## Figures from this paper

## 2,025 Citations

### The tree length of an evolving coalescent

- Mathematics
- 2009

A well-established model for the genealogy of a large population in equilibrium is Kingman’s coalescent. For the population together with its genealogy evolving in time, this gives rise to a…

### The coalescent tree of a Markov branching process with generalised logistic growth.

- MathematicsJournal of mathematical biology
- 2022

We consider a class of density-dependent branching processes which generalises exponential, logistic and Gompertz growth. A population begins with a single individual, grows exponentially initially,…

### The coalescent process in a population with stochastically varying size

- MathematicsJournal of Applied Probability
- 2003

We study the genealogical structure of a population with stochastically fluctuating size. If such fluctuations, after suitable rescaling, can be approximated by a nice continuous-time process, we…

### The coalescent tree of a branching process with generalised logistic growth

- Mathematics
- 2020

Taking the sampling time and carrying capacity simultaneously to infinity, it is proved convergence of the coalescent tree is in a sense universal over this class of density-dependent branching processes.

### A POPULATION MODEL FOR -COALESCENTS WITH NEUTRAL MUTATIONS

- Mathematics
- 2007

It is shown how this process that describes the evolution of a population, such that a sample from this population would exhibit a genealogy given by the so-called �-coalescent, or coalescent with multiple collisions, can be extended to the case where lineages can experience mutations.

### A convergence theorem for markov chains arising in population genetics and the coalescent with selfing

- MathematicsAdvances in Applied Probability
- 1998

A simple convergence theorem for sequences of Markov chains is presented in order to derive new ‘convergence-to-the-coalescent’ results for diploid neutral population models. For the so-called…

### Weak convergence to the coalescent in neutral population models

- MathematicsJournal of Applied Probability
- 1999

For a large class of neutral population models the asymptotics of the ancestral structure of a sample of n individuals (or genes) is studied, if the total population size becomes large. Under certain…

### The general coalescent with asynchronous mergers of ancestral lines

- MathematicsJournal of Applied Probability
- 1999

Take a sample of individuals in the fixed-size population model with exchangeable family sizes. Follow the ancestral lines for the sampled individuals backwards in time to observe the ancestral…

### Coalescence times for the branching process

- MathematicsAdvances in Applied Probability
- 2003

We investigate the distribution of the coalescence time (most recent common ancestor) for two individuals picked at random (uniformly) in the current generation of a branching process founded t units…

## References

SHOWING 1-7 OF 7 REFERENCES

### On the genealogy of large populations

- MathematicsJournal of Applied Probability
- 1982

A new Markov chain is introduced which can be used to describe the family relationships among n individuals drawn from a particular generation of a large haploid population. The properties of this…

### The stationary distribution of the infinitely-many neutral alleles diffusion model

- Mathematics
- 1976

An expression is found for the stationary density of the allele frequencies, in the infinitely-many alleles model. It is assumed that all alleles are neutral, that there is a constant mutation rate,…

### The population structure associated with the Ewens sampling formula.

- MathematicsTheoretical population biology
- 1977

### The coalescent

- Biology

The ancestral history of a population can be represented as a tree, or genealogy, in exactly the same manner a family tree or a species phylogeny represents the history of those lineages that have left representatives.