The timing of abscission affects dispersal distance in awind-dispersed tropical treeKyle D. Maurer*,1, Gil Bohrer1, David Medvigy2 and S. Joseph Wright3

1Department of Civil Environmental, & Geodetic Engineering, The Ohio State University, Columbus, Ohio, USA;2Department of Geosciences, Princeton University, Princeton, New Jersey, USA; and 3Smithsonian Tropical ResearchInstitute, Apartado 0843-03092, Balboa, Panama

Summary

1. Seed dispersal is a short-term phenomenon with long-term consequences for population sur-

vival and spread. Physiological mechanisms that target the release of seeds to particular sets of

environmental conditions that maximize the probability of long-distance dispersal should

evolve if long dispersal distance enhances fitness.

2. In this study, we use high-frequency censuses of seeds actually dispersed, high-frequency

within-canopy meteorological observations and long-term measurements of above-canopy

wind to investigate the environmental conditions that control the timing of seed abscission at

different time-scales for a wind-dispersed tropical tree, Luehea seemannii.

3. We show that seed abscission follows a typical seasonal pattern, is rare at night and is most

prevalent during periods of prolonged updrafts, higher temperature, with negative feedback

when the heat canopy flux is relatively high.

4. We use phenomenological (super-WALD) and mechanistic (coupled Eulerian–Lagrangianclosure) models to estimate the relative effects of the timing of seed release at different suban-

nual temporal scales (seconds–hours) on the resulting long-term (season–decade) dispersal ker-nels. We find that periods of high wind speed increase the probability of long-distance

dispersal between 100–1000 m, but decrease the probability at distances further than 1000 m

relative to unbiased environmental conditions. We also find abscission during updrafts to

increase the probability of long-distance dispersal at distances greater than 100 m.

5. Synthesis: We observe preferential abscission during updrafts in a tropical wind-dispersed

tree. We use mechanistic models and long-term wind statistics to estimate the dispersal conse-

quences of preferential seed release in specific environmental conditions. We find that the tim-

ing of the dispersal season may be influenced by wind conditions that maximize long-distance

dispersal; however, there are likely other environmental factors essential for their determina-

tion. Our approach provides a method to bridge between small turbulence scales and large eco-

system scales to predict dispersal kernels. These findings shed light on the evolutionary

processes that drive optimization of the timing of seed abscission and may be incorporated

into plant population movement models to increase their accuracy and predictive power.

Key-words: abscission, dispersal, long-distance dispersal, mechanistic modelling,

meteorology, seed trap, tropical forest, updraft, wind dispersal

Introduction

Seed dispersal determines the ability of plant populations

to sustain viable metapopulations (Bohrer, Nathan & Volis

2005; Poethke, Dytham & Hovestadt 2011), maintain

genetic diversity (Volis et al. 2005; Fayard, Klein & Lefe-

vre 2009) and respond to climate change through migra-

tion (Kuparinen et al. 2009; Nathan et al. 2011; Kremer

et al. 2012). Seed dispersal of an individual plant occurs

once in its lifetime and is, intrinsically, a short-term (milli-

seconds–minutes) phenomenon. However, over ecological

and evolutionary time-scales, patterns of many movement

events of individuals accumulate to long-term (seasons –

years) and large-scale (metres–kilometres) processes (Theo-

harides & Dukes 2007). Selection for traits that optimize

the dispersive potential of seeds may act on processes at*Correspondence author. E-mail: maurer.189@osu.edu

© 2012 The Authors. Functional Ecology © 2012 British Ecological Society

Functional Ecology 2013, 27, 208–218 doi: 10.1111/1365-2435.12028

long time-scales, such as the timing of the annual seed dis-

persal season, as well as short time-scales, such as the exact

moment a seed will be ejected from the pod or released

from the branch.

Thompson & Katul (2008) showed that it is possible to

integrate the probability density function of the expected

end point of individual dispersal events to predict long-

term dispersal kernels, if the long-term statistics of the

wind (i.e. the distributions of speed, direction and turbu-

lence) are known. However, phenomena at short time-

scales bias the distribution of wind conditions that are

encountered by the dispersing seeds relative to long-term

wind distributions. For example, at very short time-scales,

wind conditions experienced during the first few moments

of seed flight may differ significantly from block-averaged

conditions (i.e. 30-min mean wind speeds that are typically

available from meteorological stations) due to canopy-

induced turbulence (Bohrer et al. 2008), the aerodynamic

shape of seeds (Greene & Johnson 1990; Lentink et al.

2009) or the environmental conditions that lead to seed

abscission (Greene 2005; Wright et al. 2008; Greene &

Quesada 2011). At longer time-scales, the distribution of

wind conditions when seeds are available (i.e. the dispersal

season) may differ from the distribution of wind conditions

during the entire year (Wright et al. 2008). These biases in

wind conditions may change the dispersal kernel and lead

to higher mean dispersal distances and/or more frequent/

stronger events of long-distance dispersal (LDD) (Nathan

2006; Nathan et al. 2008).

For plants that are dependent on LDD, a possible set of

traits that could be optimized involves the timing of seed

abscission such that seeds are released when external con-

ditions favour LDD (Skarpaas & Shea 2007; Soons &

Bullock 2008). Traditionally, experiments have attributed

increased LDD probability to seed abscission during

strong horizontal winds (Soons et al. 2004; Greene 2005;

Jongejans et al. 2007; Greene, Quesada & Calogeropoulos

2008), by suggesting that strong horizontal winds are cor-

related with high turbulence, including upward vertical

perturbations of the wind. Over the long term and large

scale, vertical wind is a mean-zero process, which means

that strong turbulence will produce both updrafts and

downdrafts. Therefore, strong turbulence may both

enhance and hinder dispersal over the course of each

dispersal event. Dispersal models have shown that updrafts

enhance LDD (Nathan et al. 2002; Tackenberg, Poschlod

& Kahmen 2003; Bohrer et al. 2008), and therefore,

we hypothesize that updrafts should provide the preferred

release condition for wind-dispersed seeds that are

dependent on LDD.

Physiologically, targeting updrafts is not a simple task.

Forces in all directions, such as drag forces generated by

wind flowing past the seed and the turbulent shaking of

branches, will potentially detach the seeds when the wind

is strong but not necessarily upward. Therefore, seeds need

to combine directional aerodynamic shapes and release

mechanisms that favour abscission when the applied force

pulls the seed in the desired upward direction. This intui-

tive notion that wind-dispersed plants have morphological

mechanisms to preferentially release seeds during updrafts

was demonstrated in artificial settings in maple trees

(Greene & Johnson 1992) and with the forb Tragopogon

dubius (Greene & Quesada 2011).

We used field measurements (seed arrival and meteoro-

logical measurements) and long-term data sets (seed trap

and meteorology) to disentangle the effects of different sea-

sonal and meteorological forcing on seed abscission and

dispersal at different time-scales in a natural tropical forest

environment for the neotropical tree Luehea seemannii

(Triana & Planch.). We used phenomenological and mech-

anistic dispersal models to integrate the short-term out-

comes of these environmentally driven abscission

conditions and resolve the consequences of these effects for

long-term dispersal kernels.

Materials and methods

S ITE DESCRIPT ION

The study took place at the canopy crane research facility

located in the 350-ha Parque Natural Metropolitano (PNM),

Panama (8°59′N, 79°33′W). The approximately 100-year-old

natural secondary forest is classified as a dry, lowland forest

(Holdridge et al. 1971) and contains more than 300 tree species.

Canopy heights range from 20 to 40 m. Annual precipitation

averages 1740 mm. A single dry season extends from mid-Decem-

ber through April, and a single wet season that includes 90% of

annual precipitation comprises the remainder of the year (http://

biogeodb.stri.si.edu/physical_monitoring/).

SPEC IES DESCRIPT ION

Luehea seemannii (Triana & Planch.), Malvaceae, ranges through-

out Mesoamerica and northern South America and is a canopy

tree that reaches heights of 35 and 40 m at the PNM and Barro

Colorado Island (BCI), respectively. The light-demanding seed-

lings only establish in forest gaps where light reaches the forest

floor (Molofsky & Augspurger 1992). These establishment require-

ments favour LDD because forest gaps are rare, comprising less

than 2% of forest area. The fruit is a hard dry capsule that splits

open to expose the diaspores (Fig. 1). The diaspores are 4-mm-

long samaras, weigh just 2�5 mg (fresh mass; SJW, unpublished

data) and have a low fall velocity (0�7 � 0�07 ms�1, mean � 1

S.D. (Augspurger 1986)). Most fruit are oriented vertically (above

the horizontal) so that the open fruit points skyward. The diasp-

ores disperse towards the end of the dry season, when the trade

winds are strongest, the forest canopy is relatively open due to

deciduousness and the imminent wet season will provide the mois-

ture necessary for successful germination (Nathan & Katul 2005;

Wright et al. 2008; Bohlman 2010). In this study, we investigate

the sensitivity of the seasonal dispersal kernel to varying wind dis-

tributions selected from environmental conditions and temporal

ranges associated with the dispersal season.

SEED COUNT

Ten 1-m2 seed traps were placed underneath the crowns of each of

the three L. seemannii used to determine seasonal seed release.

Our dispersal models show up to 65% and 90% of seeds released

will fall within 10 m and 30 m, respectively, from the release

© 2012 The Authors. Functional Ecology © 2012 British Ecological Society, Functional Ecology, 27, 208–218

Effects of uplift on long-distance dispersal 209

point. Therefore, we are confident our seed counts will encompass

a wide range of both short- and long-distance dispersal events. We

censused the traps at 30-min intervals from 6:00 AM to 6:00 PM

from 13 to 23 April 2010, inclusive. At each census, all traps were

emptied, and the number of L. seemannii seeds in each trap was

recorded. Total night-time seed release was documented at 6:00

AM. Night-time seed release was excluded because the exact time

of abscission during the night is not known. Just 12% of seeds

were released during the night so their exclusion did not strongly

affect our results. Counts during or immediately following rain

events (17 of 335 observations) and counts influenced by the can-

opy crane knowingly shaking branches during fruit censuses (2 of

335 observations) were also removed from the data set.

METEOROLOGICAL DATA

An 11-year data set (2000–2010) of hourly mean horizontal wind

speed and temperature at the PNM crane research facility was

acquired through the Smithsonian physical monitoring program

(http://biogeodb.stri.si.edu/physical_monitoring/). A nine-month

(February through October, 2007) data set of wind speed in three

dimensions and turbulence (wind fluctuations, frictional velocity)

above the canopy, summarized as 30-min block averaged statistics

of 10 Hz measurements, was available from BCI (Bohrer 2007)

roughly 50 km north-west of the PNM. A similar two-week data

set was collected between 12 and 26 April 2010 in the PNM.

Appendix S2 (Supporting Information) describes the methods

used to process the two 10 Hz data sets and to collect ancillary

data including air temperature, relative humidity, water vapour

pressure and incoming, outgoing and net radiation at the PNM.

EMPIR ICAL ABSC ISS ION MODEL

Seed counts were used to estimate the seasonal bias of seed abscis-

sion. We call this metric seasonally adjusted seed abscission or

DSa (see Appendix S1: Dispersal Season Determination). The sea-

sonal log-normal abscission estimate had a low correlation to

actual seed count data (r2 = 0�04), but was significant (P < 0�05).We constructed a multivariate regression model between DSa and

the observed environmental variables to determine the subseasonal

scale conditions that affect seed abscission (Table S1). All data

were averaged into 90-min bins to reduce autocorrelation and

account for potential overlap between seed counts directly before

and after their corresponding 30-min wind statistics. We followed

a stepwise procedure. At the first step, first- and second-order

polynomial regression models between DSa and each environmen-

tal variable were evaluated. We then considered the subset of

regression models that were statistically significant at the 95% CI.

Of these significant models, we selected the model with the lowest

Bayesian information criterion (BIC) value (Schwarz 1978).

To determine whether the addition of other environmental vari-

ables would lead to significant model improvement, we regressed

first- and second-order polynomials of each of the environmental

variables to the residuals of the previously selected model. Statisti-

cally significant regressions (if any) were deemed to yield signifi-

cant model improvement. Of the statistically significant

regressions (if any), we selected the one with the lowest BIC as the

new best model. This procedure was repeated until no statistically

significant regressions provided a better BIC. Although this proce-

dure assumes second-order polynomials, we found that the selec-

tion of environmental variables was insensitive to this assumption.

The goodness-of-fit of the final model was evaluated by testing the

residuals for independence (Box–Ljung test), normality (Shapiro–Wilk test) and homoscedasticity (Breusch–Pagan test). Statistical

analyses were performed using R version 2�15�1.

MODEL SELECT ION CRITER IA

A Monte Carlo study was carried out to assess the skill and

significance of the model selected. The basic protocol followed

here is similar to what was presented in Beaulieu et al. (2012)

and is designed to test for Type I and Type II errors. We

started with the null hypothesis that our best-fit model is cor-

rect. To test for Type I errors, we generated a synthetic time

series by randomly drawing (with replacement) from the residu-

als of the best-fit model and then added these random draws

to the fitted values of the best-fit model. We then applied our

fitting procedure to the synthetic time series. If our original

determination of the best-fit model is correct, then this model

should be selected to describe a strong majority of the syn-

thetic series. Our procedure for testing for Type II errors was

similar, except that this time we generated a synthetic time ser-

ies by randomly drawing (with replacement) from the residuals

of the second-best-fit model and then added these random

draws to the fitted values of the second-best-fit model. We then

applied our fitting procedure to this second synthetic series and

determined the proportion of times that our best-fit model was

selected. A small proportion would indicate that we would

rarely accept the null hypothesis when it is false. These simula-

tion schemes are appropriate because, in both the best-fit

model and the second-best-fit model, the residuals can be con-

sidered independent (Ljung-Box test, 95% confidence level). A

total number of 10,000 synthetic series were generated in the

testing of both Type I and Type II errors. In a preliminary

analysis, this number of synthetic series was found to be suffi-

cient for the results to converge.

SENSIT IV ITY ANALYS IS TO DETERMINE THE EFFECTS

OF THE T IM ING OF SEED RELEASE

Different environmental conditions lead to seed abscission at dif-

ferent times. Over the long term, these differences accumulate to

form a biased sample of the actual wind conditions. To estimate

the potential effects of seed abscission timing on the dispersal ker-

nel, we used two models forced with wind distributions derived

from long-term wind observations at BCI. These distributions are

broken into subsets based on combinations of weather and wind

conditions associated with seed abscission in the best-fit abscission

model (see Methods: Empirical abscission model). Specific wind

Fig. 1. Luehea seemannii fruit in a tropical forest. Fruit pods hold

many seeds in a start orientation, typically facing upward (above

the horizontal). Cracks in the distal end of the pod widen during

the season allowing the seeds to be released.

© 2012 The Authors. Functional Ecology © 2012 British Ecological Society, Functional Ecology, 27, 208–218

210 K. D. Maurer et al.

distributions and inclusion of abscission biases in either model are

later described in the individual model methods. We use these sim-

ulations to estimate the sensitivity of the dispersal kernel (particu-

larly the mean distance and LDD probability) to the

environmental conditions affecting the timing of seed release. The

resulting kernels are not evaluated for the specific dispersal dis-

tances and probability. Instead, each kernel is compared relative

to the others and relative to a bench-mark case of unbiased, uni-

form-in-time release rate to quantify the relative long-term effects

of the bias in wind conditions due to the selective timing of seed

release under different environmental conditions.

MODELL ING LONG-TERM EFFECTS OF

ENV IRONMENTALLY TR IGGERED ABSC ISS ION – THE

SUPER-WALD KERNEL

A good approximation of the dispersal kernel for slow-falling

seeds in turbulent environments can be calculated with the WALD

phenomenological kernel (Katul et al. 2005):

W xð Þ ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

z2r4phjHx3

rexp �

V2t x� zru

Vt

� �2

4jhH uð Þ2x

0B@

1CA

264

375 eqn 1

where W xð Þ is the probability of landing at a distance x (m)

from the source, zr is the height (m) above ground at which

seeds were released from the mother plant, h is the mean

height (m) of the top of the surrounding canopy, Θ is a scal-

ing coefficient for turbulence defined as the ratio between the

standard deviation of the 10 Hz measurements over a 30-min

period of vertical wind fluctuation, rwðms�1Þ, and the mean

wind speed above the canopy, uðms�1Þ; thatis;H ¼ rw=u. Long-

term Θ is determined from the slope of the correlation between

rw and u over the data set of high-frequency wind observations.

The similarity constant, j, is assumed to be 0�6 for within-can-

opy flow conditions (Thompson & Katul 2008), and Vt is the

terminal fall velocity of the seed (m s�1). Here, we used

Vt = 0�7 � 0�07 m s�1, determined from the mean of measure-

ments of 15 seeds (Augspurger 1986). The WALD kernel

describes the distribution of dispersal distances in a given set

of wind conditions, typical of a specific 30-min period.

Thompson & Katul (2008) showed that WALD can be

expanded to represent the expected long-term dispersal kernel,

obtained as the convolution of many 30-min dispersal kernels, if

the long-term distribution of the wind is known and assumed to

fit a Weibull. A more accurate representation of the long-term

wind distribution may be obtained through explicit integration of

individual 30-min measurements over the entire period (following

the approach in Wright et al.2008). The seasonally integrated

super-WALD (SW) kernel will then follow the formulation of

SW xð Þ ¼ 1

t

Zt

W ut; xð Þdt eqn 2

where W ut; xð Þ is the WALD kernel (as a function of distance, x)

for the observed 30-min mean wind conditions at a particular time

ut (described in eqn 1). As super-WALD does not account for the

variation of wind speed with height above the canopy, we assume

the wind speed at a height of 5 m above the canopy as the effec-

tive wind speed. Super-WALD kernels were calculated using the

statistics of the 30-min mean horizontal wind at PNM for the fol-

lowing scenarios: (1) full year of uniform seed release rate; (2) dis-

persal only during the observed dispersal season (sub-sampling of

meteorological data was done following Garrity et al. 2011); (3)

dispersal during the dispersal season only during daytime hours

(6:00 AM to 6:00 PM); (4) a subset of (3) but only during strong

horizontal winds, that is, u > 0�5 m s�1 and (5) a subset of (3) but

only in relatively high (above median) temperatures, that is,

T > T50. The super-WALD kernel does not incorporate updrafts;

therefore, we include higher horizontal winds, which typically lead

to higher turbulence (i.e. more updrafts/downdrafts). We recalcu-

lated Θ based on the subset of wind observations that comply with

the conditions of each case and then recalculated the dispersal ker-

nel that corresponds with the appropriate release timing using

eqns 1 and 2. The 11-year distributions of wind speed for all cases

are presented in Figure S4. Figure S5 presents the day and night

distributions of turbulence statistics (frictional velocity and verti-

cal wind fluctuation inside the canopy) for 12–26 April 2010.

EFFECTS OF ABSC ISS ION IN UPDRAFTS

Updrafts are a short-term process and are part of the turbulent

fluctuations of vertical wind, which averages to near zero at the

30-min and longer time-scales. The coupled Eulerian–Lagrangianclosure (CELC) model (Nathan & Katul 2005) is able to simulate

turbulence by calculating random instantaneous (milliseconds–sec-onds) turbulent-driven excursions from a prescribed wind speed

field and calculate the resulting three-dimensional trajectories of

wind-dispersed seeds. In CELC, the prescribed horizontal wind

speed field is homogeneous but includes a vertical profile – weaker

wind inside the canopy and near the ground following Massman

& Weil (1999) and logarithmically increasing wind speed above

the canopy, following the Monin–Obukhov similarity theory. Sim-

ilar variation is prescribed for the turbulence statistics. The trajec-

tory calculations are repeated for many virtual seeds to produce

the large sample necessary to calculate a representative dispersal

kernel for the prescribed, half-hourly wind conditions. Repeated

CELC simulations with different sets of prescribed, observation-

based, above-canopy, half-hourly wind conditions are combined

to form an overall seasonal kernel. In this way, the resulting ker-

nel accounts for both short-term turbulence, through the effects

on the trajectories of individual seeds, and longer-term wind con-

ditions, through the combined sets of prescribed 30-min condi-

tions. We used the same CELC set-up as reported in Wright et al.

(2008). The fact that CELC utilizes both a turbulent time-scale

(during the dispersal events) and a longer time-scale (by repeated

simulations with different 30-min forcing) limit the negative effects

of time-scale choice on the estimate of the kernel (Skarpaas, Shea

& Jongejans 2011).

Inputs for CELC included the leaf drag coefficient (estimated

here as 0�25) and the half-hourly wind and turbulence statistics

above the canopy on BCI during a full dispersal season in 2007

(Bohrer 2007). Release height was assumed to be 40 m, corre-

sponding to the canopy height at BCI, where we have season-long

high-frequency measurements of wind and turbulence. Canopy

structure representation in CELC is reduced to the description of

the horizontally averaged vertical profile of leaf area density pro-

vided by Bohlman & O’Brien (2006) for BCI. Terminal velocity

for each dispersal event was randomly selected from a Gaussian

distribution, with the reported mean and standard deviation for

L. seemannii. To reduce the 2-D dispersal distribution to a 1-D

distance kernel, we converted the 2-D space to annuli centred on

the release point. The number of seeds that arrived in each dis-

tance bin were summed and then normalized by bin width and the

total number of seeds released (during the entire seasonal series of

simulations), resulting in the probability a seed fell in each dis-

tance bin. We ignore dispersal distances � 100 km, as these were

typically caused by seeds ‘caught’ at the numeric top boundary of

the model, causing unrealistically long dispersal distances due to

numerical limitations.

To directly test the effects of release in updrafts, we ran two ser-

ies of simulations with CELC: (i) bench-mark case – used to simu-

late the dispersal kernel when seed abscission rate is not affected

by updraft; (ii) updraft-biased case in which the seed is initially

© 2012 The Authors. Functional Ecology © 2012 British Ecological Society, Functional Ecology, 27, 208–218

Effects of uplift on long-distance dispersal 211

caught in an upward eddy for a period of one eddy correlation

time (calculated using formulation from Nathan & Katul (2005)).

This biased case is used to simulate abscission that is induced by

an updraft event at some point during the prescribed 30-min per-

iod. The initial vertical wind speed for each 30-min period is pre-

scribed as the median updraft velocity (i.e. the 75th percentile of

the vertical wind distribution, which includes roughly 50% up-

drafts and 50% downdrafts) assuming vertical velocity has a

Gaussian distribution with mean 0 and the observed standard

deviation, rW. This vertical eddy velocity is representative of a

typical updraft for the wind conditions during each specific half

hour and may or may not be larger than the terminal velocity of

the seed. After the initial eddy correlation time period, the seed is

allowed to experience the same wind statistics as in the bench-

mark case, driven by the observed 30-min mean and turbulence

statistics.

Results

OBSERVAT IONS : SEED ABSC ISS ION IS DETERMINED

BY METEOROLOGICAL CONDIT IONS

Seed abscission is intermittent, as can be seen by the

large deviations from predicted seasonal distribution of

seed release (DSa, Fig. S3). The majority of seeds were

released during a few large events. Over 158 half-hour

periods, we found all meteorological variables to be

significantly directly correlated with the rate of seed

abscission, with the exception of u. Because most

environmental variables were intercorrelated (Table S2),

it is not surprising that many variables show significant

effects. The variable with the highest predictive power of

seed abscission was the root mean square of the upward

wind perturbations, rWup (r2adj = 0�490, P < 0�001), whichindicates that updrafts have the strongest effect of any

environmental variable on seed abscission in L. seemannii.

In the subsequent steps of the regression analysis, the

sensible heat flux (H), temperature (T) and mean horizon-

tal wind speed (�u) also significantly affected abscission, but

the addition of further environmental variables did not

significantly improve the fit. Null hypotheses of indepen-

dence and homoscedasticity were not rejected (P = 0�72and P = 0�62, respectively). However, the residuals were

not normally distributed (P < 0�001). While non-normality

can in principle introduce biases, our parameter estimates

from ordinary least-squares were consistent with the

results of a robust regression. The seed abscission model

resulting from the stepwise procedure (r2adj = 0�714,P < 0�001) follows:DSa ¼ 1700r2Wup � 580rWup � 1040H2 þ 3�6T� 44u2 þ 45u

� 63

eqn 3

We used Markov Chain Monte Carlo analysis to test

the significance of adding each of the above model vari-

ables. rWup was selected as the first predictor variable in a

strong majority (89%) of the cases (Fig. S6a). Wmax was

selected as the first predictor variable in almost all of the

remaining cases. Thus, if our best-fit model accurately

describes the data, then rWup would be correctly identified

as the most important predictor variable with 89% proba-

bility. The probability that H was chosen as the second

predictor variable, conditional on rWup being previously

chosen, was 73% of cases (Fig. S6b). Similarly, probability

of choosing T as the third variable conditional on have

previously chosen rWup and H was 76% (Fig. S6c), and

the probability of choosing �u as the fourth variable condi-

tional on having previously chosen rWup, H and T was

74% (Fig. S6d). If �u was not chosen in the fourth step, the

next most likely outcome (23%) was that no model gave a

statistically significant improvement to the fit. Overall, the

independent variables of the best-fit model were chosen in

37% of the synthetic series. Because of the relatively low

proportion of cases for which �u was chosen, including it as

a predictor variable should be regarded as speculative. In

our analysis of Type II error, we found that the second-

best-fit model consisting of rWup, H and T was selected in

56% of the series. The best fit was (spuriously) selected

2% of the time, indicating relatively low probability of

incorrectly accepting the null hypothesis. Following the

results from the Monte Carlo study, the most significant

model (evaluated in Fig. 2) (r2adj = 0�646, P < 0�001)follows:

DSa ¼ 1700r2Wup � 600rWup � 1130H2 þ 3�3T� 43 eqn 4

This model was selected as the final abscission model,

which describes positive feedback towards abscission

during periods of updrafts and high temperature and a

negative feedback towards abscission during temperature-

driven highly convective periods. Coefficients to the model

correspond to a 30-min estimate of seed abscission.

MODELL ING: INTEGRAT ING ABSC ISS ION CONDIT IONS

TO PREDICT LONG-TERM DISPERSAL KERNELS

We created dispersal kernels using the super-WALD

model, with 11-year wind data from PNM and

−10 0 10 20 30 40 50 60

−10

0

10

20

30

40

50

60

Measured ΔSa

Mo

del

ed Δ

Sa

Fig. 2. Modeled abscission vs. measured abscission (eqn 4,

r2 = 0.646, P < 0.001). Solid line is the 1 : 1 line.

© 2012 The Authors. Functional Ecology © 2012 British Ecological Society, Functional Ecology, 27, 208–218

212 K. D. Maurer et al.

corresponding 11-year dispersal season–timing observa-

tions from BCI. The results show that kernels representing

cases 1–3 have very similar shapes (Fig. 3). The strong

wind conditions (case 4) show the highest probability of

dispersing between 20–255 m. From 255–4988 m, the high

temperature conditions (case 5) show the highest probabil-

ity, with yearly conditions (case 1) having the highest

probability of distances further than 4988 m. The dispersal

probabilities near these transitions are on the order of

10�4–10�7; however, we show for each case that roughly

1% of the seed population will travel at least 1 km and

0�1% of the seed population will travel multiple km. For

the yearly conditions, the 99�9% cumulative threshold was

not reached in the maximum search area of this study

(25 km). Although the strong wind kernel becomes less

probable than the yearly and daytime dispersal season ker-

nels, the mean dispersal distance under strong wind condi-

tions (91 m) is further than the means of the yearly,

seasonal and daytime, seasonal conditions (67, 63 and

84 m, respectively). The high-temperature kernel has the

furthest mean dispersal distance at 105 m.

MODELL ING: DETERMIN ING THE EFFECTS OF

ABSC ISS ION IN UPDRAFTS

Dispersal kernels were calculated by the CELC model

using two cases: one with an updraft bias and the other,

a control with no bias for updraft-driven seed abscission.

Dispersal distance is consistent between each case up to

roughly 100 m, as can be seen by the equivalent distance

travelled by the first cumulative 99% of seeds. At dis-

tances further than 100 m, we find a shift to higher dis-

persal distance probability in the updraft-biased scenario

relative to the control scenario (Fig. 4). At the cumula-

tive 99�9% seed population threshold, the control case

sees dispersal distances of 364 m, compared to distances

of 840 m (2�3 times as far). This roughly 2 : 1 dispersal

distance ratio of the updraft case vs. the control case

continues for the duration of the seed population, and

the difference in probability of LDD of the updraft case

becomes as large as an order of magnitude more than

the control case for dispersal distances larger than

10 km. Although this distance corresponds to a probabil-

ity on the order of 10�5–10�6, integration of the kernel

shows roughly 0�01% of the seed population will travel

further than 10 km. The mean dispersal distance during

the updraft case is 28% further than the mean dispersal

distance during the control case.

Discussion

Dispersal is a very short-term event (seconds–minutes)

which, aggregated over many events over days and sea-

sons, controls the slow, long-term dynamics (years – mil-

lennia) of population spread and survival. Therefore, we

hypothesize that the physiological traits that control the

timing of seed release should be selected to respond to

environmental conditions in a way that will optimize the

resulting dispersal. The species we studied, L. seemannii, is

shade-intolerant and depends on germination in canopy

gaps, which are rare in its closed canopy forest habitat.

These establishment limitations suggest L. seemannii

would benefit from LDD, which provides a large ‘search

area’. Selection should favour morphological traits that

promote LDD in this tree. The dispersal unit morphology

(light weight, thin ‘wings’, upward-facing capsule) suggests

10–1

10–2

10–3

10–4

10–5

10–6

10–7

10–8

100 101 102 103 104

Dispersal Distance [m]

pd

f

99%

99·9%

YearSeasonSeason (Daytime)Season (Daytime, u >0·5)Season (Daytime, T >T50)

Fig. 3. Super-WALD dispersal kernels presented as the probabil-

ity seeds disperse a given distance under five sets of environmental

conditions. The inset provides a key to the environmental condi-

tions. Both the probability of seed arrival and distance are on log-

arithmic scales. Vertical lines correspond to the distance to which

the listed percentage of seeds have traveled.

Dispersal Distance [m]

pd

f

99%

99·9%

UpdraftControl

10–1

10–2

10–3

10–4

10–5

10–6

10–7

100 101 102 103 105104

Fig. 4. The coupled Eulerian–Lagrangian closure (CELC) dis-

persal kernels presented as the probability seeds disperse a given

distance under two sets of environmental conditions. The inset

provides a key to the environmental conditions. Both the proba-

bility of seed arrival and distance are on logarithmic scales. Verti-

cal lines correspond to the distance to which the listed percentage

of seeds have traveled.

© 2012 The Authors. Functional Ecology © 2012 British Ecological Society, Functional Ecology, 27, 208–218

Effects of uplift on long-distance dispersal 213

that selection for LDD has affected the seed traits to

increase their flight time and dispersal distance. The mean

dispersal distance may also be affected by long-term

(multi-annual) interactions between population viability,

seedling survival, habitat and climate (Kuparinen et al.

2009; Nathan et al. 2011). However, in this study, we focus

on subannual time-scales. We use super-WALD kernels to

test the effects of environmental variables such as wind

speed and the seasonal and diurnal distributions of the

wind and CELC to test the effects of seed release in

updraft conditions.

EFFECTS OF THE T IM ING OF THE DISPERSAL SEASON

The year-round super-WALD kernel (case 1) had the high-

est probability of dispersing further than 4 km and the

highest mean long dispersal distance for the farthest 0�1%of seeds (Fig 3). However, the mean dispersal distance is

higher during seasonal daytime conditions (84 m) (case 3)

compared to the year-round (67 m) and dispersal season

(63 m) conditions. While the mean wind speed (�u) for the

seasonal daytime case is higher than both the seasonal and

year-round cases (Fig. S4), the year-round wind speed dis-

tribution shows a thicker tail, indicating more frequent

events of relatively strong wind. This is due to the fact that

there are more extreme turbulent wind gusts during the

wet season than during the dry season, as indicated by the

wind speed skewness and kurtosis (Table S3). Nonetheless,

our study species, and most other wind-dispersed species

in central Panama, disperse their seeds during the dry sea-

son. These findings suggest that the timing of the dispersal

season is not driven only by consideration of dispersal dis-

tance and that other factors, such as the impending rains

that favour germination and seedling establishment, may

also lead to selective forces that determine the timing of

the dispersal season.

In our simulations, we neglect the effects of spatial het-

erogeneity and the seasonality of canopy structure. It is

probable that the effects of reduced canopy density during

the dry season play an important role. During the dispersal

season, canopy density is at its minimum, which improves

dispersal distance (Nathan & Katul 2005), and the canopy

is rich with temporary gaps caused by leafless deciduous

trees surrounded by evergreen trees (Bohlman 2010), which

leads to ejection hotspots and increased LDD probability

(Bohrer et al. 2008, 2009). These effects cannot be resolved

by either the super-WALD or the CELC models as they

are driven by the spatial interaction between canopy heter-

ogeneity and turbulence. Due to these model limitations,

we cannot rule out wind as a selective driver of the timing

of the dispersal season.

EFFECTS OF DAYT IME RELEASE

As seen in our seed trap data, daytime abscission was

roughly an order of magnitude greater than night-time

abscission. Wind conditions at night tend to be weaker

than those during the day. During the strongly convective

tropical periods, daytime means of u = 0�540 m s�1,

u* = 0�280 m s�1 and rWup = 0�223 m s�1 were much lar-

ger than night-time means of u = 0�334 m s�1, u* =0�168 m s�1 and rWup = 0�158 m s�1 (Fig. S5). The day-

time vertical wind is more negatively skewed (�0�518 m

s�1) than night-time vertical wind (�0�437 m s�1), dem-

onstrating a thicker above-mean tail and higher tendency

for updrafts. These statistics, and correspondingly, our

simulation results, suggest that seeds will have higher

chances to uplift and experience LDD with the strongly

convective conditions during the day rather than during

the night.

EFFECT OF SEED ABSC ISS ION AT H IGH WIND SPEED

AND HIGH TEMPERATURE

It is interesting to note that heat flux and temperature,

which have been shown to influence seed abscission in pre-

vious studies in the same tropical environment but for a

different species, Jacaranda copaia, which disperses during

the wet season (Wright et al. 2008), were also found to sig-

nificantly influence the high-frequency seed release timing

of L. seemannii, which disperses during the dry season.

Previous studies demonstrated that drying of the dispersal

unit increases seed abscission (Greene & Johnson 1992;

Jongejans et al. 2007). It is possible that temperature pro-

vides the mechanism for the daytime release through the

drying and opening of the pod. Both temperature and

humidity have a significant positive effect on abscission;

however, the strong correlation between temperature and

humidity led to humidity not having a significant indepen-

dent effect on abscission.

Strong wind (red line, Fig. 3) and high temperature

(cyan line, Fig. 3) show enhanced dispersal probabilities

at moderate distances (100–5000 m) compared to yearly,

seasonal and seasonal daytime cases. LDD at strong

wind becomes less probable around the 99th percentile

(~1 km) of seeds released, whereas high-temperature LDD

becomes less probable around the 99�9th percentile (few

km). We found the ratio between vertical wind fluctua-

tions and mean horizontal wind speed, Θ, to be the rea-

son for the observed differences between the shape of the

dispersal kernel with strong wind and other seasonal ker-

nels. At our site and typical of other tropical sites, low

values of u are characteristic of weather conditions with

high thermally driven turbulence and therefore high Θ.

This occurs because strong wind produces more shear-

driven eddies that tend to be smaller and less energetic

than thermally driven eddies. Θ shows a twofold reduc-

tion when wind is subsampled from u > 0�5 m s�1com-

pared to the year-round and daytime dispersal season

and high temperature winds (0�59, 1�31, 1�25 and 1�18,respectively). Combined, higher u and lower Θ create

large effects on the shape of the dispersal kernel, particu-

larly, increasing the mean dispersal distance while

reducing the probability of LDD.

© 2012 The Authors. Functional Ecology © 2012 British Ecological Society, Functional Ecology, 27, 208–218

214 K. D. Maurer et al.

Table

1.Summary

ofthestatisticsfrom

thestepwiseem

piricalmodel

selectionforseed

abscission,expressed

astheresidualfrom

theexpectedseasonalseed

availabilityrate,DSa

Model:DSa=

Environmentalvariable

(x)andMonte

Carloparameter

index

BIC

TRH

W95

Wmax

Wmin

r Wr W

up

uu*

gust

rU

HSWnet

VPD

ZE

12

34

56

78

910

11

12

13

14

15

Ax+B

0.268

0.222

0.302

0.343

0.251

0.241

0.388

�0.019

0.147

0.235

0.182

0.031

0.107

0.255

0.073

–Ax2+B

0.277

0.210

0.324

0.388

0.269

0.239

0.443

�0.020

0.110

0.228

0.158

�0.012

0.048

0.291

0.066

–Ax2+Bx+C

0.318

0.243

0.318

0.401

0.258

0.226

0.490

0.021

0.178

0.219

0.197

0.094

0.165

0.279

0.054

391.7

Ar W

up2+Br W

up+Cx+D

0.509

0.491

0.533

0.480

0.480

0.517

0.519

0.514

0.488

0.501

0.544

0.480

0.498

0.483

–Ar W

up2+Br W

up+Cx2+D

0.510

0.489

0.551

0.480

0.483

0.534

0.539

0.535

0.493

0.519

0.579

0.484

0.512

0.481

372.2

Ar W

up2+Br W

up+Cx2+Dx+E

0.512

0.496

0.581

0.487

0.490

0.559

0.558

0.551

0.492

0.574

0.573

0.520

0.512

0.477

–Ar W

up2+Br W

up+CH

2+Dx+E

0.646

0.637

0.571

0.571

0.578

0.570

0.580

0.570

0.570

0.570

0.575

0.653

0.588

364.8

Ar W

up2+Br W

up+CH

2+Dx2+E

0.650

0.629

0.574

0.570

0.577

0.570

0.595

0.572

0.570

0.571

0.570

0.678

0.585

–Ar W

up2+Br W

up+CH

2+Dx2+Ex

+F

0.660

0.659

0.590

0.569

0.568

0.575

0.638

0.578

0.567

0.605

0.594

0.672

0.581

–Ar W

up2+Br W

up+CH

2+DT+Ex

+F

0.642

0.639

0.639

0.652

0.638

0.674

0.646

0.638

0.643

0.644

0.650

0.639

–.Ar W

up2+Br W

up+CH

2+DT

+Ex2+F

0.640

0.640

0.639

0.650

0.639

0.694

0.650

0.639

0.648

0.646

0.672

0.641

–Ar W

up2+Br W

up+CH

2+DT

+Ex2+Fx+G

0.668

0.640

0.631

0.646

0.639

0.714

0.645

0.634

0.655

0.640

0.675

0.635

347.6

Ar W

up2+Br W

up+CH

2+DT

+Eu

2+Fu+Gx+H

0.713

0.709

0.711

0.711

0.707

0.707

0.710

0.713

0.708

0.720

0.708

–Ar W

up2+Br W

up+CH

2+DT

+Eu

2+Fu+Gx2+H

0.710

0.710

0.711

0.710

0.707

0.707

0.709

0.711

0.709

0.738

0.710

–Ar W

up2+Br W

up+CH

2+DT

+Eu

2+Fu+Gx2+Hx+I

0.732

0.702

0.704

0.708

0.701

0.701

0.705

0.708

0.703

0.736

0.709

–

Thetable

showsther2

oflinear,

quadraticandsecond-order

polynomialregressionbetweendifferentcombinationsofenvironmentalvariables,

x,andDSa.Ateach

iteration,thevariable

withthe

highestr2

(highlightedbold)amongthose

withasignificantrelationship

wasadded

tothemodel.Thetypeofrelationship

forthisvariable

(linear,quadratic)

wasalsodetermined

accordingto

the

highestr2.Bayesianinform

ationcriterion(BIC

)analysiswasusedto

determinewhether

addingthisvariable

tothemodel

isjustified.In

each

iteration,thelowestmodel

BIC

valueisshownonthe

last

column.BIC

values

ofthelast

iterationare

leftblank,asnoBIC

waslower

thanthatofthepreviousiteration.Thesignificance

oftheim

provem

entto

themodel

incomparisonwiththesimpler

modelfrom

thepreviousiterationwastested

usingaMarkovChain

Monte

Carloanalysis(Figure

S6).

© 2012 The Authors. Functional Ecology © 2012 British Ecological Society, Functional Ecology, 27, 208–218

Effects of uplift on long-distance dispersal 215

EFFECTS OF ABSC ISS ION IN UPDRAFTS

Long-distance dispersal of wind-dispersed seeds in forests

is dependent on ejection of the seeds above the canopy

(Nathan et al. 2002; Bohrer et al. 2008). During its dis-

persal event, a seed spends a few seconds to minutes in

the air, held up by turbulent eddies that produce updrafts

that are faster than its terminal fall velocity. As the long-

term mean vertical wind is near zero, short-term turbulent

fluctuations are the major source of uplift. While at a

longer time-scale turbulence is a chaotic process, at short

time-scales turbulent motion is characterized by organized

waves – eddies. If a seed can time its release to co-occur

with the passage of an upward eddy (ejection), it can

‘ride’ this eddy for a short period before the eddy breaks

and dissipates. The average time for eddy dissipation is

the eddy dissipation time, which we used in the CELC

model. This short period (few seconds) of upward motion

may be long enough and the updraft strong enough for

the seed to be ejected above the canopy and into the

stronger horizontal winds aloft that can carry seeds long

distances.

The CELC model simulation confirmed that updraft-

targeted seed release generates a higher probability of

LDD. Dispersal events will only be meaningful when

leading to seedling establishment, which in most instances

involved LDD to escape predation and/or find suitable

habitat (Thompson et al. 2009). Yearly seedling establish-

ment events may occur at dispersal probabilities as low as

10�10 (Nathan 2006), which demonstrates our large LDD

advantage during updraft conditions at probabilities of

10�5–10�6 to be significant. Furthermore, from seed

counts per individual fruit (385 � 53, n = 18) and on the

order of 103 fruit per tree, we estimate the total annual

seed production per individual to be on the order of 105–

106 seeds, and roughly 107–109 during each tree’s lifetime.

By factoring these magnitudes into our calculated dis-

persal kernels, we show that when released in an updraft

hundreds of seeds per individual per dispersal season (and

tens-hundreds of thousands in a lifetime) will travel more

than 1 km farther than seeds whose release does not

target updrafts.

The idea that ejections (updrafts) enhance dispersal dis-

tances may seem intuitive, yet it has seldom been directly

modelled or measured. Nathan et al. (2002) used the

CELC model to show that ejected seeds would have a

large LDD advantage over those seeds not ejected from

the canopy. Our CELC simulation is the first to compare

dispersal distance of seeds that were released uniformly

without respect to updrafts with seeds released preferen-

tially in updraft conditions. Although updraft bias may

play an important role in both abscission timing and dis-

persal distance, it remains difficult to incorporate into

dispersal kernel models. The problem arises because tar-

geted abscission and turbulent momentum ejections are

coupled phenomena that operate at very short time-

scales. Timing the release to favour LDD is only possible

if short-term high-frequency information is used. The

challenge for the plant is to detect these conditions and

target the release of seeds to these turbulence ejection

events. In the case of wind-dispersed seeds, a closer

inspection of the dispersal unit may resolve the link

between morphology and LDD.

Greene & Johnson (1992) showed that drag from hori-

zontal wind (induced with a household fan) affected the

rate of seed abscission in a maple tree and that the shape

of the maple seed wings and detachment mechanisms inter-

acted with the wind direction such that under updrafts the

seeds deflected at a larger angle which increased their

probability of detachment of the peduncle. In a wind-tun-

nel experiment, Greene & Quesada (2011) showed that the

shape of the capitulum of T. dubius suppresses seed release

in downdrafts and therefore provides a morphological

mechanism for updraft-selective release. Our study is the

first to observe this updraft bias phenomenon in a natural

environment and a tropical tree. The fruits of L. seemannii

have an upward-facing cone that opens narrow cracks that

begin at its top end (Fig. 1). Bernoulli’s equation along a

vertical streamline starting from the seed location and

extending outward through the pod crack describe the

physical mechanism through which the seed pod orienta-

tion interacts with updrafts to generate lee-side wake vorti-

ces that create a pressure gradient strong enough to

dislodge the seeds.

Conclusions

To correctly estimate the movement capability of dispers-

ing seeds, the full range of time-scales of the signal that

drives seed release in plants must be represented by the

modelling methods used to predict dispersal kernels.

Super-WALD kernels that were generated with long-term

wind observations, subselected for particular seed release

dynamics, showed that the timing of the dispersal season

does not necessarily optimize dispersal distance. At shorter

time-scales, preferential dispersal timing during the day-

time with frequent updrafts increased dispersal distances

and LDD. Mechanistic dispersal simulations showed that

including an updraft bias to the abscission conditions

would further increase the probability of LDD.

Our finding of preferential abscission during updrafts is

consistent with recent hypotheses, model simulations and

laboratory experiments (Tackenberg, Poschlod & Kahmen

2003; Bohrer et al. 2008; Soons & Bullock 2008; Greene &

Quesada 2011). To date, this study and those of Greene &

Johnson (1992) and Greene & Quesada (2011) are the only

ones that report cases of morphological mechanisms for

upward-directional abscission bias. This research high-

lights the need to further investigate the mechanisms of

seed abscission in wind-dispersed plants. Specifically, we

suspect that further inspection of the morphology of their

specialized dispersal units will show how this has evolved

in many species to select release events during environmen-

tal conditions that will lead to optimal LDD.

© 2012 The Authors. Functional Ecology © 2012 British Ecological Society, Functional Ecology, 27, 208–218

216 K. D. Maurer et al.

Acknowledgements

We thank Ran Nathan for early discussion that helped inspire this

study. We thank Mirna Samaniego for data collection assistance. KM

was supported by the Smithsonian Tropical Research Institute (STRI), a

French Graduate Fellowship through the Department of Civil, Environ-

mental & Geodetic Engineering, an Ohio State University Fellowship

and an NSF IGERT Fellowship #DGE-0504552 awarded through the

University of Michigan Biosphere-Atmosphere Research Training

(BART) program. GB was supported by NSF grant #DEB-0918869.

Any opinions, findings and conclusions expressed in this material are

those of the authors and do not necessarily reflect the views of the

National Science Foundation.

References

Augspurger, C.K. (1986) Morphology and dispersal potential of wind-dis-

persed diaspores of neotropical trees. American Journal of Botany, 73,

353–363.Beaulieu, C., Sarmiento, J.L., Fletcher, S.E.M., Chen, J. & Medvigy, D.

(2012) Identification and characterization of abrupt changes in the land

uptake of carbon. Global Biogeochemical Cycles, 26, doi: 10.1029/

2010GB004024.

Bohlman, S.A. (2010) Landscape patterns and environmental controls of

deciduousness in forests of central Panama. Global Ecology and Biogeog-

raphy, 19, 376–385.Bohlman, S. & O’Brien, S. (2006) Allometry, adult stature and regeneration

requirement of 65 tree species on Barro Colorado Island, Panama. Jour-

nal of Tropical Ecology, 22, 123–136.Bohrer, G. (2007) Large eddy simulations of forest canopies for determina-

tion of biological dispersal by wind. PhD, Duke University.

Bohrer, G., Nathan, R. & Volis, S. (2005) Effects of long-distance dispersal

for metapopulation survival and genetic structure at ecological time and

spatial scales. Journal of Ecology, 93, 1029–1040.Bohrer, G., Nathan, R., Katul, G.G., Walko, R.L. & Avissar, R. (2008)

Effects of canopy heterogeneity, seed abscission, and inertia on wind-dri-

ven dispersal kernels of tree seeds. Journal of Ecology, 96, 569–580.Bohrer, G., Katul, G.G., Walko, R.L. & Avissar, R. (2009) Exploring

the effects of microscale structural heterogeneity of forest canopies

using large-eddy simulations. Boundary-Layer Meteorology, 132, 351–382.

Fayard, J., Klein, E.K. & Lefevre, F. (2009) Long distance dispersal and

the fate of a gene from the colonization front. Journal of Evolutionary

Biology, 22, 2171–2182.Garrity, S.R., Bohrer, G., Maurer, K.D., Mueller, K.L., Vogel, C.S. & Cur-

tis, P.S. (2011) A comparison of multiple phenology data sources for

estimating seasonal transitions in deciduous forest carbon exchange.

Agricultural and Forest Meteorology, 151, 1741–1752.Greene, D.F. (2005) The role of abscission in long-distance seed dispersal

by the wind. Ecology, 86, 3105–3110.Greene, D.F. & Johnson, E.A. (1990) The dispersal of winged fruits and

seeds differing in autorotative behavior. Canadian Journal of Botany-

Revue Canadienne De Botanique, 68, 2693–2697.Greene, D.F. & Johnson, E.A. (1992) Fruit abscission in Acer saccharinum

with reference to seed dispersal. Canadian Journal of Botany-Revue Cana-

dienne De Botanique, 70, 2277–2283.Greene, D.F. & Quesada, M. (2011) The differential effect of updrafts,

downdrafts and horizontal winds on the seed abscission of Tragopogon

dubius. Functional Ecology, 25, 468–472.Greene, D.F., Quesada, M. & Calogeropoulos, C. (2008) Dispersal of seeds

by the tropical sea breeze. Ecology, 89, 118–125.Holdridge, L.R., Grenke, W.C., Hathaway, W.H., Liang, T. & Tosi, J.A.

(1971) Forest Environments in Tropical Life Zones: A Pilot Study. Perg-

amon Press, New York. http://biogeodb.stri.si.edu/physical_monitoring/.

Jongejans, E., Pedatella, N.M., Shea, K., Skarpaas, O. & Auhl, R. (2007)

Seed release by invasive thistles: the impact of plant and environmental

factors. Proceedings of the Royal Society B-Biological Sciences, 274, 2457

–2464.Katul, G.G., Porporato, A., Nathan, R., Siqueira, M., Soons, M.B.,

Poggi, D., Horn, H.S. & Levin, S.A. (2005) Mechanistic analytical

models for long-distance seed dispersal by wind. American Naturalist,

166, 368–381.

Kremer, A., Ronce, O., Robledo-Arnuncio, J.J., Guillaume, F., Bohrer, G.,

Nathan, R., Bridle, J.R., Gomulkiewicz, R., Klein, E.K., Ritland, K.,

Kuparinen, A., Gerber, S. & Schueler, S. (2012) Long-distance gene flow

and adaptation of forest trees to rapid climate change. Ecology Letters,

15, 378–392.Kuparinen, A., Katul, G., Nathan, R. & Schurr, F.M. (2009) Increases in

air temperature can promote wind-driven dispersal and spread of plants.

Proceedings of the Royal Society B-Biological Sciences, 276, 3081–3087.Lentink, D., Dickson, W.B., van Leeuwen, J.L. & Dickinson, M.H. (2009)

Leading-edge vortices elevate lift of autorotating plant seeds. Science,

324, 1438–1440.Massman, W.J. & Weil, J.C. (1999) An analytical one-dimensional second-

order closure model of turbulence statistics and the Lagrangian time

scale within and above plant canopies of arbitrary structure. Boundary-

Layer Meteorology, 91, 81–107.Molofsky, J. & Augspurger, C.K. (1992) The effect of leaf litter on early

seedling establishment in a tropical forest. Ecology, 73, 68–77.Nathan, R. (2006) Long-distance dispersal of plants. Science, 313, 786–

788.

Nathan, R. & Katul, G.G. (2005) Foliage shedding in deciduous forests

lifts up long-distance seed dispersal by wind. Proceedings of the

National Academy of Sciences of the United States of America, 102,

8251–8256.Nathan, R., Katul, G.G., Horn, H.S., Thomas, S.M., Oren, R., Avissar,

R., Pacala, S.W. & Levin, S.A. (2002) Mechanisms of long-distance dis-

persal of seeds by wind. Nature, 418, 409–413.Nathan, R., Schurr, F.M., Spiegel, O., Steinitz, O., Trakhtenbrot, A. &

Tsoar, A. (2008) Mechanisms of long-distance seed dispersal. Trends in

Ecology & Evolution, 23, 638–647.Nathan, R., Horvitz, N., He, Y., Kuparinen, A., Schurr, F.M. & Katul, G.

G. (2011) Spread of North American wind-dispersed trees in future envi-

ronments. Ecology Letters, 14, 211–219.Poethke, H.J., Dytham, C. & Hovestadt, T. (2011) A metapopulation para-

dox: partial improvement of habitat may reduce metapopulation persis-

tence. American Naturalist, 177, 792–799.Schwarz, G. (1978) Estimating dimension of a model. Annals of Statistics,

6, 461–464.Skarpaas, O. & Shea, K. (2007) Dispersal patterns, dispersal mechanisms,

and invasion wave speeds for invasive thistles. American Naturalist, 170,

421–430.Skarpaas, O., Shea, K. & Jongejans, E. (2011) Watch your time step: trap-

ping and tracking dispersal in autocorrelated environments. Methods in

Ecology and Evolution, 2, 407–415.Soons, M.B. & Bullock, J.M. (2008) Non-random seed abscission, long-dis-

tance wind dispersal, and plant migration rates. Journal of Ecology, 96,

581–590.Soons, M.B., Heil, G.W., Nathan, R. & Katul, G.G. (2004) Determinants

of long-distance seed dispersal by wind in grasslands. Ecology, 85, 3056–3068.

Tackenberg, O., Poschlod, P. & Kahmen, S. (2003) Dandelion seed dis-

persal: the horizontal wind speed does not matter for long-distance dis-

persal - it is updraft!. Plant Biology, 5, 451–454.Theoharides, K.A. & Dukes, J.S. (2007) Plant invasion across space and

time: factors affecting nonindigenous species success during four stages

of invasion. New Phytologist, 176, 256–273.Thompson, S. & Katul, G.G. (2008) Plant propagation fronts and wind dis-

persal: an analytical model to upscale from seconds to decades using su-

perstatistics. American Naturalist, 171, 468–479.Thompson, S., Katul, G., Terborgh, J. & Alvarez-Loayza, P. (2009) Spatial

organization of vegetation arising from non-local excitation with local

inhibition in tropical rainforests. Physica D-Nonlinear Phenomena, 238,

1061–1067.Volis, S., Bohrer, G., Oostermeijer, G. & Van Tienderen, P. (2005) Regio-

nal consequences of local population demography and genetics in rela-

tion to habitat management in Gentiana pneumonanthe. Conservation

Biology, 19, 357–367.Wright, S.J., Trakhtenbrot, A., Bohrer, G., Detto, M., Katul, G.G., Hor-

vitz, N., Muller-Landau, H.C., Jones, F.A. & Nathan, R. (2008) Under-

standing strategies for seed dispersal by wind under contrasting

atmospheric conditions. Proceedings of the National Academy of Sciences

of the United States of America, 105, 19084–19089.

Received 20 June 2012; accepted 17 October 2012

Handling Editor: Ken Thompson

© 2012 The Authors. Functional Ecology © 2012 British Ecological Society, Functional Ecology, 27, 208–218

Effects of uplift on long-distance dispersal 217

Supporting Information

Additional Supporting Information may be found in the online

version of this article:

Appendix S1. Dispersal Season Determination.

Appendix S2. Meteorology.

Table S1. Environmental Variables.

Table S2. Environmental Correlations.

Table S3. Super-WALD Inputs.

Fig. S1. BCI Seed Trap Data.

Fig. S2. PNM Dispersal Estimates.

Fig. S3. PNM DSa.Fig. S4. Conditional Wind Distributions.

Fig. S5. Day–Night Wind Statistics.

Fig. S6. Monte Carlo Results.

© 2012 The Authors. Functional Ecology © 2012 British Ecological Society, Functional Ecology, 27, 208–218

218 K. D. Maurer et al.