Related papers: Statistical properties of genealogical trees
Ignoring the differences between countries, human reproductive and dispersal behaviors can be described by some standardized models, so whether there is a universal law of population growth hidden in the abundant and unstructured data from…
Given a gene-tree labeled topology $G$ and a species tree $S$, the "ancestral configurations" at an internal node $k$ of $S$ represent the combinatorially different sets of gene lineages that can be present at $k$ when all possible…
Phylogenetic trees represent the evolutionary relationships between extant lineages, where extinct or non-sampled lineages are omitted. Extending the work of Stadler and collaborators, this paper focuses on the branch lengths in…
Gene gains and losses have shaped the gene repertoire of species since the universal last common ancestor to species today. Genes in extant species were gained at different historical times via de novo creation of new genes, duplication of…
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…
We consider an exactly solvable model of branching random walk with random selection, which describes the evolution of a population with $N$ individuals on the real line. At each time step, every individual reproduces independently, and its…
The spread of infectious disease in a human community or the proliferation of fake news on social media can be modeled as a randomly growing tree-shaped graph. The history of the random growth process is often unobserved but contains…
This article is a presentation of specific recent results describing scaling limits of individual-based models. Thanks to them, we wish to relate the time-scales typical of demographic dynamics and natural selection to the parameters of the…
We calculate the density and expectation for the number of lineages in a reconstructed tree with $n$ extant species. This is done with conditioning on the age of the tree as well as with assuming a uniform prior for the age of the tree.
The probability that two randomly selected phylogenetic trees of the same size are isomorphic is found to be asymptotic to a decreasing exponential modulated by a polynomial factor. The number of symmetrical nodes in a random phylogenetic…
The goal of this note is to present a general approach to define the net reproduction function for a large class of nonlinear physiologically structured population models. In particular, we are going to show that this can be achieved in a…
The deterministic selection-recombination equation describes the evolution of the genetic type composition of a population under selection and recombination in a law of large numbers regime. So far, an explicit solution has seemed out of…
For a family of models of evolving population under selection, which can be described by noisy traveling wave equations, the coalescence times along the genealogical tree scale like $\log^\alpha N$, where $N$ is the size of the population,…
The hierarchical and recursive expressive capability of rooted trees is applicable to represent statistical models in various areas, such as data compression, image processing, and machine learning. On the other hand, such hierarchical…
Let $W_1,\ldots,W_N$ be a sample of $\mathrm{Pareto}(\alpha)$ random variables normalized by their sum, such that $\sum_i W_i=1$. The $W_i$ may represent the weights of valleys in a spin glass (if $0<\alpha<1$), or the frequency of…
Neutral macroevolutionary models, such as the Yule model, give rise to a probability distribution on the set of discrete rooted binary trees over a given leaf set. Such models can provide a signal as to the approximate location of the root…
Reconstructing the tree of life from molecular sequences is a fundamental problem in computational biology. Modern data sets often contain a large number of genes, which can complicate the reconstruction problem due to the fact that…
Phylogenetic networks generalize phylogenetic trees by allowing the modelization of events of reticulate evolution. Among the different kinds of phylogenetic networks that have been proposed in the literature, the subclass of binary…
Several real-world and abstract structures and systems are characterized by marked hierarchy to the point of being expressed as trees. Because the study of these entities often involves sampling (or discovering) the tree nodes in a specific…
The paper reviews the results obtained for spatial population models and the evolution of the genealogies of these populations during the last decade by the author and his coworkers. The focus is on their large scale behaviour and on the…