Pollen-mediated gene flow from glyphosate-resistant common waterhemp (Amaranthus rudis Sauer): consequences for the dispersal of resistance genes

Gene flow is an important component in evolutionary biology; however, the role of gene flow in dispersal of herbicide-resistant alleles among weed populations is poorly understood. Field experiments were conducted at the University of Nebraska-Lincoln to quantify pollen-mediated gene flow (PMGF) from glyphosate-resistant (GR) to -susceptible (GS) common waterhemp using a concentric donor-receptor design. More than 130,000 common waterhemp plants were screened and 26,199 plants were confirmed resistant to glyphosate. Frequency of gene flow from all distances, directions, and years was estimated with a double exponential decay model using Generalized Nonlinear Model (package gnm) in R. PMGF declined by 50% at <3 m distance from the pollen source, whereas 90% reduction was found at 88 m (maximum) depending on the direction of the pollen-receptor blocks. Amplification of the target site gene, 5-enolpyruvylshikimate-3-phosphate synthase (EPSPS), was identified as the mechanism of glyphosate resistance in parent biotype. The EPSPS gene amplification was heritable in common waterhemp and can be transferred via PMGF, and also correlated with glyphosate resistance in pseudo-F2 progeny. This is the first report of PMGF in GR common waterhemp and the results are critical in explaining the rapid dispersal of GR common waterhemp in Midwestern United States.


Results
Flowering Synchrony. Flowering was initiated on July 1, 2013 and July 12, 2014, with maximum flowering occurred 2 weeks after flower initiation (Table S1). The common waterhemp plants beyond 5 m distance from the pollen-donor block began flowering a few days later than those in the pollen-donor block or in the proximity of the pollen source. It was believed that the common waterhemp plants in both the pollen-donor block and the closer distances were growing in a higher density compared to the plants at the farthest distances, thus causing a brief gap (< 5 days) in the initiation of flowering. The total flowering period lasted about 5 and 4 weeks in 2013 and 2014, respectively. Therefore, a season-flowering synchrony of > 85% was ensured (Table S2).
Meteorological Data. Early and late-season temperature was slightly lower than the temperature during flowering period and mean daily temperature ranged from 17.0 to 30.5 °C in July and early-Aug in 2013 and 2014 (Fig. S1). Pearson correlation coefficients (r) showed a significant correlation between frequency of gene flow and wind parameters [wind speed, wind frequency (frequency of time/hours during which the wind blows toward a certain direction), and wind run (calculated by multiplying the average wind speed by the wind frequency for a certain direction 42 )]; however, the correlation (r ≥ 0.29) was significant up to 15 m (from the pollen source) for wind speed and 25 m for wind run (Table 1). Correlation between wind parameters and frequency of gene flow at the closer distances (within 5 m) was higher (≥ 0.48) than at the farthest distances. No negative correlation was observed, suggesting that the wind had a great influence on PMGF in common waterhemp.
Wind flow patterns were similar in 2013 and 2014, though the wind speed and wind frequency differed. Wind during both years blew mostly from the S and SE directions (Fig. 1). The average wind speed during the flowering period in 2014 was lower (1.4 m s −1 ) than the average wind speed in 2013 (2.1 m s −1 ) (Fig. S2).

Modeling PMGF and Prediction of Distances.
Determining the sample size a priori allows a researcher to reduce the sampling cost and time without losing statistical precision to quantify gene flow 43 . In 2013 and 2014, more than 130,000 common waterhemp seedlings were screened in the greenhouse to detect PMGF and a minimum power of 0.95 (α = 0.05) was ensured (Tables 2 and 3 (Tables 2 and 3). Mean PMGF frequency was recorded ≤ 0.10 at a distance ≥ 35 m. PMGF was not similar in different directional blocks of pollen-receptors or between years. The Akaike's Information Criterion (AIC)-based model selection procedure [equation (5)] revealed that the inclusion of directions in the final model provided a better estimation for gene flow than the hourly measurements of wind parameters. The Δ AIC (difference in AICs) values between the top model and rest of the models were high (≥ 398.0), showing the efficacy of the top model for predicting PMGF in common waterhemp (Table S3). Gene flow in common waterhemp declined sharply with increasing distances from the pollen source (Figs 2 and 3), following a double exponential decay model [equation (6)] where the intercepts (β 2 ) and decay rates (γ 2 ) for the second instance varied with different directions and years (see coefficient estimations in Table 4). Pearson's chi-square test showed a good fit of the model for all directions and years, where the null hypothesis (H 0 , the observed and predicted frequency of gene flow are the same) cannot be rejected due to a P-value ≥ 0.05.
The gene flow frequencies at 0 m distance were 0.77 and 0.69 in 2013 and 2014, respectively. Gene flow data from 0 m (GS plants planted inside the pollen-donor block) did not include any directions; therefore, could not be included in modeling. However, the final model [equation (6)] has predicted the PMGF frequency at 0 m for each direction and year, which was plotted later along with the original (observed) gene flow frequencies (Fig. 4).
In 2013, the model-predicted frequencies (at 0 m) in the N and NW directions were similar to the observed frequency, and in 2014, the gene flow frequency in N direction corresponded with the observed frequency at 0 m.
The predicted distances where gene flow declined by 50% (O 50 ) ranged from 0.6 to 2.4 m in 2013 and from 0.8 to 1.6 m in 2014 (Table 5) depending on the direction being investigated. The maximum distance at which 90% reduction (O 90 ) in the frequency of gene flow was predicted, was 58.3 m in the S direction in 2013 and 87.6 m in the NW direction in 2014. The variability in gene flow increased with increasing distances from the pollen source;

Wind parameters
Overall gene flow Distance from the pollen source ‡  Table 1. Pearson correlation coefficients # (r) between wind parameters (wind speed, wind frequency, and wind run) and frequency of gene flow at different distances † . # Pearson correlation coefficients were tested at two significance levels, P < 0.05 (*), and P < 0.01 (**). † Abbreviations: df, degrees of freedom. ‡ Gene flow data at 50 m was only from the four ordinal directions (NE, NW, SE, SW).  Mechanism and Inheritance of Glyphosate Resistance. To determine the mechanism and inheritance of glyphosate resistance, genomic DNA was extracted from young leaf tissues collected from GR and GS parents, F 1 , and an open-pollinated pseudo-F 2 population. EPSPS gene copy number analysis revealed that gene amplification (and the assumed overproduction of EPSPS protein 39 ) was the mechanism of glyphosate resistance in the GR common waterhemp parent used in the PMGF study. The mean relative copy number in the GR biotype was 5.3 (± 2.2, standard deviation) (Fig. 5). As expected, the GS parent biotype had, on average, one EPSPS gene copy (mean = 1.0 ± 0.2). Plants with relative EPSPS gene copy number of > 1.4 (the threshold copy number) were considered to be GR individuals 44 . Seeds of F 1 progeny (GS × GR) were directly taken from the field study (gene flow) and individuals surviving glyphosate application were selected for genomic DNA analysis. Similar to the mechanism of glyphosate resistance in the GR parent, EPSPS gene amplification was observed in 92% of the surviving individuals in the F 1 progeny. For the GR parent, the maximum number of individuals was observed near the median value (5.1) of the relative EPSPS copy number, whereas the outcrossing between GS and GR parents resulted in a greater number of plants in F 1 with a 2.0 to 4.0 EPSPS copy number (Fig. 5). EPSPS gene amplification was also observed in the pseudo-F 2 population of common waterhemp with a mean relative EPSPS gene copy number of 6.6 ± 2.6 ( Fig. 5). It is concluded that the EPSPS gene amplification is heritable in common waterhemp and can be transferred via pollen movement under field conditions. The pseudo-F 2 population of common waterhemp has segregated for both relative EPSPS gene copy number and glyphosate resistance; however, the Chi-square test showed that the segregation did not agree with the null hypothesis (Mendelian pattern of segregation for a single gene or locus), which means that F 2 individuals did not segregate in the 3GR:1GS pattern (Table 6).     Combining EPSPS Gene Amplification with the PMGF from Phenotypic Assessment. Mean relative EPSPS copy numbers (4.9 ± 2.2) from F 1 progeny were combined with the gene flow frequency (Tables 2 and 3) to predict an average EPSPS gene copy number at any given distance from the pollen source. It was assumed that all GS individuals had a similar EPSPS copy number (1.0 ± 0.2). A double exponential decay model was fit to the average copy number data at different distances from the pollen source. Average relative EPSPS gene copy number was predicted as 3.9 and 1.9 at the 0 and 10 m distances, respectively, using the equation: x x gene copy number 1 29 exp( 0 02 182 0 ) exp(0 5 0 1 ) (1) where x is the distance from the pollen source. The prediction plot ( Fig. 6) for the relative EPSPS gene copy number shows the mean relative copy number in the individuals (assumed to be the F 1 progeny) sampled randomly at a given distance from the pollen source.  Table 4. Estimation of coefficients, standard error, and test of significance for the double-exponential decay model * for prediction of pollen-mediated gene flow from glyphosate-resistant common waterhemp under field conditions.
, where p i is frequency of gene flow of the i th observation; β 0 is the overall intercept; β 1 and β 2 are the intercepts for the first and second instances, respectively; and γ 1 , and γ 2 are the decay rates. † β 2 and γ 2 vary with the direction and the year. In this table, β 2 and γ 2 show the intercept and decay rate, respectively, for one direction (East) in year 1 (2013). However, "β 2 :Direction", or "β 2 :Year 2" denote the change (from East direction and year 1) in β 2 for other directions and year 2 (2014), respectively. The same is true for γ 2 . ‡ P-values show the test of significance at P < 0.05 (*) and P < 0.01 (**).

Discussion
The PMGF estimated in this study represents hybridization (or, gene flow frequency) as a function of distance from the pollen source (i.e., actual gene flow), rather than measuring the deposition of pollen from the source to a particular distance (i.e., potential gene flow). Beckie and Hall 45 noted that it is more relevant to construct a model that predicts the actual gene flow rather than the potential gene flow, especially to understand the transfer of herbicide-resistant traits via pollen movement. PMGF depends on the mating system and reproductive biology of the plant species: for example, in highly outcrossing species such as rigid ryegrass, long-distance (up to 3 km) PMGF has been reported 19 , whereas in self-pollinating species such as barnyardgrass and common lambsquarters, the PMGF was very low (< 10%), even at closer distances from the pollen source 15,16 . In this study PMGF   has been estimated in ideal conditions with no physical or geographic barriers, other vegetation, and no GS male plants in the pollen-receptor blocks, which may have provided more opportunities for gene flow to occur. The indeterminate growth habit and pulsed flowering pattern of common waterhemp aided in a prolonged flowering period, which ensured a complete flowering synchrony in this study. Wu and Owen 46 explained that the extended flowering period of common waterhemp is an ecological adaptation to avoid harsh weather conditions and increase the chances of reproductive success. Moreover, long-distance pollen dispersal requires longer pollen  Table 6. Chi-square * analysis for the segregation in pseudo-F 2 progeny of common waterhemp based on the relative EPSPS gene copy number and phenotypic data. * The Chi-square goodness of fit test (df = 1, α = 0.05) is used to compare the observed segregation in F 2 progeny with the expected Mendelian segregation for a single gene (3GR:1GS). The calculated χ 2 > 3.84 indicates that the observed segregation does not agree with the expected segregation. † Glyphosate was applied at 1,575 g ae ha −1 and the plant survival data were recorded. viability 47 and it has been reported that the viability of common waterhemp pollen is about 120 h 32 with possibility of pollen shed throughout the day 48,49 . Gene flow declined exponentially with distance, which was due to the weaker wind near the leeward edge of the donor block, resulting maximum pollen deposition near the edge of the pollen-donor block. Du et al. 50 suggested that the wind direction near the leeward edge could also be the reverse in some cases. Results of this study also indicated that the average gene flow frequency at 50 m (the farthest distance tested in this study) was ≥ 0.05 (or ≥ 5% outcrossing) and the exponential decay model predicted that 90% reduction in gene flow occurred between 10.0 m to 87.6 m from the pollen source, depending on the direction of the pollen-receptor block. Bagavathiannan and Norsworthy 15 also reported that the average gene flow in barnyardgrass was highly variable among directions and years; therefore, it was important to develop a statistical model that incorporates the effects of direction and year in a single model. A novel statistical approach adopted in this study fulfilled our goal for modeling the PMGF in common waterhemp and can be adopted in future studies to detect PMGF from crops and herbicide-resistant weeds.
The frequency of gene flow never reached 1.00 (i.e., 100% outcrossing) in this study, though the localized GS pollen sources were removed. The presence of GS-F 1 progeny collected from the pollen-receptor blocks might have occurred for several reasons. Apomictic seed production and the presence of partially monoecious plants have been reported in common waterhemp 51 , and we have observed apomictic seed production in female GS plants grown in the greenhouse, where a few plants produced a small number of seeds without any pollen source and a partially monoecious GS plant was detected during flowering. The GR common waterhemp parent used in this study were derived from a field-collected segregating population and < 5% GS male plants were observed in this population; these plants may have contributed pollen to this study, explaining the presence of GS-F 1 progeny collected from pollen-receptor blocks. Glyphosate resistance by enhanced EPSPS copy number seems to be a dominant trait, and therefore susceptible alleles persist in phenotypically resistant plants, which would also result in GS plants in F 1 progeny. Finally, GS Amaranthus species including common waterhemp were present at a distant location from the experimental site, which could have transferred some pollen to the pollen-receptor blocks.
Mallory-Smith et al. 52 outlined the step-by-step approach for conducting a PMGF study under field conditions, and noted that the phenotypic data of herbicide resistance can be considered as an excellent marker, though it must be supplemented with molecular or morphological markers to confirm gene flow. Relative copy number analysis showed that the most GR-F 1 individuals had increased EPSPS gene copy number; however, 4 out of 48 F 1 individuals surviving glyphosate application possessed a relative EPSPS gene copy number of < 1.4, which suggested that an additional mechanism could contribute to glyphosate resistance in this biotype. In a common waterhemp biotype collected from Mississippi, Nandula et al. 53 reported both reduced glyphosate translocation and Pro106Ser point mutation in the EPSPS gene as potential glyphosate resistance mechanisms. It is possible that the parent GR population used in this study included a small proportion of individuals carrying additional, unknown mechanism(s) of resistance that might have been inherited in the F 1 progeny, though all the GR individuals selected randomly for genomic DNA analysis showed an increase (> 2.0) in EPSPS gene copy number. As reported in Palmer amaranth 41 , the results from this study suggested that EPSPS gene amplification is also heritable in common waterhemp, though inheritance of EPSPS gene amplification did not follow the 3:1 segregation ratio in pseudo-F 2 progeny. This can be explained by detecting the location of resistant allele(s) on the genome, which was not performed in this study. Recombination within the block of tandem duplication may cause GS individuals to become less frequent than expected, as a large number of individuals would inherit extra gene copies and therefore be GR. If the extra gene copies are at different locations around the genome, the probability of an F 2 individual inheriting the susceptible genotype (only 1 copy) is less than 25%, which would result in fewer GS individuals than expected.
Estimation of EPSPS gene amplification along with the prediction of gene flow provided strong evidence for the pollen-mediated transfer of the glyphosate resistant trait in common waterhemp. Here, the assessment of elevated EPSPS copy number was used not only to determine the mechanism of glyphosate resistance but also to confirm inheritance in subsequent progenies. However, EPSPS gene amplification could also be used as a molecular marker (instead of growing plants and applying herbicides for screening herbicide resistance) to detect gene flow in other important weed species (such as Italian ryegrass [Lolium multiflorum Lam.], kochia Palmer amaranth, ripgut brome [Bromus diandrus Roth.], etc.) where increased EPSPS copy number has been reported to confer glyphosate resistance 54 .
Results of this study indicated that the glyphosate-resistant trait in common waterhemp is highly mobile and its dispersal is possible via pollen movement depending on the distance from the resistant plants, the wind speed, and the wind direction. Therefore, the mobility of resistant alleles across farm enterprises should be addressed for effective management of this problem weed. Management strategies widely adapted by growers are mostly focused on preventing or delaying resistance evolution over a small area rather than preventing the large-scale movement of herbicide-resistance traits 55 . Field scouting in summer is essential for identifying patches of escaped common waterhemp plants and their management is necessary to prevent PMGF and the spread of resistant alleles. Before pollination, it is essential to identify the male and female common waterhemp plants, so that the removal of female common waterhemp plants, whether mechanically or physically, will reduce the chances of both PMGF and the spreading of herbicide resistance via seed dispersal. This is the first report describing PMGF from glyphosate-resistant to -susceptible common waterhemp under field conditions. The results of this study addressed the rapid spread of GR common waterhemp in the Midwestern United States and encourage the re-evaluation of management strategies for this troublesome weed species. Being a small-seeded broadleaf weed species, seed-mediated gene flow could play an important role in the dispersal of herbicide-resistant alleles in common waterhemp, as its seeds can also be dispersed by wind, water streams, or by the movement of tillage or harvesting implements. Contaminated crop seeds and manure can also play an important role in seed dispersal. Thus, future research should evaluate the potential for seed-mediated gene flow in common waterhemp. Modeling approach considered in this study to predict the PMGF can also be used for the risk assessment of various transgenic traits in different commercial crops.

Methods
Plant Materials. The known GR and GS common waterhemp biotypes were collected from two eastern Nebraska counties (Lancaster and Clay County, respectively); and their sensitivity to glyphosate has been evaluated. The level of glyphosate resistance was estimated 32-fold in the GR common waterhemp biotype compared to the GS biotype 31 .
Seeds from GR and GS biotypes were germinated in the greenhouse using the procedure described by Sarangi et al. 31 . The seedlings were transplanted at the cotyledon stage into 72-celled plastic germination trays containing potting mix (Berger BM1 All-Purpose Mix, Berger Peat Moss Ltd., Saint-Modeste, Quebec, Canada) and one seedling per cell was maintained. Plants were kept in the greenhouse and maintained at a constant 28/24 °C day/ night temperature, and supplemental light was provided by metal halide lamps at an intensity of 600 μ mol photon m −2 s −1 to maintain a 16 hour photoperiod. Plants were supplied with adequate water and nutrients (Miracle-Gro Water Soluble All Purpose Plant Food, Scotts Miracle-Gro Products Inc., 14111 Scottslawn Road, Marysville, OH 43041). Common waterhemp plants were then transplanted into the field at 8 to 10 cm height.

Field Experiments. Field experiments were conducted in 2013 and 2014 at South Central Agricultural
Laboratory (40.58°N, 98.14°W) at the University of Nebraska-Lincoln. The soil texture at the experimental site was Crete silt loam (montmorillonitic, mesic, Pachic Argiustolls) consisting of 17% sand, 58% silt, 25% clay, 3% organic matter, and a pH of 6.5. The experimental field was under a center-pivot irrigation system and was irrigated when needed. Based on the soil test report, starter fertilizers were applied following the University of Nebraska-Lincoln's recommendations for soybean 56  Field experiments were conducted using a concentric donor-receptor design (i.e., a Nelder wheel) where the pollen-donors were surrounded by the pollen-receptors [as described by Jhala et al. 43 ]. The common waterhemp biotype resistant to glyphosate served as the pollen-donor in this study and the GS plants served as the pollen-receptors. The experimental area was 80 m × 80 m, which also comprised a center circle (80 square m; 10 m diameter) for the pollen-donor block (Fig. 7). Approximately 550 GR common waterhemp plants were transplanted to the pollen-donor block in East-West and North-South directions in a crisscross pattern with a 0.3 m plant-to-plant distance. The transplanting was performed on the first week of June to simulate the typical growing period of common waterhemp in the Midwest for maximum growth and seed production under field conditions 46 .
The receptor area was divided into eight directional blocks (cardinal: N, S, E, and W; ordinal: NE, NW, SE, and SW) and twelve GS common waterhemp plants were transplanted at each of the thirteen specific distances (0.1, 0.5, 1, 3, 4, 5, 10, 15, 20, 25, 35 m for all cardinal and ordinal directions; and additional 45, 50 m only for the ordinal directions) from the pollen-donor block (Fig. 7). Twenty GS plants were also transplanted inside the pollen-donor area (considered as 0 m from the source) to simulate the worst-case scenario of GS plants surrounded by a dense population of GR common waterhemp. GS plants inside the pollen-donor area were marked carefully with flags and plastic tags for easy identification.
Flowering Period and Seed Harvesting. Male GS common waterhemp plants were visually detected prior to pollen shedding and removed from the pollen-receptor blocks to reduce pollen competition within the receptor blocks. Liu et al. 32 reported that common waterhemp plants can frequently be pollinated by the localized pollen source, which may reduce the chances for long-distance pollen movement. The number of flowering plants (male plants from the pollen-donor and females from the pollen-receptor blocks) was recorded at 5 d intervals and the flowering synchrony was assessed for each direction using the equation: where n is the total number of distances in direction i (i = N, S, E, W, NE, NW, SE, or SW), A% is the percentage of plants shedding pollen in the pollen-donor area, and B j % is the percentage of female flowering plants at the j th observation (distance) in the pollen-receptor blocks at that specific time. When X = 1.0, that means perfect synchrony occurs between pollen-donor and -receptor. X > 1.0 shows that sufficient pollen from GR male plants was present to pollinate GS females, but X values as low as 0.5 were not considered a good synchrony. Season-flowering synchrony (%) was assessed as the number of days pollen-donor and -receptor flowered together (X > 0.8) divided by the total number of flowering days by pollen-receptor female plants, multiplied by 100. Any GS female plants that were late (after 90% of the pollen-donors have completed pollen shedding) in flowering were removed from the receptor blocks.
Scientific RepoRts | 7:44913 | DOI: 10.1038/srep44913 At maturity, the seedheads of four GS common waterhemp plants from each distance and direction were harvested separately and labeled. Seeds were collected when ≥ 75% seeds in a seedhead turned into dark-violet or black. The seeds were then cleaned thoroughly and stored separately in airtight polythene bags at 4 °C for 2 months to overcome their limited seed dormancy.
Meteorological Data. Hourly surface meteorological data were recorded by the Bowen ratio energy balance systems (BREBS) stations of the Nebraska Water and Energy Flux Measurement, Modeling, and Research Network (NEBFLUX) available at the South Central Agricultural Laboratory, Clay Center, NE 58 . Wind frequency, wind speed, and wind run data were used for modeling PMGF in common waterhemp. Other meteorological data such as temperature, humidity, and precipitation were also recorded, as these factors can affect pollen viability and dispersal 59 . The resistance screening was performed at the 1.5 × rate (1,575 g ae ha −1 ) of glyphosate to obtain more consistency in the response of common waterhemp plants, to ensure the complete control of any GS plant present, and to assure the survival of any GR plant (as the ED 50 value, the effective dose to control 50% plant population, for GR parent plants was higher than the 1.5× rate of glyphosate; Fig. S3). The number of seedlings surviving glyphosate treatment was recorded at 21 days after herbicide application and the frequency of gene flow at each distance/direction was calculated using the equation:  probability distribution in the tail) rather than by normal distribution 52,60 . The exponential decay, or the exponential power functions, are widely reported statistical models that describe PMGF better 45 .

Resistance Screening.
In this study, all statistical analyses were carried out in R Version 3.2.2 61 . Frequency of gene flow data from all distances and directions and from both years were subjected to nonlinear regression using Generalized Nonlinear Models (package gnm). The frequency of gene flow data followed a binomial distribution, as there were two possible outcomes (dead or alive seedlings) from the resistance screening procedure. Unlike the Gaussian distribution, both mean and variance are dependent on the underlying probability, p i , in a binomial distribution. Compared to the nonlinear least square (nls) function used in several studies (e.g., Pluess et al. 62 ), gnm has two notable advantages for modeling the PMGF: (i) responses with non-Gaussian distribution can be fitted, and (ii) it is a more convenient way to represent a model with a large number of parameters by symbolic model specification 63 .
In binomial distribution, the probability of success (p i ) is a function of the covariate x (here, x is the distance from the pollen source) that can take any real value, but the p i should range between 0 and 1 (0 ≤ p i ≤ 1). Therefore, it was important to transform the frequency of gene flow data to remove the range and floor restrictions; the Logit, or log-odds, link function serves this purpose 64 : The frequency of gene flow data from both years were described using the exponential decay function in which the independent variables were distance from the pollen source, direction of the pollen-receptor blocks, average wind speed, wind frequency, wind run, and year. Therefore, 62 possible models were constructed and subjected to the test for best fit (Table S3).
Model Selection. The Akaike's Information Criterion (AIC) was used for the model comparison and selection of the best model using the equation 65 : where LL is the log-likelihood function for the models and K is the number of parameters estimated. The model with the lowest AIC value was considered as the "top model" or best candidate model tested 66 .

Top Model.
A double exponential decay model [equation (6)] where the frequency of gene flow varied with the distance from the pollen source, the direction of the pollen-receptor blocks, and the year provided the best fit to the data (Table S3) where p i is the frequency of gene flow of the i th observation; β 0 is the overall intercept; β 1 , and β 2 are the intercepts for the first and second instances, respectively; and γ 1 , and γ 2 are the decay rates where γ 1 > γ 2 . Here, β 2 and γ 2 vary with the direction and the year. The distances where the frequency of gene flow was reduced by 50% (O 50 ) and 90% (O 90 ) of the predicted frequency at 0 m were estimated from the final model [equation (6)].
Model Goodness of Fit. The difference between observed and fitted values for the final model was measured. Model goodness of fit was estimated by Pearson's chi-squared statistic using the equation 67 : where the sum of the squared difference between y i (observed values) and μ i (fitted values for the i th group of observations) was divided by the variance of y i that was μ i (n i − μ i )/n i (with μ i estimated using μ i ) and n i is the sample size for i th group. The degree of freedom for Pearson's chi-squared statistic was n − k − 1, where n was the total number of groups and k was the number of parameters.
Mechanism and Inheritance of Glyphosate Resistance. Common waterhemp individuals that survived the resistance screening procedure were considered as hybrids (GS × GR; i.e., F 1 progeny). Thirty healthy individuals from the F 1 progeny were selected and transplanted into round plastic pots (20 cm diameter and 30 cm height) containing a 3:1 mixture of soil:potting mix and grown in the greenhouses at the University of Nebraska-Lincoln. Transplanted individuals were again sprayed with glyphosate at 790 g ae ha −1 (0.75× the recommended rate) to confirm resistance. Low-level plant injury (chlorosis, stunting, frequent branching, etc.) was observed in less than 50% of the transplanted F 1 individuals. No mortality was observed, indicating that no susceptible individuals were present (ED 90 for the GS biotype was 659 g ae ha −1 ; Fig. S3). Ten F 1 individuals were selected based on their similarities in morphology and flowering initiation time and kept for open pollination in the greenhouse. Seeds were collected at maturity and designated as pseudo-F 2 , as the dioecious nature of common waterhemp prohibits self-pollination of F 1 plants to form true-F 2 progeny. Seeds from the parent biotypes (GR and GS) and the open-pollinated pseudo-F 2 were germinated in 72-celled germination trays containing potting mix. Emerged seedlings were transplanted at 2 cm height into square plastic pots (10 × 10 × 12 cm). A 50 mg sample of young meristematic leaf tissue was collected from each individual (25 individuals each from the GR and GS biotypes, and 44 individuals from the F 2 progeny) and were immediately frozen in liquid nitrogen. Individuals were then treated with glyphosate (at the rate of 1,575 g ae ha −1 ; 1.5× the recommended rate) to compare the genomic EPSPS copy number data with the greenhouse visual control. Leaf tissue samples were also collected from 48 individuals (3 randomly selected distances × 8 directions × 2 years from gene flow study) of the F 1 progeny that survived the resistance screening process.
Sample Preparation. DNA extraction and analysis were performed in the Molecular Weed Science Lab at Colorado State University. Leaf tissue samples were ground to a fine powder using a Qiagen TissueLyser II (Qiagen Inc., Valencia, CA 91355) and a metal bead for 1 min at 30 oscillations per second. Genomic DNA extraction was performed on the leaf tissue using the modified cetyltrimethylammonium bromide (CTAB) method described by Doyle 68 . The concentration and purity of the DNA was measured using a spectrophotometer (Nano Drop 2000 Spectrophotometer, Thermo Fisher Scientific, Wilmington, DE 19810) and each sample was diluted to 10 ng μ L −1 .
For both CPS and EPSPS, genomic DNA templates (10 ng) were amplified in a 25-μ L reaction volume containing forward and reverse primers (400 nM final concentration) and Quanta 2X PerfeCTa qPCR SYBR Green FastMix (Quantabio, Beverly, MA), using a real-time qPCR thermal cycler (Bio-Rad) protocol. The qPCR reactions were heated to 95 °C for 30 s, followed by 40 cycles of 30 s at 95 °C and 30 s at 60 °C. Real-time data for fluorescence of the asymmetrical cyanine dye SYBR Green were recorded at the end of the amplification step in every cycle. A melt curve analysis of the products was performed by heating the PCR products from 60 to 95 °C, in 0.5 °C increments for 5 seconds and reading fluorescence at each step. Melt curve profiles were used to verify a single melting point, indicative of a single PCR product and lack of non-specific products. As a secondary check of amplification specificity, a 5 μ L aliquot of the PCR product was run on 1% agarose gel to verify the presence of a single band (Fig. S4).
Relative quantification was conducted using the comparative cycle threshold (C T ; −∆ 2 C T ) methods described by Schmittgen and Livak 70 . Relative quantification of EPSPS for each sample was calculated using the equation:

T T T
Relative EPSPS copy number was expressed as −∆ 2 C T . Each individual sample was run in triplicate to calculate the average increase in EPSPS copy number and standard deviation.