We introduce mathematical notions used in phylogenetics and three sorts of phylogenetics polytopes. The Tight span and the Lipschitz polytope are both associated to finite metric spaces and can be connected to distance-preserving embeddings, while the balanced minimum evolution (BME) polytope is associated to natural numbers.
Resúmen
Presentamos las nociones matemáticas utilizadas en filogenética y tres clases de politopos de la filogenética. El Tight span y el politopo de Lipschitz se asocian a espacios métricos finitos y pueden conectarse a incrustaciones que conservan la distancia, mientras el politopo de evolución mínima balanceada (BME) se asocia con números naturales.
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1. Bandelt, H.-J., & Dress, A. W. M. (1992). A canonical decomposition theory for metrics on a finite set. Adv. Math., 92(1), 47-105. https://doi.org/10.1016/0001-8708(92)90061-O
2. Bollobas, B. (1998). Modern graph theory (corrected ed.). Heidelberg: Springer. https://doi.org/10.1007/978-1-4612-0619-4
3. Delucchi, E., & Hoessly, L. (2020). Fundamental polytopes of metric trees via parallel connections of matroids. European Journal of Combinatorics, 87, 103098. https://doi.org/10.1016/j.ejc.2020.103098
4. Dress, A. (1984). Trees, tight extensions of metric spaces, and the cohomological dimension of certain groups: A note on combinatorial properties of metric spaces. Advances in Mathematics, 53, 321-402. https://doi.org/10.1016/0001-8708(84)90029-X
5. Dress, A., Huber, K. T., Koolen, J., Moulton, V., & Spillner, A. (2011). Basic phylogenetic combinatorics. Cambridge University Press. https://doi.org/10.1017/CBO9781139019767
6. Eickmeyer, K., Huggins, P., Pachter, L., & Yoshida, R. (2008). On the optimality of the neighbor-joining algorithm. Algorithms for Molecular Biology, 3(1), 5. https://doi.org/10.1186/1748-7188-3-5
7. Forcey, S., Keefe, L., & Sands, W. (2016). Facets of the balanced minimal evolution polytope. Journal of Mathematical Biology, 73(2), 447-468. https://doi.org/10.1007/s00285-015-0957-1
8. Gascuel, O., & Steel, M. (2006). Neighbor-Joining Revealed. Molecular Biology and Evolution, 23(11), 1997-2000. https://doi.org/10.1093/molbev/msl072
9. Gordon, J., & Petrov, F. (2017). Combinatorics of the Lipschitz polytope. Arnold Math. J., 3(2), 205-218. https://doi.org/10.1007/s40598-017-0063-0
10. Haws, D. C., Hodge, T. L., & Yoshida, R. (2011). Optimality of the neighbor joining algorithm and faces of the balanced minimum evolution polytope. Bulletin of Mathematical Biology, 73(11), 2627-2648. https://doi.org/10.1007/s11538-011-9640-x
11. Huson, D. H., Rupp, R., & Scornavacca, C. (2010). Phylogenetic networks: Concepts, algorithms and applications. Cambridge University Press. https://doi.org/10.1017/CBO9780511974076
12. Isbell, J. R. (1964). Six theorems about injective metric spaces. Commentarii Mathematici Helvetici, 39(1), 65-76. https://doi.org/10.1007/BF02566944
13. Lefort, V., Desper, R., & Gascuel, O. (2015). FastME 2.0: A Comprehensive, Accurate, and Fast Distance-Based Phylogeny Inference Program. Molecular Biology and Evolution, 32(10), 2798-2800. https://doi.org/10.1093/molbev/msv150
14. Ostrovska, S., & Ostrovskii, M. (2019). Generalized transportation cost spaces. arXiv. https://doi.org/10.1007/s00009-019-1433-8
15. Pauplin, Y. (2000). Direct calculation of a tree length using a distance matrix. Journal of Molecular Evolution, 51(1), 41-47. https://doi.org/10.1007/s002390010065
16. Semple, C., & Steel, M. (2003). Phylogenetics. Oxford University Press.
17. Steel, M. (2016). Phylogeny: Discrete and random processes in evolution. Society for Industrial and Applied Mathematics. https://doi.org/10.1137/1.9781611974485
18. Vershik, A. M. (2015). Classification of finite metric spaces and combinatorics of convex polytopes. Arnold Math. J., 1(1), 75-81. https://doi.org/10.1007/s40598-014-0005-z
19. Ziegler, G. M. (1995). Lectures on polytopes (Vol. 152). Springer-Verlag, New York. https://doi.org/10.1007/978-1-4613-8431-1