Related papers: Takeover, fixation and identifiability in finite n…
We study the evolution of the population genealogy in the classic neutral Moran Model of finite size and in discrete time. The stochastic transformations that shape a Moran population can be realized directly on its genealogy and give rise…
In this paper we study the genealogical structure of a Galton-Watson process with neutral mutations, where the initial population is large and mutation rate is small \cite{B2}. Namely, we extend in two directions the results obtained in…
Higher-order pushdown systems and ground tree rewriting systems can be seen as extensions of suffix word rewriting systems. Both classes generate infinite graphs with interesting logical properties. Indeed, the model-checking problem for…
The goal of this work is to decompose random populations with a genealogy in subfamilies of a given degree of kinship and to obtain a notion of infinitely divisible genealogies. We model the genealogical structure of a population by…
Genotype-to-phenotype mappings translate genotypic variations such as mutations into phenotypic changes. Neutrality is the observation that some mutations do not lead to phenotypic changes. Studying the search trajectories in genotypic and…
We analyse the statistical properties of genealogical trees in a neutral model of a closed population with sexual reproduction and non-overlapping generations. By reconstructing the genealogy of an individual from the population evolution,…
We study the genealogy of a sample of $k$ individuals taken uniformly without replacement from a continuous-time multitype Bienaym\'e--Galton--Watson process at fixed times. Our results are quite general, requiring only that the process be…
We analyse the friendship paradox on finite and infinite trees. In particular, we monitor the vertices for which the friendship-bias is positive, neutral and negative, respectively. For an arbitrary finite tree, we show that the number of…
We consider a fragmentation of discrete trees where the internal vertices are deleted independently at a rate proportional to their degree. Informally, the associated cut-tree represents the genealogy of the nested connected components…
This article is concerned with the long time behavior of neutral genetic population models, with fixed population size. We design an explicit, finite, exact, genealogical tree based representation of stationary populations that holds both…
Let $\mathcal{B}$ be the set of rooted trees containing an infinite binary subtree starting at the root. This set satisfies the metaproperty that a tree belongs to it if and only if its root has children $u$ and $v$ such that the subtrees…
Consider a genetic locus carrying a strongly beneficial allele which has recently fixed in a large population. As strongly beneficial alleles fix quickly, sequence diversity at partially linked neutral loci is reduced. This phenomenon is…
We study certain consistent families $(F_\lambda)_{\lambda\ge 0}$ of Galton-Watson forests with lifetimes as edge lengths and/or immigrants as progenitors of the trees in $F_\lambda$. Specifically, consistency here refers to the property…
Phylogenetically decisive collections of taxon sets have the property that if trees are chosen for each of their elements, as long as these trees are compatible, the resulting supertree is unique. This means that as long as the trees…
Geometric trees are characterized by their tree-structured layout and spatially constrained nodes and edges, which significantly impacts their topological attributes. This inherent hierarchical structure plays a crucial role in domains such…
Interacting particle systems undergoing repeated mutation and selection steps model genetic evolution, and also describe a broad class of sequential Monte Carlo methods. The genealogical tree embedded into the system is important in both…
We consider Galton-Watson trees with ${\rm Bin}(d,p)$ offspring distribution. We let $T_{\infty}(p)$ denote such a tree conditioned on being infinite. For $d=2,3$ and any $1/d\leq p_1 <p_2 \leq 1$, we show that there exists a coupling…
The problem of comparing trees representing the evolutionary histories of cancerous tumors has turned out to be crucial, since there is a variety of different methods which typically infer multiple possible trees. A departure from the…
A new version of DNA walks, where nucleotides are regarded unequal in their contribution to a walk is introduced, which allows us to study thoroughly the "fine structure" of nucleotide sequences. The approach is based on the assumption that…
We study the path of family size decompositions of varying depth of genealogical trees. We prove that this decomposition as a function on (equivalence classes of) ultra-metric measure spaces to the Skorohod space describing the family sizes…