Jane Coons

• 
  Student Presentation: Combinatorics of k-Interval Cospeciation for Cophylogeny
  Jane Coons

  Cophylogenetics is the study of the evolutionary relationships between taxonomical units that are believed to be evolving concomitantly. We examine the combinatorial properties of the cophylogenetic distance metric, k-interval cospeciation, which was introduced by Huggins, Owen and Yoshida in their 2012 paper, "First steps toward the geometry of cophylogeny." We determined that k-interval cospeciation is a unique discrete distance metric which can quantify a degree of global congruence between two phylogenetic trees while allowing for local incongruence. We counted the size of the neighborhood of trees which satisfy the largest possible k-interval cospeciation with a given tree. Due to the way this neighborhood of trees grows as a proportion of all possible trees, we believe that k-interval cospeciation may prove useful for analyzing data obtained through simulations.