Related papers: Genealogies in Expanding Populations
Longitudinal molecular data of rapidly evolving viruses and pathogens provide information about disease spread and complement traditional surveillance approaches based on case count data. The coalescent is used to model the genealogy that…
The $N$-particle branching random walk is a discrete time branching particle system with selection. We have $N$ particles located on the real line at all times. At every time step each particle is replaced by two offspring, and each…
We investigate the $\Lambda$-Seed-Bank-Wright-Fisher process, a model describing allele frequency dynamics in populations exhibiting both skewed offspring distributions and dormancy. By performing a change of measure, we condition this…
We consider an expanding population on the plane. The genealogy of a sample from the population is modelled by coalescing Brownian motion on the circle. We establish a weak law of large numbers for the site frequency spectrum in this model.…
We investigate the nature of genetic drift acting at the leading edge of range expansions, building on recent results in [Hallatschek et al., Proc.\ Natl.\ Acad.\ Sci., \textbf{104}(50): 19926 - 19930 (2007)]. A well mixed population of two…
The measure-valued Fleming-Viot process is a diffusion which models the evolution of allele frequencies in a multi-type population. In the neutral setting the Kingman coalescent is known to generate the genealogies of the "individuals" in…
Consider a population evolving as a critical continuous-time Galton-Watson (GW) tree. Conditional on the population surviving until a large time $T$, sample $k$ individuals uniformly at random (without replacement) from amongst those alive…
A number of discrete time, finite population size models in genetics describing the dynamics of allele frequencies are known to converge (subject to suitable scaling) to a diffusion process in the infinite population limit, termed the…
We define a doubly infinite, monotone labeling of Bienayme-Galton-Watson (BGW) genealogies. The genealogy of the current generation backwards in time is uniquely determined by the coalescent point process $(A_i; i\ge 1)$, where $A_i$ is the…
Genealogical networks, also known as family trees or population pedigrees, are commonly studied by genealogists wanting to know about their ancestry, but they also provide a valuable resource for disciplines such as digital demography,…
We extend a recently developed exact schema based, or coarse grained, formulation of genetic dynamics \cite{stewael,stewael1,stewael2} and its associated exact Schema theorem to an arbitrary selection scheme and a general crossover…
We apply our general method of duality, introduced in [Giardina', Kurchan, Redig, J. Math. Phys. 48, 033301 (2007)], to models of population dynamics. The classical dualities between forward and ancestral processes can be viewed as a change…
We consider the evolution of the genealogy of the population currently alive in a Feller branching diffusion model. In contrast to the approach via labeled trees in the continuum random tree world, the genealogies are modeled as equivalence…
We consider recursion equations of the form $u_{n+1}(x)=Q[u_n](x),~n\ge 1,~x\in R$, with a non-local operator $Q[u](x)= g( u\ast q)$, where $g$ is a polynomial, satisfying $g(0)=0$, $g(1)=1$, $g((0,1)) \subseteq (0,1)$, and $q$ is a…
Recently, it has been shown that stochastic spatial Lotka-Volterra models when suitably rescaled can converge to a super Brownian motion. We show that the limit process could be a super stable process if the kernel of the underlying motion…
We review and extend results for mutation, selection, genetic drift, and migration in a one-dimensional continuous population. The population is described by a continuous limit of the stepping stone model, which leads to the stochastic…
We consider a Moran-type model of cultural evolution, which describes how traits emerge, are transmitted, and get lost in populations. Our analysis focuses on the underlying cultural genealogies; they were first described by Aguilar and…
We investigate the consensus dynamics of the voter model on large random graphs with heterogeneous and directed features, focusing in particular on networks with power-law degree distributions. By extending recent results on sparse directed…
We introduce a biologically natural, mathematically tractable model of random phylogenetic network to describe evolution in the presence of hybridization. One of the features of this model is that the hybridization rate of the lineages…
We study the voter model on Z with long-range interactions, as proposed by Hammond and Sheffield. We show a spacetime rescaling converges to a fractional Gaussian free field, which can be viewed as a one-parameter family of fractional…