Category Archives: Population genetics theory

How to infer relative fitness from a sample of genomic sequences

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How to infer relative fitness from a sample of genomic sequences
Adel Dayarian, Boris I Shraiman
(Submitted on 29 Aug 2012)

Mounting evidence suggests that natural populations can harbor extensive fitness diversity with numerous genomic loci under selection. It is also known that genealogical trees for populations under selection are quantifiably different from those expected under neutral evolution and described statistically by Kingman’s coalescent. While differences in the statistical structure of genealogies have long been used as a test for the presence of selection, the full extent of the information that they contain has not been exploited. Here we shall demonstrate that the shape of the reconstructed genealogical tree for a moderately large number of random genomic samples taken from a fitness diverse, but otherwise unstructured asexual population can be used to predict the relative fitness of individuals within the sample. To achieve this we define a heuristic algorithm, which we test {\it in silico} using simulations of a Wright-Fisher model for a realistic range of mutation rates and selection strength. Our inferred fitness ranking is based on a linear discriminator which identifies rapidly coalescing lineages in the reconstructed tree. Inferred fitness ranking correlates strongly with the actual fitness, with top 10% ranked being in the top 20% fittest with false discovery rate of 0.1-0.3 depending on the mutation/selection parameters. The ranking also enables to predict the common genotype of the future population. While the inference accuracy increases monotonically with sample size, sample sizes of 200 nearly saturate the performance. We propose that our approach can be used for inferring relative fitness of genomes obtained in single-cell sequencing of tumors and in monitoring viral outbreaks.

The impact of deleterious passenger mutations on cancer progression.

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The impact of deleterious passenger mutations on cancer progression. (arXiv:1208.6068v1 [q-bio.PE])
by Christopher D McFarland, Gregory V Kryukov, Shamil Sunyaev, Leonid Mirny

Cancer progression is driven by a small number of genetic alterations accumulating in a neoplasm. These few driver alterations reside in a cancer genome alongside tens of thousands of other mutations that are widely believed to have no role in cancer and termed passengers. Many passengers, however, fall within protein coding genes and other functional elements and can possibly have deleterious effects on cancer cells. Here we investigate a potential of mildly deleterious passengers to accumulate and alter the course of neoplastic progression. Our approach combines evolutionary simulations of cancer progression with the analysis of cancer sequencing data. In our simulations, individual cells stochastically divide, acquire advantageous driver and deleterious passenger mutations, or die. Surprisingly, despite selection against them, passengers accumulate and largely evade selection during progression. Although individually weak, the collective burden of passengers alters the course of progression leading to several phenomena observed in oncology that cannot be explained by a traditional driver-centric view. We tested predictions of the model using cancer genomic data. We find that many passenger mutations are likely to be damaging and that, in agreement with the model, they have largely evaded purifying selection. Finally, we used our model to explore cancer treatments that exploit the load of passengers by either 1) increasing the mutation rate; or 2) exacerbating their deleterious effects. While both approaches lead to cancer regression, the later leads to less frequent relapse. Our results suggest a new framework for understanding cancer progression as a balance of driver and passenger mutations.

A sequentially Markov conditional sampling distribution for structured populations with migration and recombination

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A sequentially Markov conditional sampling distribution for structured populations with migration and recombination

Matthias Steinrücken, Joshua S. Paul, Yun S. Song
(Submitted on 25 Aug 2012)

Conditional sampling distributions (CSDs), sometimes referred to as copying models, underlie numerous practical tools in population genomic analyses. Though an important application that has received much attention is the inference of population structure, the explicit exchange of migrants at specified rates has not hitherto been incorporated into the CSD in a principled framework. Recently, in the case of a single panmictic population, a sequentially Markov CSD has been developed as an accurate, efficient approximation to a principled CSD derived from the diffusion process dual to the coalescent with recombination. In this paper, the sequentially Markov CSD framework is extended to incorporate subdivided population structure, thus providing an efficiently computable CSD that admits a genealogical interpretation related to the structured coalescent with migration and recombination. As a concrete application, it is demonstrated empirically that the CSD developed here can be employed to yield accurate estimation of a wide range of migration rates.

An explicit transition density expansion for a multi-allelic Wright-Fisher diffusion with general diploid selection

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An explicit transition density expansion for a multi-allelic Wright-Fisher diffusion with general diploid selection

Matthias Steinrücken, Y. X. Rachel Wang, Yun S. Song
(Submitted on 25 Aug 2012)

Characterizing time-evolution of allele frequencies in a population is a fundamental problem in population genetics. In the Wright-Fisher diffusion, such dynamics is captured by the transition density function, which satisfies well-known partial differential equations. For a multi-allelic model with general diploid selection, various theoretical results exist on representations of the transition density, but finding an explicit formula has remained a difficult problem. In this paper, a technique recently developed for a diallelic model is extended to find an explicit transition density for an arbitrary number of alleles, under a general diploid selection model with recurrent parent-independent mutation. Specifically, the method finds the eigenvalues and eigenfunctions of the generator associated with the multi-allelic diffusion, thus yielding an accurate spectral representation of the transition density. Furthermore, this approach allows for efficient, accurate computation of various other quantities of interest, including the normalizing constant of the stationary distribution and the rate of convergence to this distribution.

The variance of identity-by-descent sharing in the Wright-Fisher model

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The variance of identity-by-descent sharing in the Wright-Fisher model

Shai Carmi, Pier Francesco Palamara, Vladimir Vacic, Todd Lencz, Ariel Darvasi, Itsik Pe’er
(Submitted on 21 Jun 2012)

Widespread sharing of long, identical-by-descent (IBD) genetic segments is a hallmark of populations that have experienced a recent bottleneck. The detection of these IBD segments is now feasible, enabling a wide range of applications from phasing and imputation to demographic inference. Here, we study the distribution of IBD sharing in the Wright-Fisher model. Using coalescent theory, we calculate the mean and variance of the total sharing between arbitrary pairs of individuals. We then study the cohort-averaged sharing: the average total sharing between one individual to the rest of the cohort. We find that for large cohorts, the cohort-averaged sharing is distributed approximately normally. Surprisingly, the variance of this distribution remains large even for large cohorts, implying the existence of “hyper-sharing” individuals. The presence of such individuals bears important consequences to the design of sequencing studies, since, if they are selected for whole-genome sequencing, a larger fraction of the cohort can be subsequently imputed. We calculate the expected gain in power of imputation by IBD, and subsequently, in power to detect an association, when individuals are either randomly selected or are specifically the hyper-sharing individuals. Finally, we study the distribution of pairwise sharing and cohort-averaged sharing in the Ashkenazi Jewish population.