SEA Working Paper 01/05

A multi-species bio-economic model for integrated weed management

Marta Monjardino, David J. Pannell, Stephen Powles
University of Western Australia, Crawley WA 6009, Australia

ABSTRACT

A multi-species version of the bio-economic model Resistance and Integrated Management (RIM) has been developed to deal with the complexities involved in the long-term integrated management of Lolium rigidum Gaud. (rigid ryegrass) and Raphanus raphanistrum L.(wild radish), which dominate and co-exist in southern Australia. In this paper, we present a review of the existing options on how to model multi-species competition in order to select the best approach for incorporation in the RIM framework. Furthermore, we show how we have extended the original single-species Ryegrass RIM model to include other aspects of the R. raphanistrum biology as well as a set of extra weed management practices used to control this weed species. We also demonstrate how the Multi-species RIM model can be used to evaluate weed management scenarios of co-existing herbicide resistant species. This is done through investigating the implications of using a new transgenic crop in the system.

Nomenclature: Lolium rigidum Gaud. LOLRI, rigid ryegrass; Raphanus raphanistrum L. RAPRA, wild radish.

Key words: RIM, Lolium rigidum, Raphanus raphanistrum, weed-crop competition, herbicide resistance, transgenic crop, scenario analysis.

INTRODUCTION

Weed infestations in agriculture usually consist of a number of co-existing weed species. Hence, interactions between weeds and crops and within weeds should be considered in studies of crop yield loss and in strategies for weed management (Combellack and Friesen, 1992; Poole and Gill, 1987). However, experiments with multiple species can be large and complex, with their thorough analyses requiring the development of appropriate mathematical tools (Ball and Shaffer, 1993; Van Acker, Lutman and Froud-Williams, 1998). Improved modelling capabilities of multi-species interactions are therefore important to the full understanding and management of current agricultural systems.

In southern Australia, Lolium rigidum Gaud. (rigid ryegrass) and Raphanus raphanistrum L. (wild radish) frequently co-exist and are economically very important. Recent field surveys conducted throughout the wheatbelt of Western Australia indicated that about 70 and 20 percent of the surveyed L. rigidum and R. raphanistrum populations showed some level of herbicide resistance, respectively (Llewellyn and Powles, 2001; Walsh, Duane and Powles, 2001). The situation is now such that farmers no longer can rely solely on herbicides for effective weed control, but rather need to combine a range of chemical and non-chemical methods (IWM) to control these species. Hence, a multi-species version of the bio-economic RIM model has been developed to deal with the complexities involved in the simultaneous integrated management of annual L. rigidum and R. raphanistrum over time.

In this paper, we present a review of the existing options on how to model multi-species competition in order to select the best approach for incorporation in the RIM framework. Furthermore, we show how we have extended the single-species L. rigidum RIM model to include other aspects of the R. raphanistrum biology as well as a set of extra weed management practices used to control this weed species. Finally, we demonstrate how the multi-species RIM model can be used to evaluate the economic trade-offs between short-term costs and long-term benefits associated with the integrated management of co-existing herbicide resistant L. rigidum and R. raphanistrum. This is done through investigating the implications of using a new transgenic crop in a realistic situation, which considers crucial biological and management interactions of two different weeds infesting the same farming system.

MODELLING MULTI-SPECIES COMPETITION

A few models relating crop yield to the presence of more than one weed have been proposed in the literature (Ball and Shaffer, 1993; Blackshaw, 1986; De Wit, 1960; Firbank and Watkinson, 1985; Halse, 1986; Hume, 1989 and 1993; Kiniry et al., 1992; Kropff and Spitters, 1991; Pannell and Gill, 1994; Sattin, Berti and Zanin, 1996; Street et al., 1985; Swinton et al., 1994; Trenbath and Stern, 1995; Wilkerson, Modena and Coble, 1991). The performance of these models is summarized in Table 1 and evaluated according to the criteria presented below.

Evaluation criteria

The selection of a particular multi-species competition approach for use in this study was based on the following criteria for the indicated reasons:

1. A single-function approach, not a short-time-step dynamic simulation model. This decision is based on the fact that a single function is more convenient, faster to solve and more compatible with the general approach in the existing RIM model. It was also found to provide a good representation of empirical data from a multi-species weed competition trial with wheat (Pannell and Gill, 1994). Biological simulation models are thus excluded from the current selection process.
2. The function should be based on plant densities rather then on leaf area indices (LAIs). Density may often not be as accurate a measure of weed quantities in a field, as it does not account for patchiness, size of the weed and emergence flushes of the weeds (Parker and Murdoch, 1996). However, advantages of the density approach are that it relies on more readily available data, allowing for validity checking, is more practical for extra data collection and, is more compatible with the existing RIM model framework than the LAI approach.
3. A function capable of capturing the realistic features of crop-weed competition. In particular, if crop yield is a function of the weed density, Y = f(W), then the function should have the following characteristics:
4. a) dY/dW < 0, for all W

   b) d2Y/dW2 > 0, for all W

   c) f(0) = max (Y) = 1, if expressed as a proportion of maximum yield.

   d) Has potential to be parameterized in such a way that f(¥ )> 0

5. Effects of a weed on crop yield may depend on the density of another weed, i.e. weed effects interact (Alex, 1970; De Wit, 1960; Kroh and Stephenson, 1980; Pannell and Gill, 1994).
6. A function capable of representing different crop plant densities. The reason for this is that high crop density is a strategy being recommended to farmers, which may as well be part of the optimal management strategy in the RIM model.
7. High densities of different weeds result in different minimum crop yields (Pannell and Gill, 1994).

Previous approaches to multi-species competition

The existing models or functions that deal with multi-species competition are listed in Table 1, following chronological order of their original publication. The performance of each model is further evaluated in terms of the selected criteria defined above. For convenience, the review is limited to models based on a single function, excluding the dynamic simulation models ALMANAC (Kiniry et al., 1992) and NTRM-MSC (Nitrogen, Tillage, Residue, Management- Multiple Species Competition) (Ball and Shaffer, 1993).

Table 1. Existing multi-species competition models according to the evaluation criteria.

Preferred multi-species approach

When weighing up all the criteria in order to select the best multi-species approach to include in RIM, four of the presented models fail only one criterion:

• Model A
• Model B
• Model E
• Model J

It is judged that criterion 6 is less important than criterion 5, since meeting criterion 5 is essential to represent a weed management strategy that is being widely advocated (increasing crop seeding rates). Therefore, approach J is not used. Model A is also rejected, because it imposes unrealistic restrictions on the function (total yield is constant regardless of the combination of plant densities). In choosing between the other two, which are actually rather similar, model B is preferred because it is convenient to base parameter values on the existing single-weed version of RIM, which uses a function similar to model B.

The preferred approach (B), estimates the effect of weed-crop competition on the production of crop grain/weed seed by using an adapted version of the model proposed by Firbank and Watkinson (1985). The single-weed version of the original function was first modified by Maxwell, Roush and Radosevich. (1990) and later by Diggle, Gill and Holmes. (1994) to become:

(1)

Where,

Y = Yield or seed produced per plant

m = Maximum seed production from the plants of species 1 in the absence of competition

P1 = Density of the producing plant species (e.g. crop)

P2 = Density of the competing plant species (e.g. weed)

a = Constant for the crop being considered

k2.1 = Competition effect of species 2 on species 1

This function has the potential to be modified in order to accommodate more species. This is done in a way similar to Halse’s model (E) by adding (kn.1Pn) to the denominator of the equation, as illustrated in the next section.

THE MULTI-SPECIES RIM MODEL

The Multi-species RIM (Resistance and Integrated Management) is a bio-economic model that simulates the population dynamics of L. rigidum and R. raphanistrum over a 20-year period. It is a decision support tool designed specifically for the evaluation of various management strategies to control herbicide-resistant weeds in dryland agriculture. The model includes approximately 1140 parameters, which represent in detail the biology of weeds, crops and pasture as well as the economics of agricultural production and management. The outputs of the model are weed seed bank/density and profit. In this section, we give an overview of the model and show how the original single-species Ryegrass RIM model (Pannell et al., 1999a). has been modified to include a second weed species, R. raphanistrum.

Weed biology

Population dynamics

The growth and mortality of L rigidum and R. raphanistrum weeds are represented in RIM according to the following equation based on Gorddard, Pannell and Hertzler (1996).

(2)

Where,

W = Density of weeds which survive to maturity

V = Viable seeds present at the beginning of a given year

G = Proportion of initial seed pool that germinates

M_s = Proportion of germinated seeds that die naturally over summer

Mn = Proportion of germinated seeds that are killed by non-chemical control

Mc = Proportion of germinated seeds that are killed by herbicide application

Seeds that remain dormant, and hence do not germinate (1-G), either die naturally or add to the following year’s seed bank. The number of seeds present at the start of each season results thus from the amount of seed produced in spring plus the viable seed carried over form the previous year.

Figure 1 illustrates the germination pattern of L. rigidum and R. raphanistrum, based on the values shown in Table 2. Despite evidence that some R. raphanistrum seeds go through cycles of increased and decreased dormancy during the growing season (secondary dormancy, possibly caused by a drop in temperature at the start of that period) (Cheam, 1986), not enough information was available to allow for quantification of this phenomenon in the model.

Figure 1. Germination pattern of L. rigidum and R. raphanistrum (adapted from Cheam, 1986 and Pannell et al., 1999a).

Table 2 summarises the model default key factors (adjustable by the user), which drive the pattern of weed population change over time. Next to weed seed germination by cohort relative to the crop, the model accounts for natural mortality of seeds and seedlings. The latter is assumed to be density-dependant at high seedling densities (two percent mortality above 5000 L. rigidum and 500 R. raphanistrum seedlings per m²). The effect of weed-crop competition on seed production and the impact of control practices to reduce weeds or seeds are dealt with in other sections of this paper.

Table 2. RIM parameters associated with population dynamics of L. rigidum and R. raphanistrum.

* Germination here refers to % of total initial seed bank, whereas in the RIM model these figures are scaled to give the % germination of seeds remaining in the seed bank.

Seed production

The preferred approach represented in (Equation 1) has been modified further to predict weed seed production in a multi-species situation (Equation 3) The multi-species equation includes features of Halse’s model (E) such as a function of total plant density and the way the third species is included.

(3)

Where,

Y = Seed produced per plant for a particular weed species

PT = A function of total plant density, which normally equals 1

m = Maximum seed production from the plants of species 1 in the absence of competition

P1 = Density of the producing plant species (e.g. the weed for which we are predicting seed production)

P2 = Density of the first competing plant species (e.g. second weed species)

P3 = Density of the second competing plant species (e.g. crop)

a = Constant for the species being considered

k2.1 = Competition effect of species 2 on species 1

k3.1 = Competition effect of species 3 on species 1

Seed production per plant is highest in weeds that emerge in the first cohort, decreasing gradually with later emerging cohorts (Cheam et al., 1998). In the RIM model, weed seed production by cohort is represented through seed production index values. L. rigidum seedlings emerging in the first wave (after the break of the season) produce 100 percent of the maximum number of seeds, whereas the second emergence wave of seedlings produces 30 percent of the seeds of an early emerging weed. Seedlings of the third emergence wave produce only 10 percent of the seeds for and, finally, a two percent seed production occurs for the L. rigidum plants emerging later in the season (Pannell et al., 1999a; J. Moore, pers. comm., 2000). For R. raphanistrum, the proportions of seed produced are 100, 50, 10 and 2 percent for each cohort, respectively. Table 3 shows the seed production index values of L. rigidum and R. raphanistrum plants competing with crops sown at the opening rains, with a 10-day, or with a 20-day delay (Cheam, 1986; J. Moore, pers. comm., 2000).

Table 3. Seed production indices representing seed production by different cohorts of L. rigidum (Lr) and R. raphanistrum (Rr), relative to seed produced by healthy (early germinating) weed plants, competing with crops sown at the opening rains, with a 10-day, or with a 20-day delay.

Finally, seed production of surviving L. rigidum and R. raphanistrum plants may be lowered by the sub-lethal effect of selective herbicides. In RIM, this is assumed to be 33 percent.

Weed-crop competition

Although only few studies have been conducted on the effects of weed complexes on crop yield, Alex (1970), Haizel and Harper (1973), Kroh and Stephenson (1980), Street et al. (1985), and Pannell and Gill (1994) have shown that weed competition in mixtures can vary widely from predictions based on studies with individual weed species. According to those authors, at high densities mixtures of weeds tend to produce less effect than the sum of their independent actions. Hence, the competitive effect on the crop of two particular weeds in mixture is not additive.

Here, the expected proportion of crop yield remaining after weed competition at high weed density is calculated through a modification of Equation 3. Thus, Equation 4 represents the weedy yield at the chosen seeding rate in competition with L. rigidum and R. raphanistrum divided by the weed-free yield at the standard crop density. The higher the seeding rate the higher the expected crop yield, and hence the higher the proportion of weed-free yield with weeds.

(4)

Where,

Y = Crop yield (as a proportion of the weed-free yield)

P0= Reference density of the crop at standard seeding rate

P1= Actual crop density

P2 = Density of weed species 1 setting seed (e.g. L. rigidum)

P3 = Density of weed species 2 setting seed (e.g. R. raphanistrum)

k2.1 = Competition factor of weed species 1 in the crop

k3.1 = Competition factor of weed species 2 in the crop

a = Crop background competition factor (plant density at which yield loss is half the maximum yield loss: 1 – PGY = M/2)

M = Maximum proportion of grain yield lost at very high weed densities

Equation 4 includes the elements M + (1 - M). Without these, the function would fail the criterion concerning the potential to be parameterized in such a way that the proportion of yield lost to weeds can remain positive when the density of weeds tends to infinity (Pannell, 1990). The maximum proportion of yield lost at high R. raphanistrum densities (80 percent) is different than for L. rigidum (60 percent). This possibility was the reason for including criterion 6. However the selected functional form allows only a single value for maximum yield loss to be represented for both weeds. Where both weeds are present, the value for R. raphanistrum is assumed to apply.

Evidence suggests that R. raphanistrum density is often patchy, meaning that portions of the field are weed-free while other areas (constrained in space) have weeds occurring at various densities. However, given the significant degree of patch site-specificity (Mortensen and Dielemen, 1998) and the dormant nature of R. raphanistrum seed banks (Cheam, 1986; Reeves, Code and Piggin, 1981; Young and Cousens, 1999), density, size and occurrence of R. raphanistrum patches can be highly unpredictable. Moreover, average crop yield in a situation where R. raphanistrum is found in patches is only slightly higher than across a uniform weed field. In any case, and despite the potential reduction in herbicide inputs, farmers do not currently spray for patches for it has proved to be a relatively unreliable and uneconomic practice (Pannell and Bennett, 1998). Therefore, a decision was made not to represent patchiness in the Multi-species RIM model.

The parameter values for Equations 3 and 4 are shown in Table 4. The parameters for L. rigidum were derived by Diggle, Gill and Holmes. (1994) and Pannell et al. (1999a). The R. raphanistrum parameters were estimated for the purpose of this study.

Table 4. Parameters used in the multi-species yield-density equations.

The competitive effect among three different species is represented by the competition factors of Species 2 competing with Species 1 in the presence of Species 3 (k2.1), and Species 3 competing with Species 1 in the presence of Species 2 (k3.1). Taking the example of wheat, the competitive effect of L. rigidum on wheat in the presence of R. raphanistrum is 0.33 (33 percent), meaning that L. rigidum is assumed to be one third of a wheat plant in terms of competitiveness. Logically, a wheat plant is then three times more competitive than a L. rigidum plant, so the competitive effect of wheat on L. rigidum in the presence of R. raphanistrum is 3. On the other hand, a R. raphanistrum plant is assumed to be twice as competitive as a wheat plant in the presence of L. rigidum; hence the competitive effect of R. raphanistrum on wheat is 2 (200 percent). Following the same rationale, the competitive effect of wheat on R. raphanistrum in the presence of L. rigidum is 0.5 (50 percent). Finally, competition between the two weed species is derived from the previous figures. The competitive effect of L. rigidum on R. raphanistrum in wheat results from multiplying the competition factor of L. rigidum on wheat (0.33) by the factor of wheat on R. raphanistrum (0.5), which is 1/6 or about 0.17. Thus, the competitive effect of R. raphanistrum on L. rigidum is 6 (600 percent) in the presence of cereals and lupins. However, inter-weed competition in the presence of canola is assumed to have a lower competitive factor (4), due to particularly low tolerance of this crop to toxic substances produced by R. raphanistrum (which have been bred out of canola) (J. Moore, pers. comm., 2000).

Figure 2 illustrates the proportion of wheat yield remaining after competition with L. rigidum and R. raphanistrum co-existing in the same system.

Figure 2. Proportion of wheat yield lost to a combination of L. rigidum and R. raphanistrum at standard crop density.

Enterprises

At present RIM comprises a selection of seven different enterprises, including four crops: wheat (Triticum aestivum L.), barley (Hordeum vulgare L.), canola (Brassica napus L.) and lupins (Lupinus angustifolius L.), as well as three types of pasture for grazing by sheep: sub-clover (Trifolium subterraneum), cadiz serradella (Ornithopus compressus) and volunteer pasture. The sequence or rotation of crops and pasture over time can be specified by the user. When any of these enterprises is chosen, production of grain, hay/silage or wool occurs. However, crop yield can be significantly reduced by weed competition, with the degree of yield loss positively related to the weed density (Maxwell, Roush and Radosevich, 1990; Pannell, 1990). In addition, short rotations (due to disease) and some control methods may affect potential crop yield, for example by delaying crop sowing or through phytotoxic damage by herbicides applied in-crop (Schmidt and Pannell, 1996b). Yield benefits provided by rotation with legume crops or pasture (due to nitrogen fixation) are also accounted for.

Weed control

In the multi-species RIM model there are 51 chemical and non-chemical control options available (for more details on each method, see Pannell et al., 1999b):

• 26 selective herbicides (including six mixes) for grass and broadleaf weeds, which provide very effective weed control, but result in a strong selection pressure for resistance when applied continuously (Powles et al., 1997).
• 5 non-selective herbicides. In spite of their widespread application, there are only relatively few cases reported of resistance to non-selective herbicides. Powles et al. (1997) suggest that this is an indication that resistance gene frequencies for such herbicides are low.
• 16 non-chemical methods, varying from cultivation and delayed sowing to seed catching and stubble burning. Grazing during a pasture phase is another important non-chemical option. Heavily weed-infested crops or pasture can be cut for hay/silage or used for green manuring.
• 4 user-defined options.

Each control strategy has its own impact on weed mortality and seed set (Table 5). However, Gill and Holmes (1997), Gorddard, Pannell and Hertzler (1996), Matthews (1996), Powles et al. (1997), and Schmidt and Pannell (1996a) suggest that no one method available provides the optimal management strategy for herbicide-resistant weeds. Instead, only a combination of a wide range of weed control methods can achieve very effective and sustainable weed control (integrated weed management, IWM). Because control methods are conducted at different times, their combined impacts are considered to be multiplicative rather than additive (Pannell et al., 1999b).

The Multi-species RIM model allows the user to specify the herbicide resistance status of L. rigidum and R. raphanistrum with respect to each of nine herbicide mode-of-action groups. Resistance status for a group is defined as the number of applications of herbicides from that group remaining before the onset of complete resistance. In the case of broadleaf herbicide mixes (of which there are six available in the model), it is assumed that each application of the mix changes the resistance status by only one half of a unit for each constituent herbicide in the mixture (compared with one unit for herbicides applied not in a mixture). This assumption is made because of the lower selection pressure for each group when a mixture is used (A. Diggle, Agriculture Western Australia, pers. comm., 2001).

Table 5. Weed control methods included in the RIM model for each weed species. The letters under each weed indicate the enterprises to which the method is applicable (dashes mean that this treatment is not an option for this weed).

Key: W- wheat; B- barley; C- canola; L- lupins; P- pasture

Economic values

The model calculates costs, revenues, profit and net present value. It also includes complexities such as tax and long-term trends on prices and yields. Costs associated with cropping, pasture and various weed control options have been estimated in detail. They account for costs of input purchasing; costs of machinery operating, maintenance and repayment; costs of contracting of labour for hay and silage making; and costs of crop insurance. There are also costs of crop yield penalty due to practices such as green manuring and delayed sowing or due to crop grain contamination with R. raphanistrum seeds. Resource degradation costs associated with some non-chemical methods such as cultivation and burning are also represented in the model. Economic returns from crops and stock are based on grain, hay and wool yields and sale prices. Sheep value is given as a gross margin per DSE. Following Gorddard, Pannell and Hertzler (1996), annual net profit from cropping one hectare is given by:

(5)

Where,

R = Annual net profit

P_W = Crop sale price

Y = Crop yield

C_n = Cost of non-chemical control

C_h = Cost of herbicides

C_f = Fixed costs (e.g. fertilizers, transport)

Because the model is run over 20 years (T), annual net profit must be discounted to make them comparable to the start of the period. A real discount rate ( r) of 5 percent per year is used for this purpose. The sum of discounted net profits gives the net present value (NPV) (Equation 6).

(6)

The model does not optimise, but is used to simulate a wide range of potential treatment strategies, so that an overall strategy which is at least near-optimal can be identified (Pannell et al., 1999a).

RESULTS AND DISCUSSION

We now present and discuss a set of model results in order to illustrate the use of the Multi-species RIM to evaluate weed management scenarios. The results show some implications of using a new transgenic crop (Ct) versus a conventional crop (C) in a Western Australian farming system.

We assume that Ct has been genetically modified to become resistant to herbicide X. Not only can herbicide X be sprayed in-crop, but Ct is also expected to perform better than C in terms of yield production and competition against weeds. On the other hand, seed purchase price is likely to be higher than that of other genotypes, due to the extra cost of the new technology. Controversy associated with genetically modified crops relates to issues of food quality, environmental impact, marketing and risks of gene flow, etc. at the farm, as discussed by Smith et al. (2000). However, none of those issues are investigated in this study.

The use of herbicide-resistant crops in agriculture can be a valuable tool in the management of herbicide-resistant weeds like L. rigidum and R. raphanistrum. The perceived advantage of growing these crops is the potential to control weeds with broad-spectrum herbicides after emergence of the crop, hence prolonging the life of selective herbicides (to which many weeds are highly resistant). On the other hand, increased usage of the herbicide to which the new crop is resistant will likely result in the development of resistance to that herbicide in weeds. These trade-offs are discussed here.

The value of the transgenic crop (Ct) was investigated for three WA farming scenarios over 20 years:

Scenario1- A continuous cropping Wheat-Ct-Wheat-Lupin rotation using the transgenic crop, which allows for extra applications of herbicide X after crop emergence and before seed set.

Scenario 2- A continuous cropping Wheat-C-Wheat-Lupin rotation using the conventional genotype C, with the traditional use of herbicide X prior to crop emergence only.

Scenario 3- A Wheat-C-Wheat-Lupin rotation punctuated by two 3-year phases of Cadiz serradella pasture in years 6-8 and 14-16. In this scenario the crop used was conventional (hence no herbicide X in-crop), but the usage of X was again increased by pasture applications in spring.

In the case where Ct was used (Scenario 1), modifications to the model involved the following:

1. adding herbicide X for use after crop emergence and before seed set in spring. Associated costs, rates (1 L ha^-1) and efficacies were also included. The values of 75 and 95 percent reduction of both L. rigidum and R. raphanistrum plant/seed numbers were used to bracket the most likely range of weed control.
2. adding a flat A$50 per hectare technology fee to the standard crop seed price (S. Powles, pers. comm., 2000).
3. A sensitivity analysis was conducted within Scenario 1 (Ct). Due to the lack of information on the new crop, different levels of yield advantage (and competition factors) were investigated: 0, +5, +10 and +20 percent over the conventional crop.

For all scenarios, a combination of several chemical and non-chemical methods was used, based on the list presented in Table 5. This was mostly carried out through a process of ‘trial and error’ until the most profitable practices were identified. As mentioned earlier, the herbicide resistance status of the weeds is dealt with in RIM through defining the number of applications of each herbicide group left available before the onset of resistance. Therefore, a maximum of five applications was allowed for (selective) herbicides of high resistance risk (Groups A and B^*), 10 for herbicides of moderate resistance risk (Groups C, D, F and G^*), and 15 for (non-selective) herbicides of low resistance risk (Groups I, L and M^*), to which herbicide X belongs.

Finally, initial weed seed densities across the three scenarios were randomly set to 1000 L. rigidum seeds m^-2 and 500 R. raphanistrum seeds m^-2. Table 6 summarizes the strategies and results for each scenario.

Table 6. Strategies and implications of using a transgenic crop (Ct) in the system versus a standard crop (C). The number of applications of each control method is shown in brackets.

^*Respectively for 0, +5, +10 and +20 percent increase in Ct yield/competition factors.

The strategies presented in Table 6 show that in Scenario 1 (Ct) the reliance on selective herbicides is lower than in Scenario 2 (C). In the former, 20 applications of selective herbicides were required (zero of Group A), whereas in the latter, 2 extra shots of a Group A and one of a Group D herbicide proved economic. This is an indication that if transgenic Ct was to be introduced in the system, a reduction in the usage of selective herbicides could be expected. This could result in a significant increase in overall profitability (the values generated in Scenario 1 were between A$37-56 ha^-1 more than Scenario 2).

It was found that changing the level of weed control had no effect on the final profitability, except in the situation where no yield advantage was considered. In that case, it proved more economic (by A$2 ha^-1) not to apply herbicide X in spring when it gave only 75 percent weed control. Regardless of the control level used, the benefits of Ct result from two aspects: 1) lower weed densities and 2) higher direct profitability of this type of crop. The higher profitability resulted from both the fact that cheaper herbicide control/control options could be used and also the yield advantage of the new crop (A$37 ha^-1 was due to better weed management only). Such results confirm the idea that the introduction of transgenic crops could be a useful tool as part of an IWM program, given the extreme situation of herbicide resistance in the state.

On the other hand, higher use of herbicide X in a Ct system (3 extra applications) increases the risk of weeds developing resistance to this herbicide in the long run. Increased selection pressure on herbicide X is thus likely to reduce its availability to farmers over time.

Figure 3. Annual gross margin (A$ ha^-1 yr^-1) and weed density in crop before harvest (m^-2) over 20 years for a W-Ct-W-L rotation with a transgenic crop (Scenario1).

Figure 4. Annual gross margin (A$ ha^-1 yr^-1) and weed density in crop before harvest (m^-2) over 20 years for a W-C-W-L rotation with a standard crop (Scenario 2).

Figures 4 and 5 illustrate the pattern of L. rigidum and R. raphanistrum density as well as enterprise gross margin over 20 years (note the difference in scale). Weed numbers were generally kept low in both scenarios, although while in Scenario 1 densities of the two weeds were driven and kept very low (1 plant m^-2 after 20 years for both weeds), in Scenario 2 they went up towards the end of the 20-year period (8 and 120 m^-2 for L. rigidum and R. raphanistrum, respectively). This was due to the allocation of herbicides over time. It would have been possible to delay usage of a herbicide until the last year, but it wasn’t economic to do so because future benefits in later years are not represented. The results conformed to the constraint imposed on the analysis that final seed numbers at the end of the last period could not exceed the starting seed numbers for year 1.

In regard to gross margins, they were generally high in both scenarios, but even higher in the transgenic scenario. As shown in Figure 3, gross margins were above A$200 ha^-1 when Ct was grown in years 2, 6, 10 14 and 18, compared to an average of A$100 ha^-1 for C. As expected, lupins presented low gross margins in both scenarios and wheat was particularly profitable after lupins due to the yield boost factor following a legume crop.

Figure 5. Annual gross margin (A$ ha^-1 yr^-1) and weed density in crop before harvest (m^-2) over 20 years for a W-C-W-L rotation (with C) punctuated with two 3-year phase of Cadiz serradella pasture in years 6-8 and 14-16 (Scenario3).

Scenario 3 (illustrated in Figure 5) proved the least profitable of all (in the current market situation) although final weed numbers were lower than in Scenario 2 (Table 6). The inclusion of two pasture phases in the rotation did provide an extra IWM tool for weed control, specially as less selective herbicides were required (16, with major reductions on moderate-risk herbicides). Conversely, the number of herbicide X applications was kept relatively high (14), for pasture allows for usage of broad-spectrum herbicides to prevent seed set in spring. The choice between herbicide X and other pasture spray-top chemicals was made upon profitability. Annual gross margins for pasture were very low, particularly in the years of establishment (6 and 14), but subsequent crops were very profitable due to yield boost and low weed densities.

CONCLUSIONS

In agricultural systems, weed populations in crops generally include several weed species. Therefore, a need exists for improving the understanding of multiple species interactions. The review of literature on multi-species competition models has led to the conclusion that most of the existing functions are not suitable for use in the RIM framework. The approach selected involves a modification of the yield-density relationship originally proposed by Firbank and Watkinson (1985) to accommodate a second weed species. Some features of Halse’s (1986) model were included in the new approach as well. The resulting functional form meets all but one of the criteria identified as relevant, while providing a great deal of flexibility in representing different crop-weed combinations.

The biological and economic additions made to the single-species RIM model have originated a new Multi-species RIM. This model provides a valuable tool for evaluating alternative long-term weed management scenarios in a more realistic situation, which considers crucial biological and management interactions of two different weeds infesting the same farming system. When using the Multi-species RIM to investigate some implications of using a new transgenic crop in a Western Australian farming system, the main conclusions are that it can be profitable and help prolong the life of selective herbicides, but it is also likely to increase resistance to the herbicide in question, thus reducing its availability to farmers over time.

AKNOWLEDGEMENTS

We are grateful for the input of a number of people in the development of the wild radish section of RIM. We particularly thank the WAHRI group and A. Cheam, A. Diggle and J. Moore from Agriculture Western Australia. We also acknowledge the help of B. Bowden, G. Gill, J. Matthews, R. Roush and B. Roy in reviewing this paper. The Grains Research and Development Corporation and the Cooperative Research Center for Weed Management Systems provided financial support for this research.

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