Permutation tests for analysing cospeciation in multiple phylogenies: Applications in tri-trophic ecology

Lazarus K. Mramba, Stuart Barber, Kerstin Hommola, Lee A. Dyer, Joseph S. Wilson, Matthew Forister, & Walter R. Gilks.
There is a need for a reliable statistical test which is appropriate for assessing cospeciation of more than two phylogenies. We have developed an algorithm using a permutation method that can be used to test for and infer tri-trophic evolutionary relationships of organisms given both their phylogenies and pairwise interactions.

An overall statistic has been developed based on the dominant eigenvalue of a covariance matrix, and compared to values of the statistic computed when tree labels are permuted. The resulting overall $p$-value is used to test for the presence or absence of cospeciation in a tri-trophic system. If cospeciation is detected, we propose new test statistics based on partial correlations to uncover more details about the relationships between multiple phylogenies.

One of the strengths of our method is that it allows more parasites than hosts or more hosts than parasites, with multiple associations and more than one parasite attached to a host (or one parasite attached to multiple hosts). The new method does not require any parametric assumptions of the distribution of the data, and unlike the old methods, which utilise several pairwise steps, the overall statistic used is obtained in one step.

We have applied our method to two published datasets where we obtained detailed information about the strength of associations among species with calculated partial p-values and one overall p-value from the dominant eigenvalue test statistic.

Our permutation method produces reliable results with a clear procedure and statistics applied in an intuitive manner. Our algorithm is useful in testing evidence for three-way cospeciation in multiple phylogenies with tri-trophic associations and determining which phylogenies are involved in cospeciation.

Some key words:
Morphometrics, Protein bioinformatics, Similarity transformations, Statistical shape analysis, Unlabelled shape analysis

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