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CROP ECOLOGY, MANAGEMENT & QUALITY

An Empirical Model for Pollen-Mediated Gene Flow in Wheat

^a Monsanto Company, 800 North Lindbergh Blvd., St. Louis, MO 63167
^b Monsanto Canada, Winnipeg, Manitoba
^c Dep. of Plant Sciences, Univ. of Saskatchewan, 51 Campus Dr., Saskatoon, SK S7N 5A8, Canada

^* Corresponding author (david.i.gustafson{at}monsanto.com)

	ABSTRACT

TOP ABSTRACT INTRODUCTION PMGF in Wheat Previous Modeling Efforts MATERIALS AND METHODS RESULTS AND DISCUSSION CONCLUSIONS REFERENCES

 
The extent of pollen-mediated gene flow (PMGF) in wheat (Triticum spp. L.) as a function of distance from a pollinator source has been measured in recent field studies. Wheat is primarily self-pollinated; however, some cross-pollination can occur depending on biological, agronomic, and environmental factors. The complexity of these interactions restricts attempts to develop a workable mechanistic model; therefore, we pursued an entirely empirical modeling approach. We fit a simple empirical regression model to all available observed data and then used it to make general predictions about the effects of field size, blending at harvest, and isolation distances on PMGF in wheat. The empirical model was derived by fitting a least squares regression line to the gene flow data when plotted as the logarithm of PMGF versus the square root distance from the edge of the source field. Linear behavior was observed when either the maximum or mean PMGF was plotted in this manner. A "General Wheat Model" (GWM) of this same mathematical form is given which provides a conservative ("high-end") prediction of PMGF in the general case: PMGF = 10^–, where PMGF is the percent gene flow at a particular point in the field (without blending), and x is the distance (m) from the edge of the source field. The GWM was used to show that the effect of source field size is minimal for sources of 10 ha or larger, where asymptotic levels of PMGF are obtained. The model was also applied to show that harvest-blending produces PMGF at the field level 10 to 50 times lower than the highest level observed at the edge of the receptor field. Significantly, isolation buffers of 0 to 10 m were predicted by the GWM to have only a minimal impact on harvest-blended PMGF, when the receptor field had an overall width of 100 m or greater. Without any isolation buffers, the harvest-blended PMGF between neighboring commercial-sized (>10 ha) fields was less than 0.1% (well below commercial thresholds for foreign material in wheat seed and grain). This is also well below any existing standards for labeling the presence of approved biotech traits in food or seed distributed or sold as conventional.

Abbreviations: , empirical factor relating percent gene flow to distance from source • GWM, General Wheat Model • Log10, logarithm base 10 • P_o, percent gene flow immediately adjacent to the source • PMGF, pollen-mediated gene flow

	INTRODUCTION

TOP ABSTRACT INTRODUCTION PMGF in Wheat Previous Modeling Efforts MATERIALS AND METHODS RESULTS AND DISCUSSION CONCLUSIONS REFERENCES

 
POLLEN-MEDIATED GENE FLOW is the transfer and incorporation of genetic information between distinct plant populations when cross-pollination occurs. PMGF is a natural biological process that occurs to some degree in all flowering plant species, including most major crops. The term "pollen-mediated gene flow" is often used synonymously with "outcrossing" or "cross-pollination." For this paper, however, we define gene flow to have taken place only when the pollination event results in the incorporation of transferred genetic information into the receptor population—that is, the production of viable seed. Gene flow can enhance the genetic diversity of plant populations and may therefore increase the population's ability to respond to changing stressors in the environment. In plants, pollen dispersal is the primary mode of gene flow among populations and occasionally between populations of different species (Levin and Kerster, 1974). Although PMGF is not unique to transgenic crops, the process has received renewed attention with their development and wide-scale introduction (Timmons et al., 1996; Klinger and Ellstrand, 1999). In this paper, we briefly discuss some general aspects of PMGF in cropping systems but confine our data and modeling analysis to the extent of PMGF in wheat (Triticum spp. L.).

The process of PMGF between two distinguishable plant populations begins when donor pollen with distinguishing genetic information from the source population, fertilizes an ovule on a maternal plant in the recipient population, resulting in the production of viable seed. The viability and/or fertility of the seed resulting from PMGF relative to the maternal parent will clearly influence the persistence of the delivered gene(s) within the recipient population. The percentage of the total seed on a plant produced by pollen from a genetically distinct population may be designated the percentage of PMGF that has occurred between the two populations. PMGF can occur either between subpopulations of a single species (intraspecific gene flow) or between different species (interspecific gene flow).

There are several factors that determine the likelihood and extent of PMGF among plant populations. These include (i) reproductive biology of a species or cultivar within a species (Suneson and Cox, 1964; Hamrick et al., 1979; Govindaraju 1988a, 1988b; Poehlman, 1987, p. 290–342). The flower structure must allow for external pollen entry and fertilization. The degree to which the species is selfing or obligate outcrossing will affect rates. Additionally, the source and receptor populations must be sexually compatible; (ii) Environmental or climatic conditions at specific vegetative and reproductive stages of plant development (Levin and Kerster 1974, Khan et al., 1973). Temperature and humidity are known to affect pollen viability and longevity of pollen and distance of pollen movement; (iii) Spatial and temporal relationship of pollen donor and recipient plants (Manasse, 1992). Plants must be within proximity such that pollen can move from plant to plant. Furthermore, plants must have synchronous flowering (Hucl and Matus-Cadiz, 2001); (iv) pollen load, which increases with source population size (Farris and Mitton, 1984).

The eventual fate and persistence of the gene(s) delivered to the recipient crop populations as a result of PMGF are variable, depending partly on what is done with the harvested grain and partly on physiological and ecological factors. In most crop production fields, the grain is harvested and removed from the field and subsequently devitalized during processing for food or feed uses. Thus in this case, although the first step in gene flow occurred, the gene was not maintained in the receptor population. A key physiological factor is whether or not seed viability is affected in the cross. The key ecological factor is whether a fitness advantage is conferred to the recipient population (Arnold and Hodges, 1995; Arriola and Ellstrand, 1997). In certain cases, particularly during interspecific PMGF, the produced seed may range from completely nonviable (does not sprout) or completely infertile (sprouts a plant that produces no seed) to partially or fully fertile.

In this paper, we define PMGF to include all such seed regardless of viability and fertility because it could produce detectable genetic material in the seed of the recipient population. However, such seed would obviously not result in the sustained presence of the gene(s) in subsequent generations if it is consumed as grain rather than planted or left in the ground as seed. Therefore, the PMGF values presented in this work should generally be treated as upper-bound estimates for use in subsequent forms of population modeling requiring PMGF as an input parameter (Hails et al., 1997; Lutman, 1993; Pekrun et al., 1997; Squire et al., 1997; Squire, 1999).

	PMGF in Wheat

TOP ABSTRACT INTRODUCTION PMGF in Wheat Previous Modeling Efforts MATERIALS AND METHODS RESULTS AND DISCUSSION CONCLUSIONS REFERENCES

 
Several studies have been conducted to measure PMGF in commercially available spring and winter wheat cultivars (Table 1). Studies involving male-sterile wheat lines are excluded from this summary, because the male sterile system is not representative of normal agronomic conditions and is therefore not relevant to the general case we are attempting to describe.

Summarizing the net impact of environmental factors, maximum levels of PMGF in wheat probably occur when a hot, dry period is followed by a period of moderate temperatures with high humidity and wind. This allows for maximum pollen viability, flower opening, and stigma receptivity as well as pollen dispersal.

	Previous Modeling Efforts

TOP ABSTRACT INTRODUCTION PMGF in Wheat Previous Modeling Efforts MATERIALS AND METHODS RESULTS AND DISCUSSION CONCLUSIONS REFERENCES

 
Clearly, the amount of PMGF in wheat or any other crop is the net result of a complex interaction among multiple factors, significantly inhibiting the development of a mechanistic model. Such a mechanistic model would, by necessity, be just as comprehensive and complex to successfully mimic all possible field situations. Nevertheless, various efforts to model PMGF have been undertaken (Di-Giovanni et al., 1989; Di-Giovanni and Beckett, 1990; Di-Giovanni and Kevan, 1991; Crawford et al., 1999; Colbach et al., 2000; Giddings, 2000; Richter et al., 2002). The historical motivations for such work have been varied, ranging from the investigation of biological evolutionary processes (Denmead and Bradley, 1985) to more practical studies involving the preservation of seed quality (Raynor et al., 1972; Ingram, 2000). In recent years, however, a primary focus of such modeling has been to quantify gene movement of transgenic crop varieties to neighboring fields, related species, and the implications for segregated grain (Timmons et al., 1996; Lavinge et al., 1998; Champolivier et al., 1999; Thompson et al., 1999; Squire et al., 2000; Rieger et al., 2002).

Most of the previous work on modeling PMGF in crops has focused on mechanistic approaches. In general, this has involved the modification of air pollution models based on the Gaussian plume equation, to simulate pollen transport from source to receptor fields. Theoretical attempts to directly model the complex fluid mechanics of air flow across, between, and within plant canopies may be broadly categorized as either Eulerian or Lagrangian (Di-Giovanni et al., 1989). The former class of models uses a fixed set of points in space as the control volume, whereas the latter considers a control volume of fluid as it moves through space. Advantages for the Lagrangian system in the case of pollen flow have been claimed (Rodean, 1996), but both theoretical systems have significant challenges in addressing the varied but specific crop reproductive biology characteristics and the topographic variations of the agricultural landscape. A further challenge to the mechanistic approach is that PMGF involves several additional steps beyond predicting how far the pollen moves and in what relative concentrations (Raynor et al., 1972; Legg and Powell, 1979; LeClerc et al., 1988; Aylor and Ferrandino, 1989). In order for successful gene flow to occur, the pollen must land on the stigma of the receptor plant, stick to the surface, germinate, and fertilize the ovule. In addition, it must compete with other native and foreign pollen that may land on the stigmatic surface. Validated mechanistic models of these processes are currently not available and may be difficult to develop without considerable empiricism.

	MATERIALS AND METHODS

TOP ABSTRACT INTRODUCTION PMGF in Wheat Previous Modeling Efforts MATERIALS AND METHODS RESULTS AND DISCUSSION CONCLUSIONS REFERENCES

 
Overview
Because of the difficulties in developing a mechanistic model, we adopted an empirical approach. We gathered available PMGF data from the literature and plotted percent gene flow as a function of distance. Transformations were simultaneously applied to both the dependent (gene flow) and independent (distance) scales until linear behavior was obtained. A line was fit to the data by minimizing the least square error on a transformed scale where the variance is relatively homogeneous. The resultant empirical model was then used to investigate a series of questions of practical importance in the management of PMGF.

1. What is the effect of the size of the source field on PMGF?
   
2. What is the effect of blending all harvested grain on average PMGF in the receptor field?
   
3. What impact would buffers have on PMGF?
   

Input Datasets
We present two data sets in which gene flow was measured as a function of distance from the source (Hucl and Matus-Cadiz, 2001; Matus-Cadiz et al., 2004). Both had 2 yr of field data each and all 4 yr of field data results were used in developing the empirical model. A third dataset from the Czech Republic provided consistent results but is not included because of its publication status (Ovesna, personal communication). Each of the field studies was conducted in a manner to produce high amounts of PMGF, relative to the size of the pollen source studied. Thus, a properly scale-adjusted empirical model based on these data is expected to be "conservative" in that it will overestimate levels of PMGF compared with that which would typically be encountered in commercial wheat production situations.

The first data set was that described by Hucl and Matus-Cadiz (2001). Four spring wheat cultivars with differing maternal receptivity to outcrossing—Katepwa (Campbell and Czarnecki, 1987a), Roblin (Campbell and Czarnecki, 1987b), Biggar (de Pauw et al., 1991), Oslo (Graf et al., 1990)—were planted in 1995 and 1996 at Saskatoon, SK. Four recipient target rows of each cultivar were planted perpendicular to the sides of a 5- x 5-m blue-grained pollinator (source) in each cardinal direction. Recipient target rows were 35 m in length (250 seeds m^–2) and spaced 30 cm apart. The four recipient cultivars were randomized within four blocks in each direction. The pollinator block was planted at a low density (60 seeds m^–2) to promote tillering and thus extend the period of pollen shed. At maturity, within each recipient row, 10-cm lengths of row were harvested at distances ranging from 0 to 33 m from the pollen source in each cardinal direction. Cross-pollination events were determined by expression of light-blue pigment in the aleurone layer of F₁ seed. Putative light blue seeds were grown out in the field for confirmation.

The second data set was that described by Matus-Cadiz et al. (2004). In 2001 and 2002, a 50- x 50-m blue-grained pollinator block, Purendo-38 (Matus-Cadiz et al., 2004), was planted and surrounded by a recipient hard red spring wheat, CDC Teal (Hughes and Hucl, 1993), to a minimum distance of 175 m in all directions, at Saskatoon, SK. A reduced seeding rate (100 seeds m^–2) and two seeding dates of the pollinator block were used to promote synchronization of flowering. CDC Teal was sown at a rate of 250 seeds m^–2 on ground cropped to pulse research plots the previous year. At maturity, 0.5- x 4-m strips of CDC Teal were harvested at eight specified distances between 0.2 and 160 m along eight transects radiating out along eight directions (N, S, E, W, NE, SE, SW, NW) from the blue-grained pollinator block. Additionally, random sampling was conducted in 2000 and 2001 in surrounding commercial wheat fields to estimate gene flow rates over distances of 180 to 2760 m.

The second data set also contained data from an amber durum (T. durum Desf.) variety, AC Navigator (Clarke et al., 2000), as the pollen recipient to measure interspecific gene flow (wheat to durum). AC Navigator was planted at a rate of 250 seeds m^–2 on ground cropped to spring cereal and flax (Linum usitatissimum L.) research plots the previous year. At maturity, 0.5- x 4-m strips of AC Navigator were harvested at eight specified distances between 0.2 and 260 m along eight transects radiating out along directions (N, S, E, W, NE, SE, SW, NW) from the blue-grained pollinator block. Cross-pollination events from Purendo-38 to recipient plants were identified by expression of light-blue pigment in the aleurone layer of F₁ seed. Putative light blue seeds were grown out in the greenhouse for confirmation.

	RESULTS AND DISCUSSION

TOP ABSTRACT INTRODUCTION PMGF in Wheat Previous Modeling Efforts MATERIALS AND METHODS RESULTS AND DISCUSSION CONCLUSIONS REFERENCES

 
Empirical Model Fit
A simple empirical model was fit to the gene flow data. After trying various transformations for the two coordinate axes, consistently linear behavior was observed when the logarithm of either the observed maximum or average PMGF was plotted as a function of the square root of the distance from the edge of the source field. The square-root dependence is consistent with the theoretical predictions of boundary-layer penetration models in mass transfer processes (Bird et al., 1960), but the approach is entirely empirical as developed here. The data from Hucl (2001) followed this pattern (not shown), as do the data from Matus-Cadiz et al. (2004) (Fig. 1 and 2). During both study years, the observed maximum and average percent gene flow data for AC Navigator and CDC Teal appear to be linear when plotted in this fashion.

View larger version (16K): [in this window] [in a new window]   Fig. 1. Average (across eight directions) and maximum intra-specific PMGF between two spring bread wheat varieties (from a blue aleurone source to CDC Teal as the receptor) measured over two years at Saskatoon, SK (Canada).

View larger version (15K): [in this window] [in a new window]   Fig. 2. Average (across eight directions) and maximum inter-specific PMGF from a blue aleurone spring bread wheat source to a spring durum wheat (AC Navigator) as the receptor, measured over two years at Saskatoon, SK (Canada).

[1]

where PMGF is the percent gene flow at a particular point in the receptor field, P_o is the percent gene flow immediately adjacent to the source, x is the distance from the edge of the source (in meters), and is an empirical factor, possibly related to a number of physical and biological factors such as wind speed, pollen size, biological compatibility, etc. However, the functional dependence of on such parameters is beyond the scope of the present study.

Best-fit parameters of Eq. [1] to the three sets of data from Fig. 1 and 2 and the other Hucl and Matus-Cadiz dataset (2001) were obtained by the standard least squares regression method and are summarized in Table 2. Also listed at the bottom of Table 2 is a "General Wheat Model" (GWM) of this same mathematical form that was derived by graphing all of the available PMGF data (Griffin, 1987; Hucl, 1996; Hucl and Matus-Cadiz, 2001; Matus-Cadiz et al., 2004; Martin, 1990) on a single plot (Fig. 3) and adjusting the two model parameters (P_o and ) until it was judged that the model was giving appropriately conservative predictions of PMGF at all distances. This is a necessarily subjective process, but the data graphed in Fig. 3 show that only a small fraction (<5%) of the observed gene flow data points at distances of more than 1 m from the source field exceed the model prediction. The GWM is simply:

[2]

View this table: [in this window] [in a new window]   Table 2. Summary of best-fit parameters for the empirical pollen-mediated gene flow (PMGF) model for maximum gene flow as a function of distance, x (m), from the edge of the source at each field site: PMGF = Po 10–

View larger version (23K): [in this window] [in a new window]   Fig. 3. Comparison of the General Wheat Model to all available individual PMGF observations in the referenced field studies, showing its conservative ("high-end") nature. Jittering (see text) around the PMGF detection limit of each study has been used to display all individual sample points on the plot. The model appears as a curve due to the use of a logarithmic scale for the x axis.

Applications of the Empirical Model
Scale Effect
The empirical model was used to simulate the effect of source size on PMGF. Two key assumptions are made in carrying out such calculations.

1. The model (which was fit to data for a 50-m source, with non-zero observations out to only 100 m) continues to remain valid for longer distances.
   
2. The PMGF produced by adjacent sources can simply be added together in a linear fashion to predict the effect of increasing source size and therefore increased pollen load. This assumption is likely valid for the rather low PMGF observed in wheat, but would obviously break down for higher gene flow percentages.
   

With these two assumptions, it is possible to investigate the predicted effect of source size by simply adding together the predicted gene flow from multiple adjacent sources. An example of this is shown in Fig. 4 for the GWM. The model appears as a concave-upward curve due to the use of the linear scale for the x axis. As the width of the source increases from 50 to 800 m (corresponding to square field sizes of 0.25 to 64 ha), only a minimal effect on PMGF is predicted. The 400 m (16 ha) and 800 m (64 ha) curves are practically indistinguishable, suggesting that asymptotic PMGF is attained for sources greater than about 10 ha. The fact that scaling effects are predicted to be so small is logically consistent with the empirical field observation that PMGF produced at a distance equal to the width of the pollinator source is near zero. Thus, the incremental PMGF arising from increasing the source width is negligible.

View larger version (12K): [in this window] [in a new window]   Fig. 4. Use of the General Wheat Model to study the effect of the size of the pollinator source. The model appears as a curve due to the use of the linear scale for the x axis.

View larger version (29K): [in this window] [in a new window]   Fig. 5. Use of the General Wheat Model to demonstrate the impact of harvest-blending on PMGF.

View larger version (20K): [in this window] [in a new window]   Fig. 6. Use of the General Wheat Model to study the influence of buffer distance on PMGF.

View larger version (34K): [in this window] [in a new window]   Fig. 7. Use of the General Wheat Model to study the influence of receptor field width for a variety of buffer distances.

	CONCLUSIONS

TOP ABSTRACT INTRODUCTION PMGF in Wheat Previous Modeling Efforts MATERIALS AND METHODS RESULTS AND DISCUSSION CONCLUSIONS REFERENCES

Empirical regression models of this form give excellent fits to the observed data for either the maximum or average (across all directions) PMGF. This same conclusion was reached for all of the datasets we were able to obtain from literature studies and by contact with researchers active in this area. We presume that the same empirical model might work well in other flowering crops, and recommend further work in this area.

In this paper, we have presented a General Wheat Model (GWM) that provides a conservative ("high-end") prediction of PMGF in the general case for wheat. The GWM is used to show that the effect of source-pollinator field size is minimal for sources of 10 ha or larger, where asymptotic levels of PMGF are obtained. The model is also applied to show that harvest-blending produces PMGF at the field level that is 10 to 50 times lower than the highest level observed at the edge of the receptor field. Significantly, isolation buffers of 0 to 10 m are predicted to have only a minimal impact on harvest-blended PMGF, when the receptor field has an overall width of 100 m or greater. Even without any isolation buffer, the harvest-blended PMGF between neighboring commercial-sized (>10 ha) fields is predicted to be less than 0.1% (well below current thresholds for foreign material in seed and grain). This is also well below any existing standards for labeling the presence of approved biotech traits in food or seed distributed or sold as conventional (Official Journal of the European Union, 2003).

	ACKNOWLEDGMENTS

 
The authors wish to acknowledge the useful comments of the reviewers and the potential contributions of two researchers in the Czech Republic, L. Kucera and J. Ovesna, whose contributions we were unfortunately obliged to remove in response to the manuscript review process.

Received for publication February 26, 2004.

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TOP ABSTRACT INTRODUCTION PMGF in Wheat Previous Modeling Efforts MATERIALS AND METHODS RESULTS AND DISCUSSION CONCLUSIONS REFERENCES

 

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