Related papers: Expectation of the Site Frequency Spectrum
The general relationship between an arbitrary frequency distribution and the expectation value of the frequency distributions of its samples is esablished. A set of combinations of expectation values whose value does not in general depend…
The relationship between sequences and secondary structures or shapes in RNA exhibits robust statistical properties summarized by three notions: (1) the notion of a typical shape (that among all sequences of fixed length certain shapes are…
Genetic drift is stochastic fluctuations of alleles frequencies in a population due to sampling effects. We consider a model of drift in an equilibrium population, with high mutation rates: few functional mutations per generation. Such…
We calculate the probability to find exactly $n$ eigenvalues in a spectral interval of a large random $N \times N$ matrix when this interval contains $s \ll N$ eigenvalues on average. The calculations exploit an analogy to the problem of…
We study an underdamped oscillator with shot-noise frequency fluctuations. The oscillator spectrum is determined by the interference of the susceptibilities for different eigenfrequencies. Depending on the parameters, it has a fine…
We consider a branching population where individuals live and reproduce independently. Their lifetimes are i.i.d. and they give birth at a constant rate b. The genealogical tree spanned by this process is called a splitting tree, and the…
Cryptic genetic sequences have attenuated effects on phenotypes. In the classic view, relaxed selection allows cryptic genetic diversity to build up across individuals in a population, providing alleles that may later contribute to…
Sequencing by synthesis is used in many next-generation DNA sequencing technologies. Some of the technologies, especially those exploring the principle of single-molecule sequencing, allow incomplete nucleotide incorporation in each cycle.…
The discovery of genetic risk factors has transformed human genetics, yet the pace of new gene identification has slowed despite the exponential expansion of sequencing and biobank resources. Current approaches are optimized for the…
We propose a Markov chain approach for the evolution of a genealogical line of genomes. Our idealized genome has $N$ sites and each site can be in state $0$ or $1$. At each time step we pick a site at random. If the site is in state $0$ we…
Phylogenetic invariants are not the only constraints on site-pattern frequency vectors for phylogenetic trees. A mutation matrix, by its definition, is the exponential of a matrix with non-negative off-diagonal entries; this positivity…
We derive exact formulae for the allele frequency spectrum under the coalescent with mutation, conditioned on allele counts at some fixed time in the past. We consider unlinked biallelic markers mutating according to a finite sites, or…
A nucleotides sequence is identified, in the two (four) letters alphabet, by the the labels of a vector state of an irreducible representation of U_q(sl(2)) (U_q(sl(2) + sl(2))), in the limit q -> 0. A master equation for the distribution…
A forward diffusion equation describing the evolution of the allele frequency spectrum is presented. The influx of mutations is accounted for by imposing a suitable boundary condition. For a Wright-Fisher diffusion with or without selection…
We study a general setting of neutral evolution in which the population is of finite, constant size and can have spatial structure. Mutation leads to different genetic types ("traits"), which can be discrete or continuous. Under minimal…
The mutant allele frequencies in oncogenes peak around 0.40 and rapidly decrease. In this article, we explain why this is the case. Invoking a key result from mathematical analysis in our model, namely, the inverse function theorem, we…
Information valuable words are the strings with the significant deviation of real frequency from the expected one. The expected frequency is determined through the maximum entropy principle of the reconstructed (extended) frequency…
It has been recently claimed that it is possible to predict the rate of de novo mutation of each site in the human genome with almost perfect accuracy (Michaelson et al. (2012) Cell, 151, 1431-1442). We show that this claim is unwarranted.…
Sequencing by synthesis is the underlying technology for many next-generation DNA sequencing platforms. We developed a new model, the fixed flow cycle model, to derive the distributions of sequence length for a given number of flow cycles…
Statistical analysis of DNA mixtures is known to pose computational challenges due to the enormous state space of possible DNA profiles. We propose a Bayesian network representation for genotypes, allowing computations to be performed…