A statistical method for analysing cospeciation in tritrophic ecology using electrical circuit theory

Colleen Nooney, Stuart Barber, Arief Gusnanto, & Walter R. Gilks.
We introduce a new method to test efficiently for cospeciation in tritrophic systems. Our method utilises electrical circuit theory to reduce higher order systems into bitrophic systems that retain the information of the original system. We use a sophisticated permutation scheme that weights interactions between two trophic layers based on their connection to the third layer in the system. Our method has several advantages compared to the method of Mramba et al. (2013). We do not require triangular interactions to connect the three phylogenetic trees and an easily interpreted p-value is obtained in one step. Another advantage of our method is the scope for generalisation to higher order systems and phylogenetic networks. The performance of our method is compared to the methods of Hommola et al. (2009) and Mramba et al. (2013) at the bitrophic and tritrophic level, respectively. This was achieved by evaluating type I error and statistical power. The results show that our method produces unbiased p-values and has greater power overall at both trophic levels. Our method was successfully applied to a dataset of leaf-mining moths, parasitoid wasps and host plants (Lopez-Vaamonde et al., 2005), at both the bitrophic and tritrophic levels.

Some key words:
cospeciation, weighted permutation test, tritrophic ecology, electrical circuit, Kirchhoff matrix

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