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Probability models for detecting transgenic plants

Published online by Cambridge University Press:  01 June 2008

Carlos M. Hernández-Suárez ,
Osval A. Montesinos-López ,
Graham McLaren  and
José Crossa
Carlos M. Hernández-Suárez
Affiliation:
Facultad de Ciencias, Universidad de Colima, Bernal Díaz del Castillo No. 340 Col. Villas San Sebastián, C.P. 28045Colima, Colima, México
Osval A. Montesinos-López
Affiliation:
Facultad de Telemática, Universidad de Colima, Bernal Díaz del Castillo No. 340 Col. Villas San Sebastián, C.P. 28045Colima, Colima, México
Graham McLaren
Affiliation:
Biometrics and Bioinformatics Unit, Crop Informatics Laboratory (CRIL), International Rice Research Institute (IRRI), DAPO Box 7777, Manila, Philippines
José Crossa*
Affiliation:
Biometrics and Statistics Unit, Crop Informatics Laboratory (CRIL), International Maize and Wheat Improvement Center (CIMMYT), Apdo. Postal 6-641, MéxicoDF, México
*
*Correspondence j.crossa@cgiar.org
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Abstract

When detecting the adventitious presence of transgenic plants (AP), it is important to use an appropriate testing method in the laboratory. Dorfman's group testing method is effective for reducing the number of laboratory analyses, but does not consider the case where AP is diluted below the sensitivity of the analyses, which causes the rate of false negatives to increase. The objective of this study is to propose binomial and negative binomial probabilistic models for determining the required sample size (n), number of pools (g), and size of the pool (k) for detecting individuals possessing AP with a probability ≥ (1 − α) (for a small α) given: (1) pool size (k); (2) estimated proportion of individuals with AP in the population (p); (3) concentration of the trait of interest (AP) in individual seeds (w); and (4) detection limit of the test (c) (AP concentration in a pool below which it cannot be detected). The proposed models consider the different rates of false positives (δ) and false negatives (λ), and the assessment of consumer and producer risks. Results have shown that when using the negative binomial, a required sample size n can be determined that guarantees a high probability that m individuals or g pools containing AP will be found. The pools formed have an optimum size, such that one element with AP will be detected at a low cost. The negative binomial distribution should be used when it is known that the proportion of individuals with AP in the population is p < 0.1; thus, it is guaranteed that m individuals or g pools of individuals with AP will be detected with high probability.

Keywords

adventitious presence of transgenic plantsbinomial distributionnegative binomial distributionpool numberpool sizesample size
Type
Research Article
Information
Seed Science Research , Volume 18 , Issue 2 , June 2008 , pp. 77 - 89
Copyright
Copyright © Cambridge University Press 2008

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