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Indifference Analysis: A Practical Method to Assess Uncertainty in IPM Decision Making

(CC)
Scott H. Hutchins
DOI: http://dx.doi.org/10.1603/IPM10002 D1-D3 First published online: 1 October 2010

Abstract

Since the publication of the integrated control concept (<xref ref-type="bibr" rid="B9">Stern et al. 1959</xref>), integrated pest management (IPM) has been based upon the principle of rational decision making with knowledge of plant-pest interactions and economic tradeoffs. In addition, although the determination of economic-injury levels and other decision benchmarks have been extraordinarily helpful with the application of IPM principles, they often are fixed, when, in fact, the situation-specific circumstances require a more dynamic approach. Moreover, in situations for which preventive control measures are preferred or required, there has been little guidance for decision makers on how to quantify payoffs to their control options. This paper introduces an approach referred to as indifference analysis, a simple and straightforward practitioner approach to support decision making in IPM programs when outcomes are unknown. The concept is based upon a basic 2 × 2 payoff matrix of prospective financial outcomes for pest management decisions taken with uncertain outcomes. Two case studies are presented to illustrate the use of indifference analysis. For each case, an indifference point is determined that provides transparency regarding the relative financial risk of various management options, leading to insights for selecting tactics under uncertainty. This approach may enlighten decision makers in choosing their IPM practices when outcomes are unknown and uncertain.

  • economic-injury level
  • preventive control
  • IPM
  • decision making

Integrated pest management (IPM), although difficult to define in specific terms, is based upon several key principles and concepts. Primary among these is the principle of rational and objective decision-making criteria, especially in the assessment of economic loss. Stern et al. (1959) clearly recognized the lack of an objective decision framework in prevailing practices when they authored their landmark paper outlining the theoretical context of an integrated control concept, incorporating benchmark decision criteria such as the general equilibrium position, economic-injury level (EIL), and economic threshold (ET). As influential as their integrated control concept was to the future of IPM, it stopped short of providing a quantitative framework from which pest managers could make decisions in the field with situation-specific economic and biological insights. A critical milestone to address this shortcoming was the simple concept of the gain threshold described by Stone and Pedigo (1972). The gain threshold is determined by dividing the cost of control (cost per unit of area) by the market value of the crop (commodity value per commodity unit), resulting in the physical yield lost (e.g., bushels per acre) that represents a resultant economic loss. Combining the gain threshold with the biological consequence of crop damage from pest injury leads to the calculated EIL. Extensive treatments of the EIL and related concepts can be found in Pedigo et al. (1986), Higley and Pedigo (1996), and Peterson and Higley (2001).

Despite outstanding progress with the principles of IPM, specifically with the determination and use of EILs, there remains a significant issue of robust utility with most EILs. Robust, characterized here as appropriate and relevant over time and space, refers to the reality that plants (and crops) respond to pest-induced injury in relation to other stresses or conditions endured by the plant. In other words, the degree and extent of physiological plant or crop tolerance is highly unpredictable, complicating the selection of the appropriate EIL.

Another shortcoming of current decision-making guidelines in IPM relates to the uncertainty inherent in using preventive control measures without complete knowledge of subsequent pest densities. The premise underlying the use of preventive control measures is belief in the likelihood that pest numbers or injury will exceed the EIL, justifying the expenditure to control the pest with a prophylactic treatment. In addition, a preventive tactic may be the only option for effective control of a given pest in many instances.

This paper describes a practical approach, referred to as indifference analysis, to place the uncertainties associated with EILs and preventive control measures within the context of simple economic payoffs.

Proposed Solution

For practical, in-season use in production agriculture and horticulture, decision-making tools in IPM must accommodate local circumstances as simply as possible and should consider the risk attitude of the grower. A key point of pest control is that intervention is never a revenue-generating enterprise for the grower. Rather, pest control only prevents or mitigates future losses that otherwise would exceed the cost of control. Indifference analysis is based upon the creation of a basic 2 × 2 payoff matrix (Boehlje and Eidman 1984) with use of the consequences and penalties (i.e., unnecessary costs) within the context of probability. The techniques for linear programming (Schrage 1984), albeit in simple form, are used in the approach.

Choosing the Correct EIL: A Case Study of Soybean Defoliation

Although EILs often are determined through controlled experimentation and are published for use as static benchmarks, an EIL in reality is highly dependent upon the crop's ability to tolerate pest stress, which also is affected by existing, cumulative stresses on the plants caused by other factors (e.g., water, level of nutrients, heat, disease, nematodes). Data from Hammond et al. (1979) documented the respective amount of injury caused by green cloverworm, Platypena scabra (F.), necessary to create soybean yield loss when plants had either adequate water or not enough water. The water-stressed soybean plants were more than twofold less tolerant to injury caused by green cloverworms than the nonstressed plants. The large difference in host response to insect defoliation in different environments complicates decision making because the damage differential between the two EILs was the equivalent of ≈94,000 larvae per acre. Multiplying the damage differential times the rate of injury in “average” (nonwater-stressed) and drought-stress conditions allows for calculation of the theoretical resultant financial penalty of choosing the wrong EIL (Table 1).

View this table:
Table 1

Variability in soybean host response and impact on the green cloverworm (Platypena scabra (F.)) EIL

EnvironmentDamage/larvaeManager's EILa
Average year0.0074 ounce /larva172,768 larvae/acre
Stressful year0.0160 ounce/larva78,872 larvae/acre
Damage differential = 172,768–78,872 = 93,896 larvae/acre
  • Financial penalty for choosing the wrong EIL: (1) For an avg year using a low EIL: 93,896 larvae/acre × 0.0074 ounce/larva = 0.72 bushel/acre loss at $11/bushel for soybean: $7.92/acre (available tolerance of crop); (2) For a stressful year using a high EIL: 93,896 larvae/acre × 0.016 ounce/larva = 1.59 bushels/acre loss at $11/bushel for soybean: $17.50/acre (yield lost before application).

  • a Gain Threshold calculated to be 1.0 bushel/acre with assumed market value of soybeans at $11/bushel and control cost at $11/acre.

Arranging these data into a payoff matrix places the relativity of the decision dilemma in context (Table 2). There are four scenarios in this payoff matrix. Scenario 1: The pest manager uses the high EIL appropriate for a crop that will not be stressed by a lack of water, and the amount of rainfall is indeed average. Under these circumstances, there is no loss or gain ($0.00 per acre, upper left) because the manager's selection of the EIL matches the correct environmental circumstance. Scenario 2: The pest manager uses the high EIL but the crop actually experiences severe drought stress. This is the worst-case scenario because the EIL is inappropriate for the situation and yield loss accrues at a faster rate per larva than would occur if the crop had adequate moisture. Under these circumstances, there is a substantial loss ($17.50 per acre, lower left). Scenario 3: The pest manager uses the low EIL appropriate for a crop that lacks adequate water, but average (not water-stressed) growing conditions prevail. Under these circumstances, there is a theoretical financial penalty for controlling an insect population whose density is less than the GT ($7.92 per acre, upper right), not accounting for available tolerance. Note that Scenario three is the most complicated and represents the financial yield still available for the crop to endure before treatment. However, this cell also could be considered the cost of the treatment itself (e.g., $11 per acre) if the treatment is applied early based solely on the payoff matrix. The pest manager can select the most appropriate entry, but this example is provided for the purpose to help him or her select an EIL early in the season based upon the Indifference Point. Scenario 4: The pest manager uses the low EIL and the crop experiences severe drought stress. This scenario results in no unexpected or unnecessary loss ($0.00 per acre, lower right) because the pest manager has selected wisely for the eventual environmental circumstances.

View this table:
Table 2

Payoff matrix of unnecessary income consequence associated with choice of EIL for each crop stress environment

Manager's decision
High EILLow EIL
EnvironmentAverage year$ 0.00$7.92a
Stressful year$17.50$0.00
  • a This payoff value represents the available yield value that could have been endured prior to initiating treatment. If a treatment is actually made with the low EIL in an avg year, the loss in the matrix would be the cost of the treatment ($11/acre in this scenario). The proposed scenario is about choosing an appropriate EIL a priori, so the tolerance value is selected.

The payoff matrix can be a useful tool, but knowing the outcomes and assessing these against the probability of occurrence is the basis for indifference analysis. Figure 1 maps the payoff matrix outcomes over a linear probability scale, with a line for each of the two pest management decision options versus their respective financial penalty for each combination on each “environmental conditions” axis. Where these two lines intersect is the point of indifference for the pest manager, 0.69 in this case. At a known probability of 69% for a drought-stressed crop, the pest manager is indifferent between using the low or the high EIL. However, each side of this indifference point provides guidance. If the pest manager is <69% confident that drought stress will affect crop tolerance, then he or she would use the lower EIL. If the pest manager is >69% confident that drought stress will not affect crop tolerance, then he or she would choose the higher EIL. The practical point is that pest managers must choose an EIL before they know the status of drought stress, so understanding the relative payoffs and consequences provides insights to make the right decision, but it does not guarantee a right decision.

Fig. 1

Example of indifference analysis for a pest management decision to choose the appropriate EIL with unknown future condition of drought stress in soybean.

A priori knowledge of historical probabilities can improve and simplify the decision by creating a single EIL that incorporates past knowledge or frequency of occurrence. In this case, assuming that an “average” year occurs 60% of the time, a single risk-adjusted EIL and “expected” income penalty that will mitigate a large loss from a worst-case decision can be calculated (Table 3). Site-specific history, historical weather patterns, and available forecasts will be useful for developing situation-specific EILs that, on balance, provide the best decision criteria for pest managers.

View this table:
Table 3

Additional probabilistic knowledge

Probability of an avg year = 60%
Probability of a stressful year = 40%
Single risk-adjusted EIL: 0.60 (172,7681 larvae/acre) + 0.40(78,872a larvae/acre) = 135,210 larvae/acre
Expected income penalty for wrong decisions: 0.60 ($7.92) + 0.40($17.50) = $11.75/acre
  • a Determined as the manager's EIL, see Table 1.

The Value of Preventive Control: Transgenic Insect Resistance Traits

Stern et al. (1959) recognized that preventing pests from reaching the EIL by changing the habitat was a valid method of control for primary pests. However, pest managers often do not know whether the primary pest will exceed the EIL or whether sporadically occurring pests that can be controlled only with preventive measures will exceed the EIL. Consequently, severe financial loss may result if the wrong decision is made. Indifference analysis can assist in placing the uncertainty of the pest management decision into perspective. As noted previously, a correct decision by a pest manager occurs only when future circumstances meet expectations. A “correct decision” does not infer a no-cost decision. Zero loss in the payoff matrix refers to avoiding unnecessary spending or yield loss.

A payoff matrix (four scenarios in a 2 × 2 payoff matrix) for the pest manager's possible decisions about using insect-resistant (IR) corn is presented in Table 4. Scenario 1: IR corn is used and the numbers of susceptible insects exceed the EIL. Under these circumstances, there is no unnecessary loss ($0.00 per acre, lower left). Scenario 2: IR corn is used and the numbers of susceptible insects do not exceed the EIL. Under these circumstances, the unnecessary loss equals the cost of the IR corn ($20.00 per acre, upper left). Scenario 3: IR corn is not used and the numbers of pests exceed the EIL. Under these circumstances, the unnecessary loss equals the damage caused by the insects (~$52.00 per acre, lower right, estimated for this example to be 10% of 150 bushels at $3.50 per bushel). Scenario 4: IR corn is not used and the numbers of pests do not exceed the EIL. Under these circumstances, there is no unnecessary loss ($0.00 per acre, upper right). Mapping these respective penalties in the context of indifference analysis (Fig. 2) demonstrates that a pest manager is indifferent about using IR corn at the 72% level of personal confidence that pest pressure will or will not exceed the EIL. Therefore, if a grower is >72% certain that pests controlled by IR corn will not be present, then the best approach would be not to use IR corn. If research or pest surveys could provide the actual probability of occurrence of these pests with confidence, then some additional decision support could be provided to the pest manager. Regarding corn rootworms (Diabrotica sp.), however, previous research and attempts to predict larval densities by sampling adults the previous year have not generated reliable results with conventional or IR corn (Foster et al. 1986, Crowder et al. 2005).

View this table:
Table 4

Payoff matrix of unnecessary income consequence associated with decision to use the preventive control tactic of IR corn under different pest pressures

Manager's decision
IR cornNon-IR corn
EnvironmentNo corn pests$20.00a$ 0.00
Corn pests$ 0.00$52.00b
  • a Assumes $20/acre IR-corn cost.

  • b Assumes ≈10% of 150 bushels lost at $3.50/bushel.

Fig. 2

Example of indifference analysis for a pest management decision about using IR corn, a preventive control measure, not knowing the future status of the pests.

Discussion and Relevance of the Solution

Although based upon science and good business principle, IPM in practice has a large component of site-specific decision making and forecasting, often with a large degree of uncertainty that must incorporate the experience and risk attitude of the pest manager. Simple decision tools that place management costs and penalties (e.g., unnecessary cost or yield loss) in context with events that cannot be predicted will provide insights on tradeoffs and consequences until additional research removes some of the uncertainty. In the case studies for selecting an EIL for green cloverworms in soybean with incomplete knowledge about the future stress condition of the crop, and the use of IR traits with incomplete knowledge of future pest damage, indifference analysis can provide useful perspective and insights for pest managers. There are many other scenarios for which this simple analysis can be adapted and helpful in providing pest managers a framework for making decisions when uncertainty prevails, especially if there is only a two-choice management decision (e.g., treat or no-treat) linked to unknown or unpredictable future conditions.

This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0/), which permits unrestricted reuse, distribution, and reproduction in any medium, providedthe original work is properly cited.

References Cited

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