Page 29 - Tequio 11

Tequio 4(11), 2021: 27-40
issn: 2594-0546

On some polytopes in phylogenetics

Politopos en filogenética

Linard Hoessly 1

Fecha de recepción: 6 de noviembre de 2020
Fecha de aceptación: 23 de diciembre de 2020

Resumen - Presentamos las nociones matemáticas Abstract - We introduce mathematical notions used
utilizadas en filogenética y tres clases de politopos de in phylogenetics and three sorts of phylogenetics
la filogenética. El Tight span y el politopo de Lipschitz polytopes. The Tight span and the Lipschitz polytope

se asocian a espacios métricos finitos y pueden are both associated to finite metric spaces and can be
conectarse a incrustaciones que conservan la distancia, connected to distance-preserving embeddings, while
mientras el politopo de evolución mínima balanceada the balanced minimum evolution (BME) polytope is
(BME) se asocia con números naturales. associated to natural numbers.

Palabras clave: Filogenética, politopo, espacio Keywords: Phylogenetics, Polytope, Finite metric
métrico finito, politopo fundamental, tight span. space, Fundamental polytope, Tight span.

1. Introduction
hylogenetics studies the methods and the practice of identifying evolutionary relationships among bi-
ological species. Finding such relationships is a current focus of research, and is usually performed via
Pphylogenetic inference based on mathematical models of evolution (Semple & Steel, 2003; Steel, 2016),
which are represented as phylogenetic trees or networks (Huson, Rupp, & Scornavacca, 2010). Usually, genet-
ic material is transferred from parents to offspring, resulting in tree-like representations. However, different
biological species can transfer genetic information between otherwise unrelated organisms. Horizontal gene
transfer e.g. is a mechanism where genetic material from one species is moved to another one which is rel-
evant in how bacteria acquire antibiotic resistance. This suggests the possibility that corresponding parts of
the evolutionary history might not be tree-like, and such relationships are often represented via phylogenetic
networks. There are different approaches to phylogenetic reconstruction. We briefly introduce and elaborate on
distance-based and likelihood-based methods. Distance-based techniques first compute a pairwise distance-like
function between the taxa to construct a phylogenetic tree T (or structure) that best represents the distances
obtained, usually via some optimality criterion. Distance-based methods are popular as they tend to be fast.
Concerning likelihood-based methods there are two main paradigms: maximum likelihood (ML) and bayesian
methods. In both, evolution is described through probabilistic model of sequence evolution, enabling in principle
computations of likelihoods of observing the data given the model and its parameters. While these methods are
assumed to be more correct from a foundational level, corresponding computations can be slow.

1 Department of Mathematical Sciences, University of Copenhagen, Copenhagen, Denmark;
email: hoessly@math.ku.dk ORCID-ID: 0000-0002-2745-2141

Tequio, enero-abril 2021, vol. 4, no. 11