1999 Fiscal Year Final Research Report Summary
Mathematical Research on Most-Parsimonious Reconstruction Problems in Phylogeny
| Project/Area Number |
10640136
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (C)
|
| Allocation Type | Single-year Grants |
|---|
| Section | 一般 |
|---|
| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
|
|---|
| Research Institution | Tokai University Junior College |
|---|
Principal Investigator |
NARUSHIMA Hiroshi Tokai University Junior College, Professor, 教授 (90056200)
|
|---|
| Co-Investigator(Kenkyū-buntansha) |
HANAZAWA Masazumi Tokai University, Science, Professor, 理学部, 教授 (50008851)
|
|---|
| Project Period (FY) |
1998 – 1999
|
| Keywords | Phylogeny / Evolutionary tree / ancestral character-state / Most-parsimonious reconstruction / ACCTRAN reconstruction / MPR-poset / complete distributivity of MPR-poset / MPR-problems on unicycle graphs |
|---|
| Research Abstract |
A mathematical theory for the subject on ancestral character-state reconstructions under the maximum parsimony in phylogeny has been developing. Recently, a clear method for the subject under a given el-tree has been presented by Hanazawa and Narushima (1995, 1997).
In the framework based on the method, Narushima and Misheva have refined and generalized the ACCTRAN reconstruction originated with Farris (1970) and defined more explicitly by Swofford and Maddison (1987), which is considered a more meaningful and useful one of the many possible most-parsimonious reconstructions (abbreviated to MPRs). Then Narushima and Misheva have showed the subtree-complete maximum-parsimonity of ACCTRAN reconstructions, and Narushima has showed another remarkable property, that is, the extremal property, of ACCTRAN reconstructions.
Furthermore, Miyakawa and Narushima have mathematically defined and generalized the MPR-poset of all MPRs, which is introduced by Minaka (1993), and then have showed the following theorems on MPR-posets : 1) an usual MPR-poset is a complete distributive lattice, 2) a σ (r)-version MPR-poset is a lower-complete semilattice, 3) any interval poset of a σ (r)-version MPR-poset is a complete distributive lattice. And also, some properties of the distortion index on all MPRs have been clarified with the ACCTRAN reconstruction.
On the other hand, Hanazawa and Narushima have given an efficient algorithm for MPR-problems on unicycle graphs.
|
