Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A class of phylogenetic networks reconstructable from ancestral profiles   Rooted phylogenetic networks provide an explicit representation of the
evolutionary history of a set $X$ of sampled species. In contrast to
phylogenetic trees which show only speciation events, networks can also
accommodate reticulate processes (for example, hybrid evolution, endosymbiosis,
and lateral gene transfer). A major goal in systematic biology is to infer
evolutionary relationships, and while phylogenetic trees can be uniquely
determined from various simple combinatorial data on $X$, for networks the
reconstruction question is much more subtle. Here we ask when can a network be
uniquely reconstructed from its `ancestral profile' (the number of paths from
each ancestral vertex to each element in $X$). We show that reconstruction
holds (even within the class of all networks) for a class of networks we call
`orchard networks', and we provide a polynomial-time algorithm for
reconstructing any orchard network from its ancestral profile. Our approach
relies on establishing a structural theorem for orchard networks, which also
provides for a fast (polynomial-time) algorithm to test if any given network is
of orchard type. Since the class of orchard networks includes tree-sibling
tree-consistent networks and tree-child networks, our result generalise
reconstruction results from 2008 and 2009. Orchard networks allow for an
unbounded number $k$ of reticulation vertices, in contrast to tree-sibling
tree-consistent networks and tree-child networks for which $k$ is at most
$2|X|-4$ and $|X|-1$, respectively.

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The categories of this paper are: bayes-an
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The categories of this paper are: alg-geom
13
The categories of this paper are: quant-ph
24
The categories of this paper are: dg-ga
31
The categories of this paper are: ao-sci
29
The categories of this paper are: funct-an
33
The categories of this paper are: plasm-ph
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The categories of this paper are: adap-org
9
The categories of this paper are: nlin
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The categories of this paper are: eess
34
The categories of this paper are: chem-ph
8
The categories of this paper are: hep-ex
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The categories of this paper are: math-ph
6
The categories of this paper are: astro-ph
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The categories of this paper are: stat
1
The categories of this paper are: cs