The purpose of computational phylogenetics is to assemble a branching diagram or tree that represents a hypothesis regarding the evolutionary relationships of an entity set. Phyletic trees and cladograms are well-known methods for expressing phyletic relationships. Although many estimating methods for cladograms have been proposed, few studies have examined automatic estimation of phyletic trees because, in our opinion, most biological entities do not have birth year information. On the other hand, targets in cultural phylogenetics may have birth year information. Therefore, we propose a method to estimate phyletic trees for cultural phylogenetics using estimated cladograms and birth order information. First, we define necessary conditions for estimating phyletic trees from cladograms and birth order. We then propose an algorithm for estimating phyletic trees that satisfy these conditions. We demonstrate that the phyletic trees estimated by the proposed algorithm satisfy the defined conditions. Our experimental results show that the proposed estimation method obtained approximately 70% estimation accuracy for some targets.