Related papers: Beta-coalescents when sample size is large
We analyse a family of two-types Wright-Fisher models with selection in a random environment and skewed offspring distribution. We provide a calculable criterion to quantify the impact of different shapes of selection on the fate of the…
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 study a one-dimensional spatial population model where the population sizes at each site are chosen according to a translation invariant and ergodic distribution and are uniformly bounded away from 0 and infinity. We suppose that the…
Reconstructing past population size from present day genetic data is a major goal of population genetics. Recent empirical studies infer population size history using coalescent-based models applied to a small number of individuals. Here we…
Kingman Coalescent was first proposed by Kingman [7] in population genetics to describe population's genealogical structure. Now it becomes a bench-mark model for coalescent process. Extensive studies have been conducted on Kingman…
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…
A density-dependent branching process is a particle system in which individuals reproduce independently, but in a way that depends on the current population size. This feature can model a wide range of ecological interactions at the cost of…
The transition distribution of a sample taken from a Wright-Fisher diffusion with general small mutation rates is found using a coalescent approach. The approximation is equivalent to having at most one mutation in the coalescent tree of…
In ecology, species can mitigate their extinction risks in uncertain environments by diversifying individual phenotypes. This observation is quantified by the theory of bet-hedging, which provides a reason for the degree of phenotypic…
We introduce a colored coalescent process which recovers random colored genealogical trees. Here a colored genealogical tree has its vertices colored black or white. Moving backward along the colored genealogical tree, the color of vertices…
We consider a population with two types of individuals, distinguished by the resources required for reproduction: type-$0$ (small) individuals need a fractional resource unit of size $\vartheta \in (0,1)$, while type-$1$ (large) individuals…
Consider a population evolving from year to year through three seasons: spring, summer and winter. Every spring starts with $N$ dormant individuals waking up independently of each other according to a given distribution. Once an individual…
The Ancestral Selection Graph (ASG) is an important genealogical process which extends the well-known Kingman coalescent to incorporate natural selection. We show that the number of lineages of the ASG with and without mutation is…
To introduce selection into a model of coalescence, I explore the use of modified integer partitions that allow the identification of a preferred lineage. I show that a partition-partition transition matrix, along with Monte Carlo discrete…
We construct a constant size population model allowing for general selective interactions and extreme reproductive events. It generalizes the idea of (Krone and Neuhauser 1997) who represented the selection by allowing individuals to sample…
Consider a birth and death process started from one individual in which each individual gives birth at rate $\lambda$ and dies at rate $\mu$, so that the population size grows at rate $r = \lambda - \mu$. Lambert and Harris, Johnston, and…
Consider a population that is expanding in two-dimensional space. Suppose we collect data from a sample of individuals taken at random either from the entire population, or from near the outer boundary of the population. A quantity of…
With novel developments in sequencing technologies, time-sampled data are becoming more available and accessible. Naturally, there have been efforts in parallel to infer population genetic parameters from these datasets. Here, we compare…
We consider population models in which the individuals reproduce, die and also migrate in space. The population size scales according to some parameter $N$, which can have different interpretations depending on the context. Each individual…
Duality plays an important role in population genetics. It can relate results from forwards-in-time models of allele frequency evolution with those of backwards-in-time genealogical models; a well known example is the duality between the…