Economic Thresholds and Response to Uncertainty in ... - Science Direct

Agricultural Systems 25 (1987) 219-227

Economic Thresholds and Response to Uncertainty in Weed Control Bruce A. Auld Agricultural Research and Veterinary Centre, Forest Rd., Orange, NSW 2800, Australia

& Clem A. Tisdell Economics Department, University of Newcastle, NSW 2308, Australia (Received 2 February 1987; revised version received 21 May 1987; accepted 22 May 1987)

S UMMA R Y The influence of uncerta&ty on economic thresholds~critical density models & weed control is examined. Two principal sources of uncertainty, potential weed density and the form of the crop loss function, are discussed. A range of criteria including maximisation of net gain, minimax gain and mean-risk analysis are considered in relation to the decision to control or not control weeds in a erop. A notional example of wild oats in wheat illustrates how the various decision criteria can also be considered as thresholds. I f risk aversion is present, uncertainty about the weed loss function and weed densities increases the likelihood that control of weeds is optimal and specOqc threshold weed densities become less relevant•

INTRODUCTION Economic threshold or critical density models are used to determine circumstances in which profit from controlling weeds exceeds the cost of doing so. Their use in decision making in weed control has recently received increasing attention (Marra & Carlson, 1983; Cousens et al., 1986; Doyle et al., 1986). Eco nom i c thresholds are influenced by variation in control costs 219 Agricultural Systems 0308-521X/87/$03"50 © Elsevier Applied Science Publishers Ltd, England, 1987. Printed in Great Britain

Bruce A. Auld, Clem A. Tisdell

220

and prices received for crop products although these can sometimes be assumed to be constant. However, if costs of weed control increase with increasing weed density, it is possible that there are two thresholds (Auld et al., 1987). In this case, control at weed densities greater than the higher threshold density is uneconomic. It is also possible that control costs increase in a stepwise fashion with weed density (e.g. Medd et al., 1987); this gives rise to the possibility of multiple thresholds. In addition, agronomic factors such as crop sowing time and rate, as well as weather, affect potential yield and, consequently, economic thresholds. Apart from these factors, many uncertainties can arise in weed control which will also influence the precision with which an economic threshold can be estimated. These include effectiveness of herbicides and phytotoxicity of herbicides to crops. In this paper, we consider the uncertainties of the weed population density and the crop loss function in relation to weed control. We discuss possible decision criteria which can be used in response to these uncertainties, given the two options: to control or not control a weed population. Several concepts of weed control thresholds exist (Cousens, 1987). This paper extends the critical density/weed control model to allow for risks and uncertainty and thereby links economic and 'safety' thresholds as described by Cousens (op. cit.). In doing so it incorporates risk in an objective manner. However, one should not assume a false sense of accuracy since the degree of risk aversion will vary among farmers.

U N C E R T A I N T I E S IN WEED C O N T R O L

Weed population A major factor in decision making about weed control is the size of the weed population in current and future years. Marra & Carlson (1983) suggest that future benefits from carryover effects of controlling weeds in one year to succeeding years may be so uncertain that it is best to ignore them. Nevertheless, increased uncertainty about the future may be taken into account by applying larger discounts to future costs and benefits, thereby putting a reduced weight on these in decision making. In the current cropping year uncertainty about the potential weed population is relevant. Particularly where pre-emergence herbicides are to be used, a farmer may be uncertain about the level of weed infestation expected in the absence of treatment; loss to be anticipated and therefore gains from treatment are uncertain. Even for emerged weeds where weed density at the economic threshold is

Economic thresholds and uncertainty in weed control

221

low, it may be difficult to obtain an accurate estimate of the weed population because of non-random distribution of weeds and difficulties in sampling low density populations in the field. Yield response function

The effect of weed density on crop yield is generally to cause increasing yield loss, but at a decreasing rate (Dew, 1972; Chisaka, 1977). Although Zimdahl (1980) has suggested a sigmoidal relationship there appears to be no empirical evidence for it and it has been refuted on theoretical grounds (Cousens et al., 1984). Marra & Carlson (op. cit.) suggest that a linear loss function is a reasonable approximation and this may be so in the region of the economic threshold. However, while the general form of the crop loss function for a specific weed/crop system may be known, its precise shape may vary with location and agronomic factors. Thus, the economic threshold derived from the value of increased yield from weed control will vary accordingly. In Fig. 1 possible revenues from weed control in relation to weed density are represented by a range of values bounded by two curves (OBD and OB'D'). The economic threshold determined by the intersection of these curves and the cost of control curve (CE) (assumed a constant for all weed densities) is represented by a range W 1 to W2. If the maximum yield loss function occurs W 1 is the economic theshold. If the minimum yield loss function occurs W2 is the economic threshold. Given that functions for the value of increased yield from treatment are positively sloped throughout, it follows that if the weed density is less than W1 it is not economic to treat the weed, but is is always economic to treat it if

D

d

c

°

ii 0

W,

w2

Weed density (W)

Fig. 1. The economic threshold is represented by the range of weed densities W 1 to W 2 where there is uncertainty about the value of increased yield function between the bounds O B D and O B ' D ' and C E represents cost of treatment.

222


the density exceeds W 2. In cases where W 1 < W < W 2 the attitude of the farmer towards uncertainty will influence the decision about whether it is optimal or not to treat the weed.

RESPONSE TO U N C E R T A I N T Y

Weed population uncertainty Figure 2 depicts the net gain function (J(W)) in relation to weed density (W) after allowing for control costs. If yield loss decreases, at a decreasing rate in the usual way, then J'(W)> 0 and J"(W) ten plants per square metre, the weeds are treated. The greater the possible range of the critical weed densities, the more likely the minimax regret criterion indicates treatment of weeds. If a farmer assumed L 2 (Fig. 3) were the loss function for his particular circumstances, uncertainty about wild oat density would be unlikely to influence his decision about whether to control or not if, expected profit maximisation were his criterion for action (because the function is almost linear in the threshold region). However, if he anticipated loss functions E(L) or L~, greater uncertainty about wild oat density increases the likelihood that non-control maximises expected gains, on average. This is because of the strict concavity of the loss functions in the threshold region. Given the original hypothesis that E(L) is the expected loss function but that possible loss functions range between L~ and L 2, the various criteria can each be considered as 'thresholds'. The minimax gain threshold is five wild oat plants per square metre, the maximax gain threshold is 20, the minimax regret threshold is 10 and the maximisation of net gain threshold is 8. CONCLUSION Increased uncertainty about either the weed density or the weed loss function increases the likelihood that weed treatment is optimal if the

226


minimax gain criterion is adopted but reduces this likelihood if the maximax criterion is adopted. In the case of the expected gain criterion and given a strictly concave weed loss function, there is a tendency for greater uncertainty about weed densities to increase the expected gain from nontreatment. F r o m the total community point of view, adoption of the maximisation of net gain criterion is the more desirable strategy; the minimax gain criterion would tend to encourage over-use of herbicides. Where risk aversion is present, increased uncertainty about weed densities or the crop loss function tends to increase the likelihood that treatment of weeds is optimal. In practice, this may be the most c o m m o n consequence. The importance of the latter finding is that where risk aversion occurs, specific economic threshold weed densities become less relevant to farmers' decision making in weed control.

ACKNOWLEDGEMENT The authors wish to thank an anonymous referee for his comments.

REFERENCES Anderson, J. R., Dillon, J. L. & Hardaker, J. B. (1977). Agricultural decision analysis. Iowa St. Univ. Press, Ames, Iowa, 90 6. Auld, B. A., Menz, K. M. & Tisdell, C. A. (1987). Weed control economics. Applied Botany and Crop Science Series. Academic Press, London, 55-6. Chisaka, H. (1977). Weed damage to crops: Yield loss due to weed competition. In: Integrated control of weeds (Fryer, J. D. & Matsunaka, S. (Eds)), Japan Scientific Societies Press, Tokyo, 1 t6. Cousens, R. (1987). Theory and reality of weed control thresholds. Plant Protection Quarterly, 2, 13-20. Cousens, R., Doyle, C. J., Wilson, B. J. & Cussans, G. W. (1986). Modelling the economics of controlling Avenuafatua in winter wheat. Pestic. Sci., 17, 1-12. Cousens, R., Peters, N. C. B. & Marshall, C. J. (1984). Models of yield loss-weed density relationships. European Weed Research Society Proceedings 7th Internat. Symp. on Weed Biology, Ecology and Systematics. Paris, 367-74. Dew, D. A. (1972). An index of competition for estimatimg crop loss due to weeds. Can. J. Plant. Sci., 52, 921 7. Doyle, C. J., Cousens, R. & Moss, S. R. (1986). A model of the economics of controlling AIopecurus myosuroides Huds. in winter wheat. Crop Protection, 5, 143-50. Luce, R. D. & Raiffa, H. (1966). Games and decisions: Introduction and critical survey. Wiley, New York, 275 87. Marra, M. C. & Carlson, G. A. (1983). An economic threshold model fbr weeds in soybeans (Glycine max). Weed Sci., 31,604 9.

Economic thresholds and uncertainty in weed control

227

Martin, R. J. (1986). Using herbicides to control wild oats in crops. In: Weed control in winter crops (Gammie, R. L. & Dellow, J. J. (Eds)). Dept. Agriculture, NSW, 26-7. Medd, R. W., Kemp, D. R. & Auld, B. A. (1987). Management of weeds in perennial pastures. In: Temperate pastures: Their production, use, management. (Wheeler, J., Pearson, C. J. & Robards, G. E. (Eds)). Australian Wool Corporation, Melbourne. (In press.) Reichelderfer, K. H. (1980). Economics of integrated pest management: Discussion. American Journal of Agricultural Economics, 62, 1012-13. Zimdahl, R. L. (1980. Weed crop competition. A review. International Plant Protection Centre, Oregon St. Univ., Corvallis, Oregon, 29-31.