Author
Baez, JC
Otter, N
Journal title
THEORY AND APPLICATIONS OF CATEGORIES
Issue
40
Volume
32
Last updated
2018-12-08T13:53:42.167+00:00
Page
1397-1453
Abstract
© John C. Baez and Nina Otter, 2017. We construct an operad Phyl whose operations are the edge-labelled trees used in phylogenetics. This operad is the coproduct of Com, the operad for commutative semigroups, and [0, ∞), the operad with unary operations corresponding to nonnegative real numbers, where composition is addition. We show that there is a homeomorphism between the space of n-ary operations of Phyl and Tn×[0, ∞)n+1, where Tn is the space of metric n-trees introduced by Billera, Holmes and Vogtmann. Furthermore, we show that the Markov models used to reconstruct phylogenetic trees from genome data give coalgebras of Phyl. These always extend to coalgebras of the larger operad Com+[0, ∞], since Markov processes on finite sets converge to an equilibrium as time approaches infinity. We show that for any operad O, its coproduct with [0, ∞] contains the operad W(O) constructed by Boardman and Vogt. To prove these results, we explicitly describe the coproduct of operads in terms of labelled trees.
Symplectic ID
734752
Download URL
http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000441757500021&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=4fd6f7d59a501f9b8bac2be37914c43e
Publication type
Journal Article
Publication date
2017
Please contact us with feedback and comments about this page. Created on 09 Oct 2017 - 10:39.