The examination of a competition matrix for transitivity and intransitive loops

Recent examinations of competition matrices for transitivity (species A > species B > species C) have used techniques that can be subject to certain biases. First, recent theoretical and empirical analyses have shown that traditional measures of competitive performance are biased in favor of the larger species. It is argued that this size bias has the potential to bias analyses of transitivity. Second, analytical techniques used to test matrices for transitivity can be shown to be insensitive to the presence of intransitive loops. Techniques are presented for exploring both these types of erros and these techniques are illustrated using the results from a six-species study of marsh plants. In addition, two published studies are partially reanalyzed using a technique designed to detect intransitivities. Results for both the new data set as well as for the published data sets fail to reveal intransitivities. For the marsh plant study, the size bias associated with traditional measures of competitive success did not bias in favor of transitivity. We conclude (1) that the studies examined do not possess intransitive loops and (2) care must be taken in order to avoid biased analyses if intransitive loops are to be detected.