Indhold

Contents

Summary

Sammendrag

1 Introduction

2 Simulation of growth

	2.1 Competition for a maximum yield potential
	2.2 Growth of crops

3 Seed bank

	3.1 Seed deposits
	3.2 Seed decay
	3.3 Germination

4 Comparison of different herbicide strategies in oilseed rape

	4.1 Introduction
	4.2 Materials and methods
	4.3 Results
	4.4 Discussion

5 Herbicide resistance

	5.1 Stellaria media
	5.2 Brassica campestris

6 Output from the sugarbeet model

	6.1 Introduction
	6.2 Materials and methods
	6.3 Results
	6.4 Discussion

7 Output from the oilseed rape model

	7.1 Introduction
	7.2 Materials and methods
	7.3 Results
	7.4 Sensitivity of selected parameters
	7.5 Discussion
	7.6 Conclusions

8 Canadian experiences

9 Final comment

Appendix 1: Sugarbeet model - equations and parameters

Appendix 2: Oilseed rape model - equations and parameters

Literature

Modelling herbicide use in genetically modified herbicide resistant crops

Description of Models and Model Output

Resumé
I rapporten beskrives modeller, der kan anvendes til at forudsige forbruget af herbicider, hvis der indføres genetisk modificerede herbicidtolerante afgrøder. Der præsenteres modelberegninger for sædskifter med sukkerroer og med raps. Endelig gøres der kort rede for erfaringerne fra Canada, hvor der dyrkes herbicidtolerante afgrøder (især raps) på kommerciel basis.

1 Introduction

Debate

The advances in biotechnology have produced transgenic crops with tolerances towards particularly the non-selective herbicides glyphosate and glufosinate. Transgenic herbicide tolerant crops have caused public debate in especially the putative uncertainties about long-term consequences of growing herbicide tolerant oilseed rape.

Crop rotations

In Denmark, the studies about transgenic herbicide tolerant crops has focused on two crops: beets (Beta vulgaris L.) and oilseed rape (Brassica napus L.). Sugarbeet rotations occupy approx. 10% of the Danish arable (land whereas oilseed rape (winter and spring varieties) occur in crop rotations on approx. 36% of the arable land (Madsen et al., 1997).

Sugarbeet

The currently used weed control strategy in sugarbeet involves a mixture of herbicides (phenmedipham, ethofumesate, metamitron, chloridazon etc.) to control dicotyledonous weeds. The current weed control strategy normally requires several applications with high doses (2000–7000 g a.i. ha^-1) of various herbicides which is reflected in a high treatment frequency of 1.94-2.69 year^-1 (Miljøstyrelsen, 1996; 1997). Introduction of herbicide tolerant varieties of sugarbeet, which will allow for use of more potent herbicides, are therefore likely to reduce herbicide use in the short-term.

Oilseed rape

Only few herbicides for dicotyledonous (dicot) weed control are presently available in oilseed rape. Propyzamide, which only controls a few dicot weed species, is used in winter varieties and napropamide and clopyralid (selective mainly against Asteraceae species) are used in spring varieties. This leaves, in particular, winter oilseed rape prone to dicot weed infestations. Growers are presently experiencing oilseed rape fields severely infested with Sinapis arvensis L., Raphanus raphanistrum L. and Capsella bursa-pastoris (L.) Medicus (Kristensen, 1997). Therefore, the introduction of herbicide tolerant oilseed rape may be of benefit to Danish farmers in the short-term.

Concerns

Both Beta vulgaris and Brassica napus hybridize within the species as well as with wild relatives. For sugarbeet these problems seem to be restricted to succeeding sugarbeet fields, but oilseed rape can, in particular, be a problematic volunteer in succeeding crops (Lutman, 1993). Furthermore, the transgenic oilseed rape can pollinate other conventional oilseed rape fields, or oilseed rape can hybridize with the related weed species Brassica campestris L. (Jørgensen & Andersen, 1994; Mikkelsen et al., 1996). The questions are: Will volunteers and hybrids with wild relatives become a more severe agronomic or environmental problem when the herbicide tolerant crop is grown? And will the amount of herbicide used in a rotation with transgenic herbicide tolerant crops decrease or increase compared with the same rotation with non-transgenic crops? These questions can only be addressed experimentally by costly perennial experiments.

Objective

The objective of this study is to substitute perennial experiments by simulating the consequences of herbicide use in a crop rotation with transgenic herbicide tolerant sugarbeet or winter oilseed rape in comparison to traditionally grown varieties. We here present two simple empirical models which aim at addressing the accumulated use of herbicides and selection of herbicide resistant weeds in particularly.

2 Simulation of growth

	2.1 Competition for a maximum yield potential
	2.2 Growth of crops

2.1 Competition for maximum yield potential

Logistic growth

Growth of the different species are modelled with sigmoid growth curves where the response variable is dry matter production in tons ha^-1 and the predictor is time in days. The model uses a time step of one day per calculation (dt).

The following equation generates a sigmoid growth curve for each species when it is integrated over time:

Y_t+1₊₁ is dry matter production from day t to day t+1.

g is the relative growth rate per day.

Y_t is dry matter production up to time t

Y_max is the maximum achievable biomass production ha^-1 for the species

Y_total is the accumulated biomass produced ha^-1 of all species in the model

Restrictions

Furthermore, each growth function has the restriction that the species stops growing when Y_Total > Y_Max , in order to avoid negative growth. This makes the total biomass produced in the model equal to Y_Max of the species with the highest potential biomass production which in most agricultural systems is the crop.

Yield potential

One question immediately arose: Was it acceptable to have this restriction on the total biomass production of the system? Trenbath (1974) analysed data from 344 mixture experiments and grouped the yield of the mixture into either 1) a yield below the yield of the lowest biomass yielding species to the average yield of the two species in monoculture or 2) a yield from the average of the monocultures to above the yield of the highest biomass yielding species in monoculture. He found that more than 60% of the experiments went into category 2.

To ensure ourselves that this restriction was appropriate for a mixture of crops and weeds, we conducted an experiment in the greenhouse in which we planted oilseed rape or spring barley in monoculture and in mixtures with two weeds.

Experimental methods

Spring barley (Alexis), spring oilseed rape (Global), Stellaria media and Chenopodium album were sown on 8 July 1996 in 0.12 m² pots in the following combinations: A) All species in monoculture. B) spring oilseed rape (Global): Stellaria media: Chenopodium album. C) Spring barley: Stellaria media: Chenopodium album and D) Stellaria media: Chenopodium album. Plant densities species^-1 pot^-1 were for all combinations: Spring barley: 36, spring oilseed rape: 10, Stellaria media: 350 and Chenopodium album: 250. There were 3 replications and 6 harvest times: 24 July, 31 July, 7 August, 14 August, 21 August and 28 August. Fresh weight and dry weight were recorded at all harvest times.

Results

The experiment showed that the crop-weed mixtures had a tendency to over-yield compared to the monocultures. However, this over-yielding in the mixtures was not significantly different from the crop yield in monoculture. This implies that the over-yielding could be explained by random variation in the data.

Conclusion In conclusion, this experiment does not reject the assumption, that yield of the mixtures of crop and weeds is likely to be similar to the yield of the crop in monoculture.

2.2 Growth of crops

The individual growth curves are essentially results of a two parameter function, a growth rate and a maximum biomass. This simplification puts restrains on the possible curves, and consequently they are considered to follow the logistic curve, which is symmetric around the point of inflection. Experimentally obtained growth curves for the crops could be found in the literature. However, usable growth curves were not available for the chosen weeds. Growth curves for the latter were therefore based on a subjective estimate. Crops and volunteers have identical growth parameters, likewise for sensitive and resistant weeds of the same species.

Winter oilseed rape

Dawkins and Almond (1984) conducted an experiment in which they measured the above ground biomass of two winter varieties of oilseed rape over time and the data shown in figure 2.4 are average values of the varieties Elvira and Jet Neuf. The English data show a higher biomass level during the winter time than the model, but otherwise the simulated curve describes the steep part of the growth.

Wheat

The simulated growth curve for winter wheat (Fig. 2.5) is compared with two experimentally determined growth curves from Denmark. The simulated growth curve overestimates the results from the variety Kraka grown 1986 (Petersen, 1987), but underestimates the results from 1994 (Jørnsgård et al., 1996).

3 Seed bank

	3.1 Seed deposits
	3.2 Seed decay
	3.3 Germination

Information concerning soil seed banks was included in the former report by Madsen, Poulsen and Streibig (1997) but as additional information was found useful for the modelling, we have included a short section in this report as well.

3.1 Seed deposits

The seed bank should literally be interpreted as a bank into which the species deposit their annual seed production. The size of the seed production is determined by the biomass production of the species at harvest time multiplied with an individual harvest index. Data on seed production are often presented as seeds per plant and not as a harvest index, but in this model we use biomass of a species rather than number of plants. Consequently we link biomass production to seed production through a harvest index.

Harvest index

Harvest index (HI) is usually a terminology used for crops and denotes the harvested part of the crop e.g. for cereal grains, relative to the total above ground biomass production. Few data are available on harvest index of weed species. Rasmussen (1993) studied seed production in Chenopodium album as a function of plant biomass. The seed production multiplied with an average seed weight from the literature of 1.2 mg (Korsmo, 1981) resulted in a HI of 40-50% for this species. Norris (1996) studied seed production in Capsella bursa-pastoris of two populations. In this species, HI varied from 10 to 28% depending on population. Andersson (1994) studied seed production and seed weight as a function of herbicide treatment with MCPA. We have recalculated HI from these results in Table 3.1.:

Harvest index for selected weed species. Recalculated after results obtained by Andersson (1994)

Predation

Before the seeds enter the seed bank many will be predated by insects, birds and small mammals. It is difficult to give an exact number for this predation, but up to 50-90% seed losses are possible (Statens Planteavlsforsøg, 1993).

Immediate germination

Depending on species many seeds are able to germinate immediately. Plants from seeds that germinate before the soil is cultivated for the succeeding crop will perish.

Estimated value

The proportion of viable seeds that enter the seed bank relative to the seed production is estimated for each weed and volunteer species in the model. This estimated value is based on the following: Is the species known to have pronounced seed dormancy, and are the seeds known to be a food source for the fauna?

3.2 Seed decay

The seed number in the total seed bank decreases exponentially (Wilson & Lawson, 1992). Decrease in cultivated soil is 2-3 times greater compared to undisturbed soil (Roberts and Feast, 1973). The rate of annual decline varies somewhat in different studies: Wilson and Lawson found a total yearly decline of 50% in a study, whereas Statens Planteavlsforsøg (1993) mentions an average of 33% per year. Roberts and Feast (1973) mention an average seed decay of 32% one year after burial of weed seeds. Decay rates for individual weed species varie as shown in Table 3.2.

Seed bank persistence of common weeds in natural, cultivated soil. After Roberts and Feast (1973)¹ and Wilson and Lawson (1992)².

In the model the exponential seed decay is based on an annual decay rate of 33%.

3.3 Germination

The number of weed seeds that germinates from the ploughing layer (the top 20 cm soil) varies considerably. Few weeds are able to germinate from lower depths and therefore the cultivation is an important factor. Roberts and Feast (1973) found that the number of seedlings were twice as great when cultivation had taken place compared to undisturbed soil. In their experiments, an average emergence of 20-25% of the seeds plants emerged as plants during the first year, and 15% during the second year after burial, and on average over the first six years after incorporation in the soil, the seeds germinated with approx. 9% annually in cultivated soil. Wilson and Lawson found 0.1-5% germination, and Hurle et al. (1988) found a germination frequency of 0.5-9%. In the model the germination frequency is assumed to be 5% for all weed species.

4 Comparison between different herbicide strategies in oilseed rape

	4.1 Introduction
	4.2 Materials and methods
	4.3 Results
	4.4 Discussion

4.1 Introduction

One of the keystones of these models is selection pressure from the herbicide on individual weed species/biotypes as a function of dose. The work presented here will later be used as input for a model that predicts herbicide use in a crop rotation with non-transgenic oilseed rape (the reference scenario), glyphosate tolerant oilseed rape and glufosinate tolerant oilseed rape (future scenarios). A similar study, conducted on weeds common to sugarbeet was presented in Madsen and Jensen (1995); however, these curves were not integrated into the presented model of a sugarbeet rotation (Chapter 6). This model uses only one rate per spraying per herbicide.

Traditional herbicides Traditional herbicides in Danish oilseed rape are currently under pressure. One reason is that herbicides commonly used in this crop are being withdrawn (benazolin), restricted in dosage (propyzamide) or banned for environmental reasons. The mentioned two herbicides accounted for 45% of the broad spectrum dicotyledon weed control in this crop (measured as treated area) in 1995 (Miljøstyrelsen, 1996). Oilseed rape is a rather competitive crop (with respect to weeds) and is therefore considered to be one of the less herbicide intensive crops which is reflected in a treatment frequencies (number of times a field is treated with the recommended dose) of 0.82-1.12 in spring varieties and 0.95-1.25 in winter varieties (Miljøstyrelsen, 1996; 1997).

Bioassay Here we present data from greenhouse (bioassay) experiments showing selection pressure from glyphosate or glufosinate on the individual weed species as a function of dose relative to a traditionally used herbicide mixture of benazolin+clopyralid. This mixture was chosen because it currently is the only foliar acting herbicide in oilseed rape (until 1997) which makes comparison of weed control strategies with the exclusively foliar acting glyphosate and glufosinate possible. Data are evaluated with the logistic dose-response model (Streibig et al., 1993) which allows for a comparison of dosages to obtain a certain efficacy level. A similar methodology is used to estimate the efficacy of the weed control on volunteers of oilseed rape in a succeeding cereal crop.

4.2 Materials and methods

Weed control - A

Four weed species were sown into square 637 ml pots (milk cartons cut of 13 cm from bottom) filled with a peat-sand mixture on 8 February 1996 and grown in the greenhouse. The pots were sub-irrigated when needed. Plants per pot were thinned 14 februar to 20 februar to 10 plants of Stellaria media, 6 of Chenopodium album, 10 of Viola arvensis and unknown of Poa annua (no thinning due to poor germination). Pots were sprayed on 26 February in a pot sprayer with a Hardi: 4110-14 nozzle applying 105 l ha^-1. Nine pots of each weed species in four replications were sprayed with glyphosate in a Roundup formulation (360 g a.i. l^-1) with 720, 360, 180, 90, 45, 23, 11, 6 and 0 g ha^-1. The remaining nine pots per weed species in four replications were sprayed with glufosinate in a Basta formulation (200 g a.i. l^-1) with 600, 300, 150, 75, 38, 19, 9, 5 and 0 g a.i. ha^-1. Plants were harvested on 11-12 March. Fresh and dry weight were recorded.

Weed control - B

Spring oilseed rape (variety: Global) and two weed species were sown into 8 l pots filled with soil-peat mixture on 9 May 1996 and grown in the greenhouse. Pots were automatically watered from above. The number of plants per pot was adjusted on 22-30 May to 20 plants of oilseed rape, 20 of Chenopodium album and 28 of Stellaria media. Plants were kept at 5° C from 3-5 June. Pots were sprayed on 6-7 June in a pot sprayer with a Hardi: 4110-16 nozzle applying 200 l volume ha^-1. Seven pots in four replications were sprayed with a commercial mixture of benazolin (500 g a.i. l^-1 formulation) and clopyralid (80 g a.i. l^-1 formulation) in a Benasalox SC formulation with 812, 406, 203, 102, 51, 25 and 0 g a.i. ha^-1, furthermore penetration oil (Agrirob) was added to the spray solution with 500 ml per ha. Another seven pots in 3 replications were sprayed with glyphosate in a Roundup formulation (360 g a.i. l^-1) with 720, 360, 180, 90, 45, 23 and 0 g ha^-1. The remaining seven pots in 4 replications were sprayed with glufosinate in a Basta formulation (200 g a.i. l^{- 1}) with 600, 300, 150, 75, 38, 19 and 0 g a.i. ha^-1. Plants were harvested and counted on 17-19 June. Fresh and dry weight were recorded.

Weed control - C

Three weed species were sown into 2 l pots filled with a soil-peat mixture on 25 juli 1996 and grown in the greenhouse. Pots were manually watered from above. Plants per pot were thinned on 5 August to 10 plants of Chenopodium album, Myosotis arvensis and Capsella bursa-pastoris. Pots were sprayed on 20 August in a pot sprayer with a Hardi: 4110-16 nozzle applying 200 l volume ha^-1. Seven pots of each weed species in four replications were sprayed on 20 August 1996 with glyphosate in a Roundup formulation (360 g a.i. l^-1) with 720, 360, 180, 90, 45, 22.5 and 0 g ha^-1. The remaining seven pots per weed species in four replications were sprayed with glufosinate in a Basta formulation (200 g a.i. l^-1) with 600, 300, 150, 75, 37.5, 18.8 and 0 g a.i. ha^-1. Plants were harvested and counted on 4 September. Fresh weight and dry weight were recorded.

Volunteer oilseed rape

Spring oilseed rape (cultivar: Global) was grown in monoculture, with spring barley (Alexis) or with winter wheat (Texana). The seeds were sown into 8 l pots with a soil-peat mixture 12 June 1996 and grown in the greenhouse. Pots were automatically watered from above. On 21-30 June plants were thinned to 9 oilseed rape plants per pot, and 12 plants per pot of the cereals, but half of the spring barley pots were thinned again due to regrowth and the rest were allowed a higher biomass. The plants were kept at 5° C from 26 June to 2 July. Pots were sprayed 4-5 July in a pot sprayer with a Hardi: 4110-16 nozzle applying 200 l volume ha^-1. Seven pots from each combination in 4 replications were sprayed with tribenuron-methyl in a commercial Express formulation (7.5 g a.i. tablet^-1) with 30, 15, 7.5, 3.8, 1.9, 0.9 and 0 g a.i. ha^-1. The remaining 7 pots from each combination in 4 rep. were sprayed with a commercial mixture of ioxynil (200 g. a.i. l^-1 formulation) and bromoxynil (200 g a.i. l^-1 formulation) in a Oxitril formulation with the following doses: 800, 400, 200, 100, 50, 25 and 0 g a.i. ha^-1. Plants were harvested and counted 18-19 July. Fresh and dry weight were recorded.

Statistical analyses

Fresh weight per pot (greenhouse) was analysed with the logarithm of the dose as predictor. The regression model of fresh weight (y) on dose (z) was a logistic curve:

where D denotes the upper limit of the curve, b is proportional to the slope around ED_50, which is the point of inflection (Streibig et al., 1993). Data were then standardized with the D-parameter to obtain relative fresh weight, and the regression was run again, now resulting in a D-parameter of approximately 100%. To stabilize the variance the Transform-Both-Sides technique was used with the optimal power of transformation ( (Carrol & Ruppert, 1988).

For practical weed control, the ED₈₅-value is of greater interest than the ED₅₀. The logistic model was reparameterized to calculate the ED₈₅-value as a parameter in the model (only greenhouse data):

LOF Lack-Of-Fit test (Weisberg, 1985) was used to determine if the model could adequately describe data.

Adjustment

The ED-values from the three greenhouse experiments were adjusted according to the ED₅₀-value from glyphosate treated S. media or C. album, to make the ED-values from the three experimental runs comparable, this resulted in almost identical curves for glufosinate treated counterparts which justifies the adjustment.

4.3 Results

Weed control

The model fitted reasonable to the data from the greenhouse, which is reflected in the confidence limits for the parameters (Table 4.1). However, the LOF-test was significant for M. arvensis and V. arvensis sprayed with glyphosate at the 5% level but not at the 2.5% level, furthermore data were very variable for S. media sprayed with benazolin and clopyralid and for oilseed rape sprayed with glufosinate. Glyphosate was more potent at the ED₅₀ and ED₈₅ level than glufosinate for C. bursa-pastoris, C. album, P. annua, however, this superiority is not statistically significant. For M. arvensis and V. arvensis, glufosinate was more potent than glyphosate; this difference was statistically significant at the 5% level for V. arvensis. The mixture of benzolin and clopyralid was less potent than glyphosate and glufosinate, however, the difference was only statistically significant for C. album at the ED₅₀ level (Figs 4.1, 4.2 and 4.3).

Ranking after sensitivity

The weed species can be ranked after their sensitivity to glyphosate or glufosinate in the greenhouse. At the ED₅₀ value of glyphosate C. bursa-pastoris > S. media > M. arvensis > C. album > P. annua > oilseed rape >V. arvensis. The ranking is almost identical at the ED₈₅ value C. bursa-pastoris > S. media > P. annua > C. album > oilseed rape > V. arvensis. For glufosinate the ranking at the ED50 value is as follows, M. arvensis > C. bursa-pastoris > V. arvensis > S. media > C. album > P. annua > oilseed rape, and at the ED₈₅ value V. arvensis > M. arvensis > C. bursa-pastoris > S. media > C. album > P. annua > oilseed rape.

Volunteer oilseed rape The LOF-test did not reject the hypothesis that the model could be used for evaluation of dose-response relationships where oilseed rape was growing in competition with different biomass of cereals. The only exception was the combination with oilseed rape in a normal biomass of barley, where LOF was significant at the 5% level but not at the 2.5% level. Tribenuron-methyl showed a significantly higher efficacy than the mixture of ioxynil and bromoxynil (Table 4.2), which is not surprising because tribenuron-methyl is considered to be a low-dose herbicide. However, there is no significant difference between different cover crop or cover crop biomass at the ED₅₀ or ED₈₅ level for tribenuron-methyl. The 85% control level of volunteer oilseed rape with tribenuron-methyl was obtained with doses from 0.53 to 1.28 g a.i. ha^-1 which is considerable less than the recommended rate of 7.5 g a.i. ha^-1 (Statens Planteavlsforsøg, 1997). This indicates that volunteer oilseed rape is highly unlikely to pose a problem in a rotation were the succeeding cereal crops are sprayed with a sulfonylurea herbicide, even though extrapolating dose rates from the greenhouse to the field is often misleading. The oilseed rape plants sprayed with the mixture of ioxynil and bromoxynil required 98.1 g a.i. ha^-1 for 85% control, this is also low compared to the allowed dose of 400 g a.i. ha^-1 for broad leaved weed control.

Integrated into model

The parameter values listed in Tables 4.1 and 4.2 are used in the oilseed rape model and these experimental data thus determine the selection pressure posed on the individual weed species present in the model.

4.4 Discussion

LOF Despite the fact that the LOF test showed lack of fit at the 5% level for three of the curves but not significant at the 2.5% level, we chose to apply the same logistic dose-response model to all data in order to obtain comparable parameters.

Field data

It would be useful to validate the relative potencies of the herbicides on different weed species with field data, however, at the time of the writing these data were not ready for being integrated in the model.

Potency

Glyphosate and glufosinate were both more potent than the traditional mixture of benazolin+clopyralid, which was expected from practical experience. In these experiments glyphosate and glufosinate seem equally potent on a mixed weed population. However, the plants were harvested after maximum effect at 2-3 weeks after the spraying. This means that regrowth of the weeds after the spraying was not included in the study, and a systemic herbicide (glyphosate) will suppress regrowth for a longer period than a contact herbicide (glufosinate). Therefore, glyphosate is probably more potent in controlling the weeds if the entire growing season is evaluated, however, this was evaluated in this study.

Greenhouse experiment. Adjusted regression parameters from regression of relative fresh weight on dose of glyphosate, glufosinate or a mixture of benazolin and clopyralid (95% confidens intervals in parenthesis). All results are based on Transform-Both-Sides transformation with =0.25.

%

%

g a.i. ha^-1

g a.i. ha^-1

(81-119)

(4-8)

(1.3-2.5)

(33.4-63.6)

(91.3-155.9)

pastoris

(83-117)

(4-9)

(1.2-2.3)

(44.0-84.1)

(127.7-224.7)

(79-121)

(1-12)

(0.9-3.79)

(67.0-144.7)

(137.6-302.8)

(85-115)

(0-8)

(1.8-5.2)

(126-196.2)

(206.3-321.4)

(90-110)

(14-37)

(0.5-6.5)

(238.6-394.6)

(288.6-751.4)

arvensis

(77-123)

(-4-11)

(0.6-1.7)

(38.3-126.6)

(120.2-624.4)

(83-116)

(4-7)

(1.9-3.4)

(44.8-69.7)

(91.3-127.7)

annua

(88-113)

(15-35)

(-0.5-8.1)

(102.2-177.9)

(100.4-332.0)

(87-113)

(-7-15)

(0.8-5.0)

(129.0-212.2)

(173.0-452.7)

media

(80-120)

(1-9)

(1.0-2.7)

(46.3-99.7)

(121.4-249.9)

(72-128)

(-6-8)

(0.7-2.5)

(30.8-99.7)

(94.0-302.9)

(71-129)

(4-52)

(-0.3-2.9)

(-4.5-172.3)

(-322.9-928.9)

arvensis

(84-116)

(0.7-1.7)

(160.0-435.4)

(727.5-1772.9)

(74-128)

(3-12)

(1.0-7.6)

(43.5-85.5)

(61.5-130.5)

(90-110)

(17-35)

(1.0-5.2)

(154.8-258.6)

(202.8-516.8)

(91-109)

(-61-138)

(-5.1-11.1)

(-181.6-924.6)

(-1280-2611)

Greenhouse experiment. Control of volunteer oilseed rape in cereal crops. Regression parameters from regression of relative fresh weight on dose of either a mixture of ioxynil and bromoxynil or tribenuron-methyl (95% confidens intervals in parenthesis). All results are based on Transform-Both-Sides transformation with individual .

%

%

g a.i. ha^-1

g a.i. ha^-1

+bromoxynil

(67-133)

(0-3)

(1.4-3.5)

(26.8-68.4)

(69.0-127.2)

-methyl

(55-145)

(4-11)

(0.6-2.2)

(0.03-0.36)

(0.29-1.03)

dense

-methyl

(54-146)

(7-19)

(0.3-2.0)

(-0.02-0.47)

(0.22-1.72)

normal

-methyl

(60-140)

(5-11)

(0.5-2.3)

(0.02-0.29)

(0.25-0.82)

dense

-methyl

(37-164)

(-3-24)

(-0.3-2.4)

(-0.17-0.63)

(-0.71-3.28)

normal

-methyl

(53-147)

(3-8)

(0.4-2.4)

(0-0.26)

(0.19-0.70)

5 Herbicide resistance

	5.1 Stellaria media
	5.2 Brassica campestris

5.1 Stellaria media

In Denmark, eight weed species have evolved resistance to atrazine (Andreasen & Jensen, 1994) and one weed, Stellaria media (common chickweed), has evolved resistance to sulfonylurea after 8 years of consecutive use of sulfonylurea herbicides (Kudsk et al. 1992). Use of the herbicide atrazine has now been banned, which leaves the sulfonylurea resistant Stellaria media the only significant herbicide resistant weed species yet found in Denmark.

Inheritance

In most cases of evolved sulfonylurea resistance, the trait is inherited by a single dominant gene (Holt et al. 1993), and the resistance mechanism does not seem to cause reduced fitness (Jensen, 1993). In the models the sulfonylurea tolerant S. media is, therefore, behaving exactly like its non-resistant counterpart.

Characteristics

S. media is an annual, winter annual and sometimes perennial herb, which emerges throughout the year. It is the most common Danish dicot weed (Andreasen, 1990), and the species is native to Europe. The species is self-pollinated and cleistogamous (Holm et al., 1977). In the models the sulfonylurea resistant S. media is treated as a separate population that is homozygous in the resistance loci, and its offspring do not segregate in a mendelian fashion. If S. medias, descending from the resistant individual, were assumed heterozygous in the resistant locus, then the offspring would segregate into homozygous resistant, heterozygous resistant and sensitive individuals. However, the fraction of sensitive individuals would rapidly diminish over the first generations (in F₁ 25% is non-resistant, in F₂ 17%, in F₃ 10% etc.).

5.2 Brassica campestris

Area grown with oilseed rape

Figure 5.1 shows the area grown with oilseed rape from 1976 to 1995. It is obvious that the area has increased almost exponentially during the first 10 years followed by a small decrease during the next 10 years. A survey on the occurrence of weed species in Danish arable fields, conducted in the period from 1987 to 1989, showed a low infestation of Brassica campestris in different crop types (Table 5.1). However, it will most likely take several decades for a weed species to stabilize its occurrence and density according to the land-use, and 10 years of intensive oilseed rape cropping is hardly enough time to expect a stabilized weed flora.

B. campestris as a weed

The herbicides used in cereal crops have traditionally been effective against B. campestris, and today large areas of cereal crops are sprayed with a sulfonylurea herbicides which are known for their efficacy against crucifeers (Chapter 4). The species is, however, tolerant to the same range of herbicides as oilseed rape, and it is therefore expected that an increased acreage with oilseed rape will increase the numbers of B. campestris.

Frequency and constancy of B. campestris and oilseed rape as weeds in Danish crops (Source: Andreasen, 1990).

B. campestris and oilseed rape are known to hybridize with relatively high frequencies. Jørgensen and Andersen (1994) found crossing frequencies of 13% on B. campestris and 9% on oilseed rape when the plants were growing in a 1:1 mixture, and if individuals of B. campestris were surrounded by oilseed rape the hybridization frequencies were up to 93% (Figure 5.2). B. campestris is known as a self-incompatible species, whereas oilseed rape is approximately 66% self-pollinating. Therefore, it is not surprising to find high hybridization frequencies on solitary B. campestris .

Fitness

Oilseed rape has a higher fitness (measured as survival in the field and seed production) than B. campestris, and the hybrid plants (F₁) seems to be intermediate the parental type (T. Hauser personal communications, 1997) but morphologically closer to oilseed rape (Jørgensen & Andersen, 1994). Seed production of the F₁ generation is not different from seed set on B. campestris. However, the next hybrid generation, F₂ or backcross BC₁, has a significantly lower seed production of only 16-28% of the seed set on B. campestris (Mikkelsen, 1996). Further backcrossings in the model are considered to be similar to B. campestris in growth habit and seed production.

Seed dormancy

Mikkelsen et al. (1996) showed that the hybrid generation has little seed dormancy, and in that respect it resembled oilseed rape. However, already in the first backcross several of the individuals were morphologically close to B. campstris and significant seed dormancy appeared in the BC₂.This means that the seed longevity in the soil will be prolonged, and thus that seeds of transgenic herbicide resistant individuals may survive several years after the seed shedding.

The model

In the model we have allowed for two hybridization scenarios: 1. The transgenic oilseed rape is homozygous for the herbicide resistance gene (used in the oilseed rape model), and 2. The transgenic oilseed rape is heterozygous for the gene. In reality we can expect a mixture of heterozygous and homozygous individuals (Kirsten Klitgaard, AgrEvo, personal communication). In the model we have simplified the process of gene transfer by only including one hybrid generation, after which, the seeds, which have the gene, are transferred to the seedbank for B. campestris. To account for the depression in seed production in BC₁ and F₂, we included a low harvest index for the F₁ generation (similar to the F₂-BC₁ generation). Oilseed rape and the F₁ have the same growth parameters and sensitive individuals of B. campestris, oilseed rape and oilseed rape volunteers are controlled with the same efficacy for each herbicide (for model equations and parameter values, see Appendix 2).

6 Output from the sugarbeet model

	6.1 Introduction
	6.2 Materials and methods
	6.3 Results
	6.4 Discussion

The content of this chapter was presented as a paper at the Second International Weed Control Congress in Copenhagen 1996 under the title ‘Simulation of herbicide use in a crop rotation with transgenic herbicide resistant sugarbeet’ by the authors K. H. Madsen, W. M. Blacklow and J. E. Jensen. The model was constructed during a five month study visit to University of Western Australia, Faculty of Agriculture in Perth.

6.1 Introduction

Background

In Denmark there is increasing public concern about the levels of pesticides used in agriculture, which has lead to an action plan to reduce pesticide use by 50% during the period from 1987 to 1997 (Haas, 1989; Thonke, 1991). This concern is, furthermore, raised in the debate over the merits of transgenic herbicide resistant crops (HRCs) in Danish agriculture. A specific concern is whether the introduction of HRCs will cause a consequential increase in herbicide use .

Concerns

It is expected that any weed population that is repeatedly treated with the same herbicides will change its composition towards species or biotypes with a higher natural tolerance to these herbicides. Furthermore, an extensive use of fewer herbicides and uncontrolled gene flow may lead to problems with resistant weeds. This may render the environmentally benign herbicides ineffective and leave the farmer with the older and not so environmentally benign herbicides if these are still available. These possibilities lead to environmental concerns about future herbicide use. Farmers need to know which combinations of resistance genes, crops, herbicide dose rates, application strategies and crop rotations will minimize the risk of losing the environmentally benign herbicides, because many of the environmentally malign herbicides may be banned in the future. Coupled to this requirement is the need to know strategies that will meet the requirements of the Danish Action Plan.

Present knowledge

Our present knowledge about the consequences of growing genetically modified HRCs on a large scale is limited because it is based primarily on small scale releases and on expected similarities with current agricultural practices.

Oilseed rape and sugarbeet

Two HCRs of current concern are oilseed rape and sugarbeet. Both species hybridize within the species as well as with wild relatives (Jørgensen & Andersen, 1994; Madsen, 1994). However, neither HRC had a greater competitive ability than non-transgenic cultivars (Fredshavn et al., 1995; Madsen, 1994). Consequently, herbicide-rates would need to be maintained in the HRCs.

Clearly, HRCs will have impacts on herbicide use. At this early stage in the release of HRCs, simulation provides a method to investigate these impacts. Specifically, the model considers herbicide use in glufosinate and glyphosate resistant sugarbeet in Denmark.

6.2 Materials and methods

STELLA

The model simulated the growth of crops and weeds in a rotation for sugarbeet and was programmed in STELLA (Peterson & Richmond, 1994). The model included four weed species (Chenopodium album, Stellaria media, Viola arvensis and Elytrygia repens). The weed species and volunteers regenerated in succeeding crops from a simulated seed bank (bank of propagules). Growth of the different species was modelled with logistic growth curves and competed for the site potential which was determined by the maximum biomass of the crop. The crop was sprayed with herbicides at a fixed biomass of weeds resulting in an efficacy of control dependent upon the weed species. Dicotyledonous (dicot) weeds in the barley and wheat crops were sprayed with a sulfonylurea herbicide. Grass weeds growing in cereal crops was controlled with a pre-harvest application of glyphosate when biomass of the grass weed exceeded a critical level at the end of the growing season.

Scenarios

The model simulated three scenarios for weed management in a rotation of sugarbeet - barley (Hordeum vulgare) - wheat (Triticum aestivum) - wheat rotation:

1. A non-transgenic sugarbeet sprayed with a mixture of metamitron, phenmedipham and ethofumesate for the control of the dicot weeds and a grass herbicide to control the grass weeds and cereal volunteers.

2. A glyphosate resistant sugarbeet sprayed only with glyphosate.

3. A glufosinate resistant sugarbeet sprayed only with glufosinate.

Input

Information for the model was from several sources (Madsen, Poulsen & Streibig, 1997):

	The crop rotation was constructed from agricultural statistics (Danmarks Statistik, 1994).
	Selection of weeds was based upon a recent Danish survey (Andreasen, 1990).
	Initial levels of weed seeds were estimated from a Danish survey (Jensen & Kjellsson, 1993).
	Initial levels of volunteers from different crops were estimated from the literature and field trials with sugarbeets (Alstedgaard, 1994).
	Herbicide doses were those currently recommended (Statens Planteavlsforsøg, 1997) and which were considered likely to be used in the future.

Appendix 1.

For specific model equations and parameter values used in the sugarbeet model, see appendix 1.

6.3 Results

Herbicide use

The model simulated the growth of crops and weeds for the three scenarios of weed control (Fig. 6.1), and the simulated levels corresponded with field experiences. In sugarbeet the critical levels of weed biomass that initiated a spraying were low and, consequently, the several herbicide applications predicted by the model agreed with the practice of weed control in this crop.

Herbicide use accumulated over time (Fig. 6.2). The greatest amounts of herbicide were applied to sugarbeet and spring barley was only sprayed between one and four times in the different scenarios (Fig. 6.2). Introduction of HR sugarbeet mainly decreased the amount of herbicide applied to that crop and had only minor influence on the amounts of herbicides applied to other crops in the rotation (Fig. 6.2). Over 20 years the total amount of herbicides used in the rotation was almost halved through the introduction of the HR sugarbeets.

6.4 Discussion

Model behaviour

The model simulated growth of crops and weeds in the four-year rotation through five cycles of the rotation. Applications of herbicides were triggered when the weed biomass reached critical levels. The simulated levels and dynamics of crops and weeds agree with those observed in the field. Furthermore, the simulated sprayings and levels of herbicides used in the rotation without HR sugarbeet agree with those used currently in the field. It can, therefore, be concluded that the model provides a basis for comparisons in herbicide use when HR sugarbeets are introduced into the rotation.

Assumptions

The introduction of HR sugarbeet into the model showed reductions in the amounts, and frequencies of herbicide use. These results were obtained under the assumptions that the introduction of HR sugarbeet will not change the current rotations, weed flora and herbicide use in other crops of the sugarbeet rotation. These assumptions can, and should, be challenged. The current simulation model can be extended to explore these assumptions.

Dose-response curves

More information is needed about herbicide efficacy on the weed species, volunteers and hybrids occurring in the HRC. These could be included in the model by experimentally determining the dose-response curves for the weedy species sprayed with (A) the herbicide used in the transgenic crop and (B) the herbicide(s) currently used. This makes it possible to compare efficacy at different dose levels of herbicide A based on practical use of herbicide B (Madsen & Jensen, 1995).

Other rotations

The simulation model can be adapted to investigate herbicide use in other rotations of Danish agriculture. Sugarbeet rotations occupy only 10% of Danish arable land and, although herbicide use on this land is currently high (Madsen et al. 1997), reductions in herbicide use in other rotations through the introduction of other HRCs have the potential to assist in meeting the objectives of the Danish Action Plan for pesticide use. Again, however, the present assumptions in the model about unchanging practices and flora as well as herbicide efficacy in different weeds need to be investigated. To these ends simulation and experiments need to be carried out on concert.

7 Output from the oilseed rape model

	7.1 Introduction
	7.2 Materials and methods
	7.3 Results
	7.4 Sensitivity of selected parameters
	7.5 Discussion
	7.6 Conclusions

7.1 Introduction

In this section we focus on the output from the oilseed rape model after 20 years under different scenarios with currently used herbicides (propyzamid and benazolin+clopyralid; only the former will be available to Danish farmers in the future), and two scenarios with transgenic glyphosate or glufosinate tolerant oilseed rape.

Crop rotation

The recommended crop rotation with oilseed rape is a six-year rotation with: oilseed rape - cereals - cereals - peas - cereals - cereals, but often oilseed rape is grown in a four-year rotation with three cereal crops in between. The main reason for this distance in time between succeeding oilseed rape crops is soil borne pests and diseases. In order to test the most simple rotation with the highest percentage of oilseed rape crops we chose to model the four-year rotation.

Thresholds

Propyzamide is normally applied to the soil during periods of cold temperatures and to simulate this, the model is restricted to spray with this herbicide during the winter period. In the cereals, the sulfonylurea (SU) herbicide: tribenuron is applied early in the season at a low threshold of weed biomass which allows for a spraying in both autumn and spring. Presently, most farmers would prefer metsulfuron in the spring, but this SU-herbicide is rather persistent in the soil which makes tribenuron the most likely herbicide choice for the future. For the scenarios with glyphosate and glufosinate, volunteer crops (crop plants acting as weeds in succeeding crops) are included in the threshold level for the oilseed rape crop, whereas the traditional oilseed rape scenarios use the same threshold based on dicotyledonous (dicot) weeds only. Elymus repens is controlled with a preharvest application with glyphosate in the cereal crops and in the traditional oilseed rape, Elymus repens and cereal volunteers can be controlled with fluazifop-P-buthyl.

Efficacy

The individual dose-response relationship of the herbicides on different weed species is (benazolin+clopyralid, glyphosat and glufosinate) based on experimental data from the greenhouse (Chapter 5). The dose-response curves for tribenuron-methyl were produced for the Danish PC-Plant Protection programme and have kindly been provided by Per Rydahl, from the Danish Agricultural Research. The dose-response relationships are well described for these herbicides, and the dose applied per spraying can therefore be changed resulting in a change of herbicide efficacy. For the remaining herbicides only efficacy at recommended dose is known, and these doses/efficacies are, therefore, fixed.

Resistance

The resistance alarm is induced when biomass of either volunteer oilseed rape, Brassica campestris or SU-resistant Stellaria media exceeds 25% of the total dicot weeds and volunteers biomass. In case of alarm, the model sprays with an additional herbicide (fluoxypyr) in the cereal crops. The frequency of resistant Stellaria media has been artificially set to initiate the SU-resistant Stellaria alarm in a hypothetical scenario with SU used in all crops.

7.2 Materials and methods

Prerequisites

The model (Fig. 7.1) is, in contrast to the ecophysiological model developed by Spitters and Kropff (Kropff, 1993), an empirical model based on alleged relationships, comparative studies between transgenic and non-transgenic crops, and practical experience from current crop rotations. The model presented here requires few growth related parameters and does not take climatic and soil conditions into account (for model parameters and equations, see Appendix 2).

Actual data

The model was based the following actual data: the crop rotation was constructed from Danish agricultural statistics (Danmarks Statistik, 1994; Madsen et al., 1997). Obtainable yields for crops were based on attainable yield levels. Selection of model weeds was based upon a recent Danish weed survey (Andreasen, 1990). Initial levels of different volunteer crops were estimated. Seed decay in the soil was assumed to be exponential. Crossing frequencies between oilseed rape and B. campestris were based on experimental data (Jørgensen & Andersen, 1994), from which inverse linear curves were extrapolated with the presence of one species relative to the other as the predictor. Data of a naturally occurring sulfonylurea-resistant Stellaria media (L.) Vill. in Denmark was from Kudsk et al. (1995) and the initial frequency was set at a high level (10^-4) corresponding to a worst case scenario which in the model caused resistance problems within 20 years in a hypothetical crop rotation with consistent sprayings with tribenuron-methyl in all crops. Herbicide resistant biotypes have similar fitness as the non-resistant biotypes of both crops and weeds (Madsen, 1994; Fredshavn et al., 1995; Jensen, 1993), however, biomass and seed production appear to be reduced in second generation hybrids (F₂ or BC₁) between oilseed rape and B. campestris (T. Hauser, personal communication). To account for the observed yield depression in later generations (which are not modelled separately), the harvest index from the hybrid was reduced in the model. The resistance trait segregated according to Mendelian principles. Recommended dose used for calculation of treatment frequency was 406 g a.i. ha^-1 for the mixture of benazolin and clopyralid and 375 g a.i. ha^-1 for fluazifop-P-butyl (Anonymous, 1995). As no recommended dose is yet available for the transgenic oilseed rape, we chose to use the Canadian recommendations for spring varieties of glyphosate tolerant ‘Roundup Ready Canola’ and the glufosinate tolerant ‘Liberty Link Canola’ for which the recommended dose was up to 445 g a.i. ha^-1 for glyphosate and up to 600 g a.i. ha^-1 for glufosinate (Anonymous, 1997).

Model development

The model (Fig. 7.1), programmed in STELLA II (Peterson & Richmond, 1994), simulated the growth of crops and weeds in a rotation with oilseed rape. It included six ‘model’ weed species.

Seed bank

The weed species and volunteers regenerate in succeeding crops from a seed bank (or for Elymus repens (L.) Gould from a bank of propagules). The number of seeds per species that yearly enter the seed bank was quantified as a linear function of the biomass present at harvest time:

N_input : Number of seeds m^-2 that enter seed bank

TCW: Thousand corn weight according to Korsmo et al. (1981)

HI: Harvest index

s: Proportion of seeds that survive from mature seed to seed bank

Y_t=h: Dry matter production g m^-2 (100 [t ha^-1]) at harvest time

Seed number that leaves the seed bank was determined by exponential seed decay and the number of seeds that germinate when the crop is sown:

N_output : Number of seeds m^-2 day^-1 that leave seed bank

N_total: Total number of seeds m^-2 in the seed bank of the species

d: Annual seed decay

e_t=s: Proportion of seeds that germinate when the crop is seeded

Growth and competition

Sigmoid growth curves described growth of the different species which competed for a yield potential determined by a maximum potential biomass of the crop:

Y_t+1₊₁: Dry matter production from day t to day t+1.

g: The relative growth rate day^-1

Y_t : Dry matter production up to time t

Y_Max: The maximum attainable biomass production ha^-1 for the species

Y_Total : The accumulated biomass produced t ha^-1 of all species in the model.

The simple competition model (eqn. 3) allowed the individual weed species to compete with each other as well as with the crop in order to obtain a share of the maximum available yield potential.

Weed control

At a fixed threshold of biomass of weeds, each crop was sprayed with herbicides. The efficacies depended upon the weed species, herbicide and dose. A realistic timing of application and numbers of sprayings was determined by the threshold levels, which were: propyzamide: 0.5 t ha^-1 of biomass of weeds and volunteers during winter; benazolin+clopyralid: 1 t ha^-1 of dicot weeds followed by fluazifop-P-butyl at 0.5 t ha^-1 of monocotyledonous weeds; glyphosate and glufosinate: 1.4 t weeds and volunteers ha^-1. Efficacy of glyphosate, glufosinate or the mixture of benazolin+clopyralid in the oilseed rape crop was determined by dose response curves (based on greenhouse experiments) for for S. media, Chenopodium album L., Capsella bursa-pastoris, Myosotis arvensis (L.) Hill, and oilseed rape (data are not shown); details on comparison of herbicide efficacy with the log-logistic dose-response model are found elsewhere (Streibig et al., 1993; Madsen & Jensen, 1995). The dose-response curves for B. campestris were assumed to be identical to the curve for oilseed rape. Dicot weeds in the barley and wheat crops were sprayed with a sulfonylurea herbicide, tribenuron-methyl (threshold: 0.1 t biomass ha^-1) with efficacy levels based on dose-response curves (P. Rydahl, personal communication). If the fraction of sulfonylurea-resistant/sensitive weeds exceeded 0.25 in the cereal crops, then fluroxypyr (144 g a.i. ha^-1) was added to the treatment. Where no dose-response relationships were available, the efficacy according to agronomic practice was used (propyzamide: 500 g a.i. ha^-1 and fluazifop-P-butyl: 188 g a.i. ha^-1). E. repens growing in cereal crops was controlled with a pre-harvest application of glyphosate (800 g ha^-1) when the development of this grass weed exceeded 0.3 t biomass ha^-1 at the end of the growing season.

The model simulated four scenarios for weed management in a rotation with winter varieties of oilseed rape - wheat (Triticum aestivum L.) - wheat - barley (Hordeum vulgare L.):

1. A non-transgenic oilseed rape sprayed only with propyzamide and fluazifop-P-butyl against E. repens and cereal volunteers.
2. A non-transgenic oilseed rape sprayed with a mixture of benazolin+clopyralid against dicot weeds and fluazifop-P-butyl against E. repens and cereal volunteers.
3. A glyphosate tolerant oilseed rape sprayed only with glyphosate.
4. A glufosinate resistant oilseed rape sprayed only with glufosinate.

7.3 Results

Simulating practice

The simulated growth of crops and weeds in Fig. 7.2 was used to evaluate different scenarios with herbicides in oilseed rape and a common herbicide for the cereal crops. The simple competition model allowed the individual weed species to compete with each other as well as with the crop in order to obtain a share of the maximum available yield potential. The thresholds were adjusted to simulate common practice with herbicide sprayings and were unchanged at different herbicide rates. When the threshold induced a spraying, it controlled the biomass of the individual weed species with a certain efficacy level, which was determined by the dose-response curve for the weed and herbicide combination. The controlled biomass then became available to the remaining crop and weeds. However, the spraying had favoured growth of the crop relative to growth of the weeds, as the relative weed biomass had diminished.

By including the greenhouse dose-response curves (Chapter 4) it was possible to test the effect of dose on accumulated herbicide use over 20 years which makes it possible to compare herbicide scenarios even though recommended dose and number of applications are not yet known. This can be used as part of a sensitivity analysis, but it also illustrates that sensitivity of herbicide-dose relationship varies with dose, because the closer the dose is to the steep part of the dose-response curves the more sensitive it becomes to adjustment. Furthermore, these runs showed that the minimum combination of dose and numbers of application, which will result in a satisfactory weed control, is not necessarily the lowest dose tested in the model.

Herbicide use

Herbicide use over 20 years was low for all scenarios compared to accumulated use in sugarbeets (Chapter 6), because current weed control in oilseed rape is conducted with relatively low herbicide doses. At the assumed recommended rate (based on Canadian recommendations) herbicide use over 20 years, measured in kg a.i. ha^-1, was similar for the scenarios with traditional and glyphosate tolerant oilseed rape, whereas it was higher in the scenario with glufosinate tolerant oilseed rape (Figs 7.3 and 7.4), however, if herbicide use was measured as treatment frequency, herbicide use was lower in the transgenic crops (Fig. 7.5). The difference in accumulated treatment frequency was rather consistent with changing rates per application, and the rotation with glyphosate or glufosinate tolerant oilseed rape had significantly lower treatment frequencies at different fractions of recommended rates (Fig 7.5). When rates were reduced below approx. 0.3 - 0.5 times recommended dose, the number of sprayings increased radically, thus making such scenarios unpractical (Fig. 7.6).

Crop yields

At the recommended rate (based on the Canadian recommendations) crop yield in the different scenarios was similar around 96-97% of the maximum yield level.

7.4 Sensitivity of selected parameters

The output from the different parameter settings used in the model varies with the chosen scenario. However, there are some general trends:

Growth rate

Growth rates of the crops and weeds are very sensitive to adjustments, because growth of a species is defined by only two parameters, growth rate and maximum biomass. However, growth is not the main focus of this model.

Dose

Sensitivity of the dose varies according to locations on the dose response curve for the individual herbicide/weed species. If doses vary around a rather flat curve at high efficacy levels, then the parameter is not sensitive, but if the dose varies around the ED₅₀ of the model (Chapter 4) then dose is a sensitive parameter.

Other parameters

The parameters that determine the loss of seed and seed decay for oilseed rape both seem sensitive at the tested range. Seed numbers and decay of Brassica campestris and Stellaria media seem less sensitive towards changes.

7.5 Discussion

Lack of data

The literature survey revealed lack of knowledge about growth characteristics of the individual weed species, and several parameters on harvest index, seed bank, growth rate and maximum biomass were estimated based on the expected behaviour in the system. Satisfactory data concerning survival and growth characteristics of weeds under field conditions would be indispensable when developing this kind of model and would not only have practical implications for predicting the herbicide use in genetically modified herbicide resistant crops, but also in any simulation model that deals with crop-weed competition.

Low dose herbicides

Compared with glyphosate and glufosinate, benazolin+clopyralid and propyzamide have low efficacy on several weed species which causes a shift toward more sprayings in the succeeding cereal crops with the SU-herbicide. Use of sulfonylureas adds only little to the amount of herbicide used, but adds equally to the other herbicides in terms of treatment frequency. This explains the contradicting conclusions about herbicide use.

SU-resistance

In the scenario where oilseed rape was sprayed with benazolin+clopyralid, the high number of SU applications, the cereal crops posed a high selection pressure on the weeds which favoured growth of SU-resistant Stellaria media, and at high rates the model induced fluoxypyr to be mixed with the SU-herbicide after 18 years of crop rotation, whereas no such problems occurred in the scenarios with glufosinate or glyphosate tolerant oilseed rape during the 20 years. It should, however, be emphasized that the initial frequency of SU-resistant Stellaria media was set at a high level in order to initiate resistance problem if SU was used in all crops.

Volunteers and hybrids Resistant volunteers and hybrids between oilseed rape and B. campestris were present but did not cause problems in any of the four scenarios. However, it is common knowledge that a SU herbicide, which was used in the cereal crops generally controls Brassica species effectively. This emphasises the importance of studying consequences for the complete rotation system, when a transgenic herbicide tolerant crop is introduced.

Number of treatment

Figures 7.4 and 7.5 leave the impression that total herbicide use can be decreased by lowering the dose indefinitely, but this strategy increases the number of treatments dramatically with a consequent unpractical increase in application costs (Fig. 7.6).

Treatment frequency 1996

In practical agriculture, average treatment frequency in 1996 was 0.95 in winter oilseed rape and 1.33 in winter cereals, which ‘all other things being equal’ means that the accumulated treatment frequency over 20 years is 25 standard recommended rates for this particular crop rotation (Miljøstyrelsen, 1996). The model predicts a treatment frequency of 25 for the traditional herbicide strategy with propyzamide and 27 for the strategy with benazolin+clopyralid. This indicates that the model simulated the crop rotation in accordance with current agricultural practices.

Predictions

The model described here is a first attempt to integrate knowledge about herbicide-tolerant crops with known agricultural practices. It should be emphasized that the model is preliminary and needs validation before any reliable predictions can be made about long-term consequences. In order to validate and adjust the model, short-term simulation results should later be compared with field data from crop rotations with transgenic herbicide tolerant crops after their release on the market. Baring these precautions in mind, we believe that the qualified prediction from the model is an improvement to just guessing, and the approach in our model could be used in revealing potential risks of growing herbicide-tolerant crops and thus prevent problems with unwise herbicide use and resistance in weeds and volunteers.

7.6 Conclusions

We constructed a simulation model of a crop rotation with oilseed rape that was able to compare different scenarios with herbicide tolerant oilseed rape. The model accounts for problems with volunteers, herbicide tolerant hybrids between oilseed rape and Brassica campestris herbicide tolerant weeds. At this stage of the model, there are still many unknown input variables, and further research into population dynamics of individual weed species is needed. It should also be emphasized that the model needs validation before any reliable predictions can be made about long-term consequences of growing transgenic herbicide tolerant oilseed rape. However, the simulation of the rotation with winter varieties of oilseed rape-wheat-wheat-barley showed ambiguous results for the two Danish defined measures of herbicide use, because herbicide use in the rotation with glyphosate or glufosinate tolerant oilseed rape was not reduced in kg a.i. ha^-1 compared to a traditional treatment, whereas treatment frequency decreased.

8 Canadian experiences

In the summer of 1997 the first author of this report went on a study visit to Saskatchewan in Canada in order to learn how herbicide tolerant oilseed rape is grown in this area. The Canadian farmers can already buy herbicide tolerant oilseed rape varieties with resistance to triazines, imidazolinones, glyphosate and glufosinate, however, only the two latter are transgenics.

General

The province of Saskatchewan stretches from 49° N to 60° N but only the southern part (the northern part of the American prairie) is cultivated. The province has less than 1 million inhabitants of which 16% live on farms. The climatic conditions with cold winter temperatures do not generally allow for winter crops (only minor areas in the north or south are grown with winter wheat). Summer temperatures vary from 5 to 25 degrees Celsius, and crops are usually planted in early May, grown to maturity within 95-100 days and harvested in September. Annual precipitation varies from 324-436 mm which limits the possibilities for continuous cropping in most regions, therefore, summer fallow is common. Soil types of Saskatchewan are to the south a brown belt (stretching from north/west to south/east) with dry soils of limited quality, a black belt and a grass belt up north which are the best soils, however, this area also has the shortest growing season. Average farm size was in 1991, 436 ha of which 329 was cultivated (Saskatchewan Agriculture and Food, 1996).

Approval procedure

One of the first transgenic crops to be developed in Canada was a sulfonylurea tolerant flax (Linum usitatissimum L.) (McHughen & Holm, 1995), and the regulatory procedures had to be constructed parallel to the development of this crop. The transgenic variety must be approved by two governmental institutions: ‘Agriculture and Agrofood Canada’ who evaluates the environmental aspects and feed safety and ‘Health Canada’ who evaluates food safety. Simultaneously, the variety is being field tested as other future varieties, and the results from two to three years of trials are evaluated by the ‘Prairie Registration Recommending Committee’.

The Saskatchewan canola area (Table 8.1) accounts for approximately 50% of the Canadian canola area and, for comparison the Danish area with oilseed rape is 152[ 10³ ha (Miljøstyrelsen, 1996). Canola is divided into ‘Argentine canola’ (Brassica napus) and ‘Polish canola’ (Brassica rapa). Polish canola needs fewer days to mature and is grown in areas where either precipitation is low or the season is short. Currently, there are no transgenic varieties of this species on the Canadian market.

Crop rotation

The typical canola rotation is a four year rotation to prevent disease problems:

	canola
	cereals
	peas or flax or another dicot crop
	cereals

Weeds

The fields inspected on this study visit were infested with Thlaspi arvense L. (Stinkweed), Sinapis arvensis (Wild mustard), Descurainia sophia L. Webb (Flixweed), Lactuca serriola L. (pricly lettuce) and/or Avena fatua (wild oats).

Main crops

Table 8.1

Traditionally trifluralin alone or in a mixture with ethalfluralin has been used to control weeds pre-emergence. The first application comes in the autumn and the second in spring . Approximately two out of three farmers will use an autumn application to get high efficacy and then spot spray post-emergence with an aryl-propanoic acid or cyclohexanedione herbicides for grass weeds, and ethametsulfuron methyl (an ALS-inhibitor) with 15-23 g a.i. ha^-1 for control of Sinapis arvensis, and clopyralid for control of thistles. In the cereal crops, the farmers can use a variety of herbicides, e.g. herbicides with auxin activity are available, in contrary to Danish conditions, and 2,4-D is an efficient option to control volunteer rapeseed. Otherwise a mixture of bromoxynil and MCPA is often chosen. ALS-inhibiting herbicides are seldomly used because of residual activity in the soil in the succeeding dicot crop (low temperatures and short seasons). The management system is slowly moving towards a no till system which relies on pre-emergence glyphosate applications for weed control followed by direct seeding of the crop.

Agronomic benefits

Herbicide resistant oilseed rape allows for post-emergence weed control and do not have to be incorporated into the soil which reduces risks of soil erosion and evaporation of soil moisture. With the traditional herbicides farmers often have to wait seeding the crop until herbicides have been incorporated into the soil, which in an area with a short growing season can be costly if early frost kills the crop (immature oilseed rape contains chlorophyll which can reduce crop value by 60%). If the problem is grass weeds, then the farmer will most likely prefer glyphosate tolerant oilseed rape, however, if wild mustard is a problem an imidazolinone resistant variety is preferable. Glufosinate is intermediate glyphosate and imidazolinones in efficacy. Farmers are not likely to use the same resistance mechanism in the next canola crop, that will depend on weed problems and seed/herbicide costs.

Herbicide tolerant varieties

Table 8.2

Seed price

Glufosinate is patented by AgrEvo, and the company covers the costs of developing the transgenic varieties by the increased sale of the herbicide. Glyphosate is off patent, therefore, Monsanto signs a ‘technology use agreement’ with the farmer before the farmer buys glyphosate tolerant seeds. This contract costs 37,5 CAD ha^-1 and furthermore restricts the farmer not to use the harvested seed for a new crop. Once the agreement is signed, the farmer will go to the grain company and buy the seed, as normally; so the contract is the costly part.

Farmer survey

Monsanto sent a questionnaire to 289 farmers who had grown glyphosate tolerant oilseed rape in 1996. The majority of these farmers had sprayed once with glyphosate with 445 g a.i. ha^-1 at the 3-4 leaf stage of the oilseed rape. A comparison was made between 31 of these farmers and 31 farmers with similar conditions growing non-transgenic oilseed rape varieties, and the net result was an average incremental return of 65 CAD ha^-1 (Monsanto, 1997).

Restrictions

There are no restrictions to the farmers management of the transgenic oilseed rape crops. However, the plant breeders must use a 10 m wide pollen catching belt of oilseed rape crop around the transgenic breeding material or 50 m distance to the nearest oilseed rape crop.

Hybrid systems

The hybrid-liberty system refers to a transgenic oilseed rape where pollen sterility is combined with glufosinate tolerance. It was developed by Plant Genetics Systems which is now part of AgrEvo. The system, which is not yet available to the farmer, allows for yield increases around 15-30% compared to normal free pollinated varieties. Glufosinate is used in the seed production to select for transgenic plants, but the farmers are likely to use the trait agronomically by spraying with glufosinate in the commercial production. AgrEvo will probably move the breeding programme towards this system. Other non-transgenic hybrid systems which uses cytoplasmatic male sterility can also be used to obtain hybrids, however the cytoplasmatic male sterility systems are more susceptible to environmental effects which can reduce the number of hybrid plants obtained (AgrEvo, 1997).

Concerns

In a minimal tillage situation, the farmer is dependent on glyphosate used pre-sowing to control weeds. Furthermore, glyphosate is used to control weeds in summer fallow. There is to date, however, only one occurrence of weed with increased tolerance to glyphosate, which is a biotype of Lolium rigidum from Australia (Heap, 1997).

Resistance to ALS-inhibitors is well-known in the Saskatchewan area and when farmers grow non-transgenic imidazolinone tolerant oilseed rape this will increase the selection pressure towards weed with resistance to these herbicides. However, Canadian farmers probably have less tradition for using ALS-inhibitors in the cereal crops compared to Danish farmers, which may delay the occurrence of resistance in weeds.

Conclusion

The transgenic varieties have only been marketed for a few years, and it is not yet possible to determine any long term effects of growing these crops. However, the weed management strategies used for the transgenic herbicide tolerant crops have already been determined and this gives an impression of how similar transgenic herbicide tolerant oilseed rape varieties will be grown in Europe.

9 Final comment

The models described in this report are first attempts to integrate knowledge about herbicide-tolerant crops with known agricultural practices. It should be emphasized that the models are preliminary and needs validation before any reliable predictions can be made about long-term consequences. The models are restricted to simulate one crop rotation with sugarbeet and one rotation with oilseed rape. The predictions from the models are therefore only valid for the chosen combination of crops, weeds and herbicide strategies .

To elaborate on the questions raised during the work requires hard data in that the data material in literature often fall short of what is needed in a simulation model

Baring these precautions in mind, we believe that the qualified predictions from this study are an improvement to just guessing, and the approach in our models could be used in revealing potential risks of growing herbicide-tolerant crops and thus prevent problems with unwise herbicide use and resistance in weeds and volunteers.

Appendix 1: Sugarbeet model - equations and parameters

BiomBarley(t) = BiomBarley(t - dt) + (GrowBarley + BarleySeed - HarvBarley) * dt

INIT BiomBarley = 0

GrowBarley = IF(MaxBarley>TotalBiom) THEN (RGRBarley*BiomBarley*(MaxBarley-TotalBiom)/MaxBarley) ELSE 0

BarleySeed = 0.18*BeginBarley

HarvBarley = IF EndBarley=1 THEN (BiomBarley+1)/DT ELSE 0

BiomSubeet(t) = BiomSubeet(t - dt) + (GrowSuBeet + SugarbeetSeed - HarvSugarBeet) * dt

INIT BiomSubeet = 0

GrowSuBeet = IF (RotationYear=1) AND (MaxSuBeet>TotalBiom) THEN(RGRSuBeet*BiomSubeet*(MaxSuBeet-TotalBiom)/(MaxSuBeet)) ELSE 0

SugarbeetSeed = 0.005*BeginSugarBeet

HarvSugarBeet = IF EndSugarBeet=1 THEN (BiomSubeet+1)/DT ELSE 0

BiomWheat(t) = BiomWheat(t - dt) + (GrowWheat + WheatSeed - HarvWheat) * dt

INIT BiomWheat = 0

GrowWheat = IF(MaxWheat>TotalBiom) THEN (Winterperiod*(RGRWheat*BiomWheat*(MaxWheat-TotalBiom)/MaxWheat))/DT ELSE 0

WheatSeed = 0.18*BeginWheat

HarvWheat = IF EndWheat=1 THEN (BiomWheat+1)/DT ELSE 0

MaxBarley = 15

MaxSuBeet = 15

MaxWheat = 18

RGRBarley = 0.075

RGRSuBeet = 0.06

RGRWheat = 0.04

BiomCHEAL(t) = BiomCHEAL(t - dt) + (GrowCHEAL + GermCHEAL - ControlCHEAL - DebriCHEAL) * dt

INIT BiomCHEAL = 0

GrowCHEAL = IF(MaxCHEAL>TotalBiom) THEN(Winterperiod*RGRCHEAL*BiomCHEAL*((MaxCHEAL-TotalBiom)/MaxCHEAL)) ELSE 0

GermCHEAL = DELAY(BeginWeed,1)*SeedbankCHEAL

ControlCHEAL = BiomCHEAL*EffiCHEAL

DebriCHEAL = EndWeed* (BiomCHEAL)

BiomELYRE(t) = BiomELYRE(t - dt) + (GrowELYRE + InitialELYRE - ControlELYRE - DebriELYRE) * dt

INIT BiomELYRE = 0

GrowELYRE = IF(BiomassCrop>0 AND MaxELYRE>TotalBiom) THEN(Winterperiod*RGRELYRE*BiomELYRE*((MaxELYRE-TotalBiom)/MaxELYRE)) ELSE 0

InitialELYRE = 0.05*ELYREinField*BeginWeed

ControlELYRE = BiomELYRE*EffiELYRE

DebriELYRE = EndWeed* (BiomELYRE)/DT*0.92

BiomSTEME(t) = BiomSTEME(t - dt) + (GrowSTEME + GermSTEME - ControlSTEME - DebriSTEME) * dt

INIT BiomSTEME = 0

GrowSTEME = IF(MaxSTEME>TotalBiom) THEN(Winterperiod*RGRSTEME*BiomSTEME*((MaxSTEME-TotalBiom)/MaxSTEME)) ELSE 0

GermSTEME = DELAY(BeginWeed,1)*SeedbankSTEME

ControlSTEME = BiomSTEME*EffiSTEME

DebriSTEME = EndWed* (BiomSTEME)

BiomVIOAR(t) = BiomVIOAR(t - dt) + (GrowVIOAR + GermVIOAR - ControlVIOAR - DebriVIOAR) * dt

INIT BiomVIOAR = 0

GrowVIOAR = IF(MaxVIOAR>TotalBiom) THEN(Winterperiod*RGRVIOAR*BiomVIOAR*((MaxVIOAR-TotalBiom)/MaxVIOAR)) ELSE 0

GermVIOAR = DELAY(BeginWeed,1)*SeedbankVIOAR

ControlVIOAR = BiomVIOAR*EffiVIOAR

DebriVIOAR = EndWeed* (BiomVIOAR)

SeedPoolCHEAL(t) = SeedPoolCHEAL(t - dt) + (NewSeedCHEAL - DeadSeedCHEAL) * dt

INIT SeedPoolCHEAL = 45297435.89744

NewSeedCHEAL = (DebriCHEAL)/DT*30000*1000/0.5

DeadSeedCHEAL = IF(BeginWeed=1) THEN SeedPoolCHEAL/3 ELSE 0

SeedPoolSTEME(t) = SeedPoolSTEME(t - dt) + (NewSeedSTEME - DeadSeedSTEME) * dt

INIT SeedPoolSTEME = 40333333.33333

NewSeedSTEME = (DebriSTEME)/DT*7000*1000/0.200

DeadSeedSTEME = IF(BeginWeed=1) THEN SeedPoolSTEME/3 ELSE 0

SeedPoolVIOAR(t) = SeedPoolVIOAR(t - dt) + (NewSeedVIOAR - DeadSeedVIOAR) * dt

INIT SeedPoolVIOAR = 35369230.76923

NewSeedVIOAR = (DebriVIOAR)/DT*600*1000/0.05

DeadSeedVIOAR = IF(BeginWeed=1) THEN SeedPoolVIOAR/3 ELSE 0

ELYREinField = 1

MaxCHEAL = 9.5

MaxELYRE = 14

MaxSTEME = 6

MaxVIOAR = 5

RGRCHEAL = 0.073

RGRELYRE = 0.034

RGRSTEME = 0.08

RGRVIOAR = 0.07

SeedbankCHEAL = SeedPoolCHEAL*0.01/1000000*0.05

SeedbankSTEME = SeedPoolSTEME*0.015/1000000*0.05

SeedbankVIOAR = SeedPoolVIOAR*0.02/1000000*0.05

BiomassCrop = BiomBarley+BiomSubeet+BiomWheat

BiomSenWeed = BiomCHEAL+BiomELYRE+BiomSTEME+BiomVIOAR

BiomSUResWeed = BiomSTEME_2

BioVolunteer = BiomBarley_2+BiomSubeet_2+BiomWheat_2

DicotWeeds = BiomCHEAL+BiomSTEME+BiomVIOAR+BiomSubeet_2+BiomSTEME_2

MonocotWeeds = BiomELYRE+BiomBarley_2+BiomWheat_2

SitePotential = 20

TotalBiom = (BiomassCrop+BiomSenWeed+BioVolunteer+BiomSUResWeed)

BiomSTEME_2(t) = BiomSTEME_2(t - dt) + (GrowSTEME_2 + GermSTEME_2 - ControlSTEME_2 - DebriSTEME_2) * dt

INIT BiomSTEME_2 = 0

GrowSTEME_2 = IF(MaxSTEME>TotalBiom) THEN(Winterperiod*RGRSTEME*BiomSTEME_2*((MaxSTEME-TotalBiom)/MaxSTEME)) ELSE 0

GermSTEME_2 = DELAY(BeginWeed,1)*SeedbankSTEME_2

ControlSTEME_2 = IF SU=0 THEN BiomSTEME_2*EffiSTEME ELSE 0

DebriTEME_2 = EndWeed* (BiomSTEME_2)

SeedPoolSTEME_2(t) = SeedPoolSTEME_2(t - dt) + (NewSeedSTEME_2 - DeadSeedSTEME_2) * dt

INIT SeedPoolSTEME_2 = 0

NewSeedSTEME_2 = (DebriSTEME_2)/DT*7000*1000/0.200

DeadSeedSTEME_2 = IF(BeginWeed=1) THEN SeedPoolSTEME_2/3 ELSE 0

IniSuSTEME_2 = 1/10000000

SeedbankSTEME_2 = (IniSuSTEME_2*SeedPoolSTEME*0.015/1000000*0.05)+(SeedPoolSTEME_2*0.015/1000000*0.05)

RotationYear(t) = RotationYear(t - dt) + (RotationYearRate - RotationYearReset) * dt

INIT RotationYear = 0

RotationYearRate = IF DaysInYear=1 THEN DaysInYear/DT ELSE 0

RotationYearReset = IF RotationYear>4 THEN ((RotationYear-1)/DT) ELSE(0)

Years(t) = Years(t - dt) + (YearRate) * dt

INIT Years = 0

YearRate = If DaysInYear=1 THEN DaysInYear/DT ELSE 0

BeginBarley = IF RotationYear=2 AND DaysInYear=75 THEN 1 ELSE 0

BeginSugarBeet = IF RotationYear=1 AND DaysInYear=90 THEN 1 ELSE 0

BeginWeed = IF (BeginBarley=1 OR BeginSugarBeet=1 OR BeginWheat=1) THEN 1 ELSE 0

BeginWheat = IF RotationYear>1 AND RotationYear<4 AND DaysInYear=258 THEN 1 ELSE 0

DaysInYear = COUNTER(1,366)

DaysTotal = TIME

EndBarley = IF RotationYear=2 AND DaysInYear=229 THEN 1 ELSE 0

EndSugarBeet = IF RotationYear=1 AND DaysInYear=304 THEN 1 ELSE 0

EndWeed = IF(EndBarley=1 OR EndSugarBeet=1 OR EndWheat=1) THEN 1 ELSE 0

EndWheat = IF RotationYear>2 AND DaysInYear=239 THEN 1 ELSE 0

Winterperiod = IF DaysInYear>325 OR DaysInYear<60 THEN 0 ELSE 1

BiomBarley_2(t) = BiomBarley_2(t - dt) + (GrowBarley_2 + BarleySeed_2 - HarvBarley_2 - WinterMortalityBarley_2 - ControlBarley_2) * dt

INIT BiomBarley_2 = 0

GrowBarley_2 = IF(MaxBarley_2>TotalBiom) THEN (Winterperiod*RGRBarley_2*BiomBarley_2*(MaxBarley_2-TotalBiom)/MaxBarley_2)/DT ELSE 0

BarleySeed_2 = DELAY(BeginWeed,1)*(SeedPoolBarley_2*0.7*0.05/1000000)

HarvBarley_2 = IF EndWeed=1 THEN (BiomBarley_2+1)/DT ELSE 0

WinterMortalityBarley_2 = IF Winterperiod=0 THEN BiomBarley_2*0.8 ELSE 0

ControlBarley_2 = BiomBarley_2*EffiBarley

BiomSubeet_2(t) = BiomSubeet_2(t - dt) + (GrowSuBeet_2 + SugarbeetSeed_2 - HarvSugarBeet_2 - ControlSBeet_2) * dt

INIT BiomSubeet_2 = 0

GrowSuBeet_2 = IF(MaxSuBeet_2>TotalBiom) THEN (Winterperiod*RGRSuBeet_2*BiomSubeet_2*(MaxSuBeet_2-TotalBiom)/(MaxSuBeet_2)) ELSE 0

SugarbeetSeed_2 = DELAY(BeginWeed,1)*(SeedPoolSugarBeet_2*0.7*0.04/1000000)

HarvSugarBeet_2 = IF EndWeed=1 THEN (BiomSubeet_2+1)/DT ELSE 0

ControlSuBeet_2 = BiomSubeet_2*EffiSugarBeet

BiomWheat_2(t) = BiomWheat_2(t - dt) + (GrowWheat_2 + WheatSeed_2 - HarvWheat_2 - ControlWheat_2) * dt

INIT BiomWheat_2 = 0

GrowWheat_2 = IF(MaxWheat_2>TotalBiom) THEN (Winterperiod*RGRWheat_2*BiomWheat_2*(MaxWheat_2-TotalBiom)/MaxWheat_2)/DT ELSE 0

WheatSeed_2 = DELAY(BeginWeed,1)*(SeedWheat_2*0.7*0.05/1000000)

HarvWheat_2 = IF EndWeed=1 THEN (BiomWheat_2+1)/DT ELSE 0

ControlWheat_2 = BiomWheat_2*EffiWheat

SeedPoolBarley_2(t) = SeedPoolBarley_2(t - dt) + (NewSeedBarley_2 - DeadSeedBarley_2) * dt

INIT SeedPoolBarley_2 = 0

NewSeedBarley_2 = (HarvBarley+HarvBarley_2-2)/DT*SeedLossBarley*0.5*1000000/0.05

DeadSeedBarley_2 = IF(BeginWeed=1) THEN SeedPoolBarley_2*95/100 ELSE 0

SeedPoolSugarBeet_2(t) = SeedPoolSugarBeet_2(t - dt) + (NewSeedSugarBeet_2 - DeadSeedSugarBeet_2) * dt

INIT SeedPoolSugarBeet_2 = 0

NewSeedSugarBeet_2 = (HarvSugarBeet+HarvSugarBeet_2-2)*(85000*2000*SeedLossSugarBeet/MaxSuBeet_2)

DeadSeedSugarBeet_2 = IF(BeginWeed=1) THEN SeedPoolSugarBeet_2*7/10 ELSE 0

SeedWheat_2(t) = SeedWheat_2(t - dt) + (NewSeedWheat_2 - DeadSeedWheat_2) * dt

INIT SeedWheat_2 = 0

NewSeedWheat_2 = (HarvWheat+HarvWheat_2-2)/DT*SeedLossWheat*0.5*1000000/0.05

DeadSeedWheat_2 = IF(BeginWeed=1) THEN SeedWheat_2*95/100 ELSE 0

MaxBarley_2 = 15

MaxSuBeet_2 = 15

MaxWheat_2 = 18

RGRBarley_2 = 0.07

RGRSuBeet_2 = 0.06

RGRWheat_2 = 0.04

SeedLossBarley = 0.05

SeedLossSugarBeet = 0.0025

SeedLossWheat = 0.05

DicotBarley(t) = DicotBarley(t - dt) + (SprayDicotBarley) * dt

INIT DicotBarley = 0

SprayDicotBarley = IF (BiomBarley>0) AND (DicotWeeds>1) THEN (DoseDicotBarley+DoseXtraBarley) ELSE 0

DicotWheat(t) = DicotWheat(t - dt) + (SprayDicotWheat) * dt

INIT DicotWheat = 0

SprayDicotWheat = IF(BiomWheat>0 AND BiomWheat<2) AND (DicotWeeds>0.5) THEN (DoseDicotWheat+DoseXtraWheat) ELSE 0

GlufHerbicidSugarBeet(t) = GlufHerbicidSugarBeet(t - dt) + (SprayGlufSugarBeet) * dt

INIT GlufHerbicidSugarBeet = 0

SprayGlufSugarBeet = IF (GlyphResSugarBeet=0 AND GlufResSugarBeet=1 AND SUResSugarBeet=0) AND (BiomSubeet>0 AND BiomSubeet<2) AND ((DicotWeeds+MonocotWeeds)>1.5) THEN DoseGlufSugarBeet ELSE 0

GlyphHerbicidSugarBeet(t) = GlyphHerbicidSugarBeet(t - dt) + (SprayGlyphSugarBeet) * dt

INIT GlyphHerbicidSugarBeet = 0

SprayGlyphSugarBeet = IF (GlyphResSugarBeet=1 AND GlufResSugarBeet=0 AND SUResSugarBeet=0 AND BiomSubeet>0.01 AND BiomSubeet<2 AND (DicotWeeds+MonocotWeeds)>1.5) THEN DoseGlyphSugarBeet ELSE 0

MonocotBarley(t) = MonocotBarley(t - dt) + (SprayMonocotBarley) * dt

INIT MonocotBarley = 0

SprayMonocotBarley = IF (BiomBarley>0) AND (DaysInYear=228) AND (BiomELYRE>1) THEN DoseMonocotBarley ELSE 0

MonocotHerbicidSugarBeet(t) = MonocotHerbicidSugarBeet(t - dt) + (SprayMonocotSugarBeet) * dt

INIT MonocotHerbicidSugarBeet = 0

SprayMonocotSugarBeet = IF (GlyphResSugarBeet=0 AND GlufResSugarBeet=0) AND (BiomSubeet>0 AND BiomSubeet<2.5) AND (MonocotWeeds>0.3) THEN DoseMonocotSugarBeet ELSE 0

MonocotWheat(t) = MonocotWheat(t - dt) + (SprayMonocotWheat) * dt

INIT MonocotWheat = 0

SprayMonocotWheat = IF (BiomWheat>10) AND (DaysInYear=238) AND (BiomELYRE>1) THEN DoseMonocotWheat ELSE 0

SUHerbicidSugarBeet(t) = SUHerbicidSugarBeet(t - dt) + (SpraySUSugarBeet) * dt

INIT SUHerbicidSugarBeet = 0

SpraySUSugarBeet = IF (GlyphResSugarBeet=0 AND GlufResSugarBeet=0 AND SUResSugarBeet=1) AND (BiomSubeet>0 AND BiomSubeet<0.9) AND (DicotWeeds>0.4) THEN (DoseSUSugarBeet+DoseXtraSugarbeet) ELSE 0

TradHerbicidSugarBeet(t) = TradHerbicidSugarBeet(t - dt) + (SprayTradSugarBeet) * dt

INIT TradHerbicidSugarBeet = 0

SprayTradSugarBeet = IF (GlyphResSugarBeet=0 AND GlufResSugarBeet=0 AND SUResSugarBeet=0) AND (BiomSubeet>0 AND BiomSubeet<0.9) AND (DicotWeeds>0.4) THEN DoseTradSugarBeet ELSE 0

DoseDicotBarley = WeedControl*0.007

DosDicotWheat = WeedControl*0.007

DoseGlufSugarBeet = 0.6*WeedControl

DoseGlyphSugarBeet = 0.72*WeedControl

DoseMonocotBarley = 3*0.360*WeedControl

DoseMonocotSugarBeet = 0.219*WeedControl

DoseMonocotWheat = 3*0.360*WeedControl

DoseSUSugarBeet = 0.007*WeedControl

DoseTradSugarBeet = 1.07*WeedControl

DoseXtraBarley = IF Problem=1 THEN 0.126 ELSE 0

DoseXtraSugarbeet = IF Problem=1 THEN 0.360 ELSE 0

DoseXtraWheat = IF Problem=1 THEN 0.144 ELSE 0

EffiBarley = EfGluBarley+EfGlyBarley+EfHalBarley

EffiCHEAL = EfGluCHEAL+EfGlyCHEAL+EfSUCHEAL+EfTradCHEAL+EfSUXtraCHEAL

EffiELYRE = EfGluELYRE+EfGlyELYRE+EfHalELYRE

EffiSTEME = EfGluSTEME+EfGlySTEME+EfSUSTEME+EfTradSTEME+EfSUXtraSTEME

EffiSugarBeet = EfGluSuBeet+EfGlySuBeet+EfSUSuBeet+EfSUXtraSuBeet

EffiVIOAR = EfGluVIOAR+EfGlyVIOAR+EfSUVIOAR+EfTradVIOAR+EfSUXtraVIOAR

EffiWheat = EfGluWheat+EfGlyWheat+EfHalWheat

EfGluBarley = IF Glufosinate>0 THEN 0.7 ELSE 0

EfGluCHEAL = IF Glufosinate>0 THEN 0.95 ELSE 0

EfGluELYRE = IF Glufosinate>0 THEN 0.7 ELSE 0

EfGluSTEME = IF Glufosinate>0 THEN 0.95 ELSE 0

EfGluSuBeet = IF GlufResSugarBeet=0 AND Glufosinate>0 THEN 0.7 ELSE 0

EfGluVIOAR = IF Glufosinate>0 THEN 0.75 ELSE 0

EfGluWheat = IF Glufosinate>0 THEN 0.7 ELSE 0

EfGlyBarley = IF SprayGlyphSugarBeet>0 THEN 0.99 ELSE 0

EfGlyCHEAL = IF SprayGlyphSugarBeet>0 THEN 0.95 ELSE 0

EfGlyELYRE = IF SprayGlyphSugarBeet>0 OR GlyphosatePreHarv>0 THEN 0.99 ELSE 0

EfGlySTEME = IF SprayGlyphSugarBeet>0 THEN 0.95 ELSE 0

EfGlySuBeet = IF GlyphResSugarBeet=0 AND SprayGlyphSugarBeet>0 THEN 0.99 ELSE 0

EfGlyVIOAR = IF SprayGlyphSugarBeet>0 THEN 0.75 ELSE 0

EfGlyWheat = IF SprayGlyphSugarBeet>0 THEN 0.99 ELSE 0

EfHalBarley = IF Haloxyfob_ethoxyethyl>0 THEN 0.95 ELSE 0

EfHalELYRE = IF Haloxyfob_ethoxyethyl>0 THEN 0.95 ELSE 0

EfHalWheat = IF Haloxyfob_ethoxyethyl>0 THEN 0.95 ELSE 0

EfSUCHEAL = IF SU>0 THEN 0.8 ELSE 0

EfSUSTEME = IF SU>0 THEN 0.8 ELSE 0

EfSUSuBeet = IF SUResSugarBeet=0 AND SU>0 THEN 0.98 ELSE 0

EfSUVIOAR = IF SU>0 THEN 0.75 ELSE 0

EfSUXtraCHEAL = IF SU&Xtra>0 THEN 0.9 ELSE 0

EfSUXtraSTEME = IF U&Xtra>0 THEN 0.9 ELSE 0

EfSUXtraSuBeet = IF SUResSugarBeet=0 AND SU&Xtra>0 THEN 0.98 ELSE 0

EfSUXtraVIOAR = IF SU&Xtra>0 THEN 0.8 ELSE 0

EfTradCHEAL = IF TradMixture>0 THEN 0.80 ELSE 0

EfTradSTEME = IF TradMixture>0 THEN 0.75 ELSE 0

EfTradVIOAR = IF TradMixture>0 THEN 0.60 ELSE 0

Glufosinate = SprayGlufSugarBeet

GlufResSugarBeet = 0

Glyphosate = SprayGlyphSugarBeet+GlyphosatePreHarv

GlyphosatePreHarv = SprayMonocotWheat+SprayMonocotBarley

GlyphResSugarBeet = 1

Haloxyfob_ethoxyethyl = SprayMonocotSugarBeet

HerbUseBarley = DicotBarley+MonocotBarley

HerbUseSugarBeet = GlufHerbicidSugarBeet+GlyphHerbicidSugarBeet+MonocotHerbicidSugarBeet+SUHerbicidSugarBeet+TradHerbicidSugarBeet

HerbUseWheat = DicotWheat+MonocotWheat

Problem = IF BiomSUResWeed/BiomSenWeed>0.25 THEN 1 ELSE 0

SU = IF Problem=0 THEN (SprayDicotBarley+SprayDicotWheat+SpraySUSugarBeet) ELSE 0

SU&Xtra = IF Problem=1 THEN (SprayDicotBarley+SprayDicotWheat+SpraySUSugarBeet) ELSE 0

SUResSugarBeet = 0

TotalHerbUse = HerbUseBarley+HerbUseSugarBeet+HerbUseWheat

TradMixture = SprayTradSugarBeet

WeedControl = 1

Appendix 2: Oilseed rape model - equations and parameters

BiomBRACARR(t) = BiomBRACARR(t - dt) + (GrowBRACARR + SowBRACARR - HarvBRACARR - ControlBRACARR) * dt

INIT BiomBRACARR = 0

GrowBRACARR = if (MaxBRACA>BiomTotal) THEN (Hybridization*Winter*RGRBRACA*BiomBRACARR*(MaxBRACA-BiomTotal)/MaxBRACA)/dt else 0

SowBRACARR = Delay(BeginWeed,1)*SeedBRACARR*GermBRACA*TKVBRACA*10000/(1000*1000000)/dt

HarvBRACARR = if EndWeed=1 then (BiomBRACARR+0.1) else 0

ControlBRACARR = BiomBRACARR*EFBRARe

BiomBRACARS(t) = BiomBRACARS(t - dt) + (GrowBRACARS + SowBRACARS - HarvBRACARS - ControlBRACARS) * dt

INIT BiomBRACARS = 0

GrowBRACARS = if (MaxBRACA>BiomTotal) THEN (Hybridization*Winter*RGRBRACA*BiomBRACARS*(MaxBRACA-BiomTotal)/MaxBRACA)/dt else 0

SowBRACARS = Delay(BeginWeed,1)*SeedBRACARS*GermBRACA*TKVBRACA*10000/(1000*1000000)/dt

HarvBRACARS = if EndWeed=1 then (BiomBRACARS+0.1) else 0

ControlBRACARS = BiomBRACARS*EFBRARe

BiomBRACASS(t) = BiomBRACASS(t - dt) + (GrowBRACASS + SowBRACASS - HarvBRACASS - ControlBRACASS) * dt

INIT BiomBRACASS = 0

GrowBRACASS = if (MaxBRACA>BiomTotal) THEN (Hybridization*Winter*RGRBRACA*BiomBRACASS*(MaxBRACA-BiomTotal)/MaxBRACA)/dt else 0

SowBRACASS = Delay(BeginWeed,1)*SeedBRACASS*GermBRACA*TKVBRACA*10000/(1000*1000000)/dt

HarvBRACASS = if EndWeed=1 then (BiomBRACASS+0.1) else 0

ControlBRACASS = BiomBRACASS*EFBRASe

SeedBRACARR(t) = SeedBRACARR(t - dt) + (NewSeedBRACARR - DeadSeedBRACARR) * dt

INIT SeedBRACARR = 0

NewSeedBRACARR = ((HarvF1*0.25*HIBRACAF1)+((HarvBRACARR*HarvBRACARR+HarvBRACARS*HarvBRACARR+0.25*HarvBRACARS*HarvBRACARS)/BRACAtot)*HIBRACA)*NonPredBRACA*1000000*1000/(TKVBRACA*10000)/dt

DeadSeedBRACARR = (SeedBRACARR*(1-EXP(LOGN(1-DecayBRACA)/365))+BeginWeed*SeedBRACARR*GermBRACA)/dt

SeedBRACARS(t) = SeedBRACARS(t - dt) + (NewSeedBRACARS - DeadSeedBRACARS) * dt

INIT SeedBRACARS = 0

NewSeedBRACARS = ((HarvF1*0.5*HIBRACAF1)+((HarvBRACARR*HarvBRACARS+2*HarvBRACARR*HarvBRACASS+0.5*HarvBRACARS*HarvBRACARS+HarvBRACARS*HarvBRACASS)/BRACAtot)*HIBRACA)*NonPredBRACA*1000000*1000/(TKVBRACA*10000)/dt

DeadSeedBRACARS = (SeedBRACARS*(1-EXP(LOGN(1-DecayBRCA)/365))+BeginWeed*SeedBRACARS*GermBRACA)/dt

SeedBRACASS(t) = SeedBRACASS(t - dt) + (NewSeedBRACASS - DeadSeedBRACASS) * dt

INIT SeedBRACASS = 200

NewSeedBRACASS = ((HarvF1*0.25*HIBRACAF1)+((0.25*HarvBRACARS*HarvBRACARS+HarvBRACASS*HarvBRACARS+HarvBRACASS*HarvBRACASS)/BRACAtot))*HIBRACA*NonPredBRACA*1000000*1000/(TKVBRACA*10000)/dt

DeadSeedBRACASS = (SeedBRACASS*(1-EXP(LOGN(1-DecayBRACA)/365))+BeginWeed*SeedBRACASS*GermBRACA)/dt

HIBRACAF1 = 0.05

BiomWBarley(t) = BiomWBarley(t - dt) + (GrowWBarley + SowWBarley - HarvWBarley) * dt

INIT BiomWBarley = 0

GrowWBarley = if (MaxWBarley>BiomTotal) THEN (Winter*RGRWBarley*BiomWBarley*(MaxWBarley-BiomTotal)/MaxWBarley)/dt else 0

SowWBarley = if BeginWBarley=1 then SeedWBarley/dt else 0

HarvWBarley = if EndWBarley=1 then (BiomWBarley+0.1)/dt else 0

BiomWRape(t) = BiomWRape(t - dt) + (GrowWRape + SowWRape - HarvWRape) * dt

INIT BiomWRape = 0

GrowWRape = if (MaxWRape>BiomTotal) THEN (Winter*RGRWRape*BiomWRape*(MaxWRape-BiomTotal)/MaxWRape)/dt else 0

SowWRape = if BeginWRape=1 then SeedWRape/dt else 0

HarvWRape = if EndWRape=1 then (BiomWRape+0.1)/dt else 0

BiomWWheat(t) = BiomWWheat(t - dt) + (GrowWWheat + SowWWheat - HarvWWheat) * dt

INIT BiomWWheat = 0

GrowWWheat = if (MaxWWheat>BiomTotal) THEN (Winter*RGRWWheat*BiomWWheat*(MaxWWheat-BiomTotal)/MaxWWheat)/dt else 0

SowWWheat = IF(BeginWWheat)=1 THEN(SeedWWheat)/dt else 0

HarvWWheat = IF (EndWWheat)=1 THEN (BiomWWheat+0.1)/dt ELSE(0)

HIWBarley = 0.4

HIWRape = 0.25

HIWWheat = 0.40

MaxWBarley = 6.5*0.85/HIWBarley

MaxWRape = 3.8*0.92/HIWRape

MaxWWheat = 8.6*0.85/HIWWheat

RGRWBarley = 0.051

RGRWRape = 0.067

RGRWWheat = 0.042

SeedWBarley = 160*0.87/1000

SeedWRape = 5*0.92/1000

SeedWWheat = 180*0.87/1000

BiomF1(t) = BiomF1(t - dt) + (GrowF1 + SowF1 - HarvF1 - ControlF1) * dt

INIT BiomF1 = 0

GrowF1 = if (MaxWRape>BiomTotal) THEN (Hybridization*Winter*RGRWRape*BiomF1*(MaxWRape-BiomTotal)/MaxWRape)/dt else 0

SowF1 = (Delay(BeginWeed,1)*SeedF1*GermWRapeVol*TKWWRape/(1000*1000000))/dt

HarvF1 = if EndWeed=1 then (BiomF1+0.1)/dt ele 0

ControlF1 = BiomF1*EFBRARe

SeedF1(t) = SeedF1(t - dt) + (NewSeedF1 - DeadSeedF1) * dt

INIT SeedF1 = 0

NewSeedF1 = IF (Bn_Rr?=0) THEN (HarvBRACASS*1/(1.075+13.293*HarvBRACASS/(HarvBRACASS+HarvWRape))+(HarvWRape*LossWRape*1/(3.03+16.299*(HarvWRape/HarvBRACASS+HarvWRape))))*DormWRape*HIBRACA*1000000*1000/TKWWRape/dt

ELSE

0.5*(HarvBRACASS*1/(1.075+13.293*HarvBRACASS/(HarvBRACASS+HarvWRape))+(HarvWRape*LossWRape*1/(3.03+16.299*(HarvWRape/HarvBRACASS+HarvWRape))))*DormWRape*HIBRACA*1000000*1000/TKWWRape/dt

DeadSeedF1 = (SeedF1*(1-EXP(LOGN(1-DecayWRape)/365))+BeginWeed*SeedF1*GermWRapeVol)/dt

Hybridization = 1

BiomWRapeVolRe(t) = BiomWRapeVolRe(t - dt) + (GrowWRapeVolRe + SowWRapeVolRe - HarvWRapeVolRe - ControlWRapeVolRe) * dt

INIT BiomWRapeVolRe = 0

GrowWRapeVolRe = if (MaxWRape>BiomTotal) THEN (Winter*RGRWRape*BiomWRapeVolRe*(MaxWRape-BiomTotal)/MaxWRape)/dt else 0

SowWRapeVolRe = (Delay(BeginWeed,1)*(SeedBnReRe*GermWRapeVol*TKWWRape)/(1000*1000000))/dt

HarvWRapeVolRe = if EndWeed=1 then (BiomWRapeVolRe+0.1)/dt else 0

ControlWRapeVolRe = BiomWRapeVolRe*EFBRARe

BiomWRapeVolReSe(t) = BiomWRapeVolReSe(t - dt) + (GrowWRapeVolReSe + SowWRapeVolReSe - HarvWRapeVolReSe - ControlWRapeVolReSe) * dt

INIT BiomWRapeVolReSe = 0

GrowWRapeVolReSe = if (MaxWRape>BiomTotal) THEN (Winter*RGRWRape*BiomWRapeVolReSe*(MaxWRape-BiomTotal)/MaxWRape)/dt else 0

SowWRapeVolReSe = (Delay(BeginWeed,1)*(SeedBnReSe)*GermWRapeVol*TKWWRape/(1000*1000000))/dt

HarvWRapeVolReSe = if EndWeed=1 then (BiomWRapeVolReSe+0.1)/dt else 0

ControlWRapeVolReSe = BiomWRapeVolReSe*EFBRARe

BiomWRapeVolSe(t) = BiomWRapeVolSe(t - dt) + (GrowWRapeVolSe + SowWRapeVolSe - HarvWRapeVolSe - ControlWRapeVolSe) * dt

INIT BiomWRapeVolSe = 0

GrowWRapeVolSe = if (MaxWRape>BiomTotal) THEN (Winter*RGRWRape*BiomWRapeVolSe*(MaxWRape-BiomTotal)/MaxWRape)/dt else 0

SowWRapeVolSe = (Delay(BeginWeed,1)*SeedBnSeSe*GermWRapeVol*TKWWRape/(1000*1000000))/dt

HarvWRapeVolSe = if EndWeed=1 then (BiomWRapeVolSe+0.1)/dt else 0

ControlWRapeVolSe = BiomWRapeVolSe*EFBRASe

SeedBnReRe(t = SeedBnReRe(t - dt) + (NewSeedBnReRe - DeadSeedBnReRe) * dt

INIT SeedBnReRe = 0

NewSeedBnReRe = IF (HarvWRape>0.01) THEN ((HarvWRapeVolRe+(HarvWRape+HarvWRapeVolReSe)*0.25)*Bn_Rr?*LossWRape*DormWRape*HIWRape*1000000*1000/TKWWRape)/dt

ELSE

((HarvWRapeVolRe+HarvWRapeVolReSe*0.25)*Bn_Rr?*DormWRape*HIWRape*1000000*1000/TKWWRape)/dt

DeadSeedBnReRe = (SeedBnReRe*(1-EXP(LOGN(1-DecayWRape)/365))+BeginWeed*SeedBnReRe*GermWRapeVol)/dt

SeedBnReSe(t) = SeedBnReSe(t - dt) + (NewSeedBnReSe - DeadSeedBn_ReSe) * dt

INIT SeedBnReSe = 0

NewSeedBnReSe = IF (HarvWRape>0.01) THEN ((HarvWRape+HarvWRapeVolReSe)*0.5*Bn_Rr?*LossWRape*DormWRape*HIWRape*1000000*1000/TKWWRape)/dt

ELSE

((HarvWRapeVolReSe*0.5*Bn_Rr?)*DormWRape*HIWRape*1000000*1000/TKWWRape)/dt

DeadSeedBn_ReSe = (SeedBnReSe*(1-EXP(LOGN(1-DecayWRape)/365))+BeginWeed*SeedBnReSe*GermWRapeVol)/dt

SeedBnSeSe(t) = SeedBnSeSe(t - dt) + (NewSeedBnSeSe - DeadSeedBnSeSe) * dt

INIT SeedBnSeSe = 0

NewSeedBnSeSe = IF (HarvWRape>0.01) THEN ((HarvWRapeVolSe+(HarvWRape+HarvWRapeVolReSe)*0.25)*Bn_Rr?*LossWRape*DormWRape*HIWRape*1000000*1000/TKWWRape)/dt

ELSE

((HarvWRapeVolSe+HarvWRapeVolReSe*0.25)*Bn_Rr?*DormWRape*HIWRape*1000000*1000/TKWWRape)/dt

DeadSeedBnSeSe = (SeedBnSeSe*(1-EXP(LOGN(1-DecayWRape)/365))+BeginWeed*SeedBnSeSe*GermWRapeVol)/dt

Bn_Rr? = 0

BiomCereals = BiomWBarley+BiomWWheat

BiomCrop = BiomWBarley+BiomWRape+BiomWWheat

BiomTotal = BiomCrop+BiomVol+BiomWeeds

BiomVol = BiomWBarleyVol+BiomWWheatVol+DicotVol

BiomWeeds = DicotWeed+BiomELYRE

BRACAhybtot = BiomF1+BRACAtot+BiomBRACA

BRACAtot = BiomBRACARR+BiomBRACARS+BiomBRACASS

DicotVol = BiomWRapeVolRe+BiomWRapeVolReSe+BiomWRapeVolSe+BiomWRapeVol

DicotWeed = BiomCABP+BiomCHEAL+BiomMYOAR+BiomSTEME+BRACAhybtot+BiomSTEMESU

DicotWeedVol = DicotWeed+DicotVol

MonocotWeedVol = BiomELYRE+BiomWBarleyVol+BiomWWheatVol

WeedsVolTotal = DicotWeedVol+MonocotWeedVol

WeedVolNoOSR = DicotWeed+MonocotWeedVol

BiomSTEMESU(t) = BiomSTEMESU(t - dt) + (GrowSTEMESU + SowSTEMESU - HarvSTEMESU - ControlSTEMESU) * dt

INIT BiomSTEMESU = 0

GrowSTEMEU = if (MaxSteme>BiomTotal) THEN ((Winter*RGRSTEME*BiomSTEMESU*(MaxSteme-BiomTotal))/MaxSteme)/dt else 0

SowSTEMESU = Delay(BeginWeed,1)*(SeedSTEME*Mutation_Frq+SeedSTEMESU)*10000*GermSTEME*TKVSTEME/(1000*1000000)/dt

HarvSTEMESU = if EndWeed=1 then (BiomSTEMESU+0.1) else 0

ControlSTEMESU = BiomSTEMESU*EFSTEMESU

SeedSTEMESU(t) = SeedSTEMESU(t - dt) + (NewSeedSTEMESU - DeadSeedSTEMESU) * dt

INIT SeedSTEMESU = 0

NewSeedSTEMESU = (HarvSTEMESU)*NonPredSTEME*HISTEME*1000000*1000/(10000*TKVSTEME)/dt

DeadSeedSTEMESU = (SeedSTEMESU*(1-EXP(LOGN(1-DecaySteme)/365))+BeginWeed*SeedSTEMESU*GermSTEME)/dt

Mutation_Frq = 1/10000

RotationYear(t) = RotationYear(t - dt) + (RotationYearRate - RotationYearReset) * dt

INIT RotationYear = 0

RotationYearRate = if DayInYear=365 then 1/DT else 0

RotationYearReset = IF(RotationYear)=4 and DayInYear=365 then (RotationYear)/DT else 0

BeginWBarley = if WBarleynr=1 and DayInYear=259 then 1 else 0

BeginWeed = if BeginWBarley=1 or BeginWRape=1 or BeginWWheat=1 then 1 else 0

BeginWRape = IF(WRapenr=1) and DayInYear=228 then 1 else 0

BeginWWheat = If (WWheatnr=1) and DayInYear=280 then 1 else 0

DayInYear = COUNTER(1,366)

EndWBarley = DELAY(BeginWBarley,308)

EndWeed = if EndWBarley=1 or EndWRape=1 or EndWWheat=1 then 1 else 0

EndWRape = DELAY(BeginWRape,351)

EndWWheat = DELAY(BeginWWheat,308)

SumAnn = If RotationYear>0 and DayInYear=76 then 1 else 0

WBarleynr = if (RotationYear=3) then 1 else 0

Winter = IF DayInYear<90 or DayInYear>320 then 0 else 1

WRapenr = IF (RotationYear=0 OR RotationYear=4) then 1 else 0

WWheatnr = if (RotationYear=1 or RotationYear=2) then 1 else 0

BiomWBarleyVol(t) = BiomWBarleyVol(t - dt) + (GrowWBarley_2 + SowWBarleyVol - HarvWBarleyVol - ControlWBarleyVol) * dt

INIT BiomWBarleyVol = 0

GrowWBarley_2 = if (MaxWBarley>BiomTotal) THEN (Winter*RGRWBarley*BiomWBarleyVol*(MaxWBarley-BiomTotal)/MaxWBarley)/dt else 0

SowWBarleyVol = (Delay(BeginWeed,1)*SeedWBarleyVol *GermWBarleyVol*TKWWBarley/(1000*1000000))/dt

HarvWBarleyVol = if EndWeed=1 then (BiomWBarleyVol+0.1)/dt ele 0

ControlWBarleyVol = BiomWBarleyVol*EFWBarley

BiomWRapeVol(t) = BiomWRapeVol(t - dt) + (GrowWRapeVol + SowWRapeVol - HarvWRapeVol - ControlWRapeVol) * dt

INIT BiomWRapeVol = 0

GrowWRapeVol = if (MaxWRape>BiomTotal) THEN (Winter*RGRWRape*BiomWRapeVol*(MaxWRape-BiomTotal)/MaxWRape)/dt else 0

SowWRapeVol = (Delay(BeginWeed,1)*SeedWRapeVol*GermWRapeVol*TKWWRape/(1000*1000000))/dt

HarvWRapeVol = if EndWeed=1 then (BiomWRapeVol+0.1)/dt else 0

ControlWRapeVol = BiomWRapeVol*EFBRARe

BiomWWheatVol(t) = BiomWWheatVol(t - dt) + (GrowWWheatVol + SowWWheatVol - HarvWWheatVol - ControlWWheatVol) * dt

INIT BiomWWheatVol = 0

GrowWWheatVol = if (MaxWWheat>BiomTotal) THEN (Winter*RGRWWheat*BiomWWheatVol*(MaxWWheat-BiomTotal)/MaxWWheat)/dt else 0

SowWWheatVol = (Delay(BeginWeed,1)*SeedWWheatVol *GermWWheatVol*TKWWWheat/(1000*1000000))/dt

HarvWWheatVol = IF (EndWeed)=1 THEN (BiomWWheatVol+0.1)/dt ELSE(0)

ControlWWheatVol = BiomWWheatVol*EFWWheat

SeedWBarleyVol(t) = SeedWBarleyVol(t - dt) + (NewSeedWBarleyVol - DeadSeedWBarleyVol) * dt

INIT SeedWBarleyVol = 0

NewSeedWBarleyVol = (((HarvWBarley+HarvWBarleyVol)*LossWBarley*DormWBarley*HIWBarley*1000000*1000)/(TKWWBarley))/dt

DeadSeedWBarleyVol = (SeedWBarleyVol*(1-EXP(LOGN(1-DecayWBarley)/365))+BeginWeed*SeedWBarleyVol*GermWBarleyVol)/dt

SeedWRapeVol(t) = SeedWRapeVol(t - dt) + (NewSeedWRapeVol - DeadSeedWRapeVol) * dt

INIT SeedWRapeVol = 0

NewSeedWRapeVol = IF (HarvWRape>0.01 AND Bn_Rr?=0) THEN ((HarvWRape+HarvWRapeVol)*LossWRape*DormWRape*HIWRape*1000000*1000/TKWWRape)/dt

ELSE

((-1)*(Bn_Rr?-1)* (HarvWRape*LossWRape+HarvWRapeVol)*DormWRape*HIWRape*1000000*1000/TKWWRape)/dt

DeadSeedWRapeVol = (SeedWRapeVol*(1-EXP(LOGN(1-DecayWRape)/365))+BeginWeed*SeedWRapeVol*GermWRapeVol)/dt

SeedWWheatVol(t) = SeedWWheatVol(t - dt) + (NewSeedWWheatVol - DeadSeedWWheatVol) * dt

INIT SeedWWheatVol = 0

NewSeedWWheatVol = ((HarvWWheat+HarvWWheatVol)*LossWwheat*DormWWheat*HIWWheat*1000000*1000)/(TKWWWheat)/dt

DeadSeedWWheatVol = (SeedWWheatVol*(1-EXP(LOGN(1-DecayWWheat)/365))+BeginWeed*SeedWWhetVol*GermWWheatVol)/dt

DecayWBarley = 0.99999

DecayWRape = 0.90

DecayWWheat = 0.99999

DormWBarley = 0.15

DormWRape = 0.025

DormWWheat = 0.15

GermWBarleyVol = 0.33

GermWRapeVol = 0.20

GermWWheatVol = 0.33

LossWBarley = 0.10

LossWRape = 0.10

LossWwheat = 0.1

TKWWBarley = 44

TKWWRape = 5.3

TKWWWheat = 44

AccCropYield(t) = AccCropYield(t - dt) + (AnnCropYield) * dt

INIT AccCropYield = 0

AnnCropYield = BiomCrop*EndWeed/dt

AccTotalYield(t) = AccTotalYield(t - dt) + (AnnTotalYield) * dt

INIT AccTotalYield = 0

AnnTotalYield = BiomTotal*EndWeed/dt

Scen125acc(t) = Scen125acc(t - dt) + (SprayScen125) * dt

INIT Scen125acc = 0

SprayScen125 = IF (BiomWRape>0 AND (Scenario?=1 OR Scenario?=2 OR Scenario?=5) AND Winter=1 AND MonocotWeedVol>0.5) THEN (WeedControl?*DoseFluazifop) ELSE (0)

Scen125TFq(t) = Scen125TFq(t - dt) + (Scen125NrRate) * dt

INIT Scen125TFq = 0

Scen125NrRate = If SprayScen125>0 THEN 1 ELSE 0

Scen1acc(t) = Scen1acc(t - dt) + (SprayScen1) * dt

INIT Scen1acc = 0

SprayScen1 = IF (BiomWRape>0 AND Scenario?=1 AND DayInYear=321 AND WeedVolNoOSR>0.5) THEN (WeedControl?*DosePropamid) ELSE (0)

Scen1TFq(t) = Scen1TFq(t - dt) + (Scen1NrRate) * dt

INIT Scen1TFq = 0

Scen1NrRate = If SprayScen1>0 THEN 1 ELSE 0

Scen2acc(t) = Scen2acc(t - dt) + (SprayScen2) * dt

INIT Scen2acc = 0

SprayScen2 = IF (BiomWRape>0 AND Scenario?=2 AND Winter=1 AND (DayInYear<165 OR DayInYear>228) AND DicotWeed>1) THEN (WeedControl?*DoseBenasa) ELSE (0)

Scen2TFq(t) = Scen2TFq(t - dt) + (Scen2NrRate) * dt

INIT Scen2TFq = 0

Scen2NrRate = If SprayScen2>0 THEN 1 ELSE 0

Scen3acc(t) = Scen3acc(t - dt) + (SprayScen3) * dt

INIT Scen3acc = 0

SprayScen3 = IF (BiomWRape>0 AND Scenario?=3 AND Winter=1 AND (DayInYear<165 OR DayInYear>228) AND WeedVolNoOSR>1.4) THEN (WeedControl?*DoseGlyphosate) ELSE (0)

Scen3TFq(t) = Scen3TFq(t - dt) + (Scen3NrRate) * dt

INIT Scen3TFq = 0

Scen3NrRate = If SprayScen3>0 THEN 1 ELSE 0

Scen4acc(t) = Scen4acc(t - dt) + (SprayScen4) * dt

INIT Scen4acc = 0

SprayScen4 = IF (BiomWRape>0 AND Scenario?=4 AND Winter=1 AND (DayInYea< 165 OR DayInYear>228) AND WeedVolNoOSR>1.4) THEN (WeedControl?*DoseGlufosinate) ELSE (0)

Scen4TFq(t) = Scen4TFq(t - dt) + (Scen4NrRate) * dt

INIT Scen4TFq = 0

Scen4NrRate = If SprayScen4>0 THEN 1 ELSE 0

Scen5acc(t) = Scen5acc(t - dt) + (SprayScen5) * dt

INIT Scen5acc = 0

SprayScen5 = IF (BiomWRape>0 AND Scenario?=5 AND Winter=1 AND Scen5TFq_2<2.9 AND (DayInYear<165 OR DayInYear>228) AND DicotWeed>0.8) THEN (WeedControl?*DoseSUWRape) ELSE (0)

Scen5TFq(t) = Scen5TFq(t - dt) + (Scen5NrRate) * dt

INIT Scen5TFq = 0

Scen5NrRate = If SprayScen5>0 THEN 1 ELSE 0

Scen5TFq_2(t) = Scen5TFq_2(t - dt) + (Scen5NrRate_2 - Reset5TFq) * dt

INIT Scen5TFq_2 = 0

Scen5NrRate_2 = If SprayScen5>0 THEN 1 ELSE 0

Reset5TFq = IF DayInYear=210 THEN Scen5TFq_2 ELSE 0

ScenCDicotacc(t) = ScenCDicotacc(t - dt) + (SprayCDicot) * dt

INIT ScenCDicotacc = 0

SprayCDicot = IF (BiomCereals>0 AND Winter=1 AND DicotWeedVol>0.1) THEN (WeedControl?*DoseSU) ELSE (0)

ScenCDicotTFq(t) = ScenCDicotTFq(t - dt) + (ScenCDicotNrRate) * dt

INIT ScenCDicotTFq = 0

ScenCDicotNrRate = If SprayCDicot>0 THEN 1 ELSE 0

ScenCELYRETFq(t) = ScenCELYRETFq(t - dt) + (ScenELYRENrRate) * dt

INIT ScenCELYRETFq = 0

ScenELYRENrRate = If SprayELYRE>0 THEN 1 ELSE 0

ScenCFLuMixacc(t) = ScenCFLuMixacc(t - dt) + (SprayCFluMix) * dt

INIT ScenCFLuMixacc = 0

SprayCFluMix = IF (BiomCereals>0 AND Winter=1 AND DicotWeedVol>0.1) THEN (WeedControl?*Dosefluroxypyr) ELSE (0)

ScenCFluroxypyrTFq(t) = ScenCFluroxypyrTFq(t - dt) + (ScenFluroxypyr) * dt

INIT ScenCFluroxypyrTFq = 0

ScenFluroxypyr = If SprayCFluMix>0 THEN 1 ELSE 0

ScenELYREacc(t) = ScenELYREacc(t - dt) + (SprayELYRE) * dt

INIT ScenELYREacc = 0

SprayELYRE = IF (BiomCereals>0 AND EndWeed=1 AND BiomELYRE>0.3) THEN (WeedControl?*DoseGlyphosatePH) ELSE (0)

BRACAResistance = IF ((SprayCDicot>0 AND Scenario?=5) OR SprayScen1>0 OR SprayScen2>0 OR SprayScen3>0 OR SprayScen4>0 OR SprayScen5>0) AND (BiomBRACARR+BiomBRACARS+BiomF1)/DicotWeedVol>0.25 THEN 1 ELSE 0

CerealTFq = ScenCDicotTFq+ScenCELYRETFq+ScenCFluroxypyrTFq

CerealUse = ScnCDicotacc+ScenCFLuMixacc+ScenELYREacc

Dose = 1

DoseBenasa = Dose*0.406

DoseFluazifop = 0.188

Dosefluroxypyr = Mix*0.144

DoseGlufosinate = Dose*0.600

DoseGlyphosate = Dose*0.445

DoseGlyphosatePH = 0.8

DosePropamid = 0.5

DoseSU = 0.0075*Dose

DoseSUWRape = 0.0075*Dose

dummy = IF (Scenario?=5) THEN 0 ELSE 1

Ef125ELYRE = IF SprayScen125>0 THEN 0.85 ELSE 0

Ef125WBarleyVol = IF SprayScen125>0 THEN 0.95 ELSE 0

Ef125WWheatVol = IF SprayScen125>0 THEN 0.95 ELSE 0

Ef1CAPB = IF SprayScen1>0 THEN 0.2 ELSE 0

Ef1CHEAL = IF SprayScen1>0 THEN 0.75 ELSE 0

Ef1ELYRE = IF SprayScen1>0 THEN 0.5 ELSE 0

Ef1MYOAR = IF SprayScen1>0 THEN 0.75 ELSE 0

Ef1STEME = IF SprayScen1>0 THEN 0.95 ELSE 0

Ef1WBarleyVol = IF SprayScen1>0 THEN 0.95 ELSE 0

Ef1WWheatVol = IF SprayScen1>0 THEN 0.95 ELSE 0

Ef2CAPB = IF SprayScen2>0 THEN (1-(0.28+(1-0.28)/(1+EXP(1.3*(LOGN(SprayScen2)-LOGN(0.600)))))) ELSE 0

Ef2CHEAL = IF SprayScen2>0 THEN (1-(0.25+(1-0.25)/(1+EXP(3.5*(LOGN(SprayScen2)-LOGN(0.3166)))))) ELSE 0

Ef2MYOAR = IF SprayScen2>0 THEN (1-(0.28+(1-0.28)/(1+EXP(1.3*(LOGN(SprayScen2)-LOGN(0.150)))))) ELSE 0

Ef2STEME = IF SprayScen2>0 THEN (1-(0.28+((1-0.28)/(1+EXP(1.3*(LOGN(SprayScen2)-LOGN(0.0839))))))) ELSE 0

Ef3BRASe = IF SprayScen3>0 THEN (1-(0.02+(1-0.02)/(1+EXP(3.1*(LOGN(SprayScen3)-LOGN(0.2067)))))) ELSE 0

Ef3CAPB = IF SprayScen3>0 THEN (1-(0.02+(1-0.02)/(1+EXP(1.9*(LOGN(SprayScen3)-LOGN(0.0485)))))) ELSE 0

Ef3CHEAL = IF SprayScen3>0 THEN (1-(0.02+(1-0.02)/(1+EXP(2.4*(LOGN(SprayScen3)-LOGN(0.1058)))))) ELSE 0

Ef3ELYRE = IF SprayScen3>0 THEN (1-(0.02+(1-0.02)/(1+EXP(1.9*(LOGN(SprayScen3)-LOGN(0.150)))))) ELSE 0

Ef3MYOAR = IF SprayScen3>0 THEN (1-(0.02+(1-0.02)/(1+EXP(1.2*(LOGN(SprayScen3)-LOGN(0.0824)))))) ELSE 0

Ef3STEME = IF SprayScen3>0 THEN (1-(0.02+(1-0.02)/(1+EXP(1.9*(LOGN(SprayScen3)-LOGN(0.073)))))) ELSE 0

Ef3WBarleyVol = IF SprayScen3>0 THEN (1-(0.02+(1-0.02)/(1+EXP(1.9*(LOGN(SprayScen3)-LOGN(0.073)))))) ELSE 0

Ef3WWheatVol = IF SprayScen3>0 THEN (1-(0.02+(1-0.02)/(1+EXP(1.9*(LOGN(SprayScen3)-LOGN(0.073)))))) ELSE 0

Ef4BRASe = IF SprayScen>0 THEN (1-(0.1+(1-0.1)/(1+EXP(3*(LOGN(SprayScen4)-LOGN(0.3715)))))) ELSE 0

Ef4CAPB = IF SprayScen4>0 THEN (1-(0.02+(1-0.02)/(1+EXP(1.7*(LOGN(SprayScen4)-LOGN(0.064)))))) ELSE 0

Ef4CHEAL = IF SprayScen4>0 THEN (1-(0.02+(1-0.02)/(1+EXP(3.5*(LOGN(SprayScen4)-LOGN(0.1613)))))) ELSE 0

Ef4ELYRE = IF SprayScen4>0 THEN (1-(0.25+(1-0.25)/(1+EXP(3*(LOGN(SprayScen4)-LOGN(0.3715)))))) ELSE 0

Ef4MYOAR = IF SprayScen4>0 THEN (1-(0.02+(1-0.02)/(1+EXP(2.7*(LOGN(SprayScen4)-LOGN(0.0573)))))) ELSE 0

Ef4STEME = IF SprayScen4>0 THEN (1-(0.02+(1-0.02)/(1+EXP(2.9*(LOGN(SprayScen4)-LOGN(0.0653)))))) ELSE 0

Ef4WBarleyVol = IF SprayScen4>0 THEN (1-(0.02+(1-0.02)/(1+EXP(2.9*(LOGN(SprayScen4)-LOGN(0.1706)))))) ELSE 0

Ef4WWheatVol = IF SprayScen4>0 THEN (1-(0.02+(1-0.02)/(1+EXP(2.9*(LOGN(SprayScen4)-LOGN(0.1706)))))) ELSE 0

EFBRARe = EfCRapeVol+EFCFluMix*(1-EfCRapeVol)

EFBRASe = Ef3BRASe+Ef4BRASe+Ef5BraSe+EfCBRASe+EFCFluMix*(1-Ef3BRASe+Ef4BRASe+Ef5BraSe+EfCBRASe)

EFCAPBP = Ef1CAPB+Ef2CAPB+Ef3CAPB+Ef4CAPB+Ef5CAPB+EfCCAPB+EFCFluMix*(1-Ef1CAPB+Ef2CAPB+Ef3CAPB+Ef4CAPB+Ef5CAPB+EfCCAPB)

EFCFluMix = IF SprayCFluMix>0 THEN 0.95 ELSE 0

EFCHEAL = Ef1CHEAL+Ef2CHEAL+Ef3CHEAL+Ef4CHEAL+Ef5CHEAL+EfCCHEAL+EFCFluMix*(1-Ef1CHEAL+Ef2CHEAL+Ef3CHEAL+Ef4CHEAL+Ef5CHEAL+EfCCHEAL)

EFELYRE = Ef125ELYRE+Ef1ELYRE+Ef3ELYRE+Ef4ELYRE+EfGlyPHELYRE

EfGlyPHELYRE = IF SprayELYRE>0 THEN 0.95 ELSE 0

EFMYOAR = Ef1MYOAR+Ef2MYOAR+Ef3MYOAR+Ef4MYOAR+Ef5MYOAR+EfCMYOAR+EFCFluMix*(1-Ef1MYOAR+Ef2MYOAR+Ef3MYOAR+Ef4MYOAR+Ef5MYOAR+EfCMYOAR)

EFSTEME = Ef1STEME+Ef2STEME+Ef3STEME+Ef4STEME+Ef5STEME+EfCSTEME

+EFCFluMix*(1-Ef1STEME+Ef2STEME+Ef3STEME+Ef4STEME+Ef5STEME+EfCSTEME)

EFSTEMESU = Ef1STEME+Ef2STEME+Ef3STEME+Ef4STEME+EFCFluMix

EFWBarley = Ef125WBarleyVol+Ef1WBarleyVol+Ef3WBarleyVol+Ef4WBarleyVol

EFWWheat = Ef125WWheatVol+Ef1WWheatVol+Ef3WWheatVol+Ef4WWheatVol

Mix = IF (BRACAResistance=1 OR SUResistance=1 OR WRapeVolResistance=1) THEN 1 ELSE 0

RapeUse = Scen125acc+Scen1acc+Scen2acc+Scen3acc+Scen4acc+Scen5acc

Scenario? = 2

SUResistance = IF (SprayCDicot>0 OR SprayScen1>0 OR SprayScen2>0OR SprayScen3>0 OR SprayScen4>0 OR SprayScen5>0) AND BiomSTEMESU/DicotWeed>0.25 THEN 1 ELSE 0

TotalTFq = CerealTFq+WRapeTFq

TotalUse = CerealUse+RapeUse

WeedControl? = 1

WRapeTFq = Scen125TFq+Scen1TFq+Scen2TFq+Scen3TFq+Scen4TFq+Scen5TFq

WRapeVolResistance = IF ((SprayCDicot>0 AND Scenario?=5) OR SprayScen1>0 OR SprayScen2>0 OR SprayScen3>0 OR SprayScen4>0 OR SprayScen5>0) AND (BiomWRapeVol+BiomWRapeVolReSe+BiomWRapeVolRe)/DicotWeedVol>0.25 THEN 1 ELSE 0

Yieldreduction = IF AccCropYield>0 THEN (AccTotalYield-AccCropYield)/AccTotalYield ELSE 0

Ef5BraSe = GRAPH(SprayScen5)

(0.00, 0.00), (0.0015, 0.895), (0.003, 0.93), (0.0045, 0.95), (0.006, 0.96), (0.0075, 0.97), (0.009, 0.975), (0.0105, 0.975), (0.012, 0.98), (0.0135, 0.98), (0.015, 0.98)

Ef5CAPB = GRAPH(SprayScen5)

(0.00, 0.00), (0.0015, 0.575), (0.003, 0.7), (0.0045, 0.755), (0.006, 0.8), (0.0075, 0.83), (0.009, 0.86), (0.0105, 0.875), (0.012, 0.89), (0.0135, 0.89), (0.015, 0.89)

Ef5CHEAL = GRAPH(SprayScen5)

(0.00, 0.00), (0.0015, 0.615), (0.003, 0.725), (0.0045, 0.775), (0.006, 0.82), (0.0075, 0.85), (0.009, 0.875), (0.0105, 0.895), (0.012, 0.905), (0.0135, 0.91), (0.015, 0.91)

Ef5MYOAR = GRAPH(SprayScen5)

(0.00, 0.00), (0.0015, 0.625), (0.003, 0.73), (0.0045, 0.77), (0.006, 0.815), (0.0075, 0.85), (0.009, 0.87), (0.0105, 0.885), (0.012, 0.9), (0.0135, 0.91), (0.015, 0.91)

Ef5STEME = GRAPH( SprayScen5)

(0.00, 0.00), (0.0015, 0.835), (0.003, 0.895), (0.0045, 0.925), (0.006, 0.945), (0.0075, 0.95), (0.009, 0.96), (0.0105, 0.965), (0.012, 0.965), (0.0135, 0.97), (0.015, 0.97)

EfCBRASe = GRAPH( SprayCDicot)

(0.00, 0.00), (0.0015, 0.895), (0.003, 0.93), (0.0045, 0.95), (0.006, 0.965), (0.0075, 0.97), (0.009, 0.97), (0.0105, 0.975), (0.012, 0.98), (0.0135, 0.98), (0.015, 0.98)

EfCCAPB = GRAPH( SprayCDicot)

(0.00, 0.00), (0.0015, 0.575), (0.003, 0.7), (0.0045, 0.74), (0.006, 0.78), (0.0075, 0.82), (0.009, 0.845), (0.0105, 0.865), (0.012, 0.885), (0.0135, 0.89), (0.015, 0.89)

EfCCHEAL = GRAPH( SprayCDicot)

(0.00, 0.00), (0.0015, 0.6), (0.003, 0.705), (0.0045, 0.77), (.006, 0.83), (0.0075, 0.85), (0.009, 0.87), (0.0105, 0.885), (0.012, 0.895), (0.0135, 0.91), (0.015, 0.91)

EfCMYOAR = GRAPH( SprayCDicot)

(0.00, 0.00), (0.0015, 0.61), (0.003, 0.72), (0.0045, 0.77), (0.006, 0.81), (0.0075, 0.85), (0.009, 0.88), (0.0105, 0.89), (0.012, 0.9), (0.0135, 0.91), (0.015, 0.91)

EfCRapeVol = GRAPH(dummy*SprayCDicot)

(0.00, 0.00), (0.0015, 0.89), (0.003, 0.925), (0.0045, 0.95), (0.006, 0.96), (0.0075, 0.97), (0.009, 0.97), (0.0105, 0.975), (0.012, 0.975), (0.0135, 0.98), (0.015, 0.98)

EfCSTEME = GRAPH(SprayCDicot)

(0.00, 0.00), (0.0015, 0.825), (0.003, 0.895), (0.0045, 0.925), (0.006, 0.95), (0.0075, 0.955), (0.009, 0.96), (0.0105, 0.965), (0.012, 0.97), (0.0135, 0.975), (0.015, 0.975)

BiomBRACA(t) = BiomBRACA(t - dt) + (GrowBRACA + SowBRACA - HarvBRACA - ControlBRACA) * dt

INIT BiomBRACA = 0

GrowBRACA = if (MaxBRACA>BiomTotal AND Hybridization=0) THEN (Winter*RGRBRACA*BiomBRACA*(MaxBRACA-BiomTotal)/MaxBRACA)/dt else 0

SowBRACA = Delay(BeginWeed,1)*SeedBRACA*GermBRACA*TKVBRACA*10000/(1000*1000000)/dt

HarvBRACA = if EndWeed=1 then (BiomBRACA+0.1) else 0

ControlBRACA = BiomBRACA*EFBRASe

BiomCABP(t) = BiomCABP(t - dt) + (GrowCABP + SowCABP - HarvCABP - ControlCABP) * dt

INIT BiomCABP = 0

GrowCABP = if (MaxCABP>BiomTotal) THEN (Winter*RGRCABP*BiomCABP*(MaxCABP-BiomTotal)/MaxCABP)/dt else 0

SowCABP = Delay(BeginWeed,1)*SeedCABP*GermCABP*TKVCABP*10000/(1000*1000000)/dt

HarvCABP = if EndWeed=1 then (BiomCABP+0.1) else 0

ControlCABP = BiomCABP*EFCAPBP

BiomCHEAL(t) = BiomCHEAL(t - dt) + (GrowCHEAL + SowCHEAL - HarvCHEAL - ControlCHEAL) * dt

INIT BiomCHEAL = 0

GrowCHEAL = if (MaxCHEAL>BiomTotal) THEN (Winter*RGRCHEAL*BiomCHEAL*(MaxCHEAL-BiomTotal)/MaxCHEAL)/dt else 0

SowCHEAL = if SumAnn=1 then SeedCHEAL*10000*GermCHEAL*TKVCHEAL/(1000*1000000)/dt else 0

HarvCHEAL = if EndWeed=1 then (BiomCHEAL+0.1) else 0

ControlCHEAL = BiomCHEAL*EFCHEAL

BiomELYRE(t) = BiomELYRE(t - dt) + (GrowELYRE + InitELYRE - HarvELYRE - ControlELYRE) * dt

INIT BiomELYRE = 0

GrowELYRE = if (MaxELYRE>BiomTotal) THEN (Winter*GRELYRE*BiomELYRE*(MaxELYRE-BiomTotal)/MaxELYRE)/dt else 0

InitELYRE = IF (TIME<365) THEN (ELYRE?*BeginWeed*0.005) ELSE (0)

HarvELYRE = DELAY(EndWeed,1)*BiomELYRE*0.975

ControlELYRE = BiomELYRE*EFELYRE

BiomMYOAR(t) = BiomMYOAR(t - dt) + (GrowMYOAR + SowMYOAR - HarvMYOAR - ControlMYOAR) * dt

INIT BiomMYOAR = 0

GrowMYOAR = if (MaxMYOAR>BiomTotal) THEN (Winter*RGRMYOAR*BiomMYOAR*(MaxMYOAR-BiomTotal)/MaxMYOAR)/dt else 0

SowMYOAR = Delay(BeginWeed,1)*SeedMYOAR*GermMYOAR*TKVMYOAR*10000/(1000*1000000)/dt

HarvMYOAR = if EndWeed=1 then (BiomMYOAR+0.1) else 0

ControlMYOAR = BiomMYOAR*EFMYOAR

BiomSTEME(t) = BiomSTEME(t - dt) + (GrowSTEME + SowSTEME - HarvSTEME - ControlSTEME) * dt

INIT BiomSTEME = 0

GrowSTEME = if (MaxSteme>BiomTotal) THEN (Winter*RGRSTEME*BiomSTEME*(MaxSteme-BiomTotal)/MaxSteme)/dt else 0

SowSTEME = Delay(BeginWeed,1)*SeedSTEME*10000*GermSTEME*TKVSTEME

/(1000*1000000)/dt

HarvSTEME = if EndWeed=1 then (BiomSTEME+0.1) else 0

ControlSTEME = BiomSTEME*EFSTEME

SeedBRACA(t) = SeedBRACA(t - dt) + (NewSeedBRACA - DeadSeedBRACA) * dt

INIT SeedBRACA = 500

NewSeedBRACA = (HarvBRACA)*NonPredBRACA*HIBRACA*1000000*1000/(TKVBRACA*10000)/dt

DeadSeedBRACA = If Hybridization=0 THEN (SeedBRACA*(1-EXP(LOGN(1-DecayBRACA)/365))+BeginWeed*SeedBRACA*GermBRACA)/dt

ELSE SeedBRACA

SeedCABP(t) = SeedCABP(t - dt) + (NewSeedCABP - DeadSeedCABP) * dt

INIT SeedCABP = 3600

NewSeedCABP = (HarvCABP)*NonPredCABP*HICABP*1000000*1000/(TKVCABP*10000)/dt

DeadSeedCABP = (SeedCABP*(1-EXP(LOGN(1-DecayCABP)/365))+BeginWeed*SeedCABP*GermCABP)/dt

SeedCHEAL(t) = SeedCHEAL(t - dt) + (NewSeedCHEAL - DeadSeedCHEAL) * dt

INIT SeedCHEAL = 1000

NewSeedCHEAL = (HarvCHEAL)*NonPredCHEAL*HICHEAL*1000000*1000/(TKVCHEAL*10000*dt)

DeadSeedCHEAL = (SeedCHEAL*(1-EXP(LOGN(1-DecayCHEAL)/365))+BeginWeed*SeedCHEAL*GermCHEAL)/dt

SeedMYOAR(t) = SeedMYOAR(t - dt) + (NewSeedMYOAR - DeadSeedMYOAR) * dt

INIT SeedMYOAR = 3400

NewSeedMYOAR = (HarvMYOAR)*NonPredMYOAR*HIMYOAR*1000000*1000/(TKVMYOAR*10000)/dt

DeadSeedMYOAR = (SeedMYOAR*(1-EXP(LOGN(1-DecayMYOAR)/365))+Begineed*SeedMYOAR*GermMYOAR)/dt

SeedSTEME(t) = SeedSTEME(t - dt) + (NewSeedSTEME - DeadSeedSTEME) * dt

INIT SeedSTEME = 10800

NewSeedSTEME = (HarvSTEME)*NonPredSTEME*HISTEME*1000000*1000/(10000*TKVSTEME)/dt

DeadSeedSTEME = (SeedSTEME*(1-EXP(LOGN(1-DecaySteme)/365))+BeginWeed*SeedSTEME*GermSTEME)/dt

DecayBRACA = 0.33

DecayCABP = 0.33

DecayCHEAL = 0.33

DecayMYOAR = 0.33

DecaySteme = 0.33

ELYRE? = 1

GermBRACA = 0.05

GermCABP = 0.05

GermCHEAL = 0.05

GermMYOAR = 0.03

GermSTEME = 0.05

HIBRACA = 0.25

HICABP = 0.25

HICHEAL = 0.5

HIMYOAR = 0.25

HISTEME = 0.5

MaxBRACA = 8

MaxCABP = 5

MaxCHEAL = 8

MaxELYRE = 8

MaxMYOAR = 5

MaxSteme = 5

NonPredBRACA = 0.8

NonPredCABP = 0.85

NonPredCHEAL = 0.5

NonPredMYOAR = 0.6

NonPredSTEME = 0.5

RGRBRACA = 0.061

RGRCABP = 0.07

RGRCHEAL = 0.15

RGRELYRE = 0.028

RGRMYOAR = 0.08

RGRSTEME = 0.067

TKVBRACA = 2

TKVCABP = 0.1

TKVCHEAL = 1.2

TKVMYOAR = 0.3

TKVSTEME = 0.6

Literature

AgrEvo (1997) Hybrid Canola. AgrEvo Canada Inc., 6 pp.

Andersson L (1994) Seed production and seed weight of six weed species treated with MCPA. Swedish Journal of agricultural Research 24, 95-100.

Anonymous (1995) Plantebeskyttelsesmidler. Landbrugs- og fiskeriministeriet, Denmark. (In Danish).

Anonymous (1997) Crop protection guide. Saskatchewan Agriculture and Food Statistics Branch, Regina, Saskatchewan, Canada.

Alstedgård (1994) Dyrkningsforsøg og undersøgelser med sukkerroer 1994. Fondet for forsøg med sukkerroedyrkning. 81 pp.

Andreasen C (1990) Ukrudtsarternes forekomst på danske sædskiftemarker. Licentiatafhandling. Den Kgl. Veterinær og Landbohøjskole. 53 pp.

Andreasen C & Jensen JE (1994) Herbicidresistens i Danmark (Herbicide resistance in Denmark). 11th Danish Plant Protection Conference - Side effects of pesticides, 261-70 (In Danish).

Carroll RJ & Ruppert D (1988) Transformation and Weighting in Regression. New York: Chapmann and Hall, 249 pp.

Danmarks Statistik (1994) Landbrugsstatistik 1993. Agricultural Statistics 1993. 302 pp.

Dawkins TCK & Almond JA (1984) The effect of a novel plant growth regulatior (EL 500) on the growth, development and yield of winter oilseed rape (Brassica napus L.) in the absence of lodging. Aspects of Applied Biology 6, 137-149.

Fredshavn J R, Poulsen G S, Huybrechts I, Rudelsheim, P (1995) Competitiveness of transgenic Oilseed rape. Transgenic Research 4, 142-148.

Haas H (1989) Danish experiences in initiating and implementing a policy to reduce herbicide use. Plant Protection Quarterly 4, 38-44.

Heap IM (1997) The occurrence of herbicide-resistant weeds worldwide. Pesticide Science 51, 235-43.

Holt, JS, Pills SB & Holtum JAM (1993) Mechanisms and agronomic aspects of herbicide resistance. Annual Review of Plant Physiology and Plant Molecular Biology 44, 203-229.

Hurle K, Maier J, Amann A, Weishaar T, Mozer B & Pulcher-Häussling M (1988) Auswirkungen unterlassener Ppflanzenschutz- und Düngungsmassnahmen auf die Unkrautflora - erste Ergebniss aus einem merhrjärighen Versuchsprogramm. Zeitschrift f¨r Pflanzenkrankheithe und Pflanzenschutz, sonderh. XI, 175-187.

Jensen, JE (1993) Fitness of herbicide resistant weed biotypes described by competition models. Proc. 8th EWRS Symposium Braunschweig 1993: Quantitative approaches in weed and herbicide research and their practical application, Volume 1, European Weed Research Society, pp. 25–32.

Jensen H A & Kjellsson G (1993) Ændringer af frøpuljens størrelse i danske marker i perioden 1964-1989. In: Supplerende bilagsmateriale i Ukrudtslære. Eds H Haas H, J C Streibig and C Andreasen. Den Kgl. Vet.- og Landbohøjskole, Danmark, 1993. 189 pp.

Jørgensen R B & Andersen B (1994) Spontaneous hybridisation between oilseed rape (Brassica napus) and weedy B. campestris (Brassicaceae): A risk of growing genetically modified oilseed rape. American Journal of Botany 81: 1620-1626.

Jørnsgård B, Rasmussen K, Hill J & Christiansen JL (1996) Influence of nitrogen on competition between cereals and their natural weed populations. Weed Research 36, 461-470.

Holm LG, Plucknett DL, Pancho JV& Herberger JP (1977) The worlds worst weeds. East-West Center Book: Honululu, Hawaii, 609 pp.

Korsmo E, Vidme T & Fykse H (1981) Korsmos ugræs plansjer. Norsk Landbruk/Landbruksforlaget, Oslo

Kristensen H (1997) Experiences with mechanical weeding in oilseed rape. 14th Danish Plant Protection Conference - side effects of pesticides, weeds, 179-82.

Kropff MJ (1993) Eco-physiological models for crop-weed interaction. In: Modelling Crop-Weed Interactions (eds MJ Kropff & HH van Laar), pp. 25-32. CAB International, Oxon, UK.

Kudsk P, Mathiassen SK & Petersen EF (1992) Resistance to sulfonylurea in Stellaria media. 9th Danish Plant Protection Conference, Weeds: 147-156.

Kudsk P, Mathiassen SK & Cotterman JC (1995) Sulfonylurea resistance in Stellaria media [L.]. Weed Research 35, 19-24.

Lutman, PJW (1993) The occurrence and persistence of volunteer oilseed rape (Brassica napus). Aspect of Applied Biology 35, Volunteer crops as weeds, 29-36.

Madsen KH (1994) Weed management and impact on ecology of growing glyphosate tolerant sugarbeets (Beta vulgaris). Ph.D.-Thesis, January 1994. The Royal Vet. and Agric. University, Copenhagen, Denmark. 62 pp.

Madsen KH & Jensen JE (1995) Weed control in glyphosate tolerant sugarbeets (Beta vulgaris L.): A comparison between glyphosate and currently used herbicides. Weed Research 35, 105-111.

Madsen KH, Poulsen ER & Streibig JC (1997) Modelling of herbicide use in genetically modified herbicide resistant crops - 1. Content and Input for models. Environmental project No. 346, Ministry of Environment and Energy, Denmark, Danish Environmental Protection Agency, 65 pp.

Madsen KH, Blacklow WM, Jensen JE & Streibig (1997) Simulation of herbicide use in a crop rotation with transgenic herbicide tolerant oilseed rape. Submitted to Weed Research.

McHughen A & Holm FA (1995) Transgenic flax with environmentally and agronomically sustainable attributes. Transgenic Research 4, 3-11.

Miljøstyrelsen (1996) Bekæmpelsesmiddelsstatistik 1995. Orientering fra Miljøstyrelsen 8. Miljø-og Energiministeriet, 38 pp.

Miljøstyrelsen (1997) Bekæmpelsesmiddelsstatistik 1996. Orientering fra Miljøstyrelsen 10. Miljø-og Energiministeriet, Denmark (in Danish).

Mikkelsen TR, Andersen B & Jørgensen RB (1996) The risk of crop transgene spread. Nature 380 (7), 31.

Mikkelsen TR (1996) Flow of engineered genes from crops to wild or weedy relatives - is there an environmental risk. A case study on oilseed rape (Brassica napus) and weedy Brassica campestris. Ph.D. thesis. Environmental Science and Technology Department, Risø National Laboratory, 96 pp.

Monsanto (1997)The Science of Farming - Changing the nature of business, Roundup Ready Canola. Monsanto Canada Inc., 8 pp.

Norris RF (1996) Weed population dynamics: seed production. Second International Weed Control Congress, Copenhagen, 1996, 15-20.

Petersen C (1987) Spektral refleksion fra landbrugsafgrøder. Licentiatafhandling. Institut for Kulturteknik og Planteernæring. Den Kgl. Veterinær og Landbohøjskole, København,

Rasmussen IA (1993) Seed production of Chenopodium Album in spring barley sprayed with different herbicides in normal to very low doses. Proc. 8th EWRS Symposium Braunschweig 1993: Quantitative approaches in weed and herbicide research and their practical application, European Weed Research Society, pp. 639-646.

Roberts HA & Feast PM (1973) Emergence and longevity of seeds of annual weeds in cultivated and undisturbed soil. Journal of Applied Ecology 10, 133-143.

Saskatchewan Agriculture and Food (1995) Agricultural statistics 1995. Saskatchewan Agriculture and Food Statistics Branch, Regina, Saskatchewan Canada, 146 pp.

Saskatchewan Agriculture and Food (1996) Agricultural statistics fact sheet, June 1996. Saskatchewan Agriculture and Food Statistics Branch, Regina, Saskatchewan Canada.

Saskatchewan Agriculture and Food (1997a) Varieties of grain crops 1997. Saskatchewan Agriculture and Food Statistics Branch, Regina, Saskatchewan Canada, 16 pp.

Saskatchewan Agriculture and Food (1997b) Crop protection guide 1997. Saskatchewan Agriculture and Food Statistics Branch, Regina, Saskatchewan Canada, 207 pp.

Statistics Canada (1997) June summerfallow and seeded area. Fact sheet from Statistics Canada, not published, 4 pp.

Statens Planteavlsforsøg (1993) Ukrudstbekæmpelse i landbruget, Planteværnscenteret, Afd. for Ukrudtsbekæmpelse, Statens Planteavlsforsøg. 400 pp.

Statens Planteavlsforsøg (1997) Vejledning i Planteværn. Statens Planteavlsforsøg og Landskontoret for Planteavl, 256 pp.

Streibig JC, Rudemo M & Jensen JE (1993) Dose-response curves and statistical models. In: Streibig JC & Kudsk P, eds. Herbicide Bioassays. Boca Raton, Florida: CRC press, pp. 29–55.

Thonke KE (1991) Political and practical approaches in Scandinavia to reduce herbicide inputs. In: Proceedings Brighton Crop Protection Conference - Weeds 1991, Volume 3, British Crop Protection Council, England, pp. 1183-1190.

Trenbath BR (1974) Biomass productivity of mixtures. In: NC Brady ed. Advances in Agronomy 26, pp.177-210

Weisberg S (1985) Applied Linear Regression, Second Edition, John Wiley & Sons, Inc., New York, 324 pp.

Wilson BJ & Lawson HM (1992) Seedbank persistence and seedling emergence of seven weed species in autumn-sown crops following a single year’s seeding. Annals of applied Biology 120, 105-116.