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| Main Authors: | , |
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| Format: | Preprint |
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2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2601.15517 |
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| _version_ | 1866915746520498176 |
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| author | Alonso, Maria Emilíia Álvarez, Ernesto |
| author_facet | Alonso, Maria Emilíia Álvarez, Ernesto |
| contents | We study the ChorHendySnir2006 evolutionary model, which consists of a rooted phylogenetic tree with three leaves, subject to the Jukes--Cantor (JC69) molecular evolutionary model and molecular clock. We show that the likelihood function associated with this model has a unique maximum which depends analytically of the parameters (as it was conjectured in ChorHendySnir2006), assuming that these parameters verify some very precise inequalities; some of which arise naturally from the model. With a typical argument of differential topology we reduce the proof to answer a question of algebra, very simple, although computationally involved, that we solve using some Maple libraries. We are very indebted to Marta Casanellas, who presented the problem to us and gave us the first insights on it. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_15517 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A computation of maximum likelihood for 4-states-triplets under Jukes-Cantor and MC Alonso, Maria Emilíia Álvarez, Ernesto Populations and Evolution 92B, 90C23 We study the ChorHendySnir2006 evolutionary model, which consists of a rooted phylogenetic tree with three leaves, subject to the Jukes--Cantor (JC69) molecular evolutionary model and molecular clock. We show that the likelihood function associated with this model has a unique maximum which depends analytically of the parameters (as it was conjectured in ChorHendySnir2006), assuming that these parameters verify some very precise inequalities; some of which arise naturally from the model. With a typical argument of differential topology we reduce the proof to answer a question of algebra, very simple, although computationally involved, that we solve using some Maple libraries. We are very indebted to Marta Casanellas, who presented the problem to us and gave us the first insights on it. |
| title | A computation of maximum likelihood for 4-states-triplets under Jukes-Cantor and MC |
| topic | Populations and Evolution 92B, 90C23 |
| url | https://arxiv.org/abs/2601.15517 |