The Maximum Pest Limit Concept Explained

The maximum pest limit (MPL) concept was developed as a practical method of implementing quarantine security measures against the import of invasive pest species of plants. The MPL itself is simply a threshold upper limit, above which the pest species in question is deemed capable of establishing a population if imported in a consignment of fruit or vegetables. This limit depends on various biological and ecological characteristics of the pest species in question. Important aspects of implementation relate to how treatment and sampling may be combined to reduce the probability that the MPL will be exceeded. If a specified level of treatment efficacy is required (for example, probit nine level), then choice of an appropriate sample size becomes the main problem for regulatory authorities seeking to maintain quarantine security. Introduction This article is intended to provide a mostly non-mathematical account of the maximum pest limit concept. Readers who would prefer to work through the mathematical details from the outset are referred to the Literature Cited section, and the articles listed therein. Notwithstanding the intention to avoid presentation of most of the mathematical details of the maximum pest limit concept, some notation used in mathematical formulations of the concept will be retained, chiefly as a form of shorthand. Quantitative aspects of the concept will be illustrated graphically. The ideas outlined in an article by Landolt et al. (5) underlie much of the subsequent work on maximum pest limits. Landolt et al. (5) pointed out that specification of a required level of treatment efficacy (usually 'probit nine', a survival rate of 32×10-6 [=10-4.5]) did not guarantee quarantine security, because the probability of pest introduction depends on the number of pests surviving treatment, rather than the number of pests killed. Treatment obviously reduces this probability, but not in any quantifiable way unless we also have information on the pre-treatment level of infestation and other biological and ecological data (as discussed later in this article) on the pest species in question. In the context of measures taken against the introduction of fruit flies, Landolt et al. (5) suggested that the risk of pest introduction, calculated as the probability of a potential mating pair arriving per consignment, provided a basis for a more consistent approach to quarantine security. The Maximum Pest Limit The term 'maximum pest limit' (MPL) appears to have been introduced to the literature by Baker et al. (1), who were concerned to avoid the establishment of fruit flies in New Zealand through imported produce. They defined the maximum pest limit as the maximum number of fruit flies that can be present in consignments imported during a specified time to a specified location, such that the smallest number of flies capable of establishing a colony is not exceeded. Baker et al. (1) set this limit at three live larvae, arguing that natural mortality should ensure that this would not subsequently result in a mating pair. Sampling to comply with an MPL, based on the cost to the exporter. Baker et al. (1) envisaged the following scenario. Consignments of fruit arrive from various sources (having been treated prior to shipping in order to qualify for a phytosanitary certificate) to be consolidated at a single destination in a specified time period (a single day is usually the time unit used for the calculations). The probability that the MPL is not exceeded after Plant Health Progress 13 November 2003 treatment in the consolidated consignment for any day is denoted Pr(B) and depends on the adopted MPL (m), the total number of fruit (N), the proportion of fruit infested (p), the mean number of pests per infested fruit (μ) and the survival rate after treatment (s). If we adopt an appropriate statistical probability distribution for Pr(B) and have agreed values for m, N, μ, and s, we can plot Pr(B) as a function of p. Pr(B) decreases with increasing p (Fig. 1). The consolidated consignment is sampled. The probability that the pest is detected in the sample is denoted 1-Pr(A) and depends on p and the sample size (n). With an appropriate statistical probability distribution for Pr(A) and a value for n, we can plot 1-Pr(A) as a function of p. 1-Pr(A) increases with increasing p (Fig. 1). Baker et al. (1) then outlined the calculation of required sample size as follows. An acceptable risk ( ) that pests will be detected in a sample taken from a consignment that is actually below the MPL is identified. Baker et al. (1) adopted =0.95. Note that Baker et al. (1) used the term ‘risk’ to refer to the probability of occurrence of an unfavorable event, a usage retained throughout the present article. A critical value of p (p*) at which Pr(B)= 0.5 is obtained, and n is then selected so that 1-Pr(A)= 0.5 when p=p*. Thus, at the critical value p*, Pr(B)×[1-Pr(A)]= . The probability that the MPL is not exceeded (after treatment) in the consolidated consignment for any day and that the pest is detected in the sample taken from this consignment is equal to a specified value when p=p* (Fig. 1). The implication appeared to be that was the maximum risk that pests will be detected in a sample taken from a consignment that is actually below the MPL, but this is not necessarily the case. In a more recent article (4) an alternative method was given for finding the value of n such that the maximum value of Pr(B)×[1-Pr(A)] as a function of p was equal to . Fig. 1. Sampling to comply with a maximum pest limit, based on the cost to the exporter. The figure shows a graphical interpretation of equation 6 from Baker et al. (1), with m=3, N=208550, μ=40, s=10-4.5, =0.95. The dashed line (-) shows the probability that the consolidated consignment is below the maximum pest limit after treatment, Pr(B), as a function of the proportion of fruit infested p. This line intersects with 0.5 (shown by a solid horizontal line) at p*=0.0041, characterizing the critical incidence of infestation for the selected parameter values above. The dotted line (---) shows the probability that the pest is detected in the sample 1-Pr(A) as a function of the proportion of fruit infested p, with Pr(A)=e-np. The sample size n is chosen so that 1-Pr(A) as a function of p intersects Pr(B) as a function of p at the previously identified critical incidence of infestation. The solid bold line then shows the probability that the consolidated consignment is below the maximum pest limit after treatment and that the pest is detected in the sample Pr(B)×[1Pr(A)] as a function of p. This probability has a value equal to at the critical incidence of infestation. The approach to sample size calculation adopted by Baker et al. (1) and Harte et al. (4) is based on setting a maximum value for the risk that pests will be detected in a sample taken from a consolidated consignment in which the pest population is actually at or below the MPL. If detection of pests in a sample taken from a consolidated consignment results in a decision not to import, this would be an erroneous decision in cases in which the pest population in a consignment was actually at or below the MPL. Such decisions represent costs to the exporter(s). Presumably, a high value of was adopted because this means that the corresponding risk of a decision, based on sampling, to import a Plant Health Progress 13 November 2003 consignment that is actually above the MPL will be low. The risk of a decision, based on sampling, to import a consignment that is actually above the MPL is not directly specified in the calculations described by Baker et al. (1), but it can be calculated retrospectively. Following on from the work of Baker et al. (1), Mangan et al. (6) adopted the same statistical probability distribution for Pr(B) and with a specified value of m and values of N, μ, and p derived from field data, defined Pr(B) (the probability that the MPL is not exceeded after treatment) as a function of survival rate after treatment (s). Pr(B) decreases with increasing s (Fig. 2). Mangan et al. (6) were interested in the critical value of s (s*) at which Pr(B)= 0.5. If this value were less than 10-4.5, the implication would be that the survival rate after treatment required to comply with the adopted MPL was lower than probit nine level. Thus, if the actual survival rate after treatment was (or was assumed to be) probit nine level, additional pest control measures designed to reduce the pretreatment level of infestation would be required in order to comply with the adopted MPL. Fig. 2. A graphical interpretation of equation 6 from Baker et al. (1), with m=2, N=141250, μ=7.427, p=0.205, =0.95 (data from Mangan et al. (6)). The solid bold line shows the probability that the consignment is below the maximum pest limit after treatment Pr(B) as a function of the survival rate after treatment s. For the selected parameter values above, this line intersects with 0.5 (shown by a solid horizontal line) between s=10-5 and s=10-6, indicating that the survival rate after treatment required to meet the adopted maximum pest limit was lower than probit nine level, s=10-4.5. Thus, if the actual survival rate after treatment was probit nine level, additional pest control measures designed to reduce the pre-treatment level of infestation would be required in order to comply with the adopted maximum pest limit. Sampling to comply with an MPL, based on the risk to the importer. The scenario envisaged by Cannon (2) differs from that outlined in the work of Baker et al. (1), in that it deals with treatment and sampling carried out on consignments of fruit at source, prior to shipping (which does not preclude further sampling of a consignment at the destination). Cannon's (2) calculation of sample size is based on setting a maximum value ( ), chosen according to the severity of the consequences, for the risk that pests will not be detected in a sample taken from a c