Fast development and commercialization of genetically modified plants have aroused concerns of transgene escape and its environmental consequences. A model that can effectively predict pollen-mediated gene flow (PMGF) is essential for assessing and managing risks from transgene escape. A pollen-trap method was used to measure the wind-borne pollen dispersal in cultivated rice and common wild rice, and effects of relative humidity, temperature and wind speed on pollen dispersal were estimated. A PMGF model was constructed based on the pollen dispersal pattern in rice, taking outcrossing rates of recipients and cross-compatibility between rice and its wild relatives into consideration. Published rice gene flow data were used to validate the model. Pollen density decreased in a simple exponential pattern with distances to the rice field. High relative humidity reduced pollen dispersal distances. Model simulation showed an increased PMGF frequency with the increase of pollen source size (the area of a rice field), but this effect levelled off with a large pollen-source size. Cross-compatibility is essential when modelling PMGF from rice to its wild relatives. The model fits the data well, including PMGF from rice to its wild relatives. Therefore, it can be used to predict PMGF in rice under diverse conditions (e.g. different outcrossing rates and cross-compatibilities), facilitating the determination of isolation distances to minimize transgene escape. The PMGF model may be extended to other wind-pollinated plant species such as wheat and barley.
The fast development of genetic engineering has greatly promoted commercialization of genetically modified (GM) plants. To date, the global cultivation area of GM plants has already exceeded 120 million hectares (James, 2008). The extensive environmental release of GM plants has aroused biosafety concerns worldwide and stimulated a large number of studies on transgene escape and its ecological consequences (Rieger et al., 2002; Ellstrand, 2003; Snow et al., 2003; Song et al., 2004b; Andow and Zwahlen, 2006). The risk assessment of transgene escape involves both estimating the frequency of gene flow and identifying the ecological impact at a given gene flow frequency (Andow and Zwahlen, 2006). Therefore, determining gene flow frequency is an essential component for risk assessment of transgene escape.
Data of pollen-mediated gene flow (PMGF) generated from worldwide field experiments of different crops provide useful information for understanding transgene escape to non-GM crops and wild relatives (Arias and Rieseberg, 1994; Amand et al., 2000; Rieger et al., 2002; Messeguer, 2003; Wilkinson et al., 2003; Chen et al., 2004; Rong et al., 2007). However, the scattered information from specific experiments under specific environmental conditions is insufficient for a general guideline that can be used to predict frequencies of PMGF. Establishing a mathematical model to summarize the general pattern of PMGF and understanding how the pattern depends on relevant factors will achieve a more accurate prediction for transgene escape under various conditions (Walklate et al., 2004).
There are two main methods for modelling the contemporary PMGF at a landscape level: mechanistic and empirical (Klein et al., 2003, 2006; Gustafson et al., 2005; Snall et al., 2007). The mechanistic modelling incorporates physical and biological factors that influence PMGF, and provides insights into the process of PMGF (Klein et al., 2003; Gustafson et al., 2005; Snall et al., 2007). This modelling method can reveal the general pattern of contemporary PMGF under influences of various factors. Therefore, it can potentially predict the PMGF under diverse conditions (Snall et al., 2007). However, mechanistic models are usually mathematically complex and computationally expensive, and often contain many parameters that are difficult to measure in natural conditions (Klein et al., 2003; Snall et al., 2007). Empirical modelling ignores the details of the dispersal process and often simulates PMGF by applying regression analysis to achieve an empirical function that fits the experimental PMGF data (Klein et al., 2003, 2006; Gustafson et al., 2005; Snall et al., 2007). The empirical method can be easily performed in practice, but cannot be extended to a wider range of environmental conditions (Klein et al., 2003; Snall et al., 2007). Therefore, quasi-mechanistic modelling has recently been proposed as an intermediate approach (Klein et al., 2003; Snall et al., 2007). The quasi-mechanistic model involves only a few major dispersal parameters that have clear physical or/and biological interpretations and are suitable for fitting to experimental data (Klein et al., 2003; Snall et al., 2007). Therefore to some extent, it resolves the conflicts between universality and practicality in mechanistic and empirical modelling and may be more useful than its predecessors. In this study, we focus on establishing a quasi-mechanistic model to simulate the PMGF in rice using the empirical pollen dispersal pattern as a baseline and adding on the outcrossing rate of recipient and the cross-compatibility between rice with different pollen recipients. In the model, some fixed fraction (s) of the ovules is selfed prior to the arrival of outcross pollen. The highest possible outcrossing rate t equals 1−s. The remaining ovules can be fertilized by outcross pollen, but they could also be selfed depending on the ratio of outcross and self pollen that reaches the stigma. Actual outcrossing rates will be lower than the maximum t, the more so when self pollen is abundant. The fraction of outcrossing from alien pollen (PMGF frequency) further relies on its cross-compatibility to the stigma while competing with conspecific pollen. Such a kind of ‘mass-action’ model was first proposed for studying evolution of plant mating systems (Holsinger, 1991; de Jong et al., 1993), and recently used to estimate the PMGF from GM to non-GM crops (Klein et al., 2006; Kuparinen et al., 2007).
Cultivated rice (Oryza sativa L.) is an important world staple food. Many GM rice lines conferring different traits have been developed and released into the environment for biosafety assessment (Lu and Snow, 2005). The insect-resistant GM rice was first commercialized in Iran in 2005 (James, 2005). As the most important cereal crop in China, commercialization of GM rice to meet the growing food demands has been advocated for years (Jia, 2004; Lei, 2004; Qiu, 2008). However, transgene escape from GM rice and its undesirable ecological consequences is still one of the major biosafety concerns, which has dramatically blocked the process of GM rice commercialization (Qiu, 2008). Previous studies indicated that PMGF commonly occurred among rice varieties and from cultivated rice to common wild rice (Oryza rufipogon Griff.) and weedy rice (O. sativa f. spontanea) (Song et al., 2003; Chen et al., 2004; Wang et al., 2006; Rong et al., 2007). Common wild rice is the ancestor of cultivated rice and the most important germplasm for cultivated rice improvement (Song et al., 2005). PMGF from cultivated rice to common wild rice could contribute to the changes of genetic diversity and genetic structure in wild rice populations, and even cause the extinctions of local wild rice populations (Song et al., 2005, 2006; Xu et al., 2006). Weedy rice is a notorious weed in rice fields worldwide (Cao et al., 2006). A recent study of weedy rice populations in China indicated that weedy rice might originate from PMGF between rice varieties (Cao et al., 2006). In addition, cultivated rice is sexually compatible with all the AA-genome wild Oryza species (Lu and Snow, 2005), indicating that the likelihood of PMGF to these wild rice species is relatively high. Therefore, rice can serve as an excellent case for studying risk assessment and management of transgene escape. Results from rice modelling can also serve as a reference for other primarily self-fertilized and wind-pollinated crops species.
For modelling PMGF, we first need to know the pollen dispersal pattern. Previous studies of pollen flow in rice indicated that pollen dispersal was significantly influenced by such factors as pollen source size, spatial distance and climate conditions (Song et al., 2004a). PMGF was significantly correlated to the relative density of pollen-donor plants (Rong et al., 2005), suggesting a direct influence between frequency of PMGF and pollen density. In addition, strong pollen competition was observed between cultivated rice and common wild rice (Song et al., 2002), indicating that the cross-compatibility of alien pollen also plays an important role in determining the frequency of PMGF.
The objectives of this study were to: (i) determine pollen dispersal pattern in rice; (ii) establish a quasi-mechanistic PMGF model for rice; (iii) evaluate the effects of pollen density, pollen competition, pollen-source size and some climate parameters on PMGF. The PMGF model will provide a useful tool to accurately predict transgene escape in rice fields and to facilitate establishing appropriate control measures for minimizing unintended PMGF from GM rice.
Pollen flow in rice
Pollen flow data were collected from hybrid rice seed production fields and a common wild rice population at a conservation site in China. High densities of pollen grains were detected within short distance intervals from pollen sources and decreased rapidly with distance. The highest pollen density detected in cultivated rice was 2234 pollen grains/cm2 (1.0 m height above ground) at the distance of 2.0 m from the pollen source in 2003. Pollen grains were detected at the distance of 85.0 m in 2002 (1.0 m height: 25.5 ± 5.0/cm2; 1.5 m height: 51.6 ± 7.5/cm2) and 70.0 m in 2003 (1.0 m height: 228.8 ± 26.7/cm2; 1.5 m height: 270.6 ± 33.6/cm2) (values following ± indicate standard errors). Pollen densities detected at the height of 1.5 m were significantly higher than those at 1.0 m height (P ≤ 0.001), except on 2 days (9 September 2002, P = 0.658 and 10 September 2002, P = 0.613). For common wild rice, the highest pollen density was about 710 pollen grains/cm2 (1.5 m height) at 5.0 m from the wild rice population. Pollen grains were detected up to 105.0 m (2.0 ± 0.2/cm2) in 2002 and 90.0 m (19.9 ± 3.8/cm2) in 2003 from the wild rice.
Linear regression analyses between natural logarithm of pollen density and distance showed that the exponential model fitted the pollen flow data of both cultivated rice and common wild rice nicely (Figure 1 showing only data from 1.5 m height). The β values (the decay parameter of the exponential function; please see the Pollen flow model section of Experimental procedures for details) estimated in cultivated rice ranged from −0.058 to −0.016 with 95% confidence intervals ranging from −0.076 to −0.009. A paired-samples t-test indicated no significant difference between β values estimated at 1.0 and 1.5 m height in cultivated rice (P = 0.136). Therefore, only data from 1.5 m height were used for further analyses. The β values of pollen flow from common wild rice were from −0.058 to −0.018 with 95% confidence intervals ranging from −0.070 to −0.012. No significant difference occurred between the β values estimated in cultivated rice and common wild rice; therefore, most likely β was only the function of climate parameters. Based on these results, we set βmin = −0.058 and βmax = −0.016 for both cultivated rice and common wild rice with 95% confidence intervals ranging from −0.076 to −0.009.
Because the values of β, relative humidity, wind speed and temperature all appear to follow normal distributions, Pearson correlation analysis was performed to calculate the pairwise correlations among them. The results indicated that the parameter β was only negatively correlated with relative humidity (n = 12, P = 0.016) in the pollen flow experiment (Table 1). This means that pollen is dispersed over wider distances on dry days. No significant effect was detected from wind speed and temperature in our study although temperature was negatively correlated with relative humidity (n = 12, P = 0.047).
Table 1. Pairwise Pearson correlation analysis (n = 12) among β (the exp decay rate of pollen density), relative humidity (H, %), wind speed (W, m/s) and temperature (T, °C). Note that β is always negative, so that a high value (just below zero) corresponds with far away dispersal and a low value with nearby dispersal
*Correlation is significant at the 0.05 level (two-tailed).
PMGF in rice
Model simulation using Eqn (9) (see details in the PMGF model section of Experimental procedures) indicated that an increase in size of the pollen source (the rice field) caused an increase in PMGF frequency (Figure 2). However, such a size effect became weaker with the increase of pollen source size (Figure 2). In addition, when β became smaller, the PMGF frequency decreased more quickly, and the effect of pollen source size on PMGF became much weaker (Figure 2). When β = βmin = −0.058 (the smallest β value estimated in the pollen flow experiments), the differences among pollen sources with different sizes were small. In this case, the PMGF frequencies estimated at different distances were almost the same between pollen sources with size parameter b = 100 and infinite (the two curves coincide with each other in Figure 2). To predict the maximum PMGF from large rice fields, we simply set b = infinite in Eqn (8), then eβb = e−∞→0, so the rate of gene flow from the pollen donating crop A to a recipient plant of type B (i.e. the fraction of the seeds on plant B that is sired by all type A plants) is:
When the pollen recipient is also cultivated rice with high cross-compatibility (δAB = 1), the frequency of PMGF can be estimated as:
Therefore, we can use the simple exponential model with β = βmax to estimate the maximum PMGF between adjacent cultivated rice fields.
Linear regression analyses using Eqn (6) indicated excellent fits to the experimental data from our previous transgene flow study (Rong et al., 2005) (for all the GM and non-GM rice combinations used, and from both of the experimental sites, R2 > 0.9 and P < 0.05). The results strongly supported our assumption that PMGF frequency from pollen donor A to recipient B was in direct proportion to the relative density of A pollen around B.
For PMGF between cultivated rice varieties, nonlinear regression analyses showed that our PMGF model (Eqn 10) could well represent the transgene flow data from the field experiments (Rong et al., 2007) (Figure 3). The average β values were −0.210 ± 0.046 (MSR), −0.229 ± 0.061 (HY1) and −0.272 ± 0.078 (HY2) for different rice varieties. All the previous experiments were conducted at the same time in the same experimental field of Shaxian, China, therefore, the climate conditions among different plots of different rice pairs were more or less the same with similar β values.
Based on the results of the pollen competition experiment by Song et al. (2002), the cross-compatibility parameter δsr between cultivated rice and common wild rice was only 0.0204, indicating that the conspecific pollen from common wild rice was much more successful in competition than the alien pollen from cultivated rice. Nonlinear regression analyses between natural logarithm of transgene flow frequency from GM rice to common wild rice and distance from GM plots [LN (F) ∼ x] indicated that the model with δsr (Eqn 11) fitted perfectly to the experimental data from Wang et al. (2006) (Figure 4). The outcrossing rates estimated for common wild rice were 20.6 ± 5.6% in Guangzhou (R2 = 0.930 and sum of squared residuals = 1.422) and 39.6 ± 9.3% in Sanya (R2 = 0.889 and sum of squared residuals = 7.983). Using the model without δ (Eqn 10) for the nonlinear regression analyses, the outcrossing rates estimated were 2.73 ± 1.26% in Guangzhou (R2 = 0.660 and sum of squared residuals = 6.878) and 3.04 ± 0.74% in Sanya (R2 = 0.860 and sum of squared residuals = 10.056). The model gained a better fit (sum of squared residuals was lower and R2 value was higher) to the experimental data by considering cross-compatibility between cultivated rice and common wild rice with δsr than those without δsr (Figure 4). In addition, without considering the pollen competition between cultivated rice and common wild rice, the estimated outcrossing rates were much lower than the highest transgene flow frequencies detected in the field experiments (18.0 ± 1.0% in Guangzhou and 11.2 ± 3.7% in Sanya) (Wang et al., 2006).
Isolation distance for minimizing PMGF in rice
For simulating the maximum PMGF from cultivated rice fields, we assume the following worst case scenario.
1 The recipient B plot is surrounded by eight pollen source A plots;
2 Wind can blow from all directions from the eight A plots to the B plot;
3 The sizes of pollen source A plots are infinite (b = infinite);
4 Pollen can be dispersed by wind to a long distance (β = βmax = −0.016).
Eqn (16) was used to estimate the isolation distances required for minimizing PMGF between cultivated rice (ts = 1% and δ = 1), as well as for minimizing PMGF from cultivated rice to common wild rice (tr = 40% and δsr = 0.0204). The results indicated that the required isolation distance was reduced when the size of the recipient plot increased (Table 2). When the recipient size was larger than 80 × 80 m2, the model simulations suggest that for cultivated rice fields only a very limited isolation distance was needed for reducing the average PMGF frequency below a threshold of 0.9%, given that all seeds from the recipient non-GM rice plot were well mixed after harvest. However, for minimizing PMGF from cultivated rice to common wild rice, even though the recipient wild rice was continuously distributed with a population size as large as 100 × 100 m2, a long isolation distance (183 m) was still required to reduce the frequency to <1%.
Table 2. Isolation distance required to keep transgene presence in the whole recipient population below 0.9% among cultivated rice (crop-to-crop) and 1% from cultivated rice to common wild rice (crop-to-wild), given a worst case scenario in which the recipient plot is surrounded by eight pollen source plots and wind can go from all different directions from these plots to the recipient plot during the flowering period
Recipient size (m2)
Isolation distance (m)
*The outcrossing rate (t) of cultivated rice is 1% and the pollen dispersal parameter β is set to the maximum value (−0.016) estimated in the rice pollen flow experiments. No cross-barrier occurs among cultivated rice (δ = 1).
†For common wild rice, t = 40% and β = −0.016. Cross-compatibility parameter between cultivated rice and common wild rice (δsr) is 0.0204.
20 × 20
40 × 40
60 × 60
80 × 80
100 × 100
Pollen flow in rice
Our experimental data showed that both cultivated and common wild rice produced a large amount of wind-borne pollen that could disperse to a long distance (Figure 1). Within the experimental scales (∼100 m), a simple exponential model can well represent pollen flow in rice (Figure 1), which serves as the basis for modelling PMGF in this study. Pollen density of cultivated rice was higher than that of common wild rice at a comparable distance, most likely because of much higher plant density and more concentrated flowering in cultivated rice. Common wild rice has a protracted flowering habit (Song et al., 2003) although it can produce more pollen per floret than cultivated rice (Oka and Morishima, 1967). In cultivated rice, pollen density was significantly higher at the vertical level of 1.5 m than that at 1.0 m, suggesting that pollen grains from cultivated rice can easily disperse to common wild rice having taller panicles. However, we can use the same estimated values of β, the key decay parameter of the exponential pollen flow model, to calculate the pollen density at different heights because no significant difference was observed between heights. The β value correlated negatively correlated with relative humidity (Table 1), suggesting that wind-borne pollen spread to a shorter spatial distance with high relative humidity. Wind speed and temperature did not have a strong effect on pollen flow, probably because of insufficient variation in wind speed and temperature during the experiments to significantly change the pollen dispersal. Further studies are needed to confirm the detailed correlations between β and climate conditions so as to predict the PMGF more precisely under different climate conditions.
PMGF in rice
We established a quasi-mechanistic model for PMGF in rice in the present study, incorporating three key biological parameters: pollen density, outcrossing rate and cross-compatibility. This model can well represent previously obtained PMGF data from cultivated rice (Rong et al., 2005, 2007) and those between cultivated rice and common wild rice (Wang et al., 2006). Compared with the previously published empirical PMGF model of wind- and self-pollinated wheat (Gustafson et al., 2005), our quasi-mechanistic PMGF model includes not only the correlation between pollen density and distance, but also biologically meaningful factors representing the mechanism of PMGF, providing a solid base for understanding the pattern of PMGF. If a model only uses empirical functions to describe the relationship between frequencies of gene flow and spatial distances, it will have a relatively low predictive power for PMGF under different circumstances, especially crop-to-wild gene flow with variable cross-compatibility. However, the parameter of cross-compatibility was rarely considered in previous PMGF models. Song et al. (2002) reported considerable competition between alien and conspecific pollen grains in rice for fertilizing a single ovule. Our results indicated that without the consideration of biological parameters such as cross-compatibility and pollen competition, a PMGF model would not accurately represent the PMGF from cultivated to common wild rice. Therefore, cross-compatibility should be included in rice PMGF modelling to avoid overestimation of PMGF.
A major concern of PMGF studies is to extend the results obtained from controlled field experiments to a large scale, owing to the ‘size effect’ that may significantly influence the generalization of experimental results. Experiments in rice indicated that pollen flow was significantly affected by the size of pollen sources, and a larger pollen-source size commonly resulted in higher pollen density (Song et al., 2003). Accordingly, higher PMGF might be expected with a larger pollen-source size. However, the largest size of pollen sources in that specific experiment was only 72 m2 (Song et al., 2003), and the actual rice fields could be as large as 10 000 m2 in the main rice planting regions in China (also in many other countries). Estimating PMGF with realistic pollen sources is essential for the relevant risk assessment and management. Our model simulations showed that for a primarily self-pollinating species, PMGF indeed increased with the increase of pollen source size, but such a size effect levelled off gradually with the increase in pollen source size (Figure 2). The influence of size approached an upper limit when pollen source size became infinite (Figure 2). Actually, when the pollen source size is as large as 100 × 100 m2, the PMGF is already close to the limit (Figure 2), suggesting PMGF is very restricted (most of the PMGF is probably within 100 m) in primarily self-pollinating plant species. Thus, we can estimate PMGF on a small or large spatial scale through the model simulation. For the primarily self-pollinating plant species such as rice in particular that has a low outcrossing rate and large amount of wind-borne pollen, the size effect can be reduced relatively quickly. Moreover, simulation of the rice PMGF indicated a clear interaction between the size effect and β, in which the small β value (e.g. −0.058) reduced the effect of pollen-source size on PMGF (Figure 2). Therefore, no significant size effect was detected on rice transgene flow in the field experiment (Rong et al., 2007) because of the small β values (about −0.2) under the experimental conditions. Such small β values also contributed to the dramatic reduction of PMGF within a short distance from pollen sources as found in Rong et al. (2007).
Isolation distance for minimizing PMGF in rice
The PMGF model can provide a practical guide for risk assessment and management of transgene escape in rice. For example, the model can estimate the isolation distances required for minimizing crop-to-crop and crop-to-wild PMGFs. Under the worst case scenario where the recipient plot is surrounded by pollen source plots with infinite sizes (b = infinite) and pollen can easily disperse to long distances (β = βmax), when outcrossing rate of cultivated rice is less than 1%, the model simulations suggest that the size of a recipient plot plays a meaningful role in setting isolation, which requires a much longer distance for small recipient plots than large recipient plots (Table 2). The model simulation showed no isolation distance to be required for large recipient plots (≥80 × 80 m2), assuming that the seeds are well mixed after harvest. In rice production practice, this illustrates that only a limited isolation distance (e.g. a few metres) could likely achieve significant reduction of gene flow frequencies in cultivated rice to <0.9% (Table 2) if large recipient plots (≥80 × 80 m2) are deployed, to minimize the potential ‘contaminations’ from GM rice. The simulations are made under the assumption of extremely limited reproductive barriers between rice cultivars (δ = 1). Sometimes, however, a certain degree of cross-incompatibility was observed between some varieties (Rong et al., 2004), particularly between the two subspecies indica and japonica rice. The frequency of PMGF here may still be overestimated, compared with the actual situation in rice fields. Therefore, for predicting rice PMGF more accurately, data on cross-compatibility between different cultivated rice varieties should be taken into consideration in future studies.
Under the same worst case scenario, the attempt to reduce the frequency of PMGF from cultivated rice to common wild rice to a low level (e.g. <1%) requires a long isolation distance when the outcrossing rate of common wild rice is about 40%, especially for small wild rice populations (Table 2). This conclusion is in agreement with the previous studies in which small populations usually received more foreign genes through PMGF than large populations (Ellstrand and Elam, 1993). The exponential model fitted the data very well over distances up to 100 m. It might be that at distances >100 m from the source some pollen is still found and that this amount is more or less constant. If this amount of pollen were significant a fat tailed model should fit better the data for long distances. Additional data for long-distance dispersal could be collected to examine if this affects our calculations or that the effect is too small to be of quantitative importance.
When the integral is used to calculate the conspecific pollen density in the wild rice population, the model simulation actually assumes that common wild rice occurs continuously with a high population density. In China, under frequent human disturbances, populations of common wild rice become small and fragmented, with low individual densities (Song et al., 2005). In this case, the density of conspecific pollen in wild rice populations would be much lower than that expected in the model simulation. According to Eqn (5)
where A indicates cultivated rice and B common wild rice, if the conspecific pollen density DB from common wild rice becomes lower, then the PMGF frequency F will be higher. Therefore, in fragmented wild rice populations, the frequencies of PMGF from nearby rice fields would be even higher than those estimated in large and continuous populations and accordingly longer isolation distances would be required. It is necessary to point out that the frequency of <1% set for crop-to-crop PMGF is definitely too high for crop-to-wild PMGF, because even a much lower than <1% transgene flow to wild population may significantly affect evolution of a wild population as indicated by Ellstrand (2003). Therefore, effective isolation should be required to reduce the crop-to-wild PMGF to a minimum level to avoid ecological consequences in rice if an escaped gene has natural selection advantage. In such a case, spatial isolation alone may not be effective to avoid crop-to-wild PMGF. As a consequence, it is suggested that GM rice varieties should not be cultivated in the vicinity of common wild rice populations to avoid possible ‘genetic contamination’ (Chen et al., 2004; Song et al., 2005).
The application of the newly established PMGF model based on rice can be extended to the prediction of PMGF in other wind-pollinated crops such as wheat and barley because the pollen dispersal patterns of these crops should be very similar and the key biological parameters, such as outcrossing rates and cross-compatibility can be easily estimated from the results of field experiments as indicated in rice.
Pollination in rice
The inflorescence (panicle) of rice has small monoclinous flowers. Each flower has one ovule with two featherlike stigmas and six anthers each with about 700–9000 pollen grains (Oka and Morishima, 1967). In cultivated rice, pollen grains disperse from anthers almost immediately after flowering and are easily attached to stigmas causing high proportion of selfing (Oka and Morishima, 1967). Outcrossing occurs through wind-borne pollen, and the estimated rate is 0%–5% (Oka and Morishima, 1967). For common wild rice, pollen dispersal after flowering takes only a few minutes (Oka and Morishima, 1967). The length of stigmas and styles are usually longer in the wild rice than in cultivated rice (Oka and Morishima, 1967). The long stigmas with long styles often stretch outside of wild rice flowers, increasing opportunities to receive foreign pollen. Therefore, outcrossing rate is much higher in common wild rice, and can be as high as 40% (Oka and Morishima, 1967).
Pollen flow in rice
Experimental data for rice pollen flow were collected using the pollen trap method of Song et al. (2004a), in three consecutive days in September 2002 and 2003 during the flowering peak for cultivated and common wild rice. For the pollen trap, two or three replicates separated for about 5 m were set at each of the measuring distances downwind from pollen sources. Pollen density was calculated as the number of pollen grains per cm2 following the methods described by Song et al. (2004a).
Pollen flow of cultivated rice was measured in a commercial hybrid rice seed production farm (250 × 350 m2) in Shanghai, China. The pollen source was 80 × 100 m2 in size with no other rice fields nearby. Based on panicle height (ca. 1 m) of cultivated rice, pollen density was measured at the heights of 1.0 and 1.5 m above ground, at around 5 m intervals between 0–85 m from pollen sources. To achieve maximum pollen flow, manual stimulation of pollen dispersal was applied by shaking rice panicles with a long cord during the daily peak of flowering (ca. 10:00–14:00). In China, this is a general treatment for seed productions of hybrid rice between male-sterile lines and male-sterile restorers (fertile) to achieve high seed sets.
Pollen flow of common wild rice was measured in the Huli Marsh, Chaling County of Hunan Province, China. The Huli Marsh is an in situ conservation site of common wild rice (about 2 ha) (Xu et al., 2006). The high density of the wild plants and absence of cultivated rice made Huli Marsh a good site for measuring wild rice pollen flow. Based on spontaneous panicle height (ca. 1.3–1.7 m above water) of the wild rice, pollen density was measured at the heights of 1.5 m above ground, at around 5 m intervals between 0–105 m from pollen sources.
At the same time, the climate parameters, including wind speed (W, m/s), temperature (T, °C) and relative humidity (H, %) were measured in the fields. Wind speed was measured every 10–15 min, and temperature and relative humidity were measured every 30 min at the height of 1.0–1.5 m, using a portable microclimate metre.
The paired-samples t-test was applied to compare the means of pollen densities at 1.0 and 1.5 m heights in cultivated rice. Linear regressions were performed to analyse the correlation between natural logarithm of pollen density and distance. All statistical analyses were performed using spss 15.0 for windows (SPSS Inc., Chicago, Illinois, USA, 2006).
Pollen flow model in rice
We used an exponential model for rice pollen dispersal because it provided an excellent fit to the experimental data of pollen flow from large rice fields. An additional advantage of the exponential model over more complex alternatives is that fewer parameters need to be estimated, facilitating the analysis. Based on a simple exponential function, the pollen density (D) at a given distance (x) from a point source can be calculated as:
where D0 indicates pollen density at 0 m from the pollen source and β determines the decrease in pollen density with the increase in distance (β < 0). A high β value (close to zero) indicates long-distance pollen dispersal.
Generally, the pollen density at the downwind direction from an a × b m2 rectangle pollen source (b is the length along wind direction) can be calculated as:
where indicates pollen density at 0 m from a line source (a m wide) and indicates pollen density at 0 m from a plane source (a × b m2).
For a simple exponential pollen flow model, only two parameters should be estimated: pollen density at 0 m from the pollen source and the value of β. According to the Eqn (4), pollen density at 0 m is the function of pollen source size and β. Therefore, β is the only parameter that should be estimated. The β values of rice pollen dispersal were estimated using the regression analysis as indicated previously. Paired-samples t-test was used to compare the values of β estimated at 1.0 and 1.5 m heights in cultivated rice. Based on the results from the study by Song et al. (2004a), rice pollen flow is probably affected by weather conditions. Therefore, effects of wind speed, temperature and relative humidity on pollen flow were evaluated by calculating the pairwise correlations among β, wind speed, temperature and relative humidity. All statistical analyses were performed using spss 15.0 for windows.
Assume that PMGF frequency (FAB) from pollen donor A to recipient B is in direct proportion to the relative pollen density around B. Therefore:
where tB indicates the maximal outcrossing rate of the recipient plant B and a fraction (s = 1 − tB) of the ovules is self-pollinated prior to the arrival of outcross pollen, DA represents the density of pollen grains dispersing from the donor plant A, DB indicates the density of pollen grains from plants of B and δAB represents cross-compatibility and it refers to the success of A in pollen competition between A and B. The δAB reflects different biological phenomena: the viability and growth rate of the pollen grains and the degree to which the maternal plant accepts different pollen types (incompatibility). For conspecific pollen, δ = 1; for alien pollen with lower cross-compatibility than conspecific pollen, 0 < δ< 1. If δAB = 0, pollen grains from A cannot hybridize with B, thus FAB = 0. For simplification, we set δ = 1 for modelling PMGF in cultivated rice because different rice varieties are the same species with relatively high cross-compatibility between each other, then:
When the pollen flow model is exponential as indicated in Eqn (4), PMGF frequency at different distances (x) from an a × b m2 rectangle pollen source (A) to an adjacent a × c m2 rectangle recipient (B) (Figure 5, r = 0) can be estimated as:
where indicates the pollen density at 0 m from a line source of A (a m wide) and the pollen density at 0 m from a line source of B (a m wide). For simplification, pollen densities at 0 m from line sources A and B are supposedly the same, i.e. , then:
For PMGF between rice cultivars, δ = 1, then:
According to Eqns (8) and (9), given pollen donor A, recipient B and constant β, PMGF frequency FAB is the function of pollen source size and distance. Set b = 5, 10, 20, 100 m or infinite, then the effects of pollen source size on PMGF were simulated using Eqn (9) with tB = 1% and β = the maximum (βmax) and minimum (βmin) values estimated in rice pollen flow experiments.
Validation of PMGF model in rice
In our previous study, transgene flow from three insect-resistant GM rice lines to their non-GM rice counterparts (isogenic lines: MSR+ & MSR−, HY1+ & HY1−, and HY2+ & HY2−) cultivated in mixture were measured at two experimental sites (Fuzhou and Sanya, China) (Rong et al., 2005). The relative densities [DGM/(DGM + Dnon-GM)] of GM pollen around non-GM recipients were: (i) 8/9 in the GM majority pattern (Experiment A: one non-GM individual was surrounded by eight GM individuals); (ii) 1/9 in the non-GM majority pattern (Experiment B: one GM individual was surrounded with eight non-GM individuals) and (iii) 1/2 in the random pattern (Experiment C: equal numbers of GM and non-GM rice were mixed and randomly planted in the plots). Using Eqn (6) from this study, linear regression analyses were applied to examine the correlations between the average transgene flow frequencies and relative GM pollen densities.
In another study, we estimated the transgene flow from the GM rice plots to adjacent non-GM rice plots (Shaxian, China) (Rong et al., 2007). The effects of pollen source size on PMGF were examined with different plot sizes of GM rice (Treatment A: b = 20 m, B: b = 10 m, C: b = 5 m, and D: b = 10 m). No significant effect of pollen source size was found in the study (Rong et al., 2007). We re-analysed the data based on Eqn (9) to validate the PMGF model in cultivated rice:
where LN represents the natural logarithm and FGM means transgene flow frequency. Nonlinear regression analyses were performed with Eqn (10) between natural logarithm of transgene flow frequency and distance from GM plots [LN (F) ∼ x] in spss 15.0 for windows. The starting values of parameters t and β were 1% and −1, respectively, with constraints of t ≥ 0 and β ≤ 0. For the loss function, ‘Sum of squared residuals’ was selected to minimize the sum of the squared residuals in the regression. The estimation method was the sequential quadratic programming algorithm (Optimality: 1E-15 and Function: 1E-15).
For PMGF from cultivated to wild rice, low cross-compatibility will lead to strong pollen competition, resulting in low PMGF frequency. In a field experiment examining pollen competition between cultivated rice and common wild rice, Song et al. (2002) demonstrated much higher success of conspecific pollen (common wild rice) than alien pollen (cultivated rice). In the study, self anthers were removed from the wild rice flowers before dehiscence, therefore, the outcrossing rate t of wild rice was supposed to be 100%. When a pollen mixture with equal amounts of pollen from cultivated rice and common wild rice (Ds = Dr) was applied to both of the common wild rice sigma branches, only 2% of the seeds were the result of alien pollination from cultivated rice (Fsr = 2%) (Song et al., 2002). The results were used to estimate the value of parameter δsr between cultivated rice and common wild rice with Eqn (5).
Transgene flow from cultivated rice to common wild rice was estimated by Wang et al. (2006) using herbicide-tolerance GM rice. The field experiments were conducted with different sizes of GM plots in Guangzhou (b = 13 m) and Sanya (b = 20 m), China (Wang et al., 2006). We re-analysed the transgene flow data based on Eqn (8) with the estimated value of δsr:
and using Eqn (10) without δ to validate the PMGF model. Nonlinear regression analyses were done between natural logarithm of transgene flow frequency and distance from GM plots [LN (F) ∼ x] in spss 15.0 for windows. The starting values of parameters t and β were 40% and −1, respectively, with constraints of t ≥ 0 and β ≤ 0. For the loss function, ‘Sum of squared residuals’ was selected to minimize the sum of the squared residuals in the regression. The estimation method was the sequential quadratic programming algorithm (Optimality: 1E-15 and Function: 1E-15).
Isolation distance for minimizing PMGF
If the pollen source A and recipient B have an isolation distance of r along the wind direction (Figure 5), PMGF frequency at distance x (x > r) from A to B is:
assuming . The average PMGF frequency from A to B is:
where c is the length of the recipient B plot along the wind direction (Figure 5). Suppose a worst case scenario, where the recipient B is an a × a m2 square plot surrounded by eight a × b m2 pollen source A plots, and wind can go from all directions from A to B during the flowering period, the maximum PMGF at distance x from A to B can be approximately estimated as:
where DA is the pollen density from one of the eight pollen source A plots. Given b = infinite (i.e. recipient B plot is surrounded by infinite pollen source A plots), then:
The average PMGF from A to B is:
We set ts = 1% and δ = 1, to simulate PMGF among cultivated rice, because all the field experiments demonstrated low gene flow frequencies in cultivated rice (usually <1%) (Lin et al., 2000; Messeguer et al., 2001, 2004; Bashir et al., 2004; Rong et al., 2004, 2005, 2007), and tr = 40% and δ = δsr, to simulate PMGF from cultivated rice to common wild rice. The given thresholds of PMGF were among cultivated rice fields (European Union labeling threshold for GM crops) and from cultivated rice to common wild rice. With β = βmax estimated in the rice pollen flow experiments, Eqn (16) was used to estimate the isolation distance (r) required among cultivation fields and from cultivated rice to common wild rice.
We are grateful to Drs F. Wang and J. Su of Fujian Provincial Key Laboratory of Genetic Engineering for Agriculture, Fujian Academy of Agricultural Sciences, Fuzhou, China, for their supports to our study and a lot of constructive discussions. We thank the reviewers and editors for their comments and suggestions in different versions of our manuscript, which were very helpful to our work. This research was supported by the National ‘973’ Basic Research and Development Programme of China (Grant nos. 2006CBI00205 and 2007CB109202), Natural Science Foundation of China (Grant no. 30730066 and 30871503) and Ministry of Agriculture 2008ZX08011-006.