High-Resolution Gene Flow Model for Assessing Environmental Impacts of Transgene Escape Based on Biological Parameters and Wind Speed

Abstract

Environmental impacts caused by transgene flow from genetically engineered (GE) crops to their wild relatives mediated by pollination are longstanding biosafety concerns worldwide. Mathematical modeling provides a useful tool for estimating frequencies of pollen-mediated gene flow (PMGF) that are critical for assessing such environmental impacts. However, most PMGF models are impractical for this purpose because their parameterization requires actual data from field experiments. In addition, most of these models are usually too general and ignored the important biological characteristics of concerned plant species; and therefore cannot provide accurate prediction for PMGF frequencies. It is necessary to develop more accurate PMGF models based on biological and climatic parameters that can be easily measured in situ. Here, we present a quasi-mechanistic PMGF model that only requires the input of biological and wind speed parameters without actual data from field experiments. Validation of the quasi-mechanistic model based on five sets of published data from field experiments showed significant correlations between the model-simulated and field experimental-generated PMGF frequencies. These results suggest accurate prediction for PMGF frequencies using this model, provided that the necessary biological parameters and wind speed data are available. This model can largely facilitate the assessment and management of environmental impacts caused by transgene flow, such as determining transgene flow frequencies at a particular spatial distance, and establishing spatial isolation between a GE crop and its coexisting non-GE counterparts and wild relatives.

Full text

RESEARCH ARTICLE
High-Resolution Gene Flow Model for
Assessing Environmental Impacts of
Transgene Escape Based on Biological
Parameters and Wind Speed
Lei Wang
1
, Patsy Haccou
2
, Bao-Rong Lu
1
*
1Ministry of Education Key Laboratory for Biodiversity and Ecological Engineering, Department of Ecology
and Evolutionary Biology, Fudan University, Handan Road 220, Shanghai 200433, China, 2Leiden
University College The Hague, P.O. Box 13228, 2501 EE The Hague, the Netherlands
*brlu@fudan.edu.cn
Abstract
Environmental impacts caused by transgene flow from genetically engineered (GE) crops to
their wild relatives mediated by pollination are longstanding biosafety concerns worldwide.
Mathematical modeling provides a useful tool for estimating frequencies of pollen-mediated
gene flow (PMGF) that are critical for assessing such environmental impacts.However, most
PMGF models are impractical for this purpose because their parameterization requires
actual data from field experiments. In addition, most of these models are usually too general
and ignored the important biological characteristics of concerned plant species; and there-
fore cannot provide accurate prediction for PMGF frequencies. It is necessary to develop
more accurate PMGF modelsbased on biological and climatic parameters that can be easily
measured in situ. Here, we present a quasi-mechanistic PMGF model that only requires the
input of biological and wind speed parameters without actual data from field experiments.
Validation of the quasi-mechanistic model based on five sets of published data from field
experiments showed significant correlations between the model-simulated and field experi-
mental-generated PMGF frequencies. These results suggest accurate prediction for PMGF
frequencies using this model, provided that the necessary biological parameters and wind
speed data are available. This model can largely facilitate the assessment and management
of environmental impacts caused by transgene flow, such as determining transgene flow fre-
quencies at a particularspatial distance, and establishing spatial isolation between a GE
crop and its coexistingnon-GE counterparts and wild relatives.
Introduction
The potential environmental impact caused by transgene flow from a genetically engineered
(GE) crop to its non-GE counterparts (crop-to-crop) and to wild relatives (crop-to-wild)
through pollen-mediated gene flow (PMGF) has aroused great biosafety concerns worldwide,
PLOS ONE | DOI:10.1371/journal.pone.0149563 March 9, 2016 1/16
OPEN ACCESS
Citation: Wang L, Haccou P, Lu B-R (2016) High-
Resolution Gene Flow Model for Assessing
Environmental Impacts of Transgene Escape Based
on Biological Parameters and Wind Speed. PLoS
ONE 11(3): e0149563. doi:10.1371/journal.
pone.0149563
Editor: Shuang-Quan Huang, Central China Normal
University, CHINA
Received: September 4, 2015
Accepted: February 1, 2016
Published: March 9, 2016
Copyright: © 2016 Wang et al. This is an open
access article distributed under the terms of the
Creative Commons Attribution License, which permits
unrestricted use, distribution, and reproduction in any
medium, provided the original author and source are
credited.
Data Availability Statement: All relevant data are
within the manuscript.
Funding: This work is supported by the Natural
Science Foundation of China (31330014, 31271683)
and National Program of Development of Transgenic
New Species of China (2011ZX08011-006). The
authors declare no conflict of interest for this work.
Competing Interests: The authors have declared
that no competing interests exist.

as a result of the extensive global cultivation of GE crops [1,2]. Field surveys and experimental
studies suggest the great likelihood of crop-to-crop and crop-to-wild PMGF for world major
crops [1,3,4]. For example, crop-to-crop PMGF is reported in a number of crop species, such
as rice [5,6], wheat [7], maize [8], oilseed rape [9], soybean [10], potato [11], and cotton [12].
Likewise, crop-to-wild PMGF is also documented in wild/weedy relative species of rice [13,14],
wheat [15], maize [16], sorghum [17], oilseed rape [18], sugar beet [19], soybean [20], and
potato [21]. All these results indicate the potential of transgene escape to non-GE crops and
wild relative species of the crops through PMGF, from which the undesired environmental
impacts become a great concern with the commercialization of GE crops worldwide. Thus, the
accurate measurement and prediction of PMGF frequencies becomes the key to assessing and
managing the environmental impact from transgene escape, particularly when crop wild rela-
tives are involved in such (trans)gene flow [1–4].
Usually, two approaches are applied to estimate PMGF frequency: conducting field experi-
ments and mathematical modelling. The estimate of PMGF frequencies based on a field experi-
ment is a common practice for environmental biosafety assessment [8,9,22,23,24]. In fact,
PMGF data generated from field experiments have played an important role in assessing envi-
ronmental consequences of transgene flow prior to the commercial production of GE crops.
However, PMGF data collected from a particular field experiment have a limited use because
these data cannot be applied to accurately assess PMGF of a crop species under diverse envi-
ronmental conditions and in different cases. It is therefore difficult, if not impossible, to
develop a general guideline that is useful for predicting PMGF frequencies of a crop species,
based only on a limited number of field experiments at a limited number of sites [25,26]. In
addition, to generate PMGF data from actual field experiments is time consuming and very
expensive.
Mathematical modelling provides an important alternative method for estimating PMGF
frequencies, which can overcome the constraints of merely relying on field experimental data.
Consequently, many models are developed and used to predict PMGF frequencies for different
crops [25–29]. These PMGF models can be roughly categorized into three types: (1) the mecha-
nistic, (2) empirical, and (3) quasi-mechanistic models, based on the various calculation meth-
ods and parameters included for modeling. The early PMGF prediction used the mechanistic
modeling that was essentially based on the physical dispersion of particles in the atmosphere
[30,31]. Mechanistic modeling can be used to estimate PMGF frequencies without field experi-
ments. However, this type of models is entirely based on the climatic parameters, without the
consideration of any biological factors that are important for PMGF prediction, such as, the
characteristics of donor’s pollen grains, the outcrossing rate of a pollen recipient, and cross-
compatibility between a pollen donor and recipient of the involved plant species. Therefore,
mechanistic models are too general and cannot accurately predict the PMGF frequency for a
particular plant species, which may not be useful for assessing environmental impacts caused
by transgene flow [32].
The empirical modeling includes actual data collected from field experiments, based on
which a consensus level of PMGF is calculated for a particular pair of plant species (e.g., crop
versus wild relative species) or populations under different environmental conditions [28,33,34].
The consensus level (or model) is then used to estimate the PMGF frequencies of that particular
pair of plant species/populations. Empirical models can provide a more accurate prediction of
PMGF, compared to the mechanistic models. However, all parameters necessary for empirical
models must be generated based on a large number of PMGF field experiments [28,33].
Combined the merits of the previous two types of models, the quasi-mechanistic modeling
can be used to predict the PMGF frequencies with an improved accuracy and a less number of
field experiments [25,26,27,35]. This type of modeling includes the climatic parameters that
Accurate Gene Flow Model Based on Biological Parameters and Wind Speed
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can be directly measured in situ. However, this type of modeling still requires some critical
parameters, such as the gene flow coefficient (GFC) [25] and synthetic parameter [27] that
must be generated from the field experiments. The requirement of these parameters makes the
PMGF modeling impractical to use and dependent of field experiments. Therefore, it is neces-
sary to develop a more practical model that can predict gene flow frequencies more accurately
but without data from actual PMGF field experiments.
To achieve the accurate description of PMGF, biological and climatic factors that determine
the PMGF frequency should be considered in the modeling. Also, it should be more practical
to predict gene flow frequencies only involving measurable parameters that are independent of
any PMGF field experiment in the modeling. Rong et al. 2010 [26] developed a quasi-mecha-
nistic model to estimate PMGF frequencies in rice, which included both biological (e.g., out-
crossing rate of a pollen recipient, and cross compatibility between a pollen donor and
recipient) and climatic (e.g., wind speed and humidity) factors. The model by Rong et al. 2010
[26] attempted to estimate PMGF frequencies more reliably than those only including climatic
parameters. However, the model included a decay parameter of an exponential function—aβ
value that describes the pollen dispersal pattern, for which one needs to conduct field experi-
ments to generate relevant data. In addition, the βvalues generated only from a few field exper-
iments may not represent the decay parameter for all environmental conditions. Therefore,
this quasi-mechanistic model [26] still has its constraint to estimate PMGF frequencies.
To overcome this constraint, we adopted the inverse Gaussian function [36] to replace the
exponential dispersal function of the quasi-mechanistic model [26]. Through this replacement,
we can avoid the inclusion of the experiment-dependent βvalues for PMGF modeling, and all
the necessary parameters can be measured directly from the target environment. Here, we
report the establishment of a modified quasi-mechanistic PMGF model using the inverse
Gaussian function. The accuracy of the developed model was validated by comparing its simu-
lation results with five sets of published PMGF data from field experiments. The modified
model can provide a useful tool to assess the environmental impact of transgene flow and
design suitable biosafety management strategies by accurately estimating PMGF frequencies
without field experiments.
Methods
Procedure of model establishment
To establish a PMGF model, we used the inverse Gaussian function (Eq 1) by Katul et al. 2005
[36], which describes the wind dispersal pattern of small particles.
fðxÞ¼ ffiffiffiffiffiffiffiffiffiffi
l
2px3
rexp lðxmÞ2
2m2x

;ð1Þ
This function was used to predict the dispersal of released seeds, including the tiny ones
such as Senecio jacobaea (~2 mm) and Solidago rigida (~3 mm) [36] from the plants onto the
ground. In our case, this function is used to predict PMGF, in which the updraft pollen grains
disperse from donors’flowers to recipients’flowers for monoclinous plants, and from male
flowers (donors) to female flowers (recipients) for diclinous plants (Fig 1). Consequently, we
made a slight modification to calculate the two key parameters included in the inverse Gaussian
function of Katul et al. 2005 [36]: the scale parameter λand the location parameter μ. As indi-
cated by Katul et al. 2005 [36], the two parameters were estimated by the release height, wind
speed, and deposition velocity. Here, we estimate the relative pollen release height, which is
defined as the height between the position of updraft pollen grains of donor’sflowers and the
position of recipient’sflowers for monoclinous plants (Fig 1, left panel), and the height between
Accurate Gene Flow Model Based on Biological Parameters and Wind Speed
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the position of updraft pollen grains of donor’s male flowers and the position of recipient’s
female flowers for diclinous plants (Fig 1, right panel). Therefore, the equations (5b) and (9) of
Katul et al. 2005 [36] to calculate λand μwere modified as follows:
l¼hU=2ksw;m¼hU =Vt;ð2Þ
where his the relative pollen release height (see Fig 1 for details); Ūis the average wind speed;
κis the von Karman’s constant (determined as 0.4) [36,37]; σ
w
is the standard deviation of ver-
tical wind speed; and V
t
is the deposition velocity of pollen grains.
The wind speed (Ū) can be directly measured, and the standard deviation of vertical wind
speed (σ
w
) is approximately equal to 1.1 × u

[36]. Let Ūequals to the wind speed at the plant
height, then u

is calculated using the following equation [25,37]:
U¼u
kln Hd
z0

;ð3Þ
where His the plant height; dis the zero-plane displacement, which was commonly determined
as 0.63 × H[25]; and z
0
is the roughness length, which was determined as 0.13 × H[37].
Fig 1. The illustration of relative pollen release height between a pollen donor and recipient under the consideration of updraft pollen grains. The
left panel indicates the relative pollen release height of monoclinous plants and the right panel indicates the relative pollen release height of diclinous plants.
doi:10.1371/journal.pone.0149563.g001
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The deposition velocity of pollen grains (V
t
) can either be obtained from previous studies or
estimated by Stoke’s Law as follows [38,39]:
Vt¼dp
2gðrpraÞ
18Z;ð4Þ
where d
p
is the diameter of a pollen grain (m); gis the gravitational acceleration (9.8 m s
−2
); ρ
p
is the density of a pollen grain (kg m
−3
); ρ
a
is the air density, which is equal to 1.178 kg m
−3
under usual conditions; and ηis the dynamic viscosity of air (~1.8×10
−5
kg m
−1
s
−1
)[40].
Through the above modification, we can describe the pollen dispersal pattern at different
distances using the inverse Gaussian function which is based on the measurable biological and
wind speed parameters. Therefore, we can establish a new model to predict PMGF frequencies
using the inverse Gaussian function to replace the negative exponential function in the equa-
tion (7) developed by Rong et al. 2010 [26].
Model validation
We used five sets of published data representing five major crop species (rice, wheat, maize, oil-
seed rape, and mustard) from field experiments [41–45] to test the accuracy of our modified
PMGF model. The first set of data included PMGF frequencies generated from a transgenic
herbicide-resistant rice (Oryza sativa) line to a wild rice (O.rufipogon) strain [41]. The second
set of data included PMGF frequencies from a blue-grained wheat variety (Triticum aestivum)
to a common wheat variety [42]. The third set of data included PMGF frequencies from a
transgenic herbicide-resistant maize line (Zea mays) to its non-transgenic counterpart [43].
The fourth set of data included PMGF frequencies from a transgenic herbicide-tolerant oilseed
rape line (Brassica napus) to a non-transgenic line [44]. The fifth set of data included PMGF
frequencies from a transgenic canola (Brassica napus, AACC genomes) line resistant to herbi-
cide (glyphosate) to its relative mustard (B.juncea, AABB genomes) for assessing PMGF
between different species with divergent genomes [45].
All the parameters used for the model validation were listed in Table 1. Among these, the rel-
ative pollen release height was estimated as 0.5 m for the monoclinous wheat and oilseed rape
assuming the updraft height of pollen grains from donor’s flowers is 0.5 m, using the updraft
height of pollen grains of rice as a reference [46], because the hermaphrodite flowers of donors
and recipients in these cases (wheat and Brassica species) are nearly at the same height
Table 1. Detail information of the five sets of gene flow data from experimental fields used for the validation of the modified model.
Type of data Relative
pollen release
height h(m)
Deposition
velocity
V
t
(m s
−1
)
Outcrossing
rate t
B
(%)
Cross
compatibility
δ
AB
(%)
Wind speed
Ū(m s
−1
)
Donor field
length b(m)
Field
space
R(m)
Crop-to-wild gene
flow in rice
0.20 0.08 18.00 (GZ)*24.00
(SY)*
70 1.8 (GZ) 2.6 (SY) 13 (GZ) 20
(SY)
0
Crop-to-crop gene
flow in wheat
0.50 0.11 0.22 (year 2000) 0.10
(year 2001)
100 4.72 50 0
Crop-to-crop gene
flow in maize
1.50 0.32 50.00 100 2.36 (year 2006)
1.92 (year 2007)
50 0
Crop-to-crop gene
flow in oilseed rape
0.50 0.03 1.7 100 2.05 100 0
Canola-to-mustard
gene flow
0.50 0.03 15.0 0.97 3.0 400 0
*GZ indicates Guangzhou site in Guangdong province; SY indicates Sanya site in Hainan province.
doi:10.1371/journal.pone.0149563.t001
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[42,44,45]. The relative pollen release height was estimated as 0.2 m for the crop-to-wild rice
gene flow, because the recipient’s flowers (wild rice) were ~0.3 m taller than the donor’s flowers
(cultivated rice) [41]. The relative pollen release height was estimated as 1.5 m for the diclinous
maize case, because the male flowers of maize were ~1.0 m higher than their female flowers [43].
The parameter of deposition velocity of pollen grains (V
t
) for the first and third sets of data
(rice and maize cases) was obtained from the published data [47,48], and that for the second
and fourth sets of data (wheat and oilseed rape case) was estimated based on the pollen diame-
ters of rice (40–50 μm), wheat (48–57 μm), maize (80–100 μm), and oilseed rape (24–26 μm)
[49–51]following Eq 4. In addition, for the parameter of cross compatibility (δ
AB
) between a
pollen donor and recipient, we set δ
AB
as 100% for the second, third, and fourth sets of data
because their pollen donors and recipients are the same species. For the first set of data, we set
δ
AB
as 70% following the literature by Oka who estimated the cross compatibility between culti-
vated rice and wild O.rufipogon [52], because the cultivated rice was used as the pollen donors
and wild rice as the pollen recipients [41]. For the fifth set of data, we set t
B
as 15.0% according
to previous studies [53–55] and calculated δ
AB
from t
B
and observed PMGF data, and the wind
speed was set as a moderate value of 3 m s
−1
because it was not provided in this experiment
[45]. In simulating the first set of data using Eq 5, we replaced the parameter of the recipient
pollen density (D
B
) by the adjusted recipient pollen density (δ
AB
×D
B
) where pollen competition
between GE and non-GE rice lines was considered because the recipient field included both
wild and non-GE rice [41].
The analyses of covariance and correlation were applied to validate the accuracy of the
model. The analysis of covariance was conducted to test the consistency of slopes (p
s
values) and
the consistency of intercepts (p
i
values) between PMGF frequencies obtained from the published
field experiment (represented by empty circles) and model simulation (represented by curves) at
different spatial distances. Correlation analysis was also conducted to test the goodness-of-fit
between the published field experiment data and model simulation results (rvalues). All the sta-
tistical analyses were conducted using the software SPSS ver. 22.0 (SPSS, Chicago, Illinois, USA).
Results
Model
We replaced the exponential function in the equation (7) of the PMGF model by Rong et al.
2010 [26] with the adjusted inverse Gaussian function of Katul et al. [36]. As a result, a modi-
fied quasi-mechanistic PMGF model is established, and can be used to predict the gene flow
frequency (F
AB
(x)) from a donor (A) to a recipient (B) as follows:
FABðxÞ¼tB
dABDA
dABDAþDB
¼tB
dABðφðxþbÞφðxÞÞ
dABðφðxþbÞφðxÞÞ þ φðxRÞ;ð5Þ
where t
B
is the outcrossing rate of a recipient plant; xis the spatial distance from the edge of a
donor field to the measured points of recipient fields; bis the length of the donor field; Ris the
spatial distance between donor and recipient fields (see Fig 1 in Rong et al. 2010 [26]); and φ(x)
is the cumulative distribution function of the inverse Gaussian function, which can be calcu-
lated as follows [56]:
φðxÞ¼Zx
0
fðyÞdy ¼Fffiffiffi
l
x
rx
m1

!
þexp 2l
m

Fffiffiffi
l
x
rx
mþ1

!
;ð6Þ
where the symbol Fdenotes the cumulative distribution function of the standard normal
distribution.
Accurate Gene Flow Model Based on Biological Parameters and Wind Speed
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Here, the modified quasi-mechanistic PMGF model (Eq 5) is used to calculate PMGF fre-
quencies for the dataset collected from a parallel donor-to-recipient field design, such as in the
case of rice-wild rice and canola-mustard gene flow [41,45]. However, we found that the model
(Eq 5) can also be applied for dataset collected from the donor-surrounded-by-recipient field
design such as in the cases of wheat, maize, and oilseed rape [42–44]. This indicates that the
modified PMGF model can produce well-fitted predicting results for datasets from the two
types of field experimental designs.
Validation
In general, the simulation results (represented by the curves) based on our modified PMGF
model from this study fitted significantly well with the observed PMGF frequencies (repre-
sented by the circles) from the five sets of published data [41–45] generated from the field
experiments for rice-wild rice, wheat-wheat, maize-maize, oilseed rape-oilseed rape, and
canola-mustard gene flow (Figs 2–6).
For the rice data validation, the PMGF frequencies estimated based on the model simulation
fitted perfectly with the frequencies obtained from the two independent crop-to-wild gene flow
field experiments at the Guangzhou and Sanya sites (Fig 2). The p
s
and p
i
values between
model-simulated and experiment-observed PMGF frequencies are 0.888 and 0.660 for data
from the Guangzhou site, and 0.961 and 0.930 for data from the Sanya site, respectively. These
values showed no significant differences (>0.05) in the slope (p
s
value) and intercept (p
i
value)
of the curves representing PMGF frequencies at different spatial distances between the model-
simulated and field-experimental results (Fig 2), indicating the similar PMGF trends of the
Fig 2. Relationships of crop-to-wild gene flow between field experiments (empty circles) and model-based simulation (solid curves) in rice (Oryza
sativa,O.rufipogon) at various spatial distances. (A) Field experiment data from the site in Guangzhou. (B) Field experiment data from the site in Sanya
[41]. Logarithmic coordinate axes (y-axis) were applied to indicate the gene flow frequencies.
doi:10.1371/journal.pone.0149563.g002
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model-simulated and experiment-observed data. In addition, the correlation coefficients (r)
between the model-simulated and experiment-observed PMGF frequencies were 0.965
(p<0.001) and 0.979 (p<0.001) for data from the Guangzhou and Sanya sites, respectively. Sig-
nificant positive correlation was observed between the PMGF frequencies obtained from the
model-simulated and field-experimental results.
For the wheat data validation, the PMGF frequencies estimated based on the model simula-
tion fitted perfectly with the frequencies obtained from the two independent crop-to-crop gene
flow field experiments conducted in 2000 and 2001 (Fig 3). The p
s
and p
i
values between
model-simulated and experiment-observed PMGF frequencies are 0.899 and 0.803 for the data
from 2000 experiment, and 0.732 and 0.699 for the data from 2001 experiment, respectively.
These values showed no significant differences (>0.05) in the slope (p
s
value) and intercept (p
i
value) of the curves representing PMGF frequencies at different spatial distances between the
model-simulated and field-experimental results (Fig 3), suggesting the similar PMGF trends of
the model-simulated and experiment-observed data. In addition, the correlation coefficients
(r) between the model-simulated and experiment-observed PMGF frequencies were 0.989
(p<0.001) and 0.993 (p<0.001) for the data from 2000 and 2001 experiments, respectively. Sig-
nificant positive correlation was observed between the PMGF frequencies obtained from the
model-simulated and field-experimental results.
For the maize data validation, the PMGF frequencies estimated based on the model simula-
tion fitted perfectly with the frequencies obtained from the two independent crop-to-crop gene
flow field experiments conducted in 2006 and 2007 (Fig 4). The p
s
and p
i
values between
model-simulated and experiment-observed PMGF frequencies are 0.741 and 0.664 for the data
Fig 3. Relationships of crop-to-crop gene flow between field experiments (empty circles) and model-based simulation (solid curves) in wheat
(Triticum aestivum) at various spatial distances. (A) Field experiment data collected in 2000. (B) Field experiment data collected in 2001 [42]. Logarithmic
coordinate axes (y-axis) were applied to indicate the gene flow frequencies.
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from 2006 experiment, and 0.728 and 0.667 for the data from 2007 experiment, respectively.
These values showed no significant differences (>0.05) in the slope (p
s
value) and intercept (p
i
value) of the curves that represented PMGF frequencies at different spatial distances between
the model-simulated and field-experimental results (Fig 4), indicating the similar PMGF trends
of the model-simulated and experiment-observed data. In addition, the correlation coefficients
(r) between the model-simulated and experiment-observed PMGF frequencies were 0.987
(p<0.001) and 0.990 (p<0.001) for the data from 2006 and 2007 experiments, respectively. Sig-
nificant positive correlation was observed between the PMGF frequencies from the model-sim-
ulated and field-experimental results.
For the oilseed rape data validation, the PMGF frequencies estimated based on the model
simulation fitted perfectly with the frequencies obtained from the two independent crop-to-
crop gene flow field experiments conducted in 2008 and 2009 (Fig 5). The p
s
and p
i
values
between model-simulated and experiment-observed PMGF frequencies are 0.779 and 0.830 for
the data from 2008 experiment, and 0.805 and 0.939 for the data from 2009 experiment,
respectively. These values showed no significant differences (>0.05) in the slope (p
s
value) and
intercept (p
i
value) of the curves that represented PMGF frequencies at different spatial dis-
tances between the model-simulated and field-experimental results (Fig 5), indicating the simi-
lar PMGF trends of the model-simulated and experiment-observed data. In addition, the
correlation coefficients (r) between the model-simulated and experiment-observed PMGF fre-
quencies were both 0.996 (p<0.01) for the data from 2008 and 2009 experiments. Significant
positive correlation was observed between the PMGF frequencies from the model-simulated
and field-experimental results.
Fig 4. Relationships of crop-to-crop gene flow between field experiments (empty circles) and model-based simulation (solid curves) in maize (Zea
mays) at various spatial distances. A. Field experiment data collected in 2006. (B) field experiment data collected in 2007 [43]. Logarithmic coordinate axes
(y-axis) were applied to indicate the gene flow frequencies.
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For the validation of canola-mustard gene flow data, the PMGF frequencies estimated based
on the model simulation fitted well with the frequencies obtained from the two independent
gene flow field experiments (Fig 6). The p
s
and p
i
values between model-simulated and experi-
ment-observed PMGF frequencies are 0.116 and 0.343 for the data from the site 1 (Fig 6A),
and 0.096 and 0.307 for the data from the site 2 (Fig 6B), respectively. These values showed no
significant differences (>0.05) in the slope (p
s
value) and intercept (p
i
value) of the curves that
represented PMGF frequencies at different spatial distances between the model-simulated and
field-experimental results, indicating the similar PMGF trends of the model-simulated and
experiment-observed data. In addition, the correlation coefficients (r) between the model-
simulated and experiment-observed PMGF frequencies were 0.996 (p<0.001) and 0.563
(p= 0.071) for the data from the site 1 and site 2, respectively.
Discussion
In this study, we established a new pollen-mediated gene flow (PMGF) model based on the
quasi-mechanistic model of Rong et al. 2010 [26], by replacing the exponential function in the
quasi-mechanistic model with the adjusted inverse Gaussian function of Katul et al. 2005 [36].
By such a modification, the new PMGF model can circumvent the input of a decay parameter
(the βvalue) that must be generated from separate PMGF field experiments. Our modified
model includes the following biological parameters: pollen diameter and relative pollen release
height of a donor, outcrossing rate of a pollen recipient, cross compatibility between a pollen
donor and recipient, spatial distance between donor and recipient fields, and the length
(depth) of a donor field, in addition to the parameter of wind speed. All of these parameters
Fig 5. Relationships of crop-to-crop gene flow between field experiments (empty circles) and model-based simulation (solid curves) in oilseed
rape (Brassica napus) at various spatial distances. (A) Field experiment data collected in 2008. (B) Field experiment data collected in 2009 [44].
Logarithmic coordinate axes (y-axis) were applied to indicate the gene flow frequencies.
doi:10.1371/journal.pone.0149563.g005
Accurate Gene Flow Model Based on Biological Parameters and Wind Speed
PLOS ONE | DOI:10.1371/journal.pone.0149563 March 9, 2016 10 / 16

can either be measured directly in the target locations or obtained from published studies/data-
bases. In contrast to the model of Rong et al. 2010 [26], some climatic factors such as the tem-
perature and relative humidity were not considered in our modified PMGF model, although
they may affect PMGF frequencies [26,57,58,59]. This is because the relationship between the
two factors and PMGF frequencies has not yet been accurately determined. Consequently, we
neglected the temperature and relative humidity in our modified PMGF model. Once the rela-
tionship is clearly determined in the future, we can include the two parameters in the PMGF
model. Thus, our modified PMGF model can be applied to accurately calculate/predict the
gene flow frequencies of plant species mediated by pollen at different spatial distances under
various environments, independent of PMGF field experiments. The new feature of our modi-
fied model makes the estimation of PMGF frequencies more practical and is easier to use, pro-
vided that the required biological parameters and wind speed data are available.
To validate the modified PMGF model, we compared the model-simulated PMGF pattern
and the gene flow frequencies obtained from the field experiments. The results of model-simu-
lated and experiment-generated PMGF showed a high level of goodness-of-fit, suggesting the
high predicting power for gene flow frequencies using the modified PMGF model. The high
probability (p
s
) and (p
i
) values (>0.05) indicate the consistency of the slopes and the intercepts
between the PMGF frequencies obtained from the model simulation and the gene flow data
from the five sets of field experiments. The high correlation coefficients (rvalues, >0.90) indi-
cate the consistency of PMGF frequencies between the results obtained from the model simula-
tion and the five sets of gene flow data, except for the site 2 of the canola-mustard PMGF
experiment in the fifth set of data [45], which showed slightly lower rvalue (~0.56). Notably,
Fig 6. Relationships of canola (Brassica napus) to mustard (B.juncea) gene flow between field experiments (empty circles) and model-based
simulation (solid curves) at various spatial distances. (A) Field experiment data collected at the site 1. (B) Field experiment data collected at the site 2
[45]. Logarithmic coordinate axes (y-axis) were applied to indicate the gene flow frequencies.
doi:10.1371/journal.pone.0149563.g006
Accurate Gene Flow Model Based on Biological Parameters and Wind Speed
PLOS ONE | DOI:10.1371/journal.pone.0149563 March 9, 2016 11 / 16

the slightly weaker correlation between the model-predicted result and observed data from the
site 2 is probably due to the unexpectedly low PMGF frequencies (0.03%) observed at the close
distance (0 m), which is unusual in PMGF experiment. These results indicate the accuracy and
effectiveness of the modified model for predicting PMGF frequencies. For example, based on
the field experiment, Langhof et al. 2010 suggested the spatial isolation distance of 50 m
between a GE maize and its non-GE counterpart with the size of 200 × 200 m
2
because the fre-
quency of transgene flow was reduced to <0.9% (the European standard for a gene flow fre-
quency between co-existing GE and non-GE crops) at this isolation distance [60]. Similarly
according to our model simulation, the predicted average PMGF frequency from a donor to a
recipient maize field with the same situation was <0.7% (data is not shown) at the spatial dis-
tance of 50 m. The two examples showed considerable consistency between the field-experi-
mental and model-simulated results. In addition, the gene flow frequencies of different wheat
varieties generated from a field experiment were <0.1% at the spatial distance of 27 m [61],
which was highly consistent with the frequencies generated from model simulation. All
these indicate the usefulness of our modified model for the accurate prediction of PMGF
frequencies.
Noticeably at the relatively long spatial distances, the model-predicted PMGF frequencies
are slightly higher than the gene flow frequencies obtained from field experiments in some
cases. This is probably due to the viability of pollen grains in the air, which can considerably
influence the actual gene flow frequencies at the long spatial distance. Pollen grains of many
plant species, particularly wind-pollination species, lose their viability quickly after being
released to the air [62,63]. The number of viable pollen grains might be considerably reduced
after a long-distance travel in the air. Therefore at the long spatial distance, the model-pre-
dicted PMGF frequency becomes greater than actually obtained gene flow frequencies from
field experiments. Nevertheless, the predicted PMGF frequencies based on our modified model
can provide useful information for assessing and monitoring environmental consequences
caused by (trans)gene flow, particularly for the worst scenario assessment [26,64] and for
establishing a safe isolation spatial distance between co-existing GE and non-GE crops [8,63].
With the rapid expansion and commercial production of GE crops over the world, trans-
gene flow and its environmental impact has aroused increasing biosafety concerns worldwide
[65]. The effective assessment and monitor of the environmental impact caused by transgene
gene flow are important to guarantee the safe and sustainable application of GE crops. To esti-
mate the frequency (exposure) of transgene flow is the critical and first step for assessing and
monitoring the environmental impact [66,67]. Our modified PMGF model provides a practical
tool to meet the objective of transgene flow estimation, particular for wind-pollinated plant
species. This model can be applied to estimate the frequency of crop-to-crop and crop-to-wild
transgene flow relatively accurately for target plant species in various locations, based only on
the required biological parameters and wind speed data that can be easily obtained. The appli-
cation of our modified PMGF model can make the prediction of transgene flow more effective
and timely, because the modeling has excluded the expensive and time-consuming gene flow
filed experiments to generate necessary parameters. In addition, the strategic design of a spatial
isolation distance can be made between coexisting GE and non-GE crops based on the model
predicted transgene flow frequencies to minimize the transgene “contamination”to a permit-
ted threshold value [60,68]. Similarly, a proper spatial isolation distance can be established
between a GE crop and its wild relative species to restrict transgene flow based on the model
predicted result for reducing the potential environmental impact [69]. This can largely facilitate
the biosafety assessment and management concerning the transgene flow and its environmen-
tal impact. Furthermore, the model-based prediction of gene flow can also be applied in the
studies of evolutionary and invasive biology [70,71].
Accurate Gene Flow Model Based on Biological Parameters and Wind Speed
PLOS ONE | DOI:10.1371/journal.pone.0149563 March 9, 2016 12 / 16

In conclusion, we established a PMGF model with a great advantage and potentially broader
use for predicting pollen-mediated gene flow, provided that the desired biological parameters
and wind speed data are available. This model retains the feature of accuracy of Rong et al.
2010 model [26], but has added a new feature that no longer requires the input of field experi-
mental data to generate parameters as in previous models [26,28,35]. The validation results
indicate the accuracy of the model prediction for gene flow of various plant species. Because
this PMGF model is practical to use and free of field experiment, it can be broadly applied in
assessing (trans)gene flow. Therefore, this PMGF model can be useful for biosafety assessment
of potential environmental impact caused by transgene flow, in addition to addressing related
questions in evolutionary biology.
Acknowledgments
This work is supported by the Natural Science Foundation of China (31330014, 31271683) and
National Program of Development of Transgenic New Species of China (2011ZX08011-006).
The authors declare no conflict of interest for this work.
Author Contributions
Conceived and designed the experiments: LW BRL. Performed the experiments: LW BRL.
Analyzed the data: LW PH BRL. Contributed reagents/materials/analysis tools: LW BRL.
Wrote the paper: LW PH BRL.
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