TY - GEN
T1 - Analytic solutions for Three-Taxon MLMC trees with variable rates across sites
AU - Chor, Benny
AU - Hendy, Michael
AU - Penny, David
N1 - Publisher Copyright:
© Springer-Verlag Berlin Heidelberg 2001.
PY - 2001
Y1 - 2001
N2 - We consider the problem of finding the maximum likelihood rooted tree under a molecular clock (MLMC), with three species and 2-state characters under a symmetric model of substitution. For identically distributed rates per site this is probably the simplest phylogenetic estimation problem, and it is readily solved numerically. Analytic solutions, on the other hand, were obtained only recently (Yang, 2000). In this work we provide analytic solutions for any distribution of rates across sites (provided the moment generating function of the distribution is strictly increasing over the negative real numbers). This class of distributions includes, among others, identical rates across sites, as well as the Gamma, the uniform, and the inverse Gaussian distributions. Therefore, our work generalizes Yang’s solution. In addition, our derivation of the analytic solution is substantially simpler. We employ the Hadamard conjugation (Hendy and Penny, 1993) and convexity of an entropy–like function.
AB - We consider the problem of finding the maximum likelihood rooted tree under a molecular clock (MLMC), with three species and 2-state characters under a symmetric model of substitution. For identically distributed rates per site this is probably the simplest phylogenetic estimation problem, and it is readily solved numerically. Analytic solutions, on the other hand, were obtained only recently (Yang, 2000). In this work we provide analytic solutions for any distribution of rates across sites (provided the moment generating function of the distribution is strictly increasing over the negative real numbers). This class of distributions includes, among others, identical rates across sites, as well as the Gamma, the uniform, and the inverse Gaussian distributions. Therefore, our work generalizes Yang’s solution. In addition, our derivation of the analytic solution is substantially simpler. We employ the Hadamard conjugation (Hendy and Penny, 1993) and convexity of an entropy–like function.
UR - http://www.scopus.com/inward/record.url?scp=84959050942&partnerID=8YFLogxK
U2 - 10.1007/3-540-44696-6_16
DO - 10.1007/3-540-44696-6_16
M3 - פרסום בספר כנס
AN - SCOPUS:84959050942
SN - 3540425160
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 204
EP - 213
BT - Algorithms in Bioinformatics - First International Workshop, WABI 2001 Århus Denmark, August 28-31, 2001 Proceedings
A2 - Moret, Bernard M. E.
A2 - Gascuel, Olivier
PB - Springer Verlag
Y2 - 28 August 2001 through 31 August 2001
ER -