Related papers: Non-extensive condensation in reinforced branching…
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…
Recent studies have shown that even in the absence of extrinsic stress, the morphologically symmetrically dividing model bacteria Escherichia coli do not generate offspring with equal reproductive fitness. Instead, daughter cells exhibit…
We consider catalytic branching populations. They consist of a catalyst population evolving according to a critical binary branching process in continuous time with a constant branching rate and a reactant population with a branching rate…
Coalescence processes have received a lot of attention in the context of conditional branching processes with fixed population size and non-overlapping generations. Here we focus on similar problems in the context of the standard…
In this paper, we consider time-inhomogeneous branching processes and time-inhomogeneous birth-and-death processes, in which the offspring distribution and birth and death rates (respectively) vary in time. A classical result of branching…
We consider branching particle processes on discrete structures like the hypercube in a random fitness landscape (i.e., random branching/killing rates). The main question is about the location where the main part of the population sits at a…
We consider a supercritical branching population, where individuals have i.i.d. lifetime durations (which are not necessarily exponentially distributed) and give birth (singly) at constant rate. We assume that individuals independently…
Traditionally evolution is seen as a process where from a pool of possible variations of a population (e.g. biological species or industrial goods) a few variations get selected which survive and proliferate, whereas the others vanish.…
Consider a continuous-state branching population constructed as a flow of nested subordinators. Inverting the subordinators and reversing time give rise to a flow of coalescing Markov processes (with negative jumps) which correspond to the…
We show how concepts from statistical physics, such as order parameter, thermodynamic limit, and quantum phase transition, translate into biological concepts in mutation-selection models for sequence evolution and can be used there. The…
We study fixation in large, but finite, populations with two types, and dynamics governed by birth-death processes. By considering a restricted class of such processes, we derive a continuous approximation for the probability of fixation…
A critical branching process $\left\{Z_{k},k=0,1,2,...\right\} $ in a random environment generated by a sequence of independent and identically distributed random reproduction laws is considered.\ Let $Z_{p,n}$ be the number of particles at…
We study the asymptotic behavior of the maximum degree in the evolving tree model with a choice based on both degree and fitness of a vertex. The tree is constructed in the following recursive way. Each vertex is assigned a parameter to it…
We provide a class of non-contracting groups containing an infinite family of fractal and weakly regular branch groups, and study certain properties including abelianization, just infiniteness, and word problem. We present an example of a…
We study age-structured branching models with reproduction law depending on the remaining lifetime of the parent. The lifespan of an individual is decided at its birth and its remaining lifetime decreases at the unit speed. The models…
We consider a (one-dimensional) branching Brownian motion process with a general offspring distribution having at least two moments, and in which all particles have a drift towards the origin where they are immediately absorbed. It is…
Preferential attachment models form a popular class of growing networks, where incoming vertices are preferably connected to vertices with high degree. We consider a variant of this process, where vertices are equipped with a random initial…
We consider branching processes with interaction in continuous time, both with values in the integers and in the reals (in the second case we restrict ourselves to continuous processes), which model the evolution of the size of a…
We study the Fleming--Viot particle system in a discrete state space, in the regime of a fast selection mechanism, namely with killing rates which grow to infinity. This asymptotics creates a time scale separation which results in the…
We consider a stochastic aggregation model on Z^d. Start with particles located at the vertices of the lattice, initially distributed according to the product Bernoulli measure with parameter \mu. In addition, there is an aggregate, which…