@inproceedings{baez_operads_2015,
title = {Operads and {Phylogenetic} {Trees}},
abstract = {We construct an operad \${\textbackslash}mathrm\{Phyl\}\$ whose operations are the edge-labelled trees used in phylogenetics. This operad is the coproduct of \${\textbackslash}mathrm\{Com\}\$, the operad for commutative semigroups, and \$[0,{\textbackslash}infty)\$, 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 \${\textbackslash}mathrm\{Phyl\}\$ and \${\textbackslash}mathcal\{T\}\_n{\textbackslash}times [0,{\textbackslash}infty){\textasciicircum}\{n+1\}\$, where \${\textbackslash}mathcal\{T\}\_n\$ 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 \${\textbackslash}mathrm\{Phyl\}\$. These always extend to coalgebras of the larger operad \${\textbackslash}mathrm\{Com\} + [0,{\textbackslash}infty]\$, 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,{\textbackslash}infty]\$ contains the operad \$W(O)\$ constucted by Boardman and Vogt. To prove these results, we explicitly describe the coproduct of operads in terms of labelled trees.},
author = {Baez, John C. and Otter, Nina},
year = {2015},
note = {ZSCC: NoCitationData[s1]
arXiv: 1512.03337},
keywords = {Biology, Coalgebras}
}