Martin Hoyle and James E. Creswell. 2007. The effect of wind direction on cross-pollination in wind-pollinated GM crops. Ecological Applications 17:1234–1243.

Appendix A. Cross-pollination rate approximation.

In this section, we show that, for the four crops studied, approximately;

.

(A.1)

The relative cross-pollination rate as a function of the angle between the GM and non-GM fields, is given in the main text as;

.

(A.2)

The cross-pollination rate of the seeds produced by a flower whose stigma is receptive to pollen over the time interval [t,t+T] is the term in brackets;

(A.3)

S_non-GM(t) is the number of receptive stigmas in the non-GM field at time t. P_GM(t) and P_non-GM(t) are the airborne concentrations of GM and non-GM pollen above their respective fields of origin at time t. A is the mean rate of deposition of pollen from the same plant (selfed pollen), where this pollen is self-compatible. (x,y) and (x´,y´) are coordinates in the GM and non-GM fields respectively. d(r) relates the decline in pollen dispersal with distance from the source, r, where . . The proportion of the total amount of GM pollen deposited at distance r from the source at time t, which is at angle is .

T similar to period of flowering (maize, sugar beet)

Maize and sugar beet stigmas are receptive to pollen over a period similar to the seasonal period of flowering. Maize stigmas are receptive for approximately 6 days (Bassetti and Westgate 1993). is approximately 2.5 days (Table A1), giving a peak flowering period of approximately 5 days (± 1 standard deviation). Sugar beet stigmas are receptive for approximately 14 days ( McGregor 1976 ). is approximately 7.9 days (see above), giving a peak flowering period of approximately 16 days.

In this case  is approximately independent of t, and Eq. A.3 is approximately proportional to as a function of t. Substituting this into Eq. A.2, the cross-pollination rate is given as in Eq. A.1.

T much smaller than period of flowering (rice, oilseed rape)

Oilseed rape and rice stigmas are receptive to pollen over a far shorter period than the seasonal period of flowering. Rice stigmas are receptive for as little as six minutes to one hour per day (Grist 1953). is approximately 7.4 days (Table S1), giving a peak flowering period of approximately 14.8 days (± 1 standard deviation). For oilseed rape, stigmas are receptive for up to five days (Hayter and Cresswell 2006). is approximately 7.8 days (Table S1), giving a flowering period of approximately 16 days (± 1 standard deviation).

In this case the cross-pollination rate for a single stigma, receptive over the period [t,t+T] (Eq. A.3), is approximately

.

(A.4)

Given that the selfing rate for rice is very high, approximately 99% (Grist 1953), then A>>P_non-GM(t), and Eq. A.4 is approximately proportional to . Substituting this into Eq. A.2, the cross-pollination rate is given as in Eq. A.1.

Oilseed rape is pollinated by bees as well as by wind (Cresswell et al. 2004). In this case, the cross-pollination rate due to wind for a single oilseed rape stigma, receptive over the period [t,t+T], is approximately

,

(A.5)

where A^bees is the selfed pollen deposited by bees, A^not-bees is the selfed pollen not deposited by bees (deposited, e.g., by the flower’s own anthers brushing the stigma) and P^bees_non-GM(t) is the non-selfed non-GM pollen deposited by bees. The selfing rate of oilseed rape is then

.

Observed values for the selfing rate are high, in the range 45–95% (Timmons et al. 1995). Hence, we assume that P_non-GM(t) is small compared with
P^bees_non-GM(t)+ A^bees + A^not-bees, and Eq. A.5 is then approximately

.

Substituting this into Eq. A.2, the cross-pollination rate is given as in Eq. A.1.

TABLE A1. Model parameter values of the crops estimated from empirical data.

LITERATURE CITED

Bassetti, P., and M. E. Westgate. 1993. Senescence and receptivity of maize silks. Crop Science 33:275–278.

Cresswell, J. E., T. W Davies, M. A. Patrick, F. Russell, C. Pennel, M. Vicot, and M. Lahoubi. 2004. Aerodynamics of wind pollination in a zoophilous flower, Brassica napus. Functional Ecology 18:861–866.

Grist, D. H. 1953. Rice. Longmans, Green & Co., London, UK.

Hayter, K. E., and J. E. Cresswell. 2006. The influence of pollinator abundance on the dynamics and efficiency of pollination in arable Brassica napus: implications for landscape-scale gene dispersal. Journal of Applied Ecology 43:1196–1202.

McGregor, S. E. 1976. Insect pollination of cultivated crop plants. < http://gears.tucson.ars.ag.gov/book>

Timmons, A. M., E. T. O’Brien, Y. M. Charters, S. J. Dubbels, and M. J. Wilkinson. 1995. Assessing the risks of wind pollination from fields of genetically modified Brassica napus ssp. oleifera. Euphytica 85:417–423.