Defining phylogenetic networks using ancestral profiles

A class of phylogenetic networks reconstructable from ancestral profiles

Rooted phylogenetic networks provide an explicit representation of the evolutionary history of a set $X$ of sampled species. In contrast to phylogenetic trees which show only speciation events, networks can also accommodate reticulate processes (for example, hybrid evolution, endosymbiosis, and lateral gene transfer). A major goal in systematic biology is to infer evolutionary relationships, and while phylogenetic trees can be uniquely determined from various simple combinatorial data on $X$, for networks the reconstruction question is much more subtle. Here we ask when can a network be unique…

Displaying trees across two phylogenetic networks

Phylogenetic networks are a generalization of phylogenetic trees to leaf-labeled directed acyclic graphs that represent ancestral relationships between species whose past includes non-tree-like events such as hybridization and horizontal gene transfer. Indeed, each phylogenetic network embeds a collection of phylogenetic trees. Referring to the collection of trees that a given phylogenetic network $N$ embeds as the display set of $N$, several questions in the context of the display set of $N$ have recently been analyzed. For example, the widely studied Tree-Containment problem asks if a given …

Defining binary phylogenetic trees using parsimony

Phylogenetic (i.e. leaf-labeled) trees play a fundamental role in evolutionary research. A typical problem is to reconstruct such trees from data like DNA alignments (whose columns are often referred to as characters), and a simple optimization criterion for such reconstructions is maximum parsimony. It is generally assumed that this criterion works well for data in which state changes are rare. In the present manuscript, we prove that each phylogenetic tree $T$ with $n\geq 20 k$ leaves is uniquely defined by the set $A_k(T)$, which consists of all characters with parsimony score $k$ on $T$. T…

用最少数量的小状态字符定义系统发育树

Defining a phylogenetic tree with the minimum number of small-state characters

本文研究用最少小状态字符唯一确定系统发育树的问题，确定 3 状态最小叶子阈值为 8，并证明 n≥16 时 ⌈(n-3)/4⌉ 个 5 状态字符足以唯一确定任意树。

使用简约性定义二元系统发育树：新的界

Defining binary phylogenetic trees using parsimony: new bounds

本文研究基于最大简约性的二元系统发育树唯一性问题，将叶子数$n$的下界从$20k$降至$4k$，将非定义区间扩展至$n \leq 2k+2$，并完全填补了最近邻交换（NNI）邻域中的空白。

通过最近公共祖先约束简化并刻画有向无环图与系统发育网络

Simplifying and Characterizing DAGs and Phylogenetic Networks via Least Common Ancestor Constraints

本文提出通过LCA约束简化有向无环图与系统发育网络，刻画LCA相关和lca相关DAG，并利用“⊖”运算符高效转换以保留关键结构。