A polynomial time algorithm for calculating the probability of a ranked gene tree given a species tree

In this paper, we provide a polynomial time algorithm to calculate the probability of a ranked gene tree topology for a given species tree, where a ranked tree topology is a tree topology with the internal vertices being ordered. The probability of a gene tree topology can thus be calculated in polynomial time if the number of orderings of the internal vertices is a polynomial number. However, the complexity of calculating the probability of a gene tree topology with an exponential number of rankings for a given species tree remains unknown.Polynomial algorithms for calculating ranked gene tree probabilities may become useful in developing methodology to infer species trees based on a collection of gene trees, leading to a more accurate reconstruction of ancestral species relationships.