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Submitted 3 March 2021
Accepted 29 June 2021
Published 21 July 2021
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Ivan Chadin, chadin@ib.komisc.ru
Academic editor
Tina Heger
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page 16
DOI 10.7717/peerj.11821
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2021 Chadin et al.
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OPEN ACCESS
A simple mechanistic model of the
invasive species Heracleum sosnowskyi
propagule dispersal by wind
Ivan Chadin1, Igor Dalke2, Denis Tishin3, Ilya Zakhozhiy2and Ruslan Malyshev2
1Molecular Biology Facility, Institute of Biology of Komi Science Centre of Ural Branch of Russian Academy
of Sciences, Syktyvkar, Komi Republic, Russian Federation
2Laboratory of Plant Ecological Physiology, Institute of Biology of Komi Science Centre of Ural Branch of
Russian Academy of Sciences, Syktyvkar, Komi Republic, Russia
3Institute of Environmental Sciences, Kazan Federal University, Kazan, Republic of Tatarstan,
Russian Federation
ABSTRACT
Background. Invasive species are one of the key elements of human-mediated
ecosystem degradation and ecosystem services impairment worldwide. Dispersal of
propagules is the first stage of plant species spread and strongly influences the dynamics
of biological invasion. Therefore, distance prediction for invasive species spread is
critical for invasion management. Heracleum sosnowskyi is one of the most dangerous
invasive species with wind-dispersed propagules (seeds) across Eastern Europe. This
study developed a simple mechanistic model for H. sosnowskyi propagule dispersal and
their distances with an accuracy comparable to that of empirical measurements.
Methods. We measured and compared the propagule traits (terminal velocity, mass,
area, and wing loading) and release height for H. sosnowskyi populations from two
geographically distant regions of European Russia. We tested two simple mechanistic
models: a ballistic model and a wind gradient model using identical artificial propagules.
The artificial propagules were made of colored paper with a mass, area, wing loading,
and terminal velocity close to those of natural H. sosnowskyi mericarps.
Results. The wind gradient model produced the best results. The first calculations of
maximum possible propagule transfer distance by wind using the model and data from
weather stations showed that the role of wind as a vector of long-distance dispersal for
invasive Heracleum species was strongly underestimated. The published dataset with H.
sosnowskyi propagule traits and release heights allows for modeling of the propagules’
dispersal distances by wind at any geographical point within their entire invasion
range using data from the closest weather stations. The proposed simple model for the
prediction of H. sosnowskyi propagule dispersal by wind may be included in planning
processes for managing invasion of this species.
Subjects Biogeography, Ecology, Plant Science, Population Biology
Keywords Heracleum sosnowskyi, Plant invasion, Seeds dispersal, Mechanistic model,
Anemochory, Long distance dispersal, Wind
INTRODUCTION
Invasive species are one of the key elements of human-mediated ecosystem degradation
and ecosystem services impairment worldwide. Dispersal of propagules is the first stage
How to cite this article Chadin I, Dalke I, Tishin D, Zakhozhiy I, Malyshev R. 2021. A simple mechanistic model of the invasive species
Heracleum sosnowskyi propagule dispersal by wind. PeerJ 9:e11821 http://doi.org/10.7717/peerj.11821
of introduction and the driving force behind biological invasion (Williamson, 1996;
Richardson et al., 2000;Nehrbass et al., 2007). The success and rate of biological invasion
directly depend on the mobility of a species, its ability to spread over long distances, and
the effectiveness of the use of dispersal agents (Pyšek & Richardson, 2007;van Kleunen et
al., 2015).
In recent decades, Heracleum sosnowskyi Manden. (Apiaceae), an invasive plant species,
has attracted considerable attention. Its invasion has significant environmental and socio-
economic impacts in Eastern Europe and the European part of Russia (Satsyperova,
1984;Chadin et al., 2017;Ozerova & Krivosheina, 2018;Gudžinskas & Žalneraviius, 2018).
A significant part of its invasion range lies between 48.6◦N in the South and 72.6◦N in the
North, and it also occupies territories between 15.0◦E on the West and 69.5◦E in the East.
H. sosnowskyi plants do not have any vegetative reproduction structures. Consequently,
the invasive success of this species depends directly on the number of propagules and their
ability to disperse (Dalke et al., 2015;Gudžinskas & Žalneraviius, 2018).
There have been several attempts to assess wind dispersal distances of Heracleum species
mericarps. Researchers have conducted experiments in wind tunnels (Clegg & Grace, 1974),
analyzed seedling density dependence on distance from the maternal plant (Pergl et al.,
2011), analyzed aerial photographs (Müllerová et al., 2005;Moravcova et al., 2007), and
directly measured propagule flight distance under field conditions (Jongejans, Skarpaas &
Shea, 2008;Wojewódzka et al., 2019).
There is consensus in the existing literature that most propagules of Heracleum
mantegazzianum Sommier & Levier, which is an invasive species that is phylogenetically and
eco-physiologically close to H. sosnowskyi, fall no further than 5 m from maternal plants.
Dispersal over distances >10 m should be considered as long-distance dispersal (LDD),
even for the tallest species of this genus (Pergl et al., 2011). Long-distance dispersal makes
a major contribution to the spread of plant species (Nathan & Muller-Landau, 2000). The
average rate of linear spread found for H. mantegazzianum in the Czech Republic was
assessed as 10.8 m/year, with a maximum value of 26.7 m/year (Müllerová et al., 2005).
Several authors have reported that streams and human activity are likely to play a major
role in LDD of H. mantegazzianum propagules. Streams may transfer H. mantegazzianum
propagules up to hundreds of meters, whereas most propagules dispersed by water are
transported over shorter(<40 m) distances (Trottier, Groeneveld & Lavoie, 2017).
Despite the LDD potential of water, wind is often the only dispersal agent at many
sites occupied by invasive Heracleum species, and we need to re-assess wind as a vector
for LDD of these species. We expect that propagule transfer distances by wind may be
strongly underestimated because of difficulties in the registration of LDD events. The
propagules of Apiaceae are adapted precisely for anemochoria. The oval-shaped mericarps
of Heracleum species are flattened with a wing-like border, and these propagules are
catapulted from mature umbels when the dry and elastic stems are pushed by gusts
of wind or moving objects (Levina, 1957;Tackenberg, 2003;Vittoz & Engler, 2007). We
found two estimates in the literature of LDD by wind for Heracleum species: up to 100 m
for H. mantegazzianum (Ochsmann, 2008) and up to 50 m for H. sosnowskyi (Kondratiev,
Budarin & Larikova, 2015), although these reports were not confirmed by any instrumental
Chadin et al. (2021), PeerJ, DOI 10.7717/peerj.11821 2/19
measurements. It is known that wind is able to transport H. sosnowskyi propagules for
distances up to hundreds of meters by dragging them along on the flat surface of icy
roads (Krivosheina, Ozerova & Petrosyan, 2020) or similar surfaces; however, modeling of
this specific process was beyond the scope of the present study.
Anemochorous seed dispersal is well studied for many plant species and has been
generalized in a number of mechanistic models of varying complexity, as reviewed by
Nathan et al. (2011). However, to date, none of these models have been used to describe
seed dispersal in Heracleum species.
The aim of this study was to develop a simple mechanistic model that enables
determination of the distance of H. sosnowskyi propagule dispersal by wind during the
period from fruit ripening until the formation of snow cover, with an accuracy comparable
to that of empirical measurements. Such a model should enable assessment of the dispersal
kernel as well as possible LDD events for different parts of the H. sosnowskyi invasion
range, where wind is the only available dispersal agent. In addition, this model should aid
in reassessing the significance of wind as an LDD agent for H. sosnowskyi, and provide
practical recommendations for invasion management using weather station data alone and
a mechanistic description of one of the factors determining H. sosnowskyi invasiveness.
METHODS
Model Development
The distance of the horizontal flight of propagules in the airflow is known to depend
mainly on three parameters: terminal velocity, release height of the propagules, and mean
horizontal wind speed (Levin et al., 2003;Dauer, Mortensen & Humston, 2006;Jongejans,
Skarpaas & Shea, 2008;Nathan et al., 2011). The simplest mechanistic model of seed
dispersal by wind is a simple ballistic model suggested by Dingler (1889) cited in Nathan
et al. (2011) and formalized as an equation by Schmidt at the beginning of the 20th
century (Nathan et al., 2011):
D=hr¯u
Vt
(1)
where Dis the distance of horizontal flight, ¯u is the mean horizontal wind speed, hris the
seed release height, and Vtis the terminal velocity (the constant velocity of a seed falling
in still air).
This simple ballistic model assumes several simplifications: (1) the seed reaches terminal
velocity immediately after release, (2) the horizontal speed of the seed is equal to the
horizontal speed of the air flow, (3) the wind does not change speed in the vertical
direction, (4) there is no turbulence, and (5) the air flow does not meet obstacles in its
path.
Currently, there are a number of models that omit all these restrictions; however, this
leads to a complication of the mathematical apparatus, for example, requiring the use of
the Navier–Stokes equations (Nathan et al., 2011). We have presumed that it is possible to
accept most of the restrictions of the simple ballistic model. Some of these restrictions may
be accepted based on H. sosnowskyi characteristics and its typical habitats in invaded areas.
Other restrictions may be accepted after experimental verification.
Chadin et al. (2021), PeerJ, DOI 10.7717/peerj.11821 3/19
The assumption of rapid deceleration of propagules to terminal velocity can be
empirically verified by measuring the time taken for a seed to fall from various heights.
The assumption that there is no significant difference between the horizontal speeds of
the wind and the propagules flying in the airflow can also be tested experimentally. Air
turbulence significantly affects the horizontal flight distance only for propagules with a
very low terminal velocity: 0.07 ≤Vt<0.3m/s(Nathan et al., 2011), and depends on
land surface heterogeneity. Our model only considers dispersal from a single plant in an
open space to allow the assumption that there is no turbulence and that the airflow is not
disrupted by obstacles. In relation to these assumptions, the H. sosnowskyi invasion range
is mainly located on flatlands, and solitary generative H. sosnowskyi plants located at a
distance of more than several dozen meters from monostands or any other tall vegetation
(>3–5 m) are not uncommon.
The vertical gradient of the horizontal wind speed may be incorporated into a simple
ballistic model. One of the equations describes the wind gradient phenomena as:
vz=vgz
zgα
(2)
where vzis the speed of the wind at height z,vgis the speed of the wind at height zgand α
is the Hellmann exponential coefficient, which represents the degree of surface roughness
and air stability Cleveland & Morris (2013). Equation (2) can be rewritten with the notation
used for the simple ballistic model (Eq. (1)):
vh=vhr h
hrα
(3)
where vhis the speed of the wind at height h,vhr is the speed of the wind at height hr(the
release height), and αis the Hellmann exponential coefficient.
Therefore, the mean horizontal wind speed (¯u) in the simple ballistic model may be
replaced by the continuously changing (decreasing) wind velocity vh. If we accept the
assumption about wind and seed velocity equivalence, then the horizontal distance of seed
flight may be determined by a definite integral of the wind velocity change rate. The hin
Eq. (3) depends on time:
h=vttf−vtt(4)
where his the height at time t,tfis the total time of seed fall from the release height to
ground level, and vtis the seed terminal velocity. Next, the h in Eq. (3) is replaced with
Eq. (4) to obtain the wind velocity change rate vh(t):
vh(t)=vhr vttf−vtt
hrα
(5)
where vhr –is the speed of the wind at height hr(the release height), his the height at time
t,tfis the total time of seed fall from the release height to the ground level, vtis the seed
terminal velocity, and αis the Hellmann exponential coefficient. The integration of Eq. (5)
allows us to determine the horizontal flight distance of the seed:
D=Ztf
0
vhr vttf−vtt
hrα
(6)
Chadin et al. (2021), PeerJ, DOI 10.7717/peerj.11821 4/19
Here after, the model represented by Eq. (6) is referred to as the gradient model. To
test whether the gradient model sufficiently described seed dispersal in H. sosnowskyi, we
collected empirical data from seed release experiments.
Data collection
The characteristics of propagules and release heights were determined for H. sosnowskyi
plants at two geographically distant sites located in two regions in Russia. Samples were
collected in the suburbs of Syktyvkar City (Komi Republic, Russia) in 2018 (the North
Group), and in the vicinity of Kazan City (Republic of Tatarstan, Russia) in 2017–2018
(the South Group). The North Group plants were from two sites with coordinates:
61.65◦N, 50.74◦E and 61.70◦N, 50.80◦E. The South Group plants were from two sites with
coordinates: 55.80◦N, 49.16◦E and 55.94◦N, 49.27◦E. The mericarps were collected, and
measurements made in typical monostands of the species. The heights of the central and
lateral umbels were measured as the distance from the root-stem junction to the top of the
main or lateral shoots of the plant.
The propagules were randomly selected from the bulk samples collected in the field. The
air-dry weight of propagules was determined using analytical balances with an accuracy
of 0.0001 g. To measure the surface area of the propagules (the area of one side), images
of the propagules were obtained using a flatbed scanner at a resolution of 600 dpi. The
area of the propagule images was determined using ImageJ software (Schneider, Rasband
& Eliceiri, 2012).
Wing loading (WL, g / cm2) was calculated as the ratio of the propagule mass (g) to the
area of one of its sides (cm2). The propagule falling velocity (Vt, m / s) was determined by
measuring the falling time (t, s) from different release heights (h, m). The measurements
were made indoors in the absence of airflow at room temperature. Propagules were dropped
from heights between 0.80 and 4.28 m. The moment of propagule landing on the floor
was visually recorded. The falling time was measured using a stopwatch. Each propagule
was dropped five times, and the median values were used for subsequent calculations. The
North Group consisted of 70 propagules, and the South Group, 60 propagules.
It was not possible to find several hundred propagules of H. sosnowskyi with the same
standard area and mass. Therefore, we used artificial models of H. sosnowskyi propagules
made of paper, the density of which was close to the average density of propagules of this
species in the air-dry state. The contours of the artificial propagules were drawn as ellipses
with a major axis of 1.35 cm and a minor axis of 0.88 cm (Fig. 1B).
The traits of the artificial propagules (median values and interquartile range, N=36)
were as follows: mass, 21.5±0.5 mg; area, 0.966 ±0.018 cm2; and wing loading,
0.0220 ±0.0004 g/cm2. The median terminal velocity measured from a release height
of 4.15 m was 1.72 ±0.11 m/s (N =10). We conducted all field measurements using
these artificial propagules. The main difference between natural and artificial propagules
was their surface structure. The artificial propagules were much smoother, and this may
have influenced their air drag force. Therefore, the difference between the horizontal
wind velocity and propagule velocity may be slightly larger for artificial propagules, and
the distances we observed may be slightly shorter for these propagules than for natural
Chadin et al. (2021), PeerJ, DOI 10.7717/peerj.11821 5/19
Figure 1 (A) Diagram of the device used for propagule dispersal measurements; (B) a real Heracleum
sosnowskyi propagule and an artificial propagule used for model testing. In (A): Two-section support
rod, 2: rings for struts and securing the rod, 3: anemometer, 4: weather-vane, 5: data recording block, 6:
removable rod for attaching the propagule-holding container, 7: propagule container, and 8: container
cover with a lock for remote propagule release.
Full-size DOI: 10.7717/peerj.11821/fig-1
propagules of similar sizes. However, the main propagule trait that influences propagule
dispersal distance by wind is the terminal velocity, and our artificial propagules reproduced
the terminal velocity of H. sosnowskyi well. This good terminal velocity match was achieved
using a form, size, and paper density close to that of real mericarps. We assumed that
we captured the main traits of H. sosnowskyi propagules that are important for dispersal
by wind. Artificial propagules were launched under natural conditions using a specially
designed and manufactured device (Fig. 1A).
Measurements of horizontal flight distances of artificial propagules were carried out in
batches of 10–20 propagules. A batch of propagules was loaded into the container and all
propagules were dropped simultaneously. The wind speed was recorded by videotaping the
anemometer readings. The horizontal flight distance of propagules was measured using a
surveyor’s tape with an accuracy of 0.01 m. Measurements were performed in Syktyvkar
on 26th January, and 11th, 12th and 17th February, 2020 during daylight hours (11:00
h–16:00 h). As a result, 37 launches of batches of paper diaspores of H. sosnowskyi were
performed at wind speeds from 0 to 9 m/s.
All data analyses were conducted in R (http://www.R-project.org). The primary data
and R-script used for performing calculations are available at the Zenodo repository
(https://doi.org/10.5281/zenodo.3837647).
Chadin et al. (2021), PeerJ, DOI 10.7717/peerj.11821 6/19
Table 1 Traits of Heracleum sosnowskyi propagules (North Group, N=70).
Summary results Mass,
mg
Area,
cm2
Wing loading,
g / cm2
Falling velocity a,
m/s
Mean 11.0 0.57 0.019 1.59
Median 11.0 0.56 0.019 1.62
Standard deviation 4.3 0.12 0.006 0.25
IQR 3.2 0.17 0.005 0.27
Standard error of mean 0.5 0.01 0.001 0.03
Notes.
aThe falling velocity was determined for a release height of 2.68 m.
RESULTS
The sample sizes of the North Group (N=70) and South Group (N=60) of propagules
were used to obtain a standard error of mean of 5% or less for all measured trait values. The
correlation between falling velocity and other H. sosnowskyi propagule traits was measured
using the North Group only. We assumed that the correlations between mericarp traits
were specific to all representatives of the species and therefore, that it would be sufficient
to make the detailed trait measurements and regression evaluation of trait relationships
for one group only. The North Group propagules were collected at two sites 7.9 km apart.
The two samples were combined into one according to the Kolmogorov–Smirnov test
(p-value =0.97 for propagule mass, p-value =0.61 for propagule area). The median mass
of H. sosnowskyi air-dry propagules of the North Group was 11 ±3 mg; the median area
of one propagule was 0.6 ±0.2 cm2; the median value of the wing loading was 0.019
±0.005 g / cm2; and the median speed of its fall from a height of 2.7 m was 1.62 ±0.27
m/s (Table 1).
The falling velocity depended on the propagule mass and propagule wing loading. The
wing loading coefficient was the most important parameter of H. sosnowskyi propagules
that affected their terminal velocity. Linear regression showed that this parameter was
responsible for more than 80% of the terminal velocity variability. For a rough estimate
of the terminal speed, one can use the propagule mass, the fluctuations of which are
responsible for approximately 50% of the terminal velocity variability (Fig. 2).
To determine the relationship between the measured mean falling speed in still air and
the release height, the propagules were dropped from heights varying from 0.80 to 4.28
m. Theoretically, as the release height increases, the measured fall rate should approach
the terminal (constant) value. Two groups (A and B) of propagules that differed in WL by
more than three times were selected for the measurements. The propagules of Group A had
an abnormally low wing load: N=4, WL=0.006 ±0.001 g / cm2, and 18 measurements
of falling velocity. The propagules of Group B had a normal wing load: N=7, WL=0.021
±0.002 g / cm2, and 42 measurements of falling velocity. The results of linear regression
showed that in the range of release heights used, it was not possible to determine the
relationship between the measured mean fall rate and the release height (Fig. 3). Because
the H. sosnowskyi propagules reached the terminal speed very quickly, we could adopt the
Chadin et al. (2021), PeerJ, DOI 10.7717/peerj.11821 7/19
0.005 0.010 0.015 0.020
1.0 1.2 1.4 1.6 1.8 2.0
A
Seed mass, g
vt, m
/
s
y=44.7x +1.1
R2=0.57
p=6.42 ⋅10−14
0.3 0.4 0.5 0.6 0.7 0.8 0.9
1.0 1.2 1.4 1.6 1.8 2.0
B
Seed area, cm2
vt, m
/
s
R2=0.03
p=0.10
0.005 0.015 0.025
1.0 1.2 1.4 1.6 1.8 2.0
C
Seed wing loading, g / cm2
vt, m
/
s
y=38.5x +0.9
R2=0.80
p<2.2 ⋅10−16
Figure 2 Relationships between H. sosnowskyi propagule terminal velocity and mass (A), area (B), and
wing loading (C). The terminal velocity was determined for a release height of 2.68 m. Linear regression is
indicated by the red line.
Full-size DOI: 10.7717/peerj.11821/fig-2
1.0 1.5 2.0 2.5 3.0 3.5 4.0
1.05 1.10 1.15 1.20
A
Release height, m
vt, m / s
R2=0.07
p=0.1582
1.0 1.5 2.0 2.5 3.0 3.5 4.0
1.2 1.4 1.6 1.8 2.0 2.2
B
Release height, m
vt, m / s
R2=−0.01
p=0.49882
Figure 3 Relationship between H. sosnowskyi propagule terminal velocity and release height. (A)
propagules with a wing loading of 0.006 ±0.001 g / cm2, and (B) propagules with a wing loading of
0.021±0.002 g / cm2. Linear regression is indicated by the red line.
Full-size DOI: 10.7717/peerj.11821/fig-3
assumption of the simple ballistic model that the propagule reaches the terminal speed
immediately after its release from the plant.
We tested the hypothesis that climate influences H. sosnowskyi propagule traits and
release height (the height of umbels above ground level). We compared these characteristics
for plants collected in two geographically distant regions: the city of Syktyvkar (North
Group) and the city of Kazan (South Group) located approximately 6◦latitude apart.
Despite some differences between the traits of the North and South plant groups, their
traits that directly affected the propagule flight distance can be considered almost identical,
as shown by the Kruskal-Wallis test p-value ≥0.04 (Fig. 4).
We performed 37 launches of paper propagule batches and 414 measurements of
horizontal propagule flight distance (8–20 measurements per launch). The wind speeds
Chadin et al. (2021), PeerJ, DOI 10.7717/peerj.11821 8/19
North Group South Group
5 10152025
A
Seed mass, mg
North Group South Group
1.0 1.2 1.4 1.6 1.8 2.0
B
vt, m / s
North Group South Group
2.0 2.5 3.0 3.5
C
Release height, m
North Group South Group
1.5 2.0 2.5 3.0 3.5
D
Release height, m
Figure 4 Characteristics of propagules and release heights of H. sosnowskyi from two geographically
distant regions. North Group: plants collected in the vicinity of Syktyvkar, and South Group: plants col-
lected in the vicinity of Kazan. (A) Propagule mass, (B) terminal velocity, (C) height of the central umbels
above ground level, and (D) height of the lateral umbels above ground level.
Full-size DOI: 10.7717/peerj.11821/fig-4
were between 0 and 9 m / s. Hereafter in the Results section, the word propagules refers to
artificial propagule models made of paper, with standard shape and wing loading.
An initial analysis of the field measurements showed two key features of the relationships
between wind speed and horizontal flight distance (Fig. 5). First, the flight distance of the
propagules was strongly correlated with wind speed (Pearson correlation coefficient: 0.78,
p-value <2.2·10−16). Second, propagules of uniform shape, weight, and size, when dropped
simultaneously from the same height, flew off and landed at different distances, and with
increasing wind speed, the distance range increased. A positive significant correlation
was observed between the values of the interquartile range of the flight distances of the
standardized propagules and the wind speed (Pearson correlation coefficient: 0.74, p-value
<1.4·10−7). The results of modeling this relationship using linear regression are described
below.
Chadin et al. (2021), PeerJ, DOI 10.7717/peerj.11821 9/19
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02468
05101520
Wind speed, m/s
Propagule wind dispersal distance, m
y=1.2x +1.4
R2=0.59
p<2.2 u10ï16
Figure 5 Raw results showing the flight distances of artificial H. sosnowskyi propagules at different
wind speeds. Linear regression is indicated by the red line.
Full-size DOI: 10.7717/peerj.11821/fig-5
We aggregated our empirical data for further analysis. We calculated the minimum
(Dmin), median (Dmedian), mean (Dmean), and maximum (Dmax ) propagule flight distances
for each launch and correlated them with the aggregated wind speed measurements:
median (vmedian), average (vmean), and maximum (vmax ). The highest Pearson correlation
coefficient (0.901, p-value <2.9·10−14) was obtained for (vmax and (Dmean). For further
analysis, we used this pair of vectors. Linear regression of the horizontal flight distance
(Dmean) on the wind speed (vmax ) showed that more than 80% of the Dmean variability was
due to variability in vmax (Fig. 6).
We calculated the theoretical horizontal flight distance of propagules using a simple
ballistic model at the wind speeds (vmax ) that we recorded during field experiments
and compared them with empirical data using the Kolmogorov–Smirnov test and linear
regression (Fig. 7A1,7B1). The simple ballistic model appeared to be effective as the range
of distances obtained from calculations using Eq. (1) did not differ significantly from
the empirical data (Kolmogorov–Smirnov test: p-value =0.52). This model enabled us to
Chadin et al. (2021), PeerJ, DOI 10.7717/peerj.11821 10/19
02468
24681012
A
vmax, m/s
Dmean, m
y=1.2x +1.4
R2=0.59
p<2.2 ⋅10−16
0 5 10 15 20 25 30 35
−4−20 2
B
Launch number
Residuals, m
Figure 6 The relationship between the artificial H. sosnowskyi propagules mean flight distance and
maximum wind speed (A), and the regression residuals (B). Linear regression is indicated by the red
line.
Full-size DOI: 10.7717/peerj.11821/fig-6
Figure 7 Relationship between the artificial H. sosnowskyi propagules empirical flight distances and
the flight distances calculated using the simple ballistic model (upper two plots) and the gradient
model with α=0.29 (lower two plots). (A) Results of linear regression (red line), dotted line is 1:1
line: (A1) Dmean = 0.77 ±0.07 (p-valu e<0.001), Intercept = 1.00 ±0.53 (p-value =0.07), (A2) Dmean =
1.00 ±0.09 (p-valu e<0.001), Intercept = 1.00 ±0.53 (p-value =0.07). (B) Kernel density estimation
of the artificial H. sosnowskyi propagules empirical flight distances (black line) and that of simulated
distances (red line). The results of the two-way Kolmogorov–Smirnov test showed that the two samples, in
both cases, belong to the same statistical population: (B1) p-value =0.52, (B2) p-value =0.35.
Full-size DOI: 10.7717/peerj.11821/fig-7
explain 80% of the variability in the experimental Dmean values. A significant shortcoming of
the simple ballistic model was that the angle of the regression line reflecting the relationship
between the calculated and experimental data differed from 45% (tangent =1) and its
tangent was equal to 0.77±0.07.
Chadin et al. (2021), PeerJ, DOI 10.7717/peerj.11821 11/19
The gradient model allowed us to consider the vertical wind speed fluctuations by
using the ground surface roughness Hellmann exponent (α). We used the same empirical
data on wind speed (vmax ) as for the simulation of propagule flight distance using the
simple ballistic model. To find the coefficient αat which the regression line angle tangent
between the calculated and empirical distances is equal to 1.00, we performed a series
of the propagule flight distance calculations using the gradient model and changing the
coefficient αfrom 0.05 to 0.50 with increments of 0.01. The value of α=0.29 provided the
optimal convergence of the calculated and empirical data (Figs. 7A2,7B2).
As shown in Fig. 5, the empirical data demonstrated that the propagule flight distance
variation increased as the wind speed increased. The range between the minimum and
maximum flight distances of the artificial propagules during the same launch linearly
depended on the wind speed and ranged from 0.75 m at zero wind speed to 5.27 m at a
wind speed of 8–9 m / s. We divided the distance measurement results into classes according
to wind speed (vmax ) and discretized them with increments of 1 m, and then calculated
the standard deviation of the propagule distance flight (Dsd ) for each wind speed class.
The results of linear regression of Dsd on vmax showed a strong relationship between these
parameters (R2=0.82, p-value =4.13·10−7). The linear regression equation is as follows:
Dsd =0.35±0.06v+0.51 ±0.29 (7)
where Dsd is the standard deviation of the flight distances of propagules released at wind
speed v. It should be noted that there were only nine pairs of vmax and Dsd because
of data discretization. The limited number of pairs did not allow for the calculation of
a statistically significant intercept (0.51 ±0.29, p-value =0.07) (see primary data and
R-script at https://doi.org/10.5281/zenodo.3837647).
DISCUSSION
The range dynamics of plant species depend on the growth rate and dispersal of the
plant population, and on the availability of suitable habitats (Higgins & Richardson, 1999).
All of these processes need to be modeled to predict plant species distribution under
global changes caused by climate change and human activity. This prediction is especially
important for invasive species that have negative impacts on humans and ecosystems.
Long-distance dispersal events are rare but have a radical effect on the spread rate (Higgins
& Richardson, 1999). Modeling of LDD with a phenomenological approach is difficult
owing to the rarity of LDD events. Mechanistic models of dispersal by wind allow us to
use a few easily measurable variables: wind statistics, seed release height, and seed terminal
velocity (Katul et al., 2005).
Simple mechanistic models with three main independent variables demonstrated
reasonable prognostic accuracy for horizontal flight distances of H. sosnowskyi propagules.
The comparison results showed that making the simple ballistic model more complex by
adding a new parameter α(Hellmann exponent) is adequate. This parameter allowed us
to account for a decrease in the wind speed in the vertical direction. The tangent of the
regression line angle between the calculated and empirical distances became equal to 1
Chadin et al. (2021), PeerJ, DOI 10.7717/peerj.11821 12/19
with an optimal value of α=0.29. These Hellmann exponent values correspond well to the
values recommended for unstable air above human inhabited areas (α=0.27) and neutral
air above human inhabited areas (α=0.34) (Cleveland & Morris, 2013).
These results are comparable with the results of field validation of a more complex
mechanistic model that has been used to predict tree seed dispersal by wind (Nathan,
Safriel & Noy-Meir, 2020). The reasonable prognostic accuracy of our simple mechanistic
model can be explained by the fact that the H. sosnowskyi stem, inflorescences, and
propagules together make up a much simpler system compared to that of tree species. H.
sosnowskyi has relatively lower release heights. Its seeds do not bear special structures for
increasing air drag force, such as samaras or long hairs, and have relatively large terminal
velocity values(>1 m / s). These H. sosnowskyi traits allowed us to ignore wind turbulence,
and the description of vertical wind velocity was limited by incorporating the Hellmann
exponent into the model.
Despite the availability of well-elaborated mechanistic models for describing and
predicting propagule dispersal by wind, to date they have not been used for Heracleum
species. Most cases of mechanistic modeling of wind seed dispersal deal with tree species
(Nathan et al., 2011). For most herb species, wind cannot serve as a LDD agent because of
the relatively lower release heights of most species. However, giant hogweeds (H. sosnowskyi,
H. mantegazzianum, and H. persicum Desf.) are outstanding herbs with diaspore release
heights of 2.5–3 m and mechanistic modeling of diaspore wind dispersal for these species
is reasonable.
The lack of mechanistic models for giant hogweed propagule dispersal by wind can
be attributed to the difficulty of testing these models by empirical dispersal distance
measurement. Hundreds of propagules with identical terminal velocities are needed to
provide sufficient replication of the measurements, and the same propagules cannot be
used for repeated measurements because the wing-like border of the propagule is very
fragile and can be easily broken after the first flight distance measuring cycle. However, our
study has shown that the use of artificial propagules with a standard shape, wing loading,
and terminal velocity close to the corresponding median values of natural propagules
enabled us to overcome these difficulties.
The idea of using artificial propagules for dispersal modeling with different dispersal
agents is not new. Artificial fruits have been used for the quantitative assessment of several
fruit characteristics and wind speed as factors for horizontal distance transfer of tropical
tree fruits (Augspurger & Franson, 1987). Artificial fruits were used to study the influence
of odor, color, and nutrient content on fruit predators and dispersers (Wang & Chen, 2009;
Oliveira Barcelos, Perônico & Eutrópio, 2012). As mentioned in the Methods section, the
artificial propagule surfaces are much smoother, which may influence the air drag force.
It should be noted that the dispersal distances obtained with the proposed model may be
shorter, but are no longer than those for natural propagules under the same conditions.
Nevertheless, we supposed that the fuzziness of horizontal flight distances (Eq. (7)) was
more significant than the difference in the air drag force between artificial and natural
propagules.
Chadin et al. (2021), PeerJ, DOI 10.7717/peerj.11821 13/19
The finding of a significant difference in the flight distance of the artificial propagules
after a simultaneous drop from the same height under the same wind conditions was
unexpected. These differences are probably due to the aerodynamic properties of
H. sosnowskyi propagules. The nearly oval propagules of the species have a strongly
flattened shape, they do not have special accessories for aerodynamic stability (e.g., wings
or a pappus), and the center of mass is close to the geometrical center of the propagule.
However, this fuzziness can be considered and introduced into our mechanistic gradient
model using Eq. (7).
In the Introduction section, we mentioned several studies performed to assess the
dispersal of mericarps of giant hogweeds by air currents (Clegg & Grace, 1974;Müllerová
et al., 2005;Moravcova et al., 2007;Jongejans, Skarpaas & Shea, 2008;Pergl et al., 2011;
Wojewódzka et al., 2019). There is agreement among these authors that most giant hogweed
propagules fall within a radius of 5–10 m from the parent plant. It has been supposed that
the main LDD agents for Heracleum species are streams and human activity. We tested this
supposition using the model proposed in this study.
Using the gradient model that we developed and weather station data, we were able to
assess the expected maximum H. sosnowskyi propagule dispersal distance. We used the
maximum wind velocity recorded at the Syktyvkar and Kazan airport weather stations
from 2013–2020 during August-October (the period of fruit readiness for dispersal before
snow cover formation). The maximum wind velocity for Syktyvkar was 16 m / s and
for Kazan, 23 m / s at a height of 10 m. Given that the maximum H. sosnowskyi release
height registered in our study was 3.85 m, and taking into account the wind gradient, the
corrected wind velocities for a height of 3.85 m were calculated as 12 m / s for Syktyvkar
and 17 m/s for Kazan. Considering that the slowest terminal velocity, determined for real
H. sosnowskyi propagules, was 0.91 m / s, the expected dispersal distance for such mericarps
was calculated as 39 ±5 m for Syktyvkar and 55 ±6 m for Kazan. For propagules with a
median terminal velocity of 1.65 m / s, the expected dispersal distance was calculated as
22±6 m for Syktyvkar and 31 ±7 m for Kazan. A quick exploration of wind gust statistics
for Syktyvkar and Kazan showed that the Kazan climate is significantly windier, and the
minimum, median, and maximum wind gust velocities were approximately 30% higher in
Kazan than in Syktyvkar.
These draft calculations show that wind should not be excluded from the list of LDD
agents for Heracleum species. The proposed mechanistic model can explain published
observations on the invasion spread rate (up to 26.7/year) of H. mantegazzianum (Müllerová
et al., 2005) as well as individual observations of the extreme flight distances of H. sosnowsky
propagules of up to 50 m (Ochsmann, 2008).
The traits and release heights of H. sosnowskyi propagules are relatively uniform over
large geographical areas with different climates. The observed differences in terminal
velocities and release heights were not sufficient to significantly affect the horizontal flight
range of the propagules. The climate significantly affects only the timing of fruit ripening
and wind conditions. A dataset with H. sosnowskyi propagule traits (measurements
for 130 propagules) and release heights (290 measurements) published in Zenodo
(https://doi.org/10.5281/zenodo.3837647) enabled us to model the propagule dispersal
Chadin et al. (2021), PeerJ, DOI 10.7717/peerj.11821 14/19
distances by wind over the entire invasion range of this species. The only additional data
needed for modeling of propagule dispersal by wind in a specific part of the invasion range
was data from the closest weather station.
Within one population, H. sosnowskyi propagules may have significant differences
in terminal velocity and may be located at different heights above ground level. These
differences can lead to significant differences in propagule dispersal by airflow. Therefore,
to calculate the entire range of distances of propagule dispersal using the proposed
mechanistic gradient model, it is necessary to develop an individual-based model (IBM), in
which the flight of each propagule is calculated separately. The values of the H. sosnowskyi
propagule terminal velocity and release heights should be selected randomly from a variety
of empirically obtained data. Wind speeds for a specific area should be available for the
period from the beginning of propagule maturation until all the propagules capable of
releasing have been dispersed.
Our observations showed that the propagules of H. sosnowskyi have different release
capacities from the inflorescence: some propagules fall off at the slightest vibration of the
plant shoot at almost zero wind speed, whereas some remain on the umbels even after
strong gusts of wind exceeding 15 m/s. The dragging of individual propagules or umbrellas
with the remaining propagules over the surface of snow by wind requires additional
studies. To model the flight distances of propagules released from umbels, it is important
to consider that different groups of propagules in the same umbel may have their own
critical wind speeds. The critical wind speed of a propagule is the minimum wind speed at
which it is released from the umbel.
An important requirement for obtaining adequate results using an IBM is the availability
of high-quality measurements of the wind speed for a given area at the highest possible
frequency. The most appropriate information for our purposes was provided by the
airport weather stations. The weather stations measure the wind speed every 30 min,
and information about the maximum wind gusts between measurement periods was also
available.
CONCLUSION
Our findings showed that the wind contribution to propagule dispersal of invasive
Heracleum species has been strongly underestimated in most studies. However, more
detailed and accurate results will be available after application of the IBM that we developed.
This will enable us to calculate the flight distances of H. sosnowskyi propagules, taking into
account real weather conditions during different years in different parts of the invasion
range of this species. We will be able to describe the direction and dynamics of H.
sosnowskyi expansion in unoccupied territories and provide practical recommendations
for the management of this invasive species.
Chadin et al. (2021), PeerJ, DOI 10.7717/peerj.11821 15/19
ADDITIONAL INFORMATION AND DECLARATIONS
Funding
The reported study was funded by RFBR and NSFB, project number 20-54-18002 and was
partially supported within the scope of State Tasks for IB FRC Komi SC UB RAS (GR no.
AAAA-A17-117033010038-7). The funders had no role in study design, data collection and
analysis, decision to publish, or preparation of the manuscript.
Grant Disclosures
The following grant information was disclosed by the authors:
RFBR and NSFB: 20-54-18002.
State Tasks for IB FRC Komi SC UB RAS: GR no. AAAA-A17-117033010038-7.
Competing Interests
The authors declare there are no competing interests.
Author Contributions
•Ivan Chadin and Igor Dalke conceived and designed the experiments, performed the
experiments, analyzed the data, prepared figures and/or tables, authored or reviewed
drafts of the paper, and approved the final draft.
•Denis Tishin and Ruslan Malyshev conceived and designed the experiments, performed
the experiments, authored or reviewed drafts of the paper, and approved the final draft.
•Ilya Zakhozhiy conceived and designed the experiments, performed the experiments,
analyzed the data, authored or reviewed drafts of the paper, and approved the final draft.
Data Availability
The following information was supplied regarding data availability:
The primary data and the R-scripts are available at Zenodo: Chadin Ivan, Dalke Igor,
Tishin Denis, Zakhozhiy Ilya, & Malyshev Ruslan. (2020). Dataset and R-script for simple
mechanistic model of Heracleum sosnowskyi seed dispersal by wind (Version 1.0) [Data
set]. Zenodo. http://doi.org/10.5281/zenodo.3837647.
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