The number of invasive species that were transported through imported commodities is increasing exponentially. The practical measure to prevent the invasion of harmful organisms are a series of phytosanitary measures, such as the prohibition of importation, disinfestation treatments of commodities, and sampling inspections of consignments. However, these measures can be used as a non-tariff barrier to trade in some countries, which may cause international conflicts. To prevent such conflicts, the Agreement on Sanitary and Phytosanitary (SPS) Measures of the General Agreement on Tariffs and Trade (GATT) requires members to base their animal, plant, and human health requirements related to trade on international standards. These plant health measures are to be based on standards developed under the auspices of the International Plant Protection Convention (IPPC), implemented by the United Nations' Food and Agriculture Organization (FAO). Although Pest Risk Analysis (PRA) is required in SPS agreement, the methodology is not yet well established.

The probability of invasion via an imported consignment (that is denoted by P_t ) can be expressed by a general form:

P_t = P₁P₂,

where P₁ is the probability that one or more individuals pass the port to enter the county, P₂ is the probability that the entered individuals find suitable locations to establish their population. (P₁ and P₂ are not strictly independent.) The estimation of P₂ is now in progress for each of the invasive species that are not yet invaded but are suspected to invade in the future. However, the quantity of P₂ contains too many uncertain components that are largely influenced by the fluctuation of environmental characteristics of the destination country. In contrast, the quantity of P₁ can be estimated more precisely if we could construct statistical models to describe the process of transportation. Hence, the estimation of P₁ seems to be practically more important for making a political decision for quarantine procedures.

Although several methods have been proposed to estimate the quantity of P₁ by researchers in the US and New Zealand, these methods do not yield a precise probability; these methods estimate P₁ for a consignment imported from a single site. In actual situations, however, many consignments are imported to a country from various exporting sites that have different levels of infestation. We derived a method to estimate P₁ by using Bayesian approach. Figure 1 shows an estimated contour of P₁ for Mexican fruit fly that has been of concern in the citrus industry in the US.

The probability of invasion will not directly give us intuitive information about whether the risk of invasion is large or not. The Expected Time required for Invasion (abbreviated by ETI) will be a superior index to express the risk. Let k be the number of consignments imported during a year. Then we approximately obtain

ETI = 1/(kP_t ) = 1/(kP₁P₂).

If we assume that P₂ =10^-5, k = 10⁴ and ETI = 1000 years, for example, we obtain P₁ = 10^-2. The contour of 10^-2 in Figure 1 indicates that, for example, if we inspect 40% of fruits after the disinfestation treatment, we can achieve ETI = 1000 by using the disinfestation treatment with a survival rate of about 10^-2.5.




Figure 1.   Contour of the probability of invasion per consignment (P₁) for the Mexican fruit fly expressed as the function of the intensity of sampling inspection and disinfestation treatment. The contour readily indicates the combination of the percentage of sampling and the disinfestation treatment to achieve a given probability of introduction. (Copyright by the Society of Population Ecology and Springer-Verlag Tokyo)