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Abstract:
The central problem of molecular phylogenetics
is the inference of evolutionary trees from biological sequence data (DNA)
of currently living species. Since standard statistical models of sequence
evolution along trees lead to parameterized algebraic varieties,
understanding these varieties better may lead to
better inference methods, which would be of great benefit to biology.
The first step is the explicit determination of the defining ideals
for a fixed model and all possible trees. After a brief introduction
to the biological origins of the problem, we outline recent progress
and point out several open problems.
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