Ecology, 95(2), 2014, pp. 505–513
Ó 2014 by the Ecological Society of America
Predicting species’ maximum dispersal distances
from simple plant traits
RIIN TAMME,
1,5
LARS GO
¨
TZENBERGER,
1,2
MARTIN ZOBEL,
1
JAMES M. BULLOCK,
3
DANNY A. P. HOOFTMAN,
3
ANTS KAASIK,
4
AND MEELIS PA
¨
RTEL
1
1
Institute of Ecology and Earth Sciences, University of Tartu, Lai 40, Tartu 51005 Estonia
2
Institute of Botany, Czech Academy of Science, Dukelska
´
135, CZ-379 82 Tr
ˇ
ebo
ˇ
n, Czech Republic
3
NERC Centre for Ecology and Hydrology, Maclean Building, Benson Lane, Wallingford OX10 8BB United Kingdom
4
Institute of Ecology and Earth Sciences, University of Tartu, Vanemuise 46, Tartu 51014 Estonia
Abstract. Many studies have shown plant species’ dispersal distances to be strongly
related to life-history traits, but how well different traits can predict dispersal distances is not
yet known. We used cross-validation techniques and a global data set (576 plant species) to
measure the predictive power of simple plant traits to estimate species’ maximum dispersal
distances. Including dispersal syndrome (wind, animal, ant, ballistic, and no special
syndrome), growth form (tree, shrub, herb), seed mass, seed release height, and terminal
velocity in different combinations as explanatory variables we constructed models to explain
variation in measured maximum dispersal distances and evaluated their power to predict
maximum dispersal distances. Predictions are more accurate, but also limited to a particular
set of species, if data on more specific traits, such as terminal velocity, are available. The best
model (R
2
¼ 0.60) included dispersal syndrome, growth form, and terminal velocity as fixed
effects. Reasonable predictions of maximum dispersal distance (R
2
¼ 0.53) are also possible
when using only the simplest and most commonly measured traits; dispersal syndrome and
growth form together with species taxonomy data. We provide a function (dispeRsal) to be
run in the software package R. This enables researchers to estimate maximum dispersal
distances with confidence intervals for plant species using measured traits as predictors. Easily
obtainable trait data, such as dispersal syndrome (inferred from seed morphology) and growth
form, enable predictions to be made for a large number of species.
Key words: dispersal syndrome; growth form; migration; mixed-effects model; predictive model; seed
mass; seed release height; taxonomy; terminal velocity; traits.
INTRODUCTION
Dispersal is the unidirectional movement of individ-
uals away from their place of birth (Levin et al. 2003).
For plants, this spatial movement occurs through
vegetative growth or seed dispersal (here we use ‘‘seed’’
as a general term for a reproductive dispersing unit).
While vegetative spread plays a great role in small-scale
patterns of species distribution (Moora et al. 2009), seed
dispersal is a process that shapes local populations and
communities as well as large-scale distribution of species
(Levin et al. 2003, Clobert et al. 2012).
In order to understand the role of dispersal at various
spatial scales, it is of primary importance to know how
far seeds disperse. However, studying seed dispersal and
measuring dispersal distances for plants is challenging.
Methods such as seed traps, direct observations, or
genetic markers are used in the field (Bullock et al.
2006). Some studies employ mechanistic models to
estimate dispersal distances using information on seed
and plant traits as well as environmental conditions
(Soons and Ozinga 2005, Nathan et al. 2011, Bullock et
al. 2012). Spatial patterns of seed dispersal are often
depicted by a dispersal curve, i.e., a dispersal distance
distribution, which displays the frequency (proportion
or probability) of seeds reaching a given distance
(Nathan et al. 2012). The shape of the dispersal curve
can vary for different species or dispersal syndromes,
but a feature of many dispersal curves is a flat tail, i.e.,
relatively rare long-distance dispersal events (Levin et al.
2003). However, such long-distance dispersal events
have disproportionate importance considering their
rarity, for example, facilitating rapid spread of species
and connecting fragmented populations (Nathan et al.
2008).
Many studies have shown dispersal distances to be
strongly related to life-hi story traits. For animals,
several recent papers highlight the strong correlation
between species traits and dispersal ability (Garrard et
al. 2012, Hein et al. 2012, Stevens et al. 2012). For
plants, it is known that dispersal distance is related to a
dispersal syndrome (Willson 1993, Pa
¨
rtel and Zobel
2007, Vittoz and Engler 2007). Dispersal syndrome may
generally be deduced from seed morphology, which is
assumed to facilitate dispersal by a specific vector (e.g.,
Manuscript received 28 May 2013; accepted 11 July 2013.
Corresponding Editor: J. Weiner.
5
E-mail: riin.tamme@ut.ee
505
animals, wind, water [Hughes et al. 1994, Thomson et al.
2010]). However, a multiplicity of vectors, as well as
variation in the behavior of these vectors, makes it
difficult to establish a direct ass ociation between
dispersal syndrome and long-distance dispersal (Nogales
et al. 2007). Even within a single dispersal syndrome,
dispersal distances vary in magnitude (e.g., Augspurger
1986, Vittoz and Engler 2007, Muller-Landau et al.
2008, Thomson et al. 2011). Additional information
about seed and plant chara cteris tics ma y help in
explaining seed dispersal distances. Models of seed
dispersal often incorporate information about seed mass
and shape (e.g., Augspurger 1986, Matlack 1987, Ernst
et al. 1992). A recent global review of seed dispersal
distances of over 300 species (Thomson et al. 2011)
revealed that plant height is more important than seed
mass in determining seed dispersal distances. Similarly,
for wind-dispersed species, seed release height is often a
good predictor of dispersal distance (Soons and Ozinga
2005).
Although many studies have examined the relation-
ship between plant traits and dispersal distances, few
have used a macroecological approach, including species
from different regions and with varying dispersal
syndromes. There are currently three attempts aiming
to generalize relationships between plant traits and
dispersal distance across multiple species. Willson (1993)
addressed the effect of dispersal syndrome on shapes of
seed shadows within growth form classes. Vittoz and
Engler (2007) did the same on the basis of a larger
sample, but included mainly species from Central
Europe, and created a more complex system of
categories where dispersal syndromes were integrated
with other plant traits. In the most recent study,
Thomson et al. (2011) included the largest data set to
date; they addressed the effect of plant height and seed
mass on dispersal distances across all species and within
particular dispersal syndromes. These three studies have
provided extremely valuable information about the
importance of dispersal syndrome as well as growth
form in determining dispersal distances across species.
However, no studies so far have explicitly evaluated the
predictive power of these traits in estimating dispersal
distances.
Here we apply a cross-validation statistical approach
to determine how well various plant traits can predict
dispersal distances by using 576 species from different
regions. We use traits that are either widely available in
databases or can be easily obtained from other sources,
such as local floras. We focus on species’ maximum
dispersal distances to emphasize the importance of long-
distance dispersal and the potential to reach a given site,
but admit that maximum dispersal distance is signifi-
cantly and strongly correlated with mean dispersal
distance (Thomson et al. 2011). In addition to providing
information on the relationship between plant traits and
dispersal distances across species, we evaluate the
possibility to use simple traits to predict dispersal
distances for species that lack distance data. We also
provide a freeware tool (dispeRsal) that can be used to
predict dispersal distances from trait data for a large
number of plant species.
M
ETHODS
Data on seed dispersal distances and plant traits
To compile our data set, we used six previous studies
that summarized published dispersal information and
addressed a large number of species (Willson 1993,
Hughes et al. 1994, Cain et al. 1998, Bullock and Clarke
2000, Ness et al. 2004, Vittoz and Engler 2007), as well
as studies in which the dispersal distances were derived
from models parameterized with field data (e.g., Sheldon
and Burrows 1973, Augspurger 1986, Matlack 1987,
Ernst et al. 1992, Sto
¨
cklin and Ba
¨
umler 1996, Kiviniemi
and Telenius 1998, Jongejans and Telenius 2001, Soons
and Ozinga 2005). We additionally searched the ISI
Web of Science for papers published up until 31 January
2012, using t he keywords ‘‘seed,’’ ‘‘dispersal,’’ and
‘‘distance.’’ We included case studies that provided data
about dispersal distances corresponding to individual
species and specific dispersal syndromes.
From each study, we extracted dispersal syndrome
and dispersal distance data. We distinguished five main
dispersal syndromes: (1) wind dispersal with special
mechanisms (e.g., plumes, wings), (2) animal dispersal
(endo-, epi-, and synzoochory by vertebrates, including
human), (3) ant dispersal, (4) ballistic dispersal, and (5)
wind dispersal without special mechanisms (i.e., seeds do
not have any special structures to enhance dispersal but
are usually dispersed by abiotic factors). We did not
further separate animal dispersal (e.g., endo-, epi-, or
synzoochory) because of too few data points within each
category. Since water dispersal distance data were
available for only four species, we excluded this
syndrome from the analyses. Dispersal distance data in
the original studies were given as the longest observed
maximum, 99th percentile, 90th percentile, mean, mode,
and median distances. Additionally, we collected infor-
mation on plant growth form from the case studies, or
from databases LEDA (Kleyer et al. 2008) and
PLANTS (available online).
6
Furthermore, we collected
additional data on seed release height (LEDA; Kleyer et
al. 2008), seed mass (Seed Information Database;
available online)
7
and terminal velocity (LEDA; Kleyer
et al. 2008).
We were able to compile data from 121 case studies
for 576 species from 102 families (see Supplement 1).
For each species, we use only the highest value reported
in the literature as the maximum dispersal distance in the
analyses. Roughly half of the data came from observa-
tional field studies, whereas the other half derived from
modeling studies that were parameterized with field
6
http://plants.usda.gov/
7
http://data.kew.org/sid/
RIIN TAMME ET AL.506 Ecology, Vol. 95, No. 2
data. Our data set is global, but data from temperate
regions in Europe and North America are more
commonly represented (468 species in temperate regions
compared to 108 in the tropics). The complete species set
could not be used for all analyses since data on seed
mass, release height, and terminal velocity were avail-
able for only 491, 292, and 247 species, respectively. For
most of the species (519), we used the furthest dispersal
distance given, which was the mea sured maximum
distance or 99th percentile (for one species we used the
90th percentile). Similar to Thomson et al. (2011), we
found in a linear regression that mean dispersal distance
was a good predictor of the maximum distance (R
2
¼
0.85) and therefore used the relationship (log
10
(max-
imum) ¼ 0.795 þ 0.984log
10
(mean)) to estimate the
maximum for species for which we only had mean values
(57 species). Maximum dispersal distances, seed release
height, seed mass, and terminal velocity were log
10
-
transformed for analyses.
Although trait data can explain plant ecol ogical
responses, taxonomy or phylogeny can add information
about functional variation among species (Reinhart et
al. 2012). Therefore, we also use taxonomy in our
predictions. The taxonomic classification was obtained
in two steps. First we used the Taxonstand (Cayuela et
al. 2012) library in R (R Development Core Team 2012)
to validate species names and to assign genera to
families. Subsequent assignment of families to orders
followed APG III for angiosperms (Angiosperm Phy-
logeny Group 2009) and Christenhusz et al. (2011) for
gymnosperms.
Data analysis
To find the most important traits affecting maximum
dispersal distances, as well as to find candidate models
for predictions, we first analyzed the relationship
between maximum dispersal distance (response variable)
and different combinations of plant traits. Using a linear
regression model, we first included all traits (dispersal
syndrome, growth form, seed mass, seed release height,
terminal velocity) as fixed effects. Since data for all traits
was available for only 155 species, we additionally tested
models that incorporated more species, but fewer traits.
Specifically, we analyzed the relationship between
maximum dispersal distance and (1) dispersal syndrome,
growth form, and terminal velocity (247 species); (2)
dispersal syndrome, growth form, seed mass, and seed
release height (264 species); (3) dispersal syndrome,
growth form, and seed release height (290 species); (4)
dispersal syndrome, growth form, and seed mass (488
species); (5) dispersal syndrome and growth form (576
species). We also tested for interactions between fixed
effects in the models. The statistical significance of fixed
effects in the linear models was evaluated using Type II
ANOVA. The linear model assumptions were evaluated
visually and all the continuous data (maximum dispersal
distance, seed mass, seed release hei ght, termi nal
velocity) were log
10
-transformed for normality.
Building the predictive models
Following the data analysis, we chose five groups of
candidate models for testing their predictive power in
estimating dispersal distances. The group 1 of candidate
models included dispersal syndrome, growth form, and
terminal velocity as explanatory factors. Group 2
included dispersal syndrome, growth form, seed mass,
and seed release height as explanatory variables. Group
3 included dispersal syndrome, growth form, and seed
release height. Group 4 included dispersal syndrome,
growth form, and seed mass. Group 5 included only
dispersal syndrome and growth form. We considered
different groups to represent different sets of plant traits
and to assess whether accurate predictions are also
possible without information on terminal velocity, for
which data are much scarcer than for release height, seed
mass, or growth form. Models with terminal velocity
only apply to species with wind or ballistic dispersal
syndrome. We did not include a ny models with
interactions for our predictions due to too few (or no)
data points for some of the trait combinations when
data were divided into two groups in testing the
predictive power of the models. Furthermore, we set
up model s that accounted for taxonomi c structure
(order, family) in the data by using the nested taxonomy
of the species as a random variable in linear mixed-effect
models (Pinheiro and Bates 2000). Altogether we fitted
15 different models (three for each group) that were
compared by Akaike information criterion (AIC) and
Bayesian information criterion (BIC) values. An addi-
tional 23 models with random slope effect (Schielzeth
and Forstmeier 2009) and genus-level taxonomy were
also fitted.
To test the ability of these models to predict seed
maximum dispersal distances accurately, we randomly
split our data set into two parts. Two-thirds of the data
was used to fit the predictive models and we used these
parameter values to predict maximum dispersal distanc-
es for the remaining species from their traits. Next, a
major axis (Type II) regression between the observed
and predicted maximum dispersa l distances (log
10
-
transformed values) was conducted, calculating R
2
,
intercept, and slope of this regression. For each model,
the results are presented as averages of 999 runs, each
with a new split of the data into model and test groups.
Because of varying number of species and different fixed
effects, AIC and BIC comparison of models are not
valid between groups. Therefore, we use R
2
from a
major axis regression between the observed and
predicted distances for a more accurate comparison of
all models.
All analyses were conducted in the software R (R
Development Core T eam 2012). We used the lm
function in the stats package (R Development Core
Team 2012) for fitting linear regression models and the
lme function in the nlme package (Pinheiro et al. 2011)
for fitting mixed-effect models. For the Type II ANOVA
test, we used the ANOVA function in the car package
February 2014 507PREDICTING SEED DISPERSAL DISTANCES
(Fox and Weisberg 2011). In testing the accuracy of
predictions, the major axis regression estimates were
calculated in the package smatr (Warton et al. 2011).
R
ESULTS
Depending on the model and the set of species used,
different factors were important in explaining maximum
dispersal distances (see Appendix A: Tables A1–A6 for
the descriptive model results). In the full model (model
R
2
¼ 0.51, P , 0.001, Table A1), only dispersal
syndrome and terminal velocity were significant. The
best model ( highest model R
2
) included dispersal
syndrome and terminal velocity (model R
2
¼ 0.61, P ,
0.001, Table A2). However, both of these models
included mostly herbs and wind-dispersed species. In
the simplest model (R
2
¼ 0.51, P , 0.001, Table A6),
including only dispersal syndrome and growth form as
explanatory variables and all 576 species, both dispersal
syndrome and growth form were statistically significant.
On average, maximum dispersal distances increase from
wind (no special mechanisms) , ballistic , ant , wind
(special mechanisms) , animal (Appendix A: Fig. A1).
Considering growth form across all species, maximum
dispersal distances increase from herb , shrub , tree
(Fig. A2).
The R
2
for the regression between observed and
predicted values ranged between 0.45 and 0.60, with the
best predictive model having dispersal syndrome,
growth form, and terminal velocity as fixed effects
(Fig. 1A). Naturally, this model cannot be used to
predict dispersal distances for animal or ant dispersal.
However, even a simple linear model incorporating only
categorical variables (growth form and dispersal syn-
drome) predicted dispersal distances with a reasonable
accuracy (predictions R
2
¼ 0.50; Fig. 1B). For predic-
tions, the models that incorporated taxonomic structure
as a random variable generally performed as well or
better than the simple linear models (Table 1) but not in
all cases (i.e., R
2
lower or equal, see Appendix B: Table
B1 for the full set of models). Regarding the relationship
between observed and predicted values, we found that
intercepts were higher than 0 and slopes of the
regression lines were ,1 for all tested models. The
average intercept estimates ranged between 0.30 and
0.44 and the slope estimates between 0.59 and 0.74.
Hence, predicted values were, in general, overestimates
for species with short-distance dispersal and underesti-
mates for species with long-distance dispersal.
To allow researchers to calculate maximum dispersal
distances with confidence intervals (CI) for their species
of interest, we provide the code for a function dispeRsal
to be run in R (see Supplement 2 for the necessary .rda
file as well as instructions). The function will work with
any species set for which at least dispersal syndrome is
available. There are no constraints on the taxonomical
affinity of the species, but prediction for species whose
order and family match the ones that are used in the
predictive models will be on average more accurate
(Table 1). This is because only for those species the
random effect of taxonomy can be considered when
predicting dispersal distances. Ho wever, for species
either lacking the taxonomic information or having no
matching taxonomical information, dispersal distances
are still predicted from the fixed effects (i.e., traits).
D
ISCUSSION
Information about dispersal distances is relevant for
understanding a multitude of ecological processes and
for addressing several conservation issues (Trakhtenbrot
et al. 2005, McConkey et al. 2012). Using a large data
set, we have shown that dispersal syndrome, growth
form, and terminal velocity explain over 60% of the
variation in maximum dispersal distances. Similarly, the
power to predict maximum dispersal distances for a
model including dispersal syndrome, growth form, and
terminal velocity is 61%. Unfor tunately , ter minal
velocity data are not available for many plant species
and also these predictions are applicable only to species
with wind or ballistic dispersal syndrome. Therefore, as
an alternative, we fitted and tested the predictive power
of more general models that include more species. Even
so, these simple and easily obtainable traits explained
maximum dispersal distances relatively well. For exam-
ple, dispersal syndrome together with plant growth form
described more tha n o ne-hal f of the variation i n
maximum dispersal distances and the predictive power
of this model increased to 53% when taxonomy data
were included. Our cross-validation approach demon-
strated strong predictive power for all of our models
(predictions R
2
. 0.45). Our main conclusion from
these results is that it is indeed possible to predict
dispersal distances for a large number of species using
easily obtainable data for a few traits.
The importance of dispersal syndrome in shaping
dispersal distance patterns is well known in ecology and
therefore our models always included this trait. Species
that have special adaptations to enhance dispersal travel
longer distances than species without such mechanisms
(Willson 1993, Vittoz and Engler 2007, Thomson et al.
2011). Generally, species specialized to ballistic or ant
dispersal have low maximum dispersal distances (on
average below 10 m) while wind dispersal with special
structures and animal dispersal result in much longer
distances (see Appendix A: Fig. A1; also Vittoz and
Engler 2007, Thomson et al. 2011). Variation in
dispersal syndromes can have significant consequences
on the distribution and assembly of plant species. For
example, Seidler and Plotkin (2006) found dispersal
syndrome to determine the spatial aggregation of species
in a tropical forest. Similarly, Drezner et al. (2001)
showed the importance of dispersal sy ndrome to
determine the species distribution patterns in a riparian
zone. Additionally, dispersal syndrome can determine
the vulnerability of species to global change (Montoya et
al. 2008).
RIIN TAMME ET AL.508 Ecology, Vol. 95, No. 2
A recent study by Thomson et al. (2011) showed the
importance of plant height in determining dispersal
distances as opposed to seed mass that is generally
deemed more important (Greene and Johnson 1993,
Xiao et al. 2005, Muller-Landau et al. 2008). According
to our cross-validation analyses, models with seed mass
had higher predictive power (higher R
2
values) than
models where seed mass was absent (Table 1, compare
groups 2 vs. 3, 3 vs. 4, and 4 vs. 5). However, all of our
models also included plant growth form (tree, shrub, or
herb), which acts as a proxy for plant height and
influences dispersal distance patterns. In addition, plant
FIG. 1. Example plots of regressions of predicted dispersal distance on observed dispersal distance (measured in meters; values
were log-transformed) for two different predictive models. The dashed line depicts the slope of unity with intercept zero, and the
solid line depicts the major axis regression slope. Points represent different species, and bars around points depict confidence
intervals of predicted values. Values of R
2
, P, intercept, and slope are for the major axis regression. (A) Simple linear regression
model with dispersal syndrome, growth form, and terminal velocity as explanatory variables. (B) Simple linear regression model
with dispersal syndrome and growth form as explanatory variables.
February 2014 509PREDICTING SEED DISPERSAL DISTANCES
