Genealogical Properties of Subsamples in Highly Fecund Populations

@article{Eldon2017GenealogicalPO,
  title={Genealogical Properties of Subsamples in Highly Fecund Populations},
  author={Bjarki Eldon and Fabian Freund},
  journal={Journal of Statistical Physics},
  year={2017},
  volume={172},
  pages={175-207}
}
We consider some genealogical properties of nested samples. The complete sample is assumed to have been drawn from a natural population characterised by high fecundity and sweepstakes reproduction (abbreviated HFSR). The random gene genealogies of the samples are—due to our assumption of HFSR—modelled by coalescent processes which admit multiple mergers of ancestral lineages looking back in time. Among the genealogical properties we consider are the probability that the most recent common… 
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A Complete Bibliography of the Journal of Statistical Physics: 2000{2009
(2 + 1) [XTpXpH12, CTH11]. + [Zuc11b]. 0 [Fed17]. 1 [BELP15, CAS11, Cor16, Fed17, GDL10, GBL16, Hau16, JV19, KT12, KM19c, Li19, MN14b, Nak17, Pal11, Pan14, RT14, RBS16b, RY12, SS18c, Sug10, dOP18]. 1

References

SHOWING 1-10 OF 79 REFERENCES
Coalescents and genealogical structure under neutrality.
TLDR
The coalescent for panmictic populations of fixed size, and its extensions to incorporate various assumptions about variation in population size and nonrandom mating caused by geographical population subdivision are described.
On the genealogy of nested subsamples from a haploid population
For the haploid genetic model of Moran, the joint distribution of the numbers of distinct ancestors of a collection of nested subsamples is derived. These results are shown to apply to the diffusion
Distortion of genealogical properties when the sample is very large
TLDR
A method for performing exact computation in the discrete-time Wright–Fisher (DTWF) model and compare several key genealogical quantities of interest with the coalescent predictions, which demonstrate that the hybrid method with only a handful of generations of the DTWF model leads to a frequency spectrum that is quite close to the prediction of the fullDTWF model.
Gene genealogies when the sample size exceeds the effective size of the population.
TLDR
It is shown that the major effect of large sample size, relative to the effective size of the population, is to increase the proportion of polymorphisms at which the mutant type is found in a single copy in the sample, and it is illustrated that, when large samples are available, it is possible to estimate the mutation rate and the effective population size separately.
Coalescent Processes When the Distribution of Offspring Number Among Individuals Is Highly Skewed
TLDR
A complex set of scaling relationships between mutation and reproduction in a simple model of a population suggests the presence of rare reproduction events in which ∼8% of the population is replaced by the offspring of a single individual.
Genealogies of rapidly adapting populations
TLDR
It is argued that lineages trace back to a small pool of highly fit ancestors, in which almost simultaneous coalescence of more than two lineages frequently occurs, and should be considered as a null model for adapting populations.
Computing likelihoods for coalescents with multiple collisions in the infinitely many sites model
TLDR
It is argued that within the (vast) family of Λ-coalescents, the parametrisable sub-family of Beta(2 − α, α)-coalesCents, where α ∈ (1, 2], are of particular relevance and obtained a method to compute (approximate) likelihood surfaces for the observed type probabilities of a given sample.
Coalescent patterns in diploid exchangeable population models
TLDR
A convergence criterium for the diploid ancestral process is proved as N goes to infinity while n remains unchanged as the class of two-sex population models is considered.
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