An Ancestral Recombination Graph for Diploid Populations with Skewed Offspring Distribution

@article{Birkner2013AnAR,
  title={An Ancestral Recombination Graph for Diploid Populations with Skewed Offspring Distribution},
  author={Matthias C. F. Birkner and Jochen Blath and Bjarki Eldon},
  journal={Genetics},
  year={2013},
  volume={193},
  pages={255 - 290}
}
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 been recently considered by various authors (cf. e.g., Eldon and Wakeley 2006, 2008) and reviewed by Hedgecock and Pudovkin (2011). Each… 

Figures and Tables from this paper

Coalescent results for diploid exchangeable population models.
We consider diploid bi-parental analogues of Cannings models: in a population of fixed size $N$ the next generation is composed of $V_{i,j}$ offspring from parents $i$ and $j$, where
The coalescent with arbitrary spatial and genetic structure
TLDR
An abstract formulation of the coalescent that applies to a broad class of neutral drift models, allowing for arbitrary spatial structure and mating patterns is introduced, and biologically relevant quantities, including coalescence time, coalescence branch length, reproductive value, number of mutations prior to coalescence, and stationary probabilities of identity-by-descent and identity- by-state are defined and analyzed.
Stochastic Models in Population Genetics: The Impact of Selection and Recombination
TLDR
Two different ways of modeling the evolution of a population which experiences a selective sweep are investigated, including a Moran model with selection and recombination and a Darwinian model with varying population size and birth and death rates depending on the current state of the population and the genetic type of an individual at the locus under selection.
Coalescent Processes with Skewed Offspring Distributions and Nonequilibrium Demography
TLDR
An extended Moran model with exponential population growth is developed, and it is demonstrated that the underlying ancestral process converges to a time-inhomogeneous psi-coalescent, and both can be estimated accurately from whole-genome data.
Genetics of the biparental Moran model.
Our goal is to study the genetic composition of a population in which each individual has 2 parents, who contribute equally to the genome of their ospring. We use a biparental Moran model, which is
Coalescent Processes with Skewed Offspring Distributions and non-Equilibrium Demography
TLDR
An extended Moran model with exponential population growth is developed, and it is demonstrated that the underlying ancestral process converges to a time-inhomogeneous psi-coalescent, allowing the process to be simulated quickly and efficiently.
The site-frequency spectrum associated with Ξ-coalescents.
TRACTABLE STOCHASTIC MODELS OF EVOLUTION FOR LOOSELY LINKED LOCI
TLDR
This paper derives two new stochastic population genetic models, one a diffusion and the other a coalescent process, which are much simpler than the standard models, but which capture their key properties for large recombination rates.
Genealogies and inference for populations with highly skewed offspring distributions
TLDR
Inference methods under the infinitely-many sites model which allow both model selection and estimation of model parameters under these coalescents are discussed.
A sequential coalescent algorithm for chromosomal inversions
TLDR
The SMC algorithm is fast, memory-efficient and accurate, making it feasible to simulate large inversions in large populations for the first time, and enables studies of patterns of genetic variation and tests of hypotheses that were previously intractable.
...
...

References

SHOWING 1-10 OF 72 REFERENCES
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.
The Two-Locus Ancestral Graph
In a population genetics two-locus model with recombination an offspring has either a single parent gene, or is a recombinant from two parent genes. The number of ancestors, backward in time, of a
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.
On Recombination-Induced Multiple and Simultaneous Coalescent Events
TLDR
It is shown that multiple and simultaneous coalescent events influence global quantities,such as total number of ancestors, but have negligible effect on local quantities, such as linkage disequilibrium.
Linkage Disequilibrium Under Skewed Offspring Distribution Among Individuals in a Population
TLDR
Correlations in coalescence times between two loci are derived under selectively neutral population models in which the offspring of an individual can number on the order of the population size and are shown to be functions of the parameters controlling the size and frequency of these large reproduction events.
The genealogy of samples in models with selection.
TLDR
It is found that when the allele frequencies in the population are already in equilibrium, then the genealogy does not differ much from the neutral case, and this is supported by rigorous results.
A coalescent dual process in a Moran model with genic selection, and the lambda coalescent limit.
The Genealogical Consequences of Fecundity Variance Polymorphism
TLDR
It is shown that the genealogical consequences of within-generation fecundity variance polymorphism are studied using coalescent processes structured by genetic backgrounds have three distinctive features, which are expected to hold in models that allow for heritable variation in other traits that affect the coalescent effective population size.
Ancestral Processes with Selection
TLDR
The main goal is to analyze the ancestral selection graph and to compare it to Kingman's coalescent process; it is found that the distribution of the time to the most recent common ancestor does not depend on the selection coefficient and hence is the same as in the neutral case.
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.
...
...