# The minimal observable clade size of exchangeable coalescents

@article{Freund2019TheMO, title={The minimal observable clade size of exchangeable coalescents}, author={Fabian Freund and Arno Siri-J'egousse}, journal={arXiv: Probability}, year={2019} }

For $\Lambda$-$n$-coalescents with mutation, we analyse the size $O_n$ of the partition block of $i\in\{1,\ldots,n\}$ at the time where the first mutation appears on the tree that affects $i$ and is shared with any other $j\in\{1,\ldots,n\}$. We provide asymptotics of $O_n$ for $n\to\infty$ and a recursion for all moments of $O_n$ for finite $n$. This variable gives an upper bound for the minimal clade size [2], which is not observable in real data. In applications to genetics, it has been…

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## References

SHOWING 1-10 OF 37 REFERENCES

### On the size of the block of 1 for $\varXi$-coalescents with dust

- Mathematics
- 2017

We study the frequency process $f_1$ of the block of 1 for a $\varXi$-coalescent $\varPi$ with dust. If $\varPi$ stays infinite, $f_1$ is a jump-hold process which can be expressed as a sum of broken…

### Cannings models, population size changes and multiple-merger coalescents

- MathematicsJournal of mathematical biology
- 2020

This article gives a more general construction of time-changed Λ - n -coalescents as limits of specific Cannings models with rather arbitrary time changes.

### Rigorous results for a population model with selection II: genealogy of the population

- Mathematics
- 2014

We consider a model of a population of fixed size $N$ undergoing selection. Each individual acquires beneficial mutations at rate $\mu_N$, and each beneficial mutation increases the individual's…

### Asymptotics of the Minimal Clade Size and Related Functionals of Certain Beta-Coalescents

- Mathematics
- 2013

The Beta(2−α,α) n-coalescent with 1<α<2 is a Markov process taking values in the set of partitions of {1,…,n}. It evolves from the initial value {1},…,{n} by merging (coalescing) blocks together into…

### Minimal clade size and external branch length under the neutral coalescent

- MathematicsAdvances in Applied Probability
- 2005

Given a sample of genes taken from a large population, we consider the neutral coalescent genealogy and study the theoretical and empirical distributions of the size of the smallest clade containing…

### On the length distribution of external branches in coalescence trees: genetic diversity within species.

- MathematicsTheoretical population biology
- 2007

### Random Recursive Trees and the Bolthausen-Sznitman Coalesent

- Mathematics
- 2005

We describe a representation of the Bolthausen-Sznitman coalescent in terms of the cutting of random recursive trees. Using this representation, we prove results concerning the final collision of the…

### The Site Frequency Spectrum for General Coalescents

- Computer ScienceGenetics
- 2016

This work derives a new formula for the expected SFS for general Λ- and Ξ-coalescents, which leads to an efficient algorithm and obtains general theoretical results for the identifiability of the Λ measure when ζ is a constant function, as well as for the identity of the function ζ under a fixed Ξ measure.

### 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…