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- Matthias Birkner, Jochen Blath, Bjarki Eldon
- Genetics
- 2013

A large offspring-number diploid biparental multilocus population model of Moran type is our object of study. At each time step, a pair of diploid individuals drawn uniformly at random contributes offspring to the population. The number of offspring can be large relative to the total population size. Similar "heavily skewed" reproduction mechanisms have… (More)

Let Λ be a finite measure on the unit interval. A Λ-Fleming-Viot process is a probability measure valued Markov process which is dual to a coalescent with multiple collisions (Λ-coalescent) in analogy to the duality known for the classical Fleming-Viot process and Kingman's coalescent, where Λ is the Dirac measure in 0. We explicitly construct a dual… (More)

- Matthias Birkner, Jochen Blath, +4 authors Anton Wakolbinger
- 2005

We determine that the continuous-state branching processes for which the genealogy, suitably time-changed, can be described by an autonomous Markov process are precisely those arising from α-stable branching mechanisms. The random ancestral partition is then a time-changed Λ-coalescent, where Λ is the Beta-distribution with parameters 2 − α and α, and the… (More)

- Matthias Birkner, Jochen Blath, Matthias Steinrücken
- Theoretical population biology
- 2011

We present and discuss new importance sampling schemes for the approximate computation of the sample probability of observed genetic types in the infinitely many sites model from population genetics. More specifically, we extend the 'classical framework', where genealogies are assumed to be governed by Kingman's coalescent, to the more general class of… (More)

- Bjarki Eldon, Matthias Birkner, Jochen Blath, Fabian Freund
- Genetics
- 2015

The ability of the site-frequency spectrum (SFS) to reflect the particularities of gene genealogies exhibiting multiple mergers of ancestral lines as opposed to those obtained in the presence of population growth is our focus. An excess of singletons is a well-known characteristic of both population growth and multiple mergers. Other aspects of the SFS, in… (More)

- Matthias Birkner, Jochen Blath, Bjarki Eldon
- Genetics
- 2013

Statistical properties of the site-frequency spectrum associated with Λ-coalescents are our objects of study. In particular, we derive recursions for the expected value, variance, and covariance of the spectrum, extending earlier results of Fu (1995) for the classical Kingman coalescent. Estimating coalescent parameters introduced by certain Λ-coalescents… (More)

- Matthias Birkner, Jochen Blath
- Journal of mathematical biology
- 2008

One of the central problems in mathematical genetics is the inference of evolutionary parameters of a population (such as the mutation rate) based on the observed genetic types in a finite DNA sample. If the population model under consideration is in the domain of attraction of the classical Fleming-Viot process, such as the Wright-Fisher- or the Moran… (More)

- Matthias Steinrücken, Matthias Birkner, Jochen Blath
- Theoretical population biology
- 2013

We apply recently developed inference methods based on general coalescent processes to DNA sequence data obtained from various marine species. Several of these species are believed to exhibit so-called shallow gene genealogies, potentially due to extreme reproductive behaviour, e.g. via Hedgecock's "reproduction sweepstakes". Besides the data analysis, in… (More)

We study a random walk pinning model, where conditioned on a simple random walk Y on Z d acting as a random medium, the path measure of a second independent simple random walk X up to time t is Gibbs transformed with Hamiltonian −L t (X, Y), where L t (X, Y) is the collision local time between X and Y up to time t. This model arises naturally in various… (More)

When we cut an i.i.d. sequence of letters into words according to an independent renewal process, we obtain an i.i.d. sequence of words. In the annealed large deviation principle (LDP) for the empirical process of words, the rate function is the specific relative entropy of the observed law of words w.r.t. the reference law of words. In the present paper we… (More)