Submitted to: World Mycotoxin Journal
Publication Type: Peer Reviewed Journal
Publication Acceptance Date: 2/3/2009
Publication Date: 8/1/2009
Citation: Toyofuku, N., Schatzki, T.F. 2009. Calculation of contaminant distribution in tree and ground nuts. World Mycotoxin Journal.2:(3):285-294. Interpretive Summary: The present manuscript discusses sampling theory for detecting contaminants in granular products. In particular it addresses the determination and use of contaminant distributions at both small and large sample sizes. It then applies these methods to a number of published distributions of aflatoxin in pistachios, almonds, and peanuts. This analysis provides insight into a number of issues with granular products of this type, including sources of contamination, control and communality, between the commodities. The model postulates that the toxin in a lot is carried in individual kernels, which may each carry a differing amount of toxin. This distribution is characterized by a distribution, given by p(c), which is the probability that any kernel carries a concentration c of toxin. The lot is assumed to be sampled at random. The sample distribution P(C;N), is the probability that a sample, containing N kernels, has an average concentration of C. Two methods of relating p(c) and P(C;N) (the non-parametric method and the negative binomial function (NBD)) are described and exemplified in this manuscript. The non-parametric method allows for freedom in matching any p(c) distribution and is ideally suited for studying the effect of pre-harvest production and post-harvest processing on toxin concentrations. The NBD is not capable of representing the small, but significant, peaks in p(c) and is therefore not suited for quality improvement research. Either method has been used successfully to predict acceptance risks for buyers and sellers, and within the limit of applicable sample sizes, to predict the impact of changes in sampling protocol.
Technical Abstract: Calculational methods have been developed for predicting the sample distribution P(C;N) of granular products at any sample size and over the entire concentration range C from an experimental distribution at a single N. Two methods have been found to yield consistent results with varying levels of precision and ranges of N. The Negative Binomial density distribution (NBD) can handle any N that is large with respect to the test size, but is limited to the precision of two parameter functions. Its application is simple and rapid, particularly at large ', which is useful for obtaining lot concentration. The non-parametric method can handle any fit to the experimental data. It is treated as a sum of Poisson (or multinomial) distributions with varying 'l=Npl, where pl is the probability of a kernel containing contaminant in concentration range cl. By the choice of c-ranges, any precision can be approximated. This method is currently restricted to 'l <2, all l, and is more laborious than the NBD, but is ideal for discerning small changes in P(C;N) at small N, indicative of pre-harvest effect of production, processing and sorting. These methods were applied to assorted processed and unprocessed aflatoxin contaminated pistachios, almonds, and peanuts. P(C;N) at low C was established in all cases, leading to a much clearer understanding of the source of contamination. The overall shapes of P(C;N) at low N were alike among tree nuts and among two very different peanut lots, indicating that aflatoxin contamination was largely mold-, not matrix-driven. The methods show great applicability for risk analysis and developing sampling protocol.