Journal of Agricultural, Biological, and Environmental Statistics
, 13:177
First online:
Collision probabilities for AFLP bands, with an application to simple measures of genetic similarity
 Gerrit GortAffiliated withWageningen University Email author
 , Wim J. M. KoopmanAffiliated withBiosystematics Group, National Herbarium Nederland, Wageningen University branch
 , Alfred SteinAffiliated withDepartment of Earth Observation Science, ITC
 , Fred A. van EeuwijkAffiliated withWageningen University
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AFLP is a frequently used DNA fingerprinting technique that is popular in the plant sciences. A problem encountered in the interpretation and comparison of individual plant profiles, consisting of band presenceabsence patterns, is that multiple DNA fragments of the same length can be generated that eventually show up as single bands on a gel. The phenomenon of two or more fragments coinciding in a band within an individual profile is a type of homoplasy, that we call collision. Homoplasy biases estimates of genetic similarity. In this study, we show how to calculate collision probabilities for bands as a function of band length, given the fragment count, the band count, or band lengths. We also determine probabilities of higher order collisions, and estimate the total number of collisions for a profile. Since short fragments occur more often, short bands are more likely to contain collisions. For a typical plant genome and AFLP procedure, the collision probability for the shortest band is 25 times larger than for the longest. In a profile with 100 bands a quarter of the bands may contain collisions, concentrated at the shorter band lengths. All calculations require a careful estimate of the monotonically decreasing fragment length distribution. Modifications of Dice and Jaccard coefficients are proposed. The principles are illustrated on data from a phylogenetic study in lettuce.
Key Words
Dice Fragment length distribution Jaccard Occupancy distribution Saddlepoint approximation Size homoplasy Title
 Collision probabilities for AFLP bands, with an application to simple measures of genetic similarity
 Journal

Journal of Agricultural, Biological, and Environmental Statistics
13:177
 Online Date
 June 2008
 DOI
 10.1198/108571108X308116
 Print ISSN
 10857117
 Online ISSN
 15372693
 Publisher
 SpringerVerlag
 Additional Links
 Topics
 Keywords

 Dice
 Fragment length distribution
 Jaccard
 Occupancy distribution
 Saddlepoint approximation
 Size homoplasy
 Industry Sectors
 Authors

 Gerrit Gort ^{(1)}
 Wim J. M. Koopman ^{(2)}
 Alfred Stein ^{(3)}
 Fred A. van Eeuwijk ^{(1)}
 Author Affiliations

 1. Wageningen University, PO Box 100, 6700 AC, Wageningen, The Netherlands
 2. Biosystematics Group, National Herbarium Nederland, Wageningen University branch, PO Box 100, 6700 AC, Wageningen, The Netherlands
 3. Department of Earth Observation Science, ITC, P.O. Box 6, 7500 AA, Enschede, The Netherlands