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Extreme long-distance seed dispersal via sheep

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The results of this study highlight the role of adhesion in long-distance dispersal and support the inclusion of migrating ungulates among forces responsible rapid plant migrations (eg following glaciations, invasion events, or in a future global change scenario).
Abstract
Extremely long seed dispersal distances occur as a result of processes such as ocean drift and tornadoes. However, we have found that large numbers of seeds with different morphologies (Trifolium angustifolium, Daucus carota, Hordeum murinum, and Plantago lagopus) are frequently dispersed equivalent distances while attached to migrating ungulates. We determined experimentally that seeds attached to the fleece of traditional nomadic (“transhumant”) sheep are transported distances of up to several hundred kilometers in substantial numbers (ranging from 5–47% of the initial seed population). Given the current and historical importance of migrating herds of sheep (wild and domestic) on different continents, the results of this study highlight the role of adhesion in long-distance dispersal and support the inclusion of migrating ungulates among forces responsible rapid plant migrations (eg following glaciations, invasion events, or in a future global change scenario). Our results also highlight an unexplored ecological consequence of abandoning nomadism.

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B
iogeographers have long considered the presence of
organisms outside their normal distribution range to
be important, since this will indicate where the tails of
dispersal curves might lie and what the species migration
potential might be. Long-distance dispersal (LDD; ie the
dispersal of seeds or propagules over distances several
orders of magnitude greater than median distances;
Higgins et al. 2003a), is a major topic in plant dispersal
biology, linked with biogeography (Cain et al. 1998) and
conservation ecology issues (Soons and Ozinga 2005).
However, studies have been severely constrained by the
low proportion of seeds that travel long distances and
therefore by the difficulty of gathering data (Higgins et al.
2003a). There is a discrepancy of several orders of magni-
tude between observed migration rates of plants in the
fossil record (100–1000 m yr
–1
) and the dispersal capacity
actually measured by experimental studies (up to
10 m yr
–1
). Known as Reid’s paradox, it has been a contro-
versial issue in seed dispersal ecology since the end of the
19th century (Clark et al. 1998). Exceptional abiotic dis-
persal factors such as tornadoes are extremely infrequent
and unpredictable, so they do not provide a plausible
explanation. Recently, modeling approaches have focused
on wind dispersal (Nathan et al. 2002) and dispersal in
feces (Pakeman 2001); however, these processes cannot
produce sufficiently high dispersal rates to explain the
rapid migrations observed in the paleorecord, except in a
limited number of plant species and under special circum-
stances (Higgins et al. 2003b). Only some wind dispersal
models and limited experimental data for tropical bird-
dispersed trees provide dispersal distance data per year
consistent with that found in the paleorecord (Higgins et
al. 2003a), and only by a small margin. The paleomigra-
tion rates for herbs remain unexplained (Cain et al. 1998)
and their predicted migration rates are lower than those
for trees (Higgins et al. 2003a).
Seed dispersal by adhesion, or epizoochory (the trans-
port of seeds attached to animal skin), is well-known in
biology (Ridley 1930), but little systematic data has been
available until recently, mainly because of the method-
ological difficulty of studying such phenomena
(Sorensen 1986). Even fewer studies have examined the
efficacy of epizoochory over great distances. However,
research on epizoochory by sheep (Fischer et al. 1996)
has shown its potential importance in terms of retention
time and dispersal distance. Studies have also high-
lighted the potential of other animals to disperse seeds in
this way (Couvreur et al. 2004), even facilitating the
spread of non-native species (Sorensen 1986; Constible
et al. 2005). Perhaps most striking is the diversity of plant
species that can be dispersed by epizoochory (Fischer et
al. 1996), among which herbs are especially notable
(Sorensen 1986).
Transhumance involves seasonal drives of animals for
hundreds of kilometers in search of productive pastures.
An ancient method of livestock management in Spain
(Ruiz and Ruiz 1986) and other countries (Fischer et al.
1996), it has been progressively abandoned as a result of
economic development. The similarities between trans-
humance and the migratory movements of wild animal
herds (Fryxell and Sinclair 1988) provide an opportunity
to evaluate the LDD potential of herbivores in general. In
this study we used one of the last transhumant sheep
flocks in Spain to determine actual seed retention times
and dispersal potential.
RESEARCH COMMUNICATIONS RESEARCH COMMUNICATIONS
Extreme long-distance seed dispersal via
sheep
Pablo Manzano and Juan E Malo
Extremely long seed dispersal distances occur as a result of processes such as ocean drift and tornadoes.
However, we have found that large numbers of seeds with different morphologies (Trifolium angustifolium,
Daucus carota, Hordeum murinum, and Plantago lagopus) are frequently dispersed equivalent distances
while attached to migrating ungulates. We determined experimentally that seeds attached to the fleece of
traditional nomadic (“transhumant”) sheep are transported distances of up to several hundred kilometers in
substantial numbers (ranging from 5–47% of the initial seed population). Given the current and historical
importance of migrating herds of sheep (wild and domestic) on different continents, the results of this study
highlight the role of adhesion in long-distance dispersal and support the inclusion of migrating ungulates
among forces responsible rapid plant migrations (eg following glaciations, invasion events, or in a future
global change scenario). Our results also highlight an unexplored ecological consequence of abandoning
nomadism.
Front Ecol Environ 2006; 4(5): 244–248
TEG, Dpto Ecología, Universidad Autónoma de Madrid, E-28049
Madrid, Spain (pablo.manzano@uam.es)

P Manzano and JE Malo Long-distance seed dispersal
245
© The Ecological Society of America www.frontiersinecology.org
Methods
The route of the merino flock (the
breed traditionally used in Spanish
transhumance), a herd of about 1500
animals, follows the traditional cat-
tle paths (“cañadas reales”) ranging
from the Cantabric Mountains,
through Spain’s northern plateau,
Madrid, and the Tajo valley, and
finally ending in Extremadura, in
SW Spain (Figure 1a). This live-
stock movement takes place over a
period of 1.5 months or more and
provides a unique, linear dispersal
vector over extremely large dis-
tances. The seeds of four herb species
common in central Spain, together
with their dispersal structures, were
collected in the field in September
2003, at the time the sheep flock
began the move towards winter pas-
tures. These herb species were narrowleaf crimson clover
(Trifolium angustifolium), carrot (Daucus carota), foxtail
barley (Hordeum murinum), and hare’s-foot plantain
(Plantago lagopus). The propagules were then color-
marked with previously tested, water-based lacquer
(Fischer et al. 1996; Figure 1b) and placed in three differ-
ent positions (front, center, and back) on the fleece of
each of five castrated rams (wethers) during the annual
drive, near the municipality of Coca (Segovia; Figure 1a).
In each position, 40 propagules of T angustifolium, 50 of D
carota, 12 of H murinum, and 40 of P lagopus were placed
by hand. Wethers are used to help guide the flock by
being regularly hand-fed and by wearing cowbells, and
were chosen for the experiment because they are easier to
handle and similar in behavior to ewes. In fact, they walk
within the flock most of the time.
On November 8th, 2003, seeds were spread over one
hand which was then gently pressed onto the fleece for a
few seconds, simulating the effect of the animal lying on
the ground. A sample of wool taken from each animal
was used to measure the amount of curling of the wool, by
dividing the length of the hair stretched out by length in
its curled state. We then followed the flock from Coca
(Segovia, 41˚ 13’ N and 4˚ 32’ W) to Torrejón el Rubio
(Cáceres, 39˚ 46’ N and 6˚ 00’ W), a 28-day journey with
a total distance of about 400 km (Figure 1a).
Visual counts of the propagules were made while the
flock was resting so as not to disturb the animals. The
adherence of each plant species was measured as the per-
centage of propagules remaining on the fleece 2.5 hours
after placement. Differences between plant species were
assessed using a nested analysis of variance (ANOVA),
controlling for the effects of individual (factor “wether”)
and propagule position (see below). Significance level
was set at P = 0.05.
To determine the persistence of the propagules on the
fleece during the rest of the journal, eight further counts
were made on November 10th–12th, 14th, 16th, 19th,
26th, and December 3rd. Persistence was measured as the
proportion of seeds in the initial count (at 2.5 hours) that
remained attached to the the fleece (Figure 1c). A sig-
nificant number of propagules were still present at the
end of the route, so three more counts were carried out on
December 17th, January 7th, and February 17th, before
the animals were sheared on May 2nd, 2004.
An algebraically tailed dispersal curve (Portnoy and
Willson 1993) was fitted to the resulting dataset for every
case (four plant species x five individual sheep x three posi-
tions on each sheep = 60 in total). The fitted model was:
(1) n = 100 ( t + 1)
a
where n is the percentage of initially attached propagules
present, t is the time, expressed in hours, elapsed since
propagule adhesion, and a is the parameter estimated. In
order to ensure robust least squares estimates (Quinn and
Keough 2002), data were log-transformed to adjust the
linearized function:
(2) ln(n) = ln(100) + a ln( t + 1).
The estimate a was used as a descriptor for each of the 60
persistence datasets, and introduced as a dependent vari-
able in an ANOVA test performed with the factors
species, wether, and position (nested within factor
“wether”) as independent variables. A cubic root trans-
formation of a was performed to achieve normality, and
significance level was set at P = 0.05. Only one of the 60
regressions was non-significant (P = 0.1625) and was
therefore dropped from further analyses. The other 59
regressions were highly significant (mean P-value
0.00013; sd = 0.00049; all cases P < 0.003) and explained
Figure 1. Phases of the experiment. (a) Route followed by merino sheep flock before
(green) and after (red) application of seeds to fleece of focal animals. (b) Marked seeds
in the lab. (c) Marked seeds on fleece. (d) Flock used in the experiment crossing Madrid
city center.
(a) Courtesy of NASA (d) Courtesy of E García
Daucos carota
Plantago lagopus
Hordeum murinum
Trifolium angustifolium
(a)
(c)
(b)
(d)

Long-distance seed dispersal P Manzano and JE Malo
246
www.frontiersinecology.org © The Ecological Society of America
models that adequately describe dispersal data (Cain et al.
2000), and offers a useful approach to quantifying attach-
ment potential of plant propagules.
Seeds attached to sheep fleece show extremely high per-
sistence; following the 28-day, 400-km journey (Figure 2a;
WebFigure 1), a total of 46.9% of T angustifolium, 12.3% of
D carota, 9.6% of H murinum, and 4.9% of P lagopus
propagules remained attached to the fleece. At the time of
shearing (4000 h after seed placement), persistence of
seeds in the fleece was still 38.1%, 6.93%, 5.06%, and
2.15%, respectively. For each of the studied plant species,
these data are the greatest dispersal distances ever
recorded. They exceed the greatest dispersal distances
measured so far in other animals by at least two orders of
magnitude (4 km vs 400 km; Higgins et al. 2003a), and
provide enough distance to solve Reid’s paradox on
Holocene migration of herbs (Cain et al. 1998; Clark et al.
1998; Pakeman 2001; Higgins et al. 2003b). The final tail
of the distribution is so large (Figure 2a; WebFigure 1)
that, by some definitions, it cannot be described as LDD,
as this concept is sometimes identified as the final 1% of
the distribution spectrum (Cain et al. 2000).
Epizoochory differs from other mechanisms of animal-
mediated dispersal, such as endozoochory (dispersal by
ingestion and later defecation), in that the resulting seed
deposition is not clumped in space and time, but evenly
distributed (Sorensen 1986). Seed detachment from the
fleece over the entire dispersal period can be mathemati-
cally described as a seed rain function (Figure 2b). Its
decay is slower for more persistent propagules, so that seed
dispersal among species with efficient attachment struc-
tures continues for a greater length of time (and over a
potentially greater distance). They are therefore able to
disperse more efficiently. Dispersal efficiency by means of
epizoochory also has the advantage, compared to endozoo-
chory, that attached seeds are not subjected to losses via
digestion or secondary seed predation in feces.
65% of the variance (mean r
2
= 0.648; average data can
be found in WebTable 1). Afterwards, the correlation
between mean propagule persistence on wethers and
wool curling was tested.
To describe the seed deposition with time (seed rain, sr)
inferred from the mean values of the above model, we
used the negative of the derivative of equation (1), ie:
(3) sr = – (100 a (t+1) a–1)
whose linearized form for representation purposes is:
(4) ln(sr) = ln(100) + ln(–a)+(a–1) ln (t+1).
Results and discussion
The mean adherence potential of propagules after 2.5
hours differed significantly between plant species (F
3,42
=
8.49; P < 0.001), with T angustifolium showing the great-
est attachment potential (mean 51.5%; sd = 4.48). The
adherence values for the three other species (D carota
33.73%, sd = 4.66; H murinum 29.44%, sd = 4.22; P lago-
pus 32%, sd = 6.33) were similar, even though their
propagules have very distinct morphologies. In fact, P
lagopus capsules get attached by means of sparse hairs pre-
sent on corolla-lobes, a structure that contrasts with the
hook- or spine-bearing appendages considered typical for
epizoochory (Weiher et al. 1999). Several studies have
noted that seeds lacking obvious adaptations for adhesion
can nonetheless become attached to animal furs (Fischer
et al. 1996; Couvreur et al. 2004).
The selected model proved to be a good descriptor of
the persistence curve (WebTable 1) and persistence is
easily described by a linear equation after log-transforma-
tion of variables. The high goodness-of-fit contrasts with
the usual difficulties of finding appropriate statistical
Figure 2. Retention pattern of propagules and seed loss in fleece. (a) Plots display equation (1) for average persistence parameter
values. The end of the 400 km-long journey is represented by a vertical dashed line, and the time of shearing by a vertical dotted line.
(b) Seed rain, calculated for the mean persistence parameter values in equation (4).
(a)
(b)
100
80
60
40
20
0
4
2
0
-2
-4
-6
-8
0 1000 2000 3000 4000
Time (h)
0 2 4 6 8
Time (In [h + 1])
Seeds remaining in fleece (%)
Seeds loss (In [% seed over h])
T angustifolium
D carota
H murinum
P lagopus

P Manzano and JE Malo Long-distance seed dispersal
247
© The Ecological Society of America www.frontiersinecology.org
Conclusions and future guidelines
Assuming that the behavior of propagules on the fur of
wild animals is comparable to that in our findings
(Couvreur et al. 2004), part of the answer to the paradox
of LDD may lie in adhesive dispersal. Epizoochory has
long been observed in migrating wild animals (eg
Berthoud 1892) and such migrations were both important
and widespread in the Pleistocene (Rivals et al. 2004) and
still take place in some regions. Large, migrating herbi-
vores play an important role in the dispersal of plants, and
this may have been complemented or supplanted by
nomadic herds in regions ranging from the Mediterranean
(Ruiz and Ruiz 1986) to the Arctic (Ingold 1986). Sheep’s
wool contains large numbers of viable seeds at the time of
shearing and the total number of seeds transported can be
high (Manzano and Malo unpublished). Furthermore, epi-
zoochory is not the only way plants are dispersed by
nomadic animals; dispersal via the feces of both wild and
domesticated animals can also result in long dispersal
times (Ridley 1930; Manzano et al. 2005).
LDD may be a critical mechanism for plants to escape
the effects of global climate change. Many plants have
specific genetic adaptations to local conditions (eg the
North American prairie plant Chamaecrista fasciculata;
Etterson 2004), highlighting the potential importance of
migration mechanisms to plant species faced with rapid
climatic changes. However, if LDD depends on large her-
bivore migrations, this is highly unlikely to continue in
today’s world. Large wild herbivores have either disap-
peared or are no longer able to migrate long distances,
while the vectors that could substitute for them (ie
nomadic herds) are disappearing as a result of economic
development. In view of increasing habitat fragmenta-
tion, losses caused by human activities, and the conse-
quences for plant migrations (Higgins et al 2003b), the
waning of nomadism may have important implications
for future plant biodiversity, as it had for soil fertility and
plant productivity in Africa in the 1970s and 1980s that
culminated in the Sahel famine crisis (Fryxell and
Sinclair 1988). In addition, the spread of invasive plant
species may be increased by unnatural adhesive dispersal,
a more common LDD mechanism for non-native species
than endozoochory (Sorensen 1986; Constible et al.
2005), on artificially transported animals.
Research should now focus on the current relevance for
plant dispersal of long-range animal movements (either
wild or nomadic herds, or agricultural and recreational
transport) and on better assessing factors that determine
the efficiency of epizoochory. A better understanding of
seed transport by animals along corridors and between
landscape patches is also needed, in order to guide con-
servation actions for species and landscapes (Soons and
Ozinga 2005). In addition, trade-offs potentially involved
in plant traits associated with adhesive dispersal need fur-
ther assessment. Those trade-offs include a more adhesive
morphology causing increased grooming behavior
(Sorensen 1986), thus reducing the final dispersal dis-
Even among sheep of the same breed, we found that the
“wether” factor had a significant effect on seed retention
time (WebTable 2). Mean persistence seems to be related
to the curliness of the fleece (Pearson r = 0.733; df = 4;
P = 0.158) but no significant difference was found, proba-
bly because of the small number of wethers used in the
study. A similar relation has been observed among the
furs of several mammal species in the laboratory
(Couvreur et al. 2004), where the greater range of hair
types used in the study results in major retention differ-
ences among animals.
Persistence of seeds in fleece varied significantly between
plant species (WebTable 2), but T angustifolium was the
only species to show a significantly higher persistence on
the animals than the others (HSD test: P <0.001 in all
comparisons). Nevertheless, a significant retention was
found even among propagules without specialized attach-
ment morphology. The fact that nearly 5% of P lagopus
propagules reached the winter pastures 400 km away and
one month after propagule attachment (2% persisted for 6
months in the fleece) has important implications.
Propagules that are able to disperse effectively, despite
the lack of obvious adhesion adaptations, seem to be
quite common (Ridley 1930; Fischer et al. 1996); this
means that epizoochory linked to migratory species can
be an important LDD vector for seeds/fruits with diverse
morphologies. In fact, experimental approaches have
shown that propagules of many species can attach to, and
remain within, the sheep fleece or the straight fur of wild
and domestic species, for the equivalent of several hours
under natural conditions (Couvreur et al. 2004;
Römermann et al. 2005). Such retention times corre-
spond to dispersal distances of several kilometers if the
animals are moving in a single direction. However,
morphology did play a role in the attachment and
retention of the seeds studied, and the propagules with
the most efficient adhesive mechanism (T angusti-
folium) showed the greatest dispersal distance
(Römermann et al. 2005).
Our study was carried out using plant species that had
ripe seeds available in the field at the time of the experi-
ment (autumn). However, in regions with a
Mediterranean climate, seed availability and therefore
number of seeds potentially transported is higher in
spring. We therefore expect transport to be a frequent
phenomenon both northwards and southwards. In other
arid and semiarid environments where migrating herds are
moved in response to changing pasture productivity (and
seeding) peaks (Fryxell and Sinclair 1988), we can expect
the same pattern of sustained LDD. However, in higher
latitudes, where seed production is concentrated at the
end of summer (Hülber et al. 2005) northward dispersal
events could happen only during itinerant grazing move-
ments (up to 100 km long; Fischer et al. 1996) within a
single season. An alternative option would imply seed per-
manence in fleece during the winter dormancy typical of
species from cold areas (Ortega et al. 1997).

Long-distance seed dispersal P Manzano and JE Malo
248
www.frontiersinecology.org © The Ecological Society of America
tance, or a reduced seed mass that increases the adhesive
transport efficiency (Römermann et al. 2005) but also
decreases the recruitment success.
Acknowledgements
We thank L Álvarez and ME Hidalgo for allowing us to
work with their animals; J Garzón for making this work
possible; S Martos, AM Baena, SD Pastor, Q Wauquiez,
JG Vicente, T Sainz, and AI del Cueto for field assis-
tance; and L Manzano for literature assistance. F Suárez,
CC Nice, JR Ott, and especially MA Huston thoroughly
reviewed earlier versions of this manuscript. This study
was supported by the Spanish Ministry of Education and
Science (project CICYT REN2003-01562 and FPU fel-
lowship to PM).
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Reid's Paradox of Rapid Plant Migration Dispersal theory and interpretation of paleoecological records

TL;DR: Clark, Lynch, and Wyckoff as discussed by the authors have been employed at the American Institute of Biological Sciences (AIBS) since 1998, where they were employed in the Department of Botany, Duke University, Durham, NC 27708; Chris Fastie and Stephen T. Jackson are at the University of Wyoming, Laramie, WY 82701; George Hurtt and Stephen Pacala are at Princeton University, Princeton, NJ 08544-1003; Carter Johnson is at South Dakota State University, Brookings, SD 57007; George A. King is
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Q1. What are the contributions in this paper?

Seed dispersal by adhesion, or epizoochory ( the transport of seeds attached to animal skin ), is well-known in biology ( Ridley 1930 ), but little systematic data has been available until recently, mainly because of the methodological difficulty of studying such phenomena ( Sorensen 1986 ). The similarities between transhumance and the migratory movements of wild animal herds ( Fryxell and Sinclair 1988 ) provide an opportunity to evaluate the LDD potential of herbivores in general. In this study the authors used one of the last transhumant sheep flocks in Spain to determine actual seed retention times and dispersal potential. However, research on epizoochory by sheep ( Fischer et al. 1996 ) has shown its potential importance in terms of retention time and dispersal distance. Studies have also highlighted the potential of other animals to disperse seeds in this way ( Couvreur et al. 2004 ), even facilitating the spread of non-native species ( Sorensen 1986 ; Constible et al. 2005 ). 

In view of increasing habitat fragmentation, losses caused by human activities, and the consequences for plant migrations ( Higgins et al 2003b ), the waning of nomadism may have important implications for future plant biodiversity, as it had for soil fertility and plant productivity in Africa in the 1970s and 1980s that culminated in the Sahel famine crisis ( Fryxell and Sinclair 1988 ). In addition, trade-offs potentially involved in plant traits associated with adhesive dispersal need further assessment. However, in regions with a Mediterranean climate, seed availability and therefore number of seeds potentially transported is higher in spring. Evolutionary potential of Chamaecrista fasciculata in relation to climate change. 

In view of increasing habitat fragmentation, losses caused by human activities, and the consequences for plant migrations (Higgins et al 2003b), the waning of nomadism may have important implications for future plant biodiversity, as it had for soil fertility and plant productivity in Africa in the 1970s and 1980s that culminated in the Sahel famine crisis (Fryxell and Sinclair 1988). 

The seeds of four herb species common in central Spain, together with their dispersal structures, were collected in the field in September 2003, at the time the sheep flock began the move towards winter pas-tures. 

epizoochory is not the only way plants are dispersed by nomadic animals; dispersal via the feces of both wild and domesticated animals can also result in long dispersal times (Ridley 1930; Manzano et al. 2005).LDD may be a critical mechanism for plants to escape the effects of global climate change. 

At the time of shearing (4000 h after seed placement), persistence of seeds in the fleece was still 38.1%, 6.93%, 5.06%, and 2.15%, respectively. 

In addition, the spread of invasive plant species may be increased by unnatural adhesive dispersal, a more common LDD mechanism for non-native species than endozoochory (Sorensen 1986; Constible et al. 2005), on artificially transported animals. 

Given the current and historical importance of migrating herds of sheep (wild and domestic) on different continents, the results of this study highlight the role of adhesion in long-distance dispersal and support the inclusion of migrating ungulates among forces responsible rapid plant migrations (eg following glaciations, invasion events, or in a future global change scenario). 

This livestock movement takes place over a period of 1.5 months or more and provides a unique, linear dispersal vector over extremely large distances. 

The authors determined experimentally that seeds attached to the fleece of traditional nomadic (“transhumant”) sheep are transported distances of up to several hundred kilometers in substantial numbers (ranging from 5–47% of the initial seed population). 

In fact, experimental approaches have shown that propagules of many species can attach to, and remain within, the sheep fleece or the straight fur of wild and domestic species, for the equivalent of several hours under natural conditions (Couvreur et al. 2004; Römermann et al. 2005). 

Many plants have specific genetic adaptations to local conditions (eg the North American prairie plant Chamaecrista fasciculata; Etterson 2004), highlighting the potential importance of migration mechanisms to plant species faced with rapid climatic changes. 

The fact that nearly 5% of P lagopus propagules reached the winter pastures 400 km away and one month after propagule attachment (2% persisted for 6 months in the fleece) has important implications. 

Valid n include only regressions with P-value < 0.05 (all cases but one) which are used for further analysis (see Methods)Variance explained by model parameters Mean sd Range Valid nT angustifolium 0.720 0.208 0.257 – 0.956 15 D carota 0.667 0.159 0.364 – 0.919 15 H murinum 0.483 0.209 0.216 – 0.776 14 P lagopus 0.712 0.186 0.213 – 0.923 15WebTable 2. Effects of plant species, wether, and placement position on propagule persistence measured through the parameter a. 

In fact, P lagopus capsules get attached by means of sparse hairs present on corolla-lobes, a structure that contrasts with the hook- or spine-bearing appendages considered typical for epizoochory (Weiher et al. 1999). 

The Ecological Society of Americamodels that adequately describe dispersal data (Cain et al. 2000), and offers a useful approach to quantifying attachment potential of plant propagules. 

The fitted model was:(1) n = 100 ( t + 1) awhere n is the percentage of initially attached propagules present, t is the time, expressed in hours, elapsed since propagule adhesion, and a is the parameter estimated. 

The estimate a was used as a descriptor for each of the 60 persistence datasets, and introduced as a dependent variable in an ANOVA test performed with the factors species, wether, and position (nested within factor “wether”) as independent variables.