AbstractThe transfer distance (TD) was introduced in the classification framework and studied in the context of phylogenetic tree matching. Recently, Lemoine et al. (2018) showed that TD can be a powerful tool to assess the branch support of phylogenies with large data sets, thus providing a relevant alternative to Felsenstein’s bootstrap. This distance allows a reference branch β in a reference tree 𝒯 to be compared to a branch b from another tree T, both on the same set of n taxa. The TD between these branches is the number of taxa that must be transferred from one side of b to the other in order to obtain β. By taking the minimum TD from β to all branches in T we define the transfer index, denoted by ϕ(β, T), measuring the degree of agreement of β with T. Let us consider a reference branch β having p tips on its light side and define the transfer support (TS) as 1 – ϕ(β, T)/(p – 1). The aim of this article is to provide evidence that p 1 is a meaningful normalization constant in the definition of TS, and measure the statistical significance of TS, assuming that β is compared to a tree T drawn according to a null model. We obtain several results that shed light on these questions in a number of settings. In particular, we study the asymptotic behavior of TS when n tends to ∞, and fully characterize the distribution of ϕ when T is a caterpillar tree.
On global solutions and asymptotic behavior of planar magnetohydrodynamics with large data
