25 problems

Let $n$-leaved phylogenetic trees be compared using the quartet distance, whose diameter is the maximum distance between two such trees. Bandelt–Dress conjecture. The diameter is a…

Let two rooted balanced phylogenetic trees have the same leaf set of size $n$. Martin–Thatte conjecture. The two trees must agree on at least … leaves. This conjecture concerns the…

Cardwell's conjecture. Every GL-binomial BMT-derived model derived from a phylogenetic tree with colored nodes must be vertex regular.

Let $L_{\mathcal{T}}$ be the ultrametric Laplacian of a finite ultrametric phylogenetic tree, and let its eigenbasis and spectral parameters be used to represent functions on the t…

Let Towering distance be the metric on the space of phylogenetic trees with non-identical leaves, and let the preliminary algorithm described in Section compute Towering distances.…

Let Towering space be the complete length space of phylogenetic trees with non-identical leaves, with tree space denoted by $\mathcal{T}^{\mathbf{P}(\mathcal{N})}$. Consider trees…

Let $T\in\widehat{\mathcal{RBT}}_n$ be a fixed phylogenetic tree, and let $T'$ be a random tree differing from $T$ by a single subtree-prune-and-regraft (SPR) move, chosen uniforml…

Tropicalization conjecture. The tropicalization $\operatorname{Trop}\mathcal{M}_{\mathrm{C}_{n-1}}$ is the space of ASPTs: the fan formed by the cones $C_{T,\varphi}$ with…

Let $k$ be a positive integer, and consider sets of three trees on $2^k$ taxa: two caterpillar trees and a fully balanced tree whose leaves are equally distant from the root. Maxim…

The Wald space is the subspace of phylogenetic forests referred to in the cited literature. Stickiness conjecture. The Wald space features stickiness. Stickiness is known to occur…

A rooted phylogenetic tree has a sound Colless-like index if the index satisfies the soundness properties under discussion, and let $f:\mathbb{N}\rightarrow\mathbb{N}$ be a functio…

Let $T_1$ and $T_2$ be equidistant rooted phylogenetic trees with $n$ leaves in $X$, and let $\Gamma_{T_1,T_2}$ be the tropical line segment between them. A nearest neighbor interc…

Let ${\mathcal S}$ and ${\mathcal T}$ be balanced rooted binary phylogenetic $X$-trees, meaning that each has $2^m$ leaves for some non-negative integer $m$ and height $m$, and let…

Nonexistence conjecture. No function $f:\mathbb{N}\to\mathbb{N}$ satisfies this property.

Li et al.'s conjecture. For any rooted binary ultrametric phylogenetic tree and a simple model of evolution, the Fitch algorithm using all taxa for ancestral state reconstruction i…

Li, Steel and Zhang's conjecture. For any ultrametric phylogenetic tree and a symmetric model, the Fitch parsimony method using all terminal taxa is more accurate, or at least as a…

The cluster-count criterion. One has

Let $\mathcal T_n$ be the space of unrooted trees on $n$ labelled leaves, equipped with the tree distance under consideration. A caterpillar is an unrooted tree whose internal vert…

Let $T$ be a tree with a finite set of leaves, and choose a sequence of leaves at random according to the sampling scheme in the paper. Let $W_k$ denote the length of the minimal s…

Let $(\gamma,\alpha)$ be covariance parameters in a general tree growth model, and suppose that $(\gamma,\alpha)$ is microergodic, meaning that it can be consistently estimated und…

A gene tree is a phylogenetic tree representing the evolutionary history of a particular gene, while a species tree represents the evolutionary history of the species. Given a coll…

A bounding hypersurface is a hypersurface bounding a vistal cell in a global NPC cubical complex. High-degree bounding hypersurface conjecture. The bounding hypersurface can have c…

Let $T_1$ and $T_2$ be binary phylogenetic trees with the same leaf-set, and let a maximum agreement subtree be a largest common subtree on a subset of their leaves. In the balance…

Let $T_1$ and $T_2$ be balanced, rooted, binary trees of height $m$. An agreement subtree is a common subtree of the two trees on a shared set of leaves. The square-root agreement-…

Weighted-tree tropical Grassmannian conjecture. For $m\geq 5$, one has