# The general coalescent with asynchronous mergers of ancestral lines

@article{Sagitov1999TheGC, title={The general coalescent with asynchronous mergers of ancestral lines}, author={Serik Sagitov}, journal={Journal of Applied Probability}, year={1999}, volume={36}, pages={1116 - 1125} }

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 process. We describe a class of asymptotic structures for the ancestral process via a convergence criterion. One of the basic conditions of the criterion prevents simultaneous mergers of ancestral lines. Another key condition implies that the marginal distribution of the family size is attracted by an…

## 372 Citations

### On sampling distributions for coalescent processes with simultaneous multiple collisions

- Mathematics
- 2006

Recursions for a class of sampling distributions of allele configurations are derived for the situation where the genealogy of the underlying population is modelled by a coalescent process with…

### A Classification of Coalescent Processes for Haploid Exchangeable Population Models

- Mathematics
- 2001

We consider a class of haploid population models with nonoverlapping generations and fixed population size N assuming that the family sizes within a generation are exchangeable random variables. A…

### A CHARACTERIZATION OF ANCESTRALLIMIT PROCESSES ARISING IN HAPLOIDPOPULATION GENETICS

- Mathematics
- 1998

The classical n-coalescent introduced by Kingman is not the only possible limit process arising in ancestral population genetics. Under smooth conditions other limit processes do appear, where…

### The fixation line in the Λ -coalescent.

- Mathematics
- 2015

We define a Markov process in a forward population model with backward genealogy given by the -coalescent. This Markov process, called the fixation line, is related to the block counting process…

### Exchangeable partitions derived from Markovian coalescents

- Mathematics
- 2006

Kingman derived the Ewens sampling formula for random partitions describing the genetic variation in a neutral mutation model defined by a Poisson process of mutations along lines of descent governed…

### CONVERGENCE TO THE COALESCENT WITH SIMULTANEOUS MULTIPLE MERGERS

- Mathematics
- 2003

The general coalescent process with simultaneous multiple mergers of ancestral lines was initially characterized by Mohle and Sagitov (2001) in terms of a sequence of measures defined on the…

### Structured coalescent processes from a modified Moran model with large offspring numbers.

- Environmental ScienceTheoretical population biology
- 2009

### On the number of segregating sites for populations with large family sizes

- MathematicsAdvances in Applied Probability
- 2006

We present recursions for the total number, S n , of mutations in a sample of n individuals, when the underlying genealogical tree of the sample is modelled by a coalescent process with mutation rate…

### Convergence to the coalescent in populations of substantially varying size

- MathematicsJournal of Applied Probability
- 2004

Kingman's classical theory of the coalescent uncovered the basic pattern of genealogical trees of random samples of individuals in large but time-constant populations. Time is viewed as being…

## References

SHOWING 1-10 OF 11 REFERENCES

### Robustness results for the coalescent

- MathematicsJournal of Applied Probability
- 1998

A variety of convergence results for genealogical and line-of-descendent processes are known for exchangeable neutral population genetics models. A general convergence-to-the-coalescent theorem is…

### 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…

### More Exact Statements of Several Theorems in the Theory of Branching Processes

- Mathematics
- 1957

Theorems proved by A. N. Kolmogorov [2], A. M. Yaglom [3] and B. A. Sevastyanov [1] on regular branching processes with particles of one type homogeneous in time (parameter t being continuous) are…

### An Introduction to Probability Theory and Its Applications

- Mathematics
- 1950

Thank you for reading an introduction to probability theory and its applications vol 2. As you may know, people have look numerous times for their favorite novels like this an introduction to…

### Exchangeability and the evolution of large populations

- Exchangeability in Probability and Statistics