Summary and full report, May 2002
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Summary
1. Introduction
This report is based on two papers that will be submitted for publication in a peer-reviewed journal.. The authors are Eva Novotny (Institute of Astronomy, University of Cambridge) and Jean Perdang (Institut d’Astrophysique, University of Liège, Belgium.) To investigate how pollen may spread from a field to its surroundings, and to what degree the pollen is capable of fertilising another variety of the same crop, a computer programme has been written that simulates the main processes in pollen transport, deposition and fertilisation.
2. The Cellular Automation (CA) Model
The physical region to be studied, typically a field on which a crop is growing and providing pollen (the source field) and a surrounding region, is imagined as having superimposed upon it a rectangular lattice. The lattice may also include one or more receptor regions for the pollen and, usually, some land surrounding the areas already mentioned. The lattice is divided into cells by a grid of rectangular co-ordinates. Pollen is created in the source field and is carried off by the wind; and its progress across the lattice and its ultimate fate are tracked in a series of time steps. As it travels, the pollen is subject to being deposited and lost to the air-stream, either by falling on the ground (or on leaves, stems, etc.) or by impacting on a stigma with the possibility of causing fertilisation.
Essential quantities to be represented at each time-step and for each cell individually are wind velocity (both speed and direction), amount and state of the pollen (of each type present) — that is, how much has just been created, how much has just become air-borne and how much has just been deposited. Also, if required, the number of fertilisations by particular varieties of pollen are recorded at each time-step for each cell.
At each time-step, pollen may travel from one cell to an adjacent cell, under the action of the wind. Whether or not motion takes place, and in which direction, is determined probabilistically. A probability Psis assigned, at each cell, that pollen will be trapped (i.e., will ‘stick’) and will thus make a transition from the state of being air-borne to the state of being deposited. In our current programme, this probability is constant for all time and over all cells that are occupied by the same type of crop or ground. We require values of PsF, the probability of deposit in the source field and any other region of the same crop, and PsE,, the probability for the exterior region. In practice, the probability of deposition would depend on various factors such as humidity and height above the ground.
All calculations are done in dimensionless variables. Physical dimensions are obtained by assigning physical values to cell size, unit time step and unit amount of pollen. Thus a single numerical experiment represents many physical situations.
If sufficient memory capacity is available for computing, multiple layers of the lattice can be used to compute 3-dimensional transport of pollen. In this case, the wind velocity is 3-dimensional and may carry pollen from one layer to an adjacent layer during a single time-step. Changes in ground elevation and barriers can be introduced, although these affect not only deposition but also the airflow pattern. For realistic modelling, a 3-dimensional wind would be required, as well as the barrier. Other extensions are also possible, given enough computer capacity, including more sophisticated formulations of the phenomena we have described.
3. Computer Modelling
In most of the numerical experiments the same geometry of the donor field has been used. The field is modelled by a square area of 20´ 20 cells, on a lattice of 150´ 50 cells. Two exceptional geometries are discussed as well: one experiment has a rectangular source field of 40´ 20 cells, and another has a field reducing to a single row (1´ 50 cells).
The wind-velocity field, which has components parallel to the long and short sides of the lattice, is briefly discussed for each specific numerical experiment. It may be comprised of (i) a uniform (time- and space- independent) velocity component, w, directed along the length of the lattice; (ii) a wavelike propagating component, of zero average over space and time; (iii) a component localised in space and time; and (iv) a randomly fluctuating component of zero average. Contributions (ii) and (iv) simulate the non-steady and turbulent wind components, respectively; effect (iii) describes a gust of wind. Colour contour-plots display the pollen deposition patterns resulting from various types of wind.
Input data such as wind velocity and amount of created pollen can be approximated with guidance from observations. A quantity for which no measurements exist, on the other hand, is the probability of deposition. To obtain measured values, it would be necessary to make observations of pollen deposition as a function of distance while keeping detailed records of wind-velocity, humidity, temperature, etc. on a continual basis during the time of deposition. In the absence of measured values, we experimented numerically with our computer simulations to determine the sensitivity of our results to the values assumed for the deposition probabilities in the donor and recipient fields and to ascertain whether we might obtain preliminary estimates for these values.
4. Comparison With Observed Data
Tables of measured wind-speed and direction were obtained from the UK Meteorological Office. Also shown are analytical approximations, consisting of summations of sine and cosine terms, which use less memory than would the tabulations.
No empirical information is available on probabilities of deposition of pollen. However, only a limited range of values produces distributions of deposited pollen with distance that resemble observed distributions. This has guided us in finding, by trial and error, values of Ps for the donor and recipient fields.
We have been able to reproduce the general behaviour of the relative amount of pollen deposited as a function of distance from the source field, as measured in the field by Jones and Newell for seven species of grasses. Similarly, our models have approximated the relative amounts of hybridisation of maize with distance from the source field as measured by Jones and Brooks.
No attempt has been made to include in our calculations a small effect that has, nevertheless, important consequences for avoidance of cross-contamination between crops. It is found experimentally that a very long tail of the profile of deposited pollen persists to large distances from the source. In one experiment, in spite of the fact that the receptor maize was in the direction opposite to that of the prevailing winds, the percentages of outcrossed maize at five distances from 80 m to 160 m were, respectively, 0.02. 0.08, 0.79, 0.18, and 0.21. One of these values is dangerously close to the 1 percent level of contamination permitted in farm-scale trials of GM maize in the United Kingdom, where separation distances are required to be no more than 50 m from fields of conventional maize and 200 m from fields of organic maize. Pollen can be carried to large distances at higher altitudes, from where it drifts downwards.
5. Conclusions
While precise quantitative conclusions cannot be drawn from this work, for lack of sufficient observational data, certain qualitative features are apparent and will be present in all real cases, regardless of actual numerical values. One characteristic common to all contour plots of deposited pollen is the patchiness of the deposit. Even in a calm breeze, a degree of patchiness will be present, because the release and deposition of pollen are probabilistic; in a real breeze or wind, eddies in the air currents will move pollen about at random. This point is of particular relevance when plants growing in the field may cause cross-pollination with plants in the exterior; it becomes difficult to set a fixed distance at which some specified maximum level of cross-pollination will occur. When winds are unusually strong, pollen is dispersed to much larger distances than at times of normal conditions, and these distances scale with the wind strength. Our contour plots show isolated cells of high pollen deposit amid regions of low deposit at considerable distances from the field. Thus even if, on average, the amount of pollen carried beyond a given distance is low, there may be islands or fingers of higher pollen count at greater distances.