Comparing risks among pesticides has substantial utility for decision makers. However, if rating schemes to compare risks are to be used, they must be conceptually and mathematically sound. We address limitations with pesticide risk rating schemes by examining in particular the Environmental Impact Quotient (EIQ) using, for the first time, a probabilistic analytic technique. To demonstrate the consequences of mapping discrete risk ratings to probabilities, adjusted EIQs were calculated for a group of 20 insecticides in four chemical classes. Using Monte Carlo simulation, adjusted EIQs were determined under different hypothetical scenarios by incorporating probability ranges. The analysis revealed that pesticides that have different EIQs, and therefore different putative environmental effects, actually may be no different when incorporating uncertainty. The EIQ equation cannot take into account uncertainty the way that it is structured and provide reliable quotients of pesticide impact. The EIQ also is inconsistent with the accepted notion of risk as a joint probability of toxicity and exposure. Therefore, our results suggest that the EIQ and other similar schemes be discontinued in favor of conceptually sound schemes to estimate risk that rely on proper integration of toxicity and exposure information.

Numerous methods to rate pesticide risks have been introduced over the past two decades. The methods are typically qualitative or semi-quantitative and involve rating and weighting hazard, toxicity, and exposure factors for pesticide active ingredients. The purpose of these rating schemes is to provide growers and other decision makers with information so that they can discriminate among pesticides based on their risk to such entities as people, other non-target organisms, and water quality.

Comparing risks among pesticides has substantial utility for decision makers (

The most influential scheme is arguably the Environmental Impact Quotient (EIQ) by

The EIQ method essentially is a mathematical formula that determines environmental impact for pesticide active ingredients based on converting a raft of physicochemical and toxicological information, such as acute dermal toxicity, toxicity to birds, long-term health effects, and soil runoff potential, into an arbitrary ratings scale of 1, 3, and 5 and then combining and weighting those ratings through multiplication, division, and addition. This computation results in EIQs for farm worker, consumer, and environment. The EIQs from these three component categories are then averaged to determine a total EIQ. The EIQ equation is:

Here, we examine pesticide risk rating schemes and the EIQ in particular using, for the first time, a probabilistic analytic technique. Our purpose is not to repeat the mathematical proofs of

The ratings of 1, 3, and 5 in the EIQ method are surrogates for low, medium, and high risk or impact or toxicity or persistence, depending on the factor of interest. For demonstration purposes only, we show how converting the ratings to estimates of risk probabilities for only four of the factors limits the value of the EIQ method. The EIQ factors, “long-term health effects”, “leaching potential”, and “surface runoff potential”, and ratings of “little-none”, “possible”, “definite”, “small”, “medium”, and “large” imply that they are risks. Therefore, they have a probability of occurrence rather than an absolute certainty of occurring. Similarly, the factor “beneficial arthropod toxicity” has ratings of “low impact”, “moderate impact”, and “severe impact”. Degrees of impact also have associated uncertainty.

Because the ratings of 1, 3, and 5 are surrogates for risk, they can be converted to risk intervals that incorporate the underlying probabilities. Therefore, the simplest, yet coarse, way to do this is to assume the ratings of 1, 3, and 5 span the range of risk from 0 to 1 (or 0 to 100%). A rating of 1, when mapped onto an interval of risks would be 0 to 0.32. A score of 3 would be 0.33 to 0.66 and a score of 5 would be 0.67 to 1. Consequently, if a pesticide has a “surface runoff potential” factor that has a score of 3, it is at medium risk of runoff. However, a discrete score of 3 does not capture the probabilistic nature of risk, yet the score of 3 is intended to represent medium risk. Therefore, the score needs to be mapped to an estimate of risk. This can be done most simply by assuming a uniform probability density function of risk values from 0.32 to 0.66 for medium risk. Medium risk implies uncertainty and probability, but a score of 3 does not accommodate that risk estimate. An interval of 0.33 to 0.66, however crudely, accommodates the probability of occurrence.

To demonstrate the consequences of mapping discrete risk ratings to probabilities, we calculated adjusted EIQs for a group of 20 actual insecticide active ingredients with unadjusted EIQs ranging from 22.1 (methiocarb) to 44 (diazinon). The insecticides evaluated were chosen randomly from lists of active ingredients in

Using Monte Carlo simulation (Oracle Crystal Ball^{®} 11.2, Denver, CO), we calculated adjusted EIQs under different hypothetical scenarios by incorporating the probability ranges associated with the four factors (

For each bar, the bottom line is the 10th, the middle line is the 50th, and the top line is the 90th percentile value from the simulation. The number at the top of each bar is the original EIQ value. The original EIQ value reported for naled, 49, is incorrect. The correct value is 41.

Results demonstrate overlaps of adjusted EIQs for insecticides that have discrete EIQs (

Another example can be shown with imidacloprid and dinotefuran, two neonicotinoid insecticides. The adjusted EIQs range from 0.88 to 1.29 for imidacloprid and 0.65 to 1.04 for dinotefuran. More than 26% of the adjusted EIQ values overlap with each other. The unadjusted EIQs are 36.7 and 22.3, respectively, a 14.4 EIQ unit difference. Consequently, these examples show that pesticides with different EIQs, and therefore different putative environmental effects, actually may not be different because of the potential overlap in EIQ values when incorporating uncertainty. Therefore, for example, a decision maker choosing acetamiprid over cypermethrin because of the nearly 8-unit difference in EIQs is choosing between two insecticides in which there may be no difference in EIQs when considering uncertainty (i.e., the EIQs overlapped 90% of the time in the simulation).

Our results demonstrate the problems with qualitative risk ratings in which uncertainty is not taken into account. Uncertainty cannot be ignored because the rating scores are surrogates for probabilities of occurrence or impact. However, the EIQ equation cannot take into account uncertainty the way that it is structured and provide reliable quotients of pesticide impact. As demonstrated by

In addition to the analyses above and those of

If the EIQ method and others like it are not conceptually or mathematically sound, then what should be used in their place? Risk is the joint probability of effect and exposure. In the case of pesticides, risk is the joint probability of toxicity and exposure. Therefore, for risk rating systems to be informative, toxicity and exposure must be integrated in an estimate of risk.

Risk rating systems for pesticides initially emerged when methods and models for estimating environmental exposure were in nascent stages of development. However, the ability to estimate the joint probability of exposure and toxicity (i.e., risk) currently is relatively simple and there are several acceptable models for estimating environmental exposures, e.g., FOCUS, PRZM-EXAMS, T-REX (

The purpose of this article is not to examine a specific alternative to qualitative rating systems for pesticides. However, a starting point to create a useful quantitative rating system is the risk quotient (RQ) that is used in concept, but not necessarily by that specific term, by regulatory agencies throughout the world. An RQ is simply the ratio of estimated or actual environmental or dietary concentration of the pesticide to a toxic effect level or threshold. Some other terms for this ratio include hazard quotient (HQ), hazard index (HI), margin of safety (MOS), toxicity-exposure ratio (TER), and margin of exposure (MOE).

A risk rating system for pesticides is attractive and has potential benefits. However, our results suggest that qualitative rating systems should not be used for pesticide risk assessment, management, or decision making because they cannot properly discriminate between different levels of risk the way they are currently structured. We suggest that quantitative risk models be used for both risk assessment and risk management of pesticides.

We thank LG Higley and SH Hutchins for their reviews of earlier versions of this paper.

The authors declare they have no competing interests.