experience lower levels of predation, were found in all studies
where the principal predator was an insect that attacks developing seeds, and in just four of nine studies where the principal
predator was a vertebrate or attacked after seed dispersal. Each study compared predation for at least two years with different
levels of seed production. The original author identified the principal predator.
? ??Yes?? and ??opposite?? indicate that predation was significantly lower and higher in years with greater seedfall, respec-
tively. ??Null?? indicates that the null hypothesis of no difference in predation with seedfall was accepted.
? Predation declined with the ratio of floret production for the present to the previous year.
tiation of animal pests leading to increased survival of
flowers, seeds, or seedlings following large reproduc-
tive efforts (Kelly 1994). Of course, if large reproduc-
tive efforts have the opposite effect and satiate mutu-
alists or attract disproportionate numbers of pests, then
selection may act to favor constant seed production or
to minimize interannual variation.
These considerations suggest that interannual vari-
ation in seed production should vary geographically.
Kelly and Sork (2002) reasoned that seed production
should be relatively constant among years in the tropics
because (1) low climate variability minimizes resource
variation, (2) high tropical productivity minimizes the
time required to recover resources after large seed
crops, (3) high plant species diversity makes it difficult
for any one species to satiate generalist seed predators,
and (4) most plant species are pollinated and have their
seeds dispersed by animals, whose numbers and ser-
vices would be adversely affected if host reproductive
effort was highly variable. Interannual variation has
rarely been quantified in the tropics, and Kelly and Sork
(2002) were unable to evaluate their hypothesis con-
vincingly because their exhaustive review of the lit-
erature, which documented patterns for 579 plant pop-
ulations, included just 10 tropical populations. Even
fewer studies have evaluated resource matching, re-
source prediction, or economy of scale hypotheses, or
otherwise investigated factors that might influence in-
terannual variation in the tropics.
Of those studies at any latitude that have tested econ-
omies of scale, most have focused on predispersal pro-
cesses such as pollination and predispersal seed pre-
dation (Table 1). Few studies have tested for postdis-
persal economies of scale by evaluating annual vari-
ation in seedling recruitment relative to annual
variation in seedfall, and those few studies indicate that
economies of scale are less likely after seeds disperse
(Table 1; Fisher Exact Test, P 5 0.029 for interaction
between predispersal insect predator vs. another pred-
ator and an economy of scale). There are at least two
reasons to expect this outcome. The first concerns dif-
ferences between pre- and postdispersal predators
(Nilsson 1985, Sork 1993). The most important pre-
dispersal seed predators tend to be relatively host-spe-
cific insects (Janzen 1980). Large host seed crops sa-
tiate these insects because, lacking alternative hosts,
insect numbers decline when host seed crops are small
and because larval development times limit reproduc-
tive recruitment before seed dispersal. In contrast, post-
dispersal predators include a mix of insects, pathogens,
and vertebrates. Pathogens and vertebrates are less like-
ly to be satiated because most pathogens are capable
of rapid reproductive responses, while most vertebrates
have relatively broad diets and are unlikely to decline
in numbers when one food source fails. Predispersal
predators tend to favor economies of scale, while post-
dispersal predators do not.
The second reason that economies of scale are un-
likely after seeds are dispersed concerns the effects of
850 S. JOSEPH WRIGHT ET AL. Ecology, Vol. 86, No. 4
interannual variation in seed production on the average
local densities of conspecifics experienced by dispersed
seeds. Postdispersal performance (survival or growth)
is often negatively density dependent or inversely re-
lated to the local density of conspecific seeds or seed-
lings (reviewed by Wright [2002] for tropical forest
plants). This raises the possibility that spatial and tem-
poral variation in seedfall density may interact. When
all else is equal, negative density dependence insures
that seed and seedling performance will be reduced in
years characterized by high seedfall density. This is
exactly the opposite of an economy of scale. More
generally, temporally variable seedfall will increase the
local density of conspecific seeds experienced by a rep-
resentative seed, and this will decrease negatively den-
sity-dependent seed performance (see Introduction:
Theory). This, in turn, sets the stage for selection to
act to minimize interannual variation unless negative
density dependence is alleviated or seed dispersal is
more effective when seed crops are large.
In this study, we document interannual variation in
seed production for 108 woody plant species from Bar-
ro Colorado Island (BCI), Panama, and evaluate the
hypothesis that annual seedfall is less variable on BCI
than at higher latitudes. We also document annual var-
iation in seedling recruitment for 32 of these species
using spatially explicit data. We use these data to quan-
tify annual and spatial variation in seedfall, to update
analyses of density dependence during the seed-to-
seedling transition (Harms et al. 2000), to investigate
how interannual variation in seedfall interacts with neg-
ative density dependence, and to test for economies of
scale in seedling recruitment.
Theory
Seedfall varies spatially because of variation in seed
production among parent trees, variation in seed dis-
persal with distance to parent trees, and further spatial
variation in seed dispersal due to microhabitat (directed
dispersal) and other factors (Nathan and Muller-Landau
2000). Seeds are thus clumped in space, rather than
being randomly or evenly distributed. This spatial var-
iation is important because seed survival and seedling
establishment are negatively dependent on local con-
specific seed density (Harms et al. 2000). As a result,
spatial variation in seedfall decreases mean recruitment
success per seed in the population as a whole because
it increases the mean local density of conspecific seeds
experienced by a seed. Similarly, temporal variation in
seedfall also increases the perceived local density of
conspecific seeds of the same cohort, and thus also
decreases recruitment per seed.
We can analytically illustrate how local density de-
pendence interacts with spatial and temporal variation
in seedfall. Consider a population with total seed pro-
duction F, whose seeds land in location x with prob-
ability p(x). Then the expected seed density S(x) at
location x is simply as follows:
S(x) 5 Fp(x).
Assume further that seed survival to recruitment is a
power-law function of local expected seed density.
Thus, the expected density of recruits, R(x), at location
x is
b b bR(x) 5 a[S(x)] 5 aF [p(x)]
where 0 , a , 1 and b , 1, so that survival is neg-
atively density dependent (as shown in Harms et al.
2000 and in the analyses below). We can then obtain
the total number of surviving seedlings that year, Rtotal,
by integrating over the total area:
b bR 5 R(x) dx 5 F a [ p(x)] dx.total E E
Note that the total number of recruits scales as Fb times
a constant that depends on the parameters of dispersal
and density dependence, which we will henceforth de-
note k.
If seed production is constant among years, then the
total number of recruits in T years is simply
bR 5 TkF .constant
If instead seed production varies among years and is
lognormally distributed with distribution p(F), mean
log seed production m, and standard deviation of log
seed production s, then we must integrate over the
distribution of seed production to obtain the expected
number of seedlings in T years:
`
R 5 T R (F )p(F ) dFvariable E total
0
` 21 2[log(F ) 2 m]b
5 T kF exp dF
E 2
5 62sFs?2p0
2 2b s
5 Tk exp bm 1 .
1 22
Because the mean seed production F? , is exp(m 1 (s2/2)),
this can be rewritten as simply
2
sb
?R 5 TkF exp 2 b(1 2 b) .variable [ ]2
We can calculate the expected decrease in recruitment
due to variable seedfall as the ratio
2R svariable
5 exp 2 b(1 2 b) . (1)[ ]R 2constant
Note that this ratio depends only on the strength of
density dependence (b) and the magnitude of annual
variation in seedfall (s), and is not sensitive to the form
of the seed shadow. This ratio is always less than one
when 0 , b , 1. Moreover, when 0 , b , 1, the larger
the annual variation in seedfall (larger s), the smaller
this ratio and the greater the reduction in recruitment.
If there is no density dependence (b 5 1) or if the
April 2005 851SEEDFALL AND SEEDLING RECRUITMENT
number of recruits is independent of the number of
seeds (b 5 0), then variation in seedfall has no effect.
If b , 0, that is, if negative density dependence is so
extreme that the number of recruits decreases as the
number of seeds increases, then increased annual var-
iation in seedfall leads to increased recruitment. Intu-
itively, when b , 0, gains in recruitment in years of
very low seedfall more than offset losses in recruitment
in years of very high seedfall, relative to cumulative
recruitment when all years have intermediate seedfall.
Such overwhelming negative density dependence could
lead to selection for low seedfall in all years (possibly
with freed resources allocated to seed/seedling de-
fense), but not to selection for more variable seedfall,
because years of high seedfall would bring only fewer
recruits at a higher cost. Data and theory both suggest
that b values are unlikely to be negative (Hubbell 1980,
Harms et al. 2000). Thus, variable annual seedfall and
negatively density-dependent, postdispersal seed sur-
vival are most likely to interact to reduce numbers of
recruits.
This simple analysis succinctly illustrates how var-
iable fecundity reduces recruitment when postdispersal
seed survival is negatively density dependent and dis-
persal and density dependence act identically in years
of high and low seedfall. We will calculate the expected
decrease in seedling recruitment due to observed an-
nual variation in seedfall given observed levels of den-
sity dependence and spatial variation in the probability
of seed arrival, and assess whether variation in density
dependence among years of high and low seedfall could
compensate for this handicap. We analyze seed dis-
persal distances, including variation in dispersal dis-
tances among years, elsewhere (Dalling et al. 2002,
Muller-Landau et al. 2002, in press).
METHODS
Study site
Annual rainfall averages 2600 mm and supports
semideciduous tropical forest on BCI (98109 N, 798519
W) (Windsor 1990). This study was conducted in a 50-
ha Forest Dynamics Plot, where all trees and shrubs
.1 cm in diameter at breast height have been mapped
and identified (Condit 1998). Humans have had little
impact on this forest since at least 1500 BP (Piperno
1990), with the exception of a small (,2 ha) patch of
secondary forest perhaps 120 years old. BCI has a di-
verse, and, with the exception of macaws (Ara spp.)
and white-lipped peccaries (Tayassu pecari), intact
community of vertebrate seed dispersers, seed preda-
tors, and seedling herbivores. Because of a well-en-
forced ban on hunting, densities of mammalian her-
bivores are comparable with those at much more remote
sites (Wright et al. 1994, Peres 1996, Wright et al.
2000).
Seed and recruit censuses
The rain of seeds and flowers was censused weekly
from 1 January 1987 through 21 May 2003, using 200
seed traps set along 2.7 km of trails within the 50-ha
plot (Wright and Caldero?n 1995, Wright et al. 1999).
Each seed trap consisted of a square, 0.5-m2 PVC frame
supporting a shallow, open-topped, 1-mm mesh bag,
and suspended 0.8 m above the ground on four PVC
posts. Traps were located at 13.5-m intervals on alter-
nating sides of the trail and randomly between 4 and
10 m from the trail so that distances between the nearest
traps averaged 18.9 6 3.6 m (mean 6 1 SD). All flow-
ers, seeds, fruits, capsules, and other reproductive parts
of plants that fell into the traps were identified to spe-
cies and counted (only presence was recorded for flow-
ers). Fruits and seeds were further categorized as abort-
ed, immature, mature (endosperm-filled), or damaged
by insects or vertebrates. For each species, the number
of undamaged, mature fruit was multiplied by the spe-
cies-specific average seed-to-fruit ratio and added to
the number of undamaged seeds to estimate the total
number of viable seeds falling into each trap.
All woody seedlings ,50 cm tall in 600 1-m2 seed-
ling plots were censused between January and March
each year from 1994 through 2003 (Harms et al. 2000,
Wright 2002). Seedling plots were located 2 m from
the three sides of each seed trap away from the nearby
trail. Henceforth, ??station?? will refer to a seed trap
and its three associated seedling plots. Each seedling
was tagged and identified when it was first censused,
and measured (height and number of leaves) every year.
The analyses here consider seedlings only when they
first enter, or recruit into, the census. The age of seed-
lings at recruitment varies among species due to dif-
ferences in the timing of seedfall and different lag times
until germination (see Discussion: Spatial density de-
pendence).
Criteria to include species
We considered only trees, shrubs, and lianas; other
life forms were excluded. We also excluded species
whose seeds passed through the 1-mm mesh (Cecropia,
Conostegia, Marcgravia, Miconia, Mikania); species
whose seeds could not be reliably identified to species
(Ficus, Inga excepting I. marginata, Zanthoxylum pan-
amense and Z. procerum, Abuta racemosa and Chon-
drodendron tomentosum); and the single species that
reproduced twice each year (Hyeronima alchorneo-
ides).
We included only species for which we could be
confident that the 200 stations monitored a minimum
of four seed-bearing individuals. The locations of traps,
the number of seeds captured, and the presence of flow-
ers were compared with the locations and sizes of all
conspecific trees and shrubs present in the 50-ha plot.
Discrete clusters of trees and traps were identified,
where each cluster included one or more traps that
captured both flowers and seeds located near a large
conspecific that was presumed to bear seeds and where
clusters were separated by two or more traps that failed
to capture conspecific flowers. We included tree and
852 S. JOSEPH WRIGHT ET AL. Ecology, Vol. 86, No. 4
shrub species represented by four or more clusters and
presumably by four or more seed-bearing adults located
above a station. These species were each represented
by many more reproductively sized individuals in the
50-ha plot that were not directly over a census station
so that the 200 stations collectively monitored a larger
population.
Lianas are not mapped in the 50-ha plot, necessi-
tating a different criterion to ensure that a population
of individuals was being monitored. Each tree and
shrub species represented by four or more discrete clus-
ters of traps (see previous paragraph) also had seeds
or fruit captured in 10 or more traps in at least one
year. We therefore included liana species captured in
10 or more traps in at least one year to maintain con-
sistent criteria across life forms.
Finally, we also excluded species with fewer than 75
seeds plus fruit captured during 15 annual reproductive
events. For each species, the month of minimum seed-
fall defined start and end dates of annual reproductive
events. After 15 yr, cumulative seedfall was zero for
at least one month for every species examined here.
The first reproductive event started in 1987 and the
15th ended in 2002 for each species.
Recruitment was evaluated for species with seedling
recruits recorded at 30 or more stations in nine years,
10 or more recruits recorded for at least one station in
at least one year, and seeds or fruit recorded for 50 or
more stations for the appropriate nine years. For seed-
lings, the nine years included 1995 through 2003, be-
cause new recruits could not be distinguished during
the initial 1994 seedling census. The timing of seedfall,
species-specific germination lags (Garwood 1983), and
the timing of the annual seedling census were incor-
porated to associate recruits with the appropriate es-
timate of annual seedfall. The 1998 fruiting of Dipteryx
panamensis will illustrate this association. No seeds of
D. panamensis have ever fallen into traps in July, the
mean date for seed dispersal is in January, and seeds
germinate in May and June. Seedfall occurring largely
during January and February 1998 (recorded from 16
July 1997 through 15 July 1998) led to germination in
May and June 1998 and to recruits first recorded be-
tween January and March 1999. Thus, our seed-to-
seedling transition spans 11?13 months for D. pana-
mensis, including 4 months of postdispersal exposure
of seeds and 7?9 months of postgermination exposure
of seedlings. The seed-to-seedling transition can be
much shorter for other species (see Discussion: Spatial
density dependence).
Annual and spatial variation in seedfall
To quantify annual variation (CVyears), coefficients of
variation were calculated using seedfall averaged over
the 200 seed traps for each annual reproductive event
(Kelly 1994). Skewness and kurtosis were evaluated
for both untransformed and log-transformed values of
annual seedfall for each species. To quantify spatial
variation (CVtraps), coefficients of variation were cal-
culated using seedfall averaged over the 15 years for
each seed trap.
Mann-Whitney U tests were used to evaluate the
hypothesis that CVyears differed between plant species
from BCI and those from extratropical latitudes. Shi-
bata et al. (2002) used similar methods (121 0.5-m2
seed traps in a regular grid over a 1.2-ha plot) to doc-
ument seedfall for nine years and 14 temperate tree
species from the Ogawa Forest, Japan. A second com-
parison was made using extratropical populations taken
from the literature review of Herrera et al. (1998). Only
those populations with seedfall recorded for 12?18
years were used because this brackets the 15 years
recorded for BCI, and variation tends to increase with
the length of ecological time series (Pimm and Red-
fearn 1988).
Relationships between seedfall and recruitment
An initial analysis explored the relationship between
stand-level recruitment and stand-level seedfall for the
nine years. Let R? t and S? t represent mean recruit and
mean seedfall density taken over the 200 stations for
year t, respectively. Stepwise multiple regression was
used to evaluate the following quadratic equation:
2
? ? ?R 5 c 1 c S 1 c St 0 1 t 2 t (2)
where c0, c1 and c2 are fitted coefficients. An economy
of scale is realized if R? t is an accelerating function of
S? t, that is, if the second-order coefficient, c2, is signif-
icant and positive and the first-order coefficient, c1, is
insignificant or significant and positive. This stand-lev-
el analysis most closely approximates earlier studies
that compared annual seedfall and recruitment (Hett
1971, Jensen 1985, Crawley and Long 1995).
We then pooled data from all stations and all year
cohorts to describe the overall relationship between
local recruit and seedfall density for each species. Let
Sit and Rit represent the density of seeds and conspecific
recruits for station i and year t, respectively. We used
maximum likelihood methods to compare the following
functions:
linear R 5 aS (3a)it it
2bSitexponential R 5 aS e (3b)it it
bpower R 5 aS (3c)it it
using both Poisson and negative binomial error distri-
butions. Model selection is unaffected by data values
with Sit 5 Rit 5 0 because their likelihood equals one
under all models. Data values with Sit , Rit or Sit 5 0
, Rit do present a problem, however, because they are
infinitely unlikely and thus their likelihood functions
are undefined under the Poisson and negative binomial
error distributions, respectively. HilleRisLambers et al.
(2002) simply set Sit equal to Rit whenever Sit , Rit in
a similar analysis. We adopted their convention even
April 2005 853SEEDFALL AND SEEDLING RECRUITMENT
though it introduces a conservative bias against de-
tecting negative density dependence by systematically
increasing seedfall density whenever observed seedfall
fell below observed recruit density. The negative bi-
nomial error distribution invariably provided a signif-
icant improvement over the Poisson error distribution.
This was expected given the large variation associated
with clumped seed dispersal, and fits with the Poisson
error distribution were not considered further. The ex-
ponent b differs significantly from one (zero) when the
power (exponential) function provides a significantly
better fit than the linear function, and this outcome is
consistent with density-dependent survival during the
seed-to-seedling transition. Asymptotic standard errors
and Wald confidence intervals were used to determine
whether b values differed significantly from zero for
power function fits.
Two analyses were performed to evaluate how re-
cruitment responded to simultaneous spatial and tem-
poral variation in seedfall. The first quantified the po-
tential consequences of temporal variation in seedfall
for recruitment given the observed negative density
dependence (see Introduction: Theory). We did not use
Eq. 1 for this purpose because it only incorporates log-
normal variation in seed production. Instead, we used
a numerical analog of Eq. 1 that incorporates all ob-
served temporal variation. Let pi represent the propor-
tion of seeds arriving at station i over T years, let Ft
be the seed production in year t, let F? be the mean
annual seed production, and assume the relationship
between recruit and seedfall density, R(S), is unchang-
ing and equals the function selected using the methods
described in the previous paragraph. Then the number
of recruits expected at I stations over T years of con-
stant seedfall is
I
?R9 5 T R(Fp ) (4)
Oconstant i
i51
and the number of recruits expected given annually
variable seedfall and the same spatial pattern of seed
rain is
T I
R9 5 R(F p ). (5)
O Ovariable t i
t51 i51
The empirically determined ratio R9variable:R9constant quan-
tifies the potential consequences of observed variable
seed production for recruitment given observed spatial
variation in seedfall density and an unchanging func-
tion for seed-to-seedling survival.
The final analysis used maximum likelihood methods
to determine whether the spatial relationship between
recruit and seedfall densities varied among years. The
single year of highest seedfall was contrasted with the
eight pooled years of lower seedfall, unless seedfall for
a second year fell within 10% of seedfall in the highest
year, in which case the two pooled years of highest
seedfall were contrasted with the seven pooled years
of lower seedfall. The following models with different
combinations of year-dependent parameters were com-
pared (only power functions were used because these
proved significantly better than exponential or linear
functions for all species):
intercepts and exponents in common,
bR 5 aS (6a)it it
intercepts in common, exponents different,
bhaS if t is a high seedfall yearitR 5 (6b)it b l
5aS otherwiseit
intercepts different, exponents in common,
ba S if t is a high seedfall yearh itR 5 (6c)it b
5a S otherwisel it
both intercepts and exponents different,
bha S if t is a high seedfall yearh itR 5 (6d)it b l
5a S otherwise.l it
Analyses
The Akaike Information Criterion (AIC) was used
to select the best model from among the models de-
scribed by Eqs. 3a?c and 6a?d (note that Eqs. 3c and
6a are identical). AIC is calculated as 22L 1 2P, where
L is the log likelihood of the model and P is the number
of parameters. We tabulated the difference (DAIC) be-
tween the AIC value observed for each model and the
smallest AIC value observed for that same species fol-
lowing the recommendation of Burnham and Anderson
(1998). If this difference exceeds 10 for two models,
then there is no empirical support for the model with
the larger AIC value. If this difference is less than two,
then the two models cannot be distinguished (Burnham
and Anderson 1998).
We also compared the models described by Eqs. 3
and 6 in a hypothesis-testing mode. Less parsimonious
models with additional parameters were evaluated rel-
ative to more parsimonious models with fewer param-
eters using likelihood ratio tests (chi-squared tests on
the differences in log likelihoods between the models,
with degrees of freedom determined by the differences
in the number of parameters (Hilborn and Mangel
1997)). This approach has the twin advantages that it
is familiar to more ecologists and the sequential Bon-
ferroni procedure (Rice 1989) can be used to protect
against Type II error when multiple tests are performed,
and the disadvantage that it cannot be used to compare
models with the same number of parameters. The se-
quential Bonferroni procedure was also applied to anal-
yses of the quadratic relationship between annual re-
cruitment and annual seedfall (Eq. 2). Two-tailed tests
were used throughout. Analyses were performed with
SYSTAT 10.0 (SPSS 2000).
854 S. JOSEPH WRIGHT ET AL. Ecology, Vol. 86, No. 4
FIG. 1. Frequency histograms of coefficients of variation
for seedfall density recorded for 15 years and 108 species
from Barro Colorado Island, Panama (this study); for 12?18
years and 35 populations from extratropical latitudes (Herrera
et al. 1998); and for 9 years and 14 tree species from the
Ogawa Forest, Japan (Shibata et al. 2002).
FIG. 2. The ratio of temporal (CVyears) to spatial (CVtraps)
variation in seedfall for 59 tree, 43 liana, and 6 shrub species.
Temporal variation is represented by the coefficient of vari-
ation of annual seedfall summed over 200 traps for each of
15 years. Spatial variation is represented by the coefficient
of variation of seedfall summed over 15 years for each of
200 traps.
RESULTS
Annual and spatial variation in seedfall
The 200 seed traps collected 960 872 undamaged
seeds and fruits representing 494 species in 853 weekly
censuses between 1 January 1987 and 21 May 2003.
Six shrub, 59 tree, and 43 liana species fulfilled the
criteria to be included in analyses of seedfall (Appendix
A). The 15 annual values of seedfall were significantly
skewed (kurtotic) for 62 (48) of these 108 species. All
significant values of skewness and kurtosis were pos-
itive for untransformed values of seedfall, which in-
dicates a long tail of large values. When annual seedfall
was log transformed, the number of significantly
skewed (kurtotic) species was just 16 (10). Distribu-
tions of annual seedfall were approximately lognormal
for most species.
The median coefficient of variation (CVyears) of annual
seedfall was 1.01 for the 108 BCI populations (Fig. 1).
CVyears was significantly larger for 35 extratropical plant
populations and also for 14 tree populations from the
Ogawa Forest, Japan (Fig. 1, Mann-Whitney U tests,
P , 0.01 and P , 0.001, respectively). Spatial variation
in seedfall among traps (CVtraps) was greater than tem-
poral variation in seedfall among years (CVyears) for ev-
ery BCI species (Fig. 2).
Relationships between seedfall and recruitment
The 600 seedling plots included 29 312 recruits rep-
resenting 282 species in nine annual censuses between
1995 and 2003. Three shrub, 16 tree, and 13 liana spe-
cies fulfilled the criteria to be included in analyses of
recruitment (Appendix B). A quadratic model (Eq. 2)
was used to evaluate the stand-level relationship be-
tween annual recruitment and seedfall. The first-order
coefficient (c1) was always positive when significant.
The second-order coefficient (c2) was significant and
positive for eight species after the sequential Bonfer-
roni correction. Realized recruitment per seed in-
creased with annual seedfall for these eight species
(Fig. 3).
Power functions (Eq. 3c) best described the rela-
tionship between local recruit and seedfall densities for
all 32 species when the nine-year cohorts were pooled.
Power functions provided significantly better fits than
linear functions (Table 2, minimum DAIC 5 23.52;
minimum likelihood ratio test x2 5 19.72, P , 0.001
after the sequential Bonferroni correction) and sub-
stantially better fits than exponential functions for all
species (Table 2, minimum DAIC 5 20.90). The ex-
ponent (b) of the best fit power function was signifi-
cantly less than one for all 32 species. The test based
on asymptotic standard errors further indicated that b
values were significantly greater than zero for 11 spe-
cies and significantly smaller than zero for no species.
Sample size was important for the latter test. Numbers
of recruits and seeds were significantly greater for the
11 species with positive b values than for the 21 species
whose b values were indistinguishable from zero
(Mann-Whitney U tests, P , 0.001 and P , 0.01, re-
spectively). We believe that b values will prove to fall
between zero and one for ever more species as we
accumulate additional years of data and sample size
increases. To summarize, significant negative density
dependence characterized the seed-to-seedling transi-
tion for every species; nonetheless recruit density tend-
ed to increase with seedfall density (Harms et al. 2000).
April 2005 855SEEDFALL AND SEEDLING RECRUITMENT
FIG. 3. Mean recruit and seedfall flux densities for nine
years (with means taken over 200 census stations), and the
best-fit quadratic functions (Eq. 2), for the eight BCI species
that realized an economy of scale after seed dispersal. Re-
cruits are seedlings that are known to have germinated and
recruited within the past year.
The ratio R9variable:R9constant (Eq. 5:Eq. 4) quantifies the
potential consequences of variable seedfall for recruit-
ment given observed spatial variation in seedfall den-
sity and an unvarying function for density-dependent
survival during the seed-to-seedling transition. This ra-
tio was less than one for 29 of the 32 species evaluated
(Fig. 4). The three exceptional species had estimated
b values , 0 for Eq. 3c. Although R9variable:R9constant . 1
is expected when b values are negative, there are rea-
sons to doubt whether negative density dependence ac-
tually takes this extreme form (see Introduction: The-
ory and previous paragraph). We conclude that variable
annual seedfall will tend to reduce recruitment given
observed spatial variation in seedfall density if nega-
tively density-dependent survival acts identically
across years.
The final analysis contrasted the relative strength of
density dependence during the seed-to-seedling tran-
sition in the year(s) of greatest seedfall and in the re-
maining years of lower seedfall (Eqs. 6). Survival dur-
ing the seed-to-seedling transition was significantly
larger for the year(s) of greatest seedfall than for the
remaining years of lower seedfall for 12 species when
the sequential Bonferroni procedure was applied to
likelihood ratio tests (Table 2). This included the eight
species in Fig. 3 and also Hirea reclinata, Pouteria
reticulata, Psychotria horizontalis and Simarouba
amara. The exponent (b value) alone was significantly
larger for 10 species (Eq. 6b), the intercept alone was
significantly larger for Faramea occidentalis (Eq. 6c),
and both the intercept and exponent were significantly
larger for Trichilia tuberculata (Eq. 6d). Fig. 5 presents
the relationship between recruit and seedfall densities
for 4 of these 12 species. Finally, the b value was
significantly smaller for the year(s) of greatest seedfall
than for the remaining years of lower seedfall for Mac-
fadyena unguis-cati and Randia armata (Table 2). To
summarize, survival during the seed-to-seedling tran-
sition was significantly larger in the year(s) of greatest
seedfall for 12 species, and significantly smaller for 2
species.
DISCUSSION
Annual and spatial variation in seedfall
Annual variation in seedfall on BCI was substantial
(CVyears . 1 for 50% of species), but was still signifi-
cantly smaller than for higher latitudes (Fig. 1). The
BCI-Ogawa forest comparison is particularly compel-
ling because both studies used seed traps located in-
dependently of seed-bearing trees to quantify seedfall
so that both studies sampled the more abundant and
fecund species at their respective sites The BCI data
support the hypothesis that annual variation in seedfall
is lower in the tropics than at higher latitudes (Kelly
and Sork 2002). There is, however, ample evidence that
CVyears varies geographically within both the tropics
(e.g., greater for the Dipterocarp forests of Southeast
Asia) and at higher latitudes (e.g., greater for New
Zealand). Additional seedfall studies from the tropics
will be required to substantiate a tropical?extratropical
dichotomy and to evaluate possible causes.
Spatial variation in seedfall density was greater than
annual variation for all 108 BCI species (Fig. 2). The
rarity of seed-bearing adults, variation in seed depo-
sition with distance, and clumped seed deposition by
frugivores are the most important sources of this spatial
variation (Muller-Landau 2001, Muller-Landau et al.
2002). Spatial variation in seedfall density sets the
stage for density-dependent performance.
856 S. JOSEPH WRIGHT ET AL. Ecology, Vol. 86, No. 4
TABLE 2. Species, life forms, sample sizes, model selection criteria, and parameters from the best-fit model to describe the
relationship between recruit and seedfall density.
Species
Life
form
No.
seeds
No.
recruits
Difference from minimum Akaike
Information Criterion for model
3a 3b 3c or 6a
Beilschmiedia pendula? T 870 822 53.00 52.00 30.16
Brosimum alicastrum T 4870 69 154.98 147.88 71.40
Chrysophyllum cainito T 479 132 47.78 43.24 0
Doliocarpus major? L 1342 478 197.02 183.58 66.18
D. multiflorus L 1456 78 47.82 45.88 10.86
D. olivaceus L 455 142 99.96 95.32 34.04
Eugenia oerstedeana T 903 529 264.12 210.90 33.78
Faramea occidentalis? T 5506 4143 501.76 446.16 275.28
Guapira standleyanum T 419 99 88.92 41.24 0
Heisteria concinna T 503 187 74.66 63.28 1.98
Hippocratea volubilis L 1015 227 128.48 111.58 0
Hiraea reclinata L 933 258 218.08 169.20 24.18
H. faginea L 247 129 24.46 20.90 6.34
H. grandifolia L 329 128 45.76 44.62 3.36
Hybanthus prunifolius? S 9231 2781 386.78 293.54 3.84
Jacaranda copaia? T 64 713 116 23.52 77.4 0
Macfadyena unguis-cati L 436 150 98.28 83.98 14.70
Maripa panamensis L 478 359 200.90 143.10 0
Mascagnia hippocrateoides? L 1144 626 60.08 44.88 0
M. nervosa? L 17 978 1042 281.92 248.08 3.00
Paragonia pyramidata L 771 202 71.44 54.24 5.66
Pouteria reticulata? T 349 202 101.06 81.76 10.18
Prionostemma aspera L 244 131 55.96 41.52 0
Psychotria horizontalis S 1028 768 325.04 271.34 10.86
Quararibea asterolepis T 16 473 866 391.38 345.94 3.2
Randia armata? T 3227 1637 184.26 165.18 10.92
Simarouba amara T 773 68 56.62 54.70 18.64
Sorocea affinis S 387 363 216.02 158.52 0.16
Tetragastris panamensis? T 2248 380 78.88 71.20 0
Thinouia myriantha T 7804 309 284.16 240.48 5.24
Trichilia tuberculata? T 17 659 3097 786.80 763.16 458.28
Triplaris cumingiana T 455 93 58.86 52.34 0
Notes: Life forms are tree (T), liana (L), and shrub (S). Numbers of seeds and recruits are summed over nine years and
200 0.5-m2 seed traps and 600 1-m2 seedling plots, respectively. Model selection criteria are differences between the values
of the Akaike Information Criterion observed for each model and the minimum (best) AIC observed for the six models under
consideration (DAIC). Models are identified by equation numbers (see Methods: Relationships between seedfall and recruit-
ment). Parameter values are from the best-fit model as determined by likelihood ratio tests after sequential Bonferroni
correction: a single value is presented for a and b if model 3c (or 6a) provided the best fit; separate values are presented for
years of low (subscript l) and high (h) seedfall if models 6b, 6c, or 6d provided the best fit. Models 3a and 3b never provided
the best fit.
? The b value was significantly greater than zero for model 3c. All b values were significantly less than 1.
Spatial density dependence
We evaluated density dependence during the seed-
to-seedling transition. The duration of this transition
varied among species due to the timing of seedfall and
germination. For example, the transition includes four
months between seedfall and germination and seven to
nine months after germination for Dipteryx panamensis
(see Methods: Relationships between seedfall and re-
cruitment). At the other extreme, the transition includes
a few days between seedfall and germination and two
to five months after germination for Trichilia tuber-
culata. These differences necessitate caution when in-
terpreting interspecific comparisons; however, the in-
traspecific comparisons among years conducted here
are unaffected.
Analytical methods influence the frequency with
which density dependence is detected (HilleRis-
Lambers et al. 2002). Two different analyses have now
been used to evaluate density dependence during the
seed-to-seedling transition, with the same outcome for
BCI. Visual inspection of the data, linear regression
analyses, and maximum-likelihood analyses all indi-
cate that power functions, with exponents indicative of
negative density dependence, describe the relationship
between conspecific recruit and seedfall density for ev-
ery BCI species examined (Fig. 5, Table 2; Harms et
al. 2000).
Negative density dependence enhances species co-
existence in spatially structured plant communities
(Chave et al. 2002). Pervasive negative density depen-
dence characterizes postdispersal seed survival on BCI
(Fig. 5, Table 2). Negative density dependence contin-
ues to characterize growth and survival as seedlings
mature and even large saplings are affected in tropical
forests (reviewed by Wright 2002). The full conse-
quences for tree demography and species coexistence
April 2005 857SEEDFALL AND SEEDLING RECRUITMENT
TABLE 2. Extended.
Difference from minimum Akaike
Information Criterion for model
6b 6c 6d
Power function parameters
a(al) ah b(bl) bh
0.84 2.18 0 0.532 0.428 0.825
0 45.00 0.12 0.616 20.743 0.244
1.26 1.12 3.06 0.663 0.169
0 22.72 1.60 0.814 20.016 0.540
0 3.92 1.92 0.773 20.227 0.234
0 20.12 1.70 0.929 20.428 0.277
0 13.26 1.70 1.083 20.074 0.270
38.88 2.26 0 0.943 5.042 0.285
0.90 1.32 2.90 1.014 20.239
0 0.32 1.64 0.738 0.176
0.60 2.00 1.42 1.068 0.012
0.10 15.44 0 1.092 20.369 0.048
0 6.86 0.70 0.761 0.305
0 4.86 0.12 0.889 0.164
0 2.14 1.34 0.985 0.312
1.40 1.80 2.58 0.014 0.360
1.02 0 0.98 0.952 0.075 20.504
2.00 1.88 3.80 1.030 0.076
1.60 0.76 2.38 0.859 0.440
0 0.30 1.88 0.196 0.383
0.54 0 1.54 0.584 0.229
0 4.10 1.52 0.999 20.043 0.292
1.74 1.96 3.52 0.834 0.075
0 7.82 1.98 1.324 0.002 0.262
2.64 0 1.68 0.806 0.087
0 5.44 1.74 1.219 0.474 0.250
1.72 0 0.06 0.505 20.252 0.353
0.68 0 1.92 1.115 20.007
0.82 1.50 2.68 0.659 0.277
0 2.94 1.54 0.288 0.109
47.50 22.66 0 0.487 1.928 0.180 0.417
1.98 1.58 2.96 0.618 0.187
FIG. 4. Frequency histogram of the ratio of the number
of seedling recruits expected given variable seedfall (Eq. 5)
to the number expected given constant seedfall (Eq. 4) for
16 tree, 13 liana, and three shrub species from Barro Colorado
Island, Panama. Temporally variable seedfall and subsequent
density-dependent seed survival have the potential to reduce
recruitment when the ratio R9variable:R9constant is less than 1.
These values incorporate observed spatial variation in seed-
fall density and assume that density-dependent seed survival
acts identically across years (see Methods: Relationships be-
tween seedfall and recruitment).
will be underappreciated until density-dependent ef-
fects are integrated over all life history stages (Alvarez-
Buylla 1994).
Implications for variable seed production
Variable annual seedfall and negatively density-de-
pendent, postdispersal seed survival will combine to
reduce numbers of recruits when seed dispersal and
density dependence act identically across years (see
Introduction: Theory). This reduction can be substan-
tial, with variable seedfall resulting in excess nega-
tively density-dependent mortality of up to 28% of the
recruits expected if seedfall were constant across years
(Fig. 4). This handicap must be overcome for larger
seed crops to realize greater per seed recruitment after
dispersal (a postdispersal economy of scale) and for
selection acting after dispersal to favor more variable
annual seedfall.
The handicap was overcome for the eight species for
which per seed recruitment increased with seed crop
size (Fig. 3). We could not identify any traits that set
these species apart: they were not distinguished by sig-
nificantly higher or lower annual or spatial variation
in seedfall, or seed mass (Kruskal-Wallis tests). These
eight species plus four additional species exhibited
858 S. JOSEPH WRIGHT ET AL. Ecology, Vol. 86, No. 4
FIG. 5. Survival during the seed-to-seedling transition was significantly larger during the year(s) of greatest seedfall (open
circles, dashed line) than during years of lower seedfall (solid circles, solid line) for 12 species from Barro Colorado Island,
Panama (just four are shown). The lines represent best-fit power functions determined using maximum-likelihood methods
(note the log?log scale). Survival was significantly smaller during the year(s) of greatest seedfall for an additional two species
(not shown).
weaker density dependence when seed crops were larg-
est; however, two other species exhibited stronger neg-
ative density dependence when seed crops were largest
(Table 2).
To summarize, per seed recruitment was significantly
greater when seed crops were largest for 12 species,
significantly lower for 2 species, and the null hypoth-
esis could not be rejected for 18 species. Published
studies provide similar numbers (4:1:3, species, re-
spectively; Table 1), given the bias against publication
when the null hypothesis is accepted. Collectively,
these studies suggest that the frequency of postdisper-
sal economies of scale is low at least in part because
the impact of negative density dependence is enhanced
when seedfall varies among years. Additional studies
of annual variation in seedfall and postdispersal seed
fate will be required to evaluate this tentative conclu-
sion.
Mechanisms contributing to postdispersal
economies of scale
At least four mechanisms could contribute to post-
dispersal economies of scale. Large seed crops might
attract disproportionate numbers of frugivores leading
to greater seed dispersal and hence greater seed survival
(Vander Wall 2002). Alternatively, large seed crops
might satiate postdispersal seed or seedling predators,
thereby improving survival (Jensen 1985, Nilsson and
Wa?stljung 1987, Crawley and Long 1995, Wolff 1996).
A third possibility hinges on predispersal pollinator ac-
tivity causing an apparent postdispersal economy of
scale. Outcrossing often enhances seed and seedling per-
formance. If large flower displays led to increased levels
of outcrossing, then per-seed recruitment might increase
with seed crop size as a consequence of outcrossing
rather than with events that occur during or after seed
April 2005 859SEEDFALL AND SEEDLING RECRUITMENT
dispersal. Finally, successful resource prediction could
also lead to an apparent economy of scale because seeds
produced in larger numbers in years characterized by
conditions favorable for seedling establishment recruit
in disproportionately larger numbers. All four mecha-
nisms will lead to greater recruitment per dispersed seed
when seedfall is greater (Fig. 3).
The form of density dependence in years with large
and small seed crops may help discriminate among
these four mechanisms (Fig. 5). Specialized natural en-
emies are a primary cause of negatively density-de-
pendent seed survival (Janzen 1970). Weaker negative
density dependence, as reflected by a greater slope of
the relationship between recruits and seeds, is consis-
tent with satiation of enemies. Higher quality, out-
crossed seeds, or improved conditions for establish-
ment are more likely to increase survival everywhere
(increased intercept a), while leaving the strength of
density dependence (the slope, or more strictly the ex-
ponent, b) unchanged. Better dispersal should insure
that fewer seeds experience high densities of conspe-
cifics (no effect on the density-dependent relationship),
and may take seeds to better sites where resources are
enhanced (increasing the intercept), but also seems
likely to have little impact on the slope. The frugivore
attraction hypothesis can be further discounted because
dispersal distances tend to be lower in years of high
seedfall for the majority of animal-dispersed species
on BCI (Muller-Landau 2001). We conclude that the
most likely explanation for the economies of scale ob-
served in this study is that some unknown postdispersal
pest of seeds or seedlings is partially satiated in the
year(s) of greatest seedfall.
Conclusions
Kelly (1994) suggested that CVyears . 1 characterizes
mast fruiting. Fifty-four of 108 BCI species satisfy this
criterion (Fig. 1). The only other reports of mast fruit-
ing from the tropics are for single species that dominate
extensive forest stands (Newbery 1998), or for trees
from the family Dipterocarpaceae that dominate many
forests in Southeast Asia (Curran et al. 1999). Domi-
nance is absent from the forests of BCI, where CVyears
. 1 characterizes several species with less than one
reproductive adult per hectare. Such rare species are
unlikely to attract disproportionate numbers of mutu-
alists or satiate their pests independently of the rest of
the plant community; however, interspecific synchrony
in reproductive effort among species may allow rare
species to benefit from community-level satiation of
generalist pests on BCI (Wright et al. 1999).
Most studies of annual variation in reproductive ef-
fort in plants have focused on predispersal stages (Her-
rera et al. 1998, Kelly and Sork 2002). All else equal,
negative density dependence, which is widespread
among plants after seeds are dispersed (Harms et al.
2000, HilleRisLambers et al. 2002, Wright 2002), will
reduce recruitment as annual variation in seedfall in-
creases (Eq. 1). This increased mortality will tend to
offset predispersal advantages that may be associated
with annual variation in reproductive effort. Thus, our
understanding of the evolution of temporal variation in
seed production will only be complete when its eco-
logical consequences have been evaluated and inte-
grated across reproductive stages (flowers, predispersal
seed development, and postdispersal seed fate) for the
same plant populations. Such studies have yet to occur
(Kelly and Sork 2002).
ACKNOWLEDGMENTS
Allen Herre, Jean-Franc?ois Molino, and an anonymous re-
viewer provided thoughtful comments that improved this pa-
per. The Environmental Sciences Program of the Smithsonian
Institution supported this study. H.C. Muller-Landau was sup-
ported by a postdoctoral fellowship at the National Center
for Ecological Analysis and Synthesis, a Center funded by
NSF (Grant No. DEB-0072909), the University of California,
and the Santa Barbara campus.
LITERATURE CITED
Alvarez-Buylla, E. R. 1994. Density dependence and patch
dynamics in tropical rain forests: matrix models and appli-
cations to a tree species. American Naturalist 143:155?191.
Burnham, K. P., and D. R. Anderson. 1998. Model selection
and inference: a practical information-theoretic approach.
Springer, New York, New York, USA.
Chave, J., H. C. Muller-Landau, and S. A. Levin. 2002. Com-
paring classical community models: theoretical consequences
for patterns of diversity. American Naturalist 159:1?23.
Condit, R. 1998. Tropical forest census plots. Springer-Ver-
lag, Berlin, Germany.
Crawley, M. J., and C. R. Long. 1995. Alternate bearing,
predator satiation and seedling recruitment in Quercus rob-
ur L. Journal of Ecology 83:683?696.
Curran, L. M., I. Caniago, G. D. Paoli, D. Astianti, M. Kus-
neti, M. Leighton, C. E. Nirarita, and H. Haeruman. 1999.
Impact of El Nin?o and logging on canopy tree recruitment
in Borneo. Science 286:2184?2188.
Dalling, J. W., H. C. Muller-Landau, S. J. Wright, and S. P.
Hubbell. 2002. Role of dispersal in the recruitment limi-
tation of neotropical pioneer species. Journal of Ecology
90:714?727.
DeSteven, D. 1982. Seed production and seed mortality in a
temperate forest shrub (witch-hazel, Hamamelis virgini-
ana). Journal of Ecology 70:437?443.
DeSteven, D. 1983. Reproductive consequences of insect seed
predation in Hamamelis virginiana. Ecology 64:89?98.
Gardner, G. 1977. The reproductive capacity of Fraxinus
excelsior on the Derbyshire limestone. Journal of Ecology
65:107?118.
Garwood, N. C. 1983. Seed germination in a seasonal tropical
forest in Panama: a community study. Ecological Mono-
graphs 53:159?181.
Harms, K. E., S. J. Wright, O. Caldero?n, A. Herna?ndez, and
E. A. Herre. 2000. Pervasive density-dependent recruit-
ment enhances seedling diversity in a tropical forest. Nature
404:493?495.
Herrera, C. M., P. Jordano, J. Guitian, and A. Traveset. 1998.
Annual variability in seed production by woody plants and
the masting concept: reassessment of principles and rela-
tionship to pollination and seed dispersal. American Nat-
uralist 152:576?594.
Hett, J. M. 1971. A dynamic analysis of age in sugar maple
seedlings. Ecology 52:1071?1074.
Hilborn, R., and M. Mangel. 1997. The ecological detective:
confronting models with data. Princeton University Press,
Princeton, New Jersey, USA.
860 S. JOSEPH WRIGHT ET AL. Ecology, Vol. 86, No. 4
HilleRisLambers, J., J. S. Clark, and B. Beckage. 2002. Den-
sity-dependent mortality and the latitudinal gradient in spe-
cies diversity. Nature 417:732?735.
Hubbell, S. P. 1980. Seed predation and the coexistence of
tree species in tropical forests. Oikos 35:214?229.
Janzen, D. H. 1970. Herbivores and the number of tree spe-
cies in tropical forests. American Naturalist 104:501?528.
Janzen, D. H. 1980. Specificity of seed-attacking beetles in
a Costa Rican deciduous forest. Journal of Ecology 68:
929?952.
Jensen, T. S. 1985. Seed-seed predator interactions of Eu-
ropean beech, Fagus silvatica and forest rodents, Cleth-
rionomys glareolus and Apodemus flavicollis. Oikos 44:
149?156.
Jones, C. G., R. S. Ostfeld, M. P. Richard, E. M. Schauber,
and J. O. Wolff. 1998. Chain reactions linking acorns to
gypsy moth outbreaks and Lyme disease risk. Science 279:
1023?1026.
Kelly, D. 1994. The evolutionary ecology of mast seeding.
Trends in Ecology and Evolution 9:465?470.
Kelly, D., and V. L. Sork. 2002. Mast seeding in perennial
plants: why, how, where? Annual Review of Ecology and
Systematics 33:427?447.
Kelly, D., and J. J. Sullivan. 1996. Quantifying the benefits
of mast seeding on predator satiation and wind pollination
in Chionochloa pallens (Poaceae). Oikos 78:143?150.
McQuilkin, R. A., and R. A. Musbach. 1977. Pin oak acorn
production on green tree reservoirs in southeastern Mis-
souri. Journal of Wildlife Management 41:218?225.
Muller-Landau, H. C. 2001. Seed dispersal in a tropical for-
est: empirical patterns, their origins and their consequences
for forest dynamics. Dissertation. Princeton University,
Princeton, New Jersey, USA.
Muller-Landau, H. C., J. W. Dalling, K. E. Harms, S. J.
Wright, R. Condit, S. P. Hubbell, and R. B. Foster. In press.
Seed dispersal and density-dependent seed and seedling
mortality in Trichilia tuberculata and Miconia argentea. In
E. G. Leigh, editor. Forest diversity and dynamism: findings
from a network of large-scale tropical forest plots. Uni-
versity of Chicago Press, Chicago, Illinois, USA.
Muller-Landau, H. C., S. J. Wright, O. Caldero?n, S. P. Hub-
bell, and R. B. Foster. 2002. Assessing recruitment limi-
tation: concepts, methods and case-studies from a tropical
forest. Pages 35?53 in M. Galetti, editor. Seed dispersal
and frugivory: ecology, evolution and conservation. CAB
International, Wallingford, Oxfordshire, UK.
Nathan, R., and H. C. Muller-Landau. 2000. Spatial patterns
of seed dispersal, their determinants and consequences for
recruitment. Trends in Ecology and Evolution 15:278?285.
Newbery, D. M., N. C. Songwe, and G. B. Chuyong. 1998.
Phenology and dynamics of an African rainforest at Korup,
Cameroon. Pages 267?307 in D. M. Newbery, H. H. T.
Prins, and N. D. Brown, editors. Dynamics of tropical com-
munities. Blackwell Science, London, UK.
Nilsson, S. G. 1985. Ecological and evolutionary interactions
between reproduction of beech Fagus sylvatica and seed
eating animals. Oikos 44:157?164.
Nilsson, S. G., and A. U. Wa?stljung. 1987. Seed predation
and cross-pollination in mast-seeding beech (Fagus syl-
vatica) patches. Ecology 68:260?265.
Peres, C. A. 1996. Population status of white-lipped Tayassu
pecari and collared peccaries T. tajacu in hunted and un-
hunted Amazonian forests. Biological Conservation 77:
115?123.
Pimm, S. L., and A. Redfearn. 1988. The variability of pop-
ulation-densities. Nature 334:613?614.
Piperno, D. R. 1990. Fitolitos, arquelogia y cambios prehis-
toricos de la vegetacion en un lote de cincuenta hectareas
de la isla de Barro Colorado. Pages 153?156 in E. G. J.
Leigh, A. S. Rand, and D. M. Windsor, editors. Ecologia
de un bosque tropical. Smithsonian Institution Press, Wash-
ington, D. C., USA.
Rice, W. R. 1989. Analyzing tables of statistical tests. Evo-
lution 43:223?225.
Schupp, E. W. 1990. Annual variation in seedfall, postdis-
persal predation, and recruitment of a Neotropical tree.
Ecology 71:504?515.
Shibata, M., H. Tanaka, S. Iida, S. Abe, T. Masaki, K. Nii-
yama, and T. Nakashizuka. 2002. Synchronized annual
seed production by 16 principal tree species in a temperate
deciduous forest, Japan. Ecology 83:1727?1742.
Shibata, M., H. Tanaka, and T. Nakashizuka. 1998. Causes
and consequences of mast seed production of four co-oc-
curring Carpinus species in Japan. Ecology 79:54?64.
Silvertown, J. W. 1980. The evolutionary ecology of mast
seeding in trees. Biological Journal of the Linnean Society
14:235?250.
Sork, V. L. 1993. Evolutionary ecology of mast-seeding in
temperate and tropical oaks (Quercus spp.). Vegetatio 107/
108:133?147.
Spere, U. 1997. Fruit production in Sorbus aucuparia L. (Ro-
saceae) and pre-dispersal seed predation by the apple fruit
moth (Argyresthia conjugella Zell.). Oecologia 110:368?373.
SPSS. 2000. SYSTAT 10.0. SPSS, Chicago, Illinois, USA.
Vander Wall, S. B. 2002. Masting in animal-dispersed pines
facilitates seed dispersal. Ecology 83:3508?3516.
Waller, D. M. 1979. Models of mast fruiting in trees. Journal
of Theoretical Biology 80:223?232.
Windsor, D. M. 1990. Climate and moisture variability in a
tropical forest: long-term records from Barro Colorado Is-
land, Panama?. Smithsonian Institution Press, Washington,
D.C., USA.
Wolff, J. O. 1996. Population fluctuations of mast-eating ro-
dents are correlated with production of acorns. Journal of
Mammalogy 77:850?856.
Wright, S. J. 2002. Plant diversity in tropical forests: a review
of mechanisms of species coexistence. Oecologia 130:1?14.
Wright, S. J., and O. Caldero?n. 1995. Phylogenetic patterns
among tropical flowering phenologies. Journal of Ecology
83:937?948.
Wright, S. J., C. Carrasco, O. Caldero?n, and S. Paton. 1999.
The El Nin?o Southern Oscillation, variable fruit production
and famine in a tropical forest. Ecology 80:1632?1647.
Wright, S. J., M. E. Gompper, and B. Deleon. 1994. Are large
predators keystone species in Neotropical forests?the ev-
idence from Barro Colorado Island. Oikos 71:279?294.
Wright, S. J., H. Zeballos, I. Dominguez, M. M. Gallardo,
M. C. Moreno, and R. Ibanez. 2000. Poachers alter mam-
mal abundance, seed dispersal, and seed predation in a
Neotropical forest. Conservation Biology 14:227?239.
APPENDIX A
A table showing annual seedfall for 108 species from Barro Colorado Island, Panama is available in ESA?s Electronic Data
Archive: Ecological Archives E086-044-A1.
APPENDIX B
A table showing annual number of seedling recruits for 32 species from Barro Colorado Island, Panama is available in
ESA?s Electronic Archive: Ecological Archives E086-044-A2.