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- Title
Counting phylogenetic networks of level 1 and 2.
- Authors
Bouvel, Mathilde; Gambette, Philippe; Mansouri, Marefatollah
- Abstract
Phylogenetic networks generalize phylogenetic trees, and have been introduced in order to describe evolution in the case of transfer of genetic material between coexisting species. There are many classes of phylogenetic networks, which can all be modeled as families of graphs with labeled leaves. In this paper, we focus on rooted and unrooted level-k networks and provide enumeration formulas (exact and asymptotic) for rooted and unrooted level-1 and level-2 phylogenetic networks with a given number of leaves. We also prove that the distribution of some parameters of these networks (such as their number of cycles) are asymptotically normally distributed. These results are obtained by first providing a recursive description (also called combinatorial specification) of our networks, and by next applying classical methods of enumerative, symbolic and analytic combinatorics.
- Subjects
COMBINATORICS; COUNTING; ASYMPTOTIC distribution; GAUSSIAN distribution; GENERATING functions
- Publication
Journal of Mathematical Biology, 2020, Vol 81, Issue 6/7, p1357
- ISSN
0303-6812
- Publication type
Article
- DOI
10.1007/s00285-020-01543-5