37,904 research outputs found
Capturing a phylogenetic tree when the number of character states varies with the number of leaves
We show that for any two values for which
then there is a value so that for all the
following holds. For any binary phylogenetic tree on leaves there is a
set of characters that capture , and for which
each character takes at most distinct states. Here
`capture' means that is the unique perfect phylogeny for these characters.
Our short proof of this combinatorial result is based on the probabilistic
method.Comment: 3 pages, 0 figure
Tracing evolutionary links between species
The idea that all life on earth traces back to a common beginning dates back
at least to Charles Darwin's {\em Origin of Species}. Ever since, biologists
have tried to piece together parts of this `tree of life' based on what we can
observe today: fossils, and the evolutionary signal that is present in the
genomes and phenotypes of different organisms. Mathematics has played a key
role in helping transform genetic data into phylogenetic (evolutionary) trees
and networks. Here, I will explain some of the central concepts and basic
results in phylogenetics, which benefit from several branches of mathematics,
including combinatorics, probability and algebra.Comment: 18 pages, 6 figures (Invited review paper (draft version) for AMM
An Arrow-type result for inferring a species tree from gene trees
The reconstruction of a central tendency `species tree' from a large number
of conflicting gene trees is a central problem in systematic biology. Moreover,
it becomes particularly problematic when taxon coverage is patchy, so that not
all taxa are present in every gene tree. Here, we list four desirable
properties that a method for estimating a species tree from gene trees should
have. We show that while these can be achieved when taxon coverage is complete
(by the Adams consensus method), they cannot all be satisfied in the more
general setting of partial taxon coverage.Comment: 5 pages, 0 figure
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