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

We introduce a new method to test efficiently for cospeciation in tritrophic systems. Our method utilises an analogy with electrical circuit theory to reduce higher order systems into bitrophic data sets 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. [Mramba, L. K., S. Barber, K. Hommola, L. A. Dyer, J. S. Wilson, M. L. Forister and W. R. Gilks (2013): "Permutation tests for analyzing cospeciation in multiple phylogenies: applications in tri-trophic ecology," Stat. Appl. Genet. Mol. Biol., 12, 679-701.]. 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. [Hommola, K., J. E. Smith, Y. Qiu and W. R. Gilks (2009): "A permutation test of host-parasite cospeciation," Mol. Biol. Evol., 26, 1457-1468.] and Mramba et al. [Mramba, L. K., S. Barber, K. Hommola, L. A. Dyer, J. S. Wilson, M. L. Forister and W. R. Gilks (2013): "Permutation tests for analyzing cospeciation in multiple phylogenies: applications in tri-trophic ecology," Stat. Appl. Genet. Mol. Biol., 12, 679-701.] 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 comparable 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, C., H. Godfray, S. West, C. Hansson and J. Cook (2005): "The evolution of host use and unusual reproductive strategies in achrysocharoides parasitoid wasps," J. Evol. Biol., 18, 1029-1041.], at both the bitrophic and tritrophic levels.