Related papers: Re-imagining the Hardy-Weinberg Law
We study the probability that a random polynomial with integer coefficients is reducible when factored over the rational numbers. Using computer-generated data, we investigate a number of different models, including both monic and non-monic…
We consider a population of N individuals, whose dynamics through time is represented by a biparental Moran model with two types: an advantaged type and a disadvantaged type. The advantage is due to a mutation, transmitted in a Mendelian…
We present Lilac, a separation logic for reasoning about probabilistic programs where separating conjunction captures probabilistic independence. Inspired by an analogy with mutable state where sampling corresponds to dynamic allocation, we…
Resistance to insecticide is considered nowadays one of the major threats to insect control, as its occurrence reduces drastically the efficiency of chemical control campaigns, and may also perturb the application of other control methods,…
The key findings of classical population genetics are derived using a framework based on information theory using the entropies of the allele frequency distribution as a basis. The common results for drift, mutation, selection, and gene…
Conditional on the extended Riemann hypothesis, we show that with high probability, the characteristic polynomial of a random symmetric $\{\pm 1\}$-matrix is irreducible. This addresses a question raised by Eberhard in recent work. The main…
Replication helps ensure that a genotype-phenotype association observed in a genome-wide association (GWA) study represents a credible association and is not a chance finding or an artifact due to uncontrolled biases. We discuss…
Testing for Hardy-Weinberg equilibrium (HWE) is a fundamental component of genetic data analysis, widely used for quality control and model validation. Although HWE testing is well established for autosomal loci, inference on the X…
One of the most challenging issues of evolutionary biology concerns speciation, the emergence of new species from an initial one. The huge amount of species found in nature demands a simple and robust mechanism. Yet, no consensus has been…
When predicting the fate and consequences of recurring deleterious mutations in self-fertilising populations most models developed make the assumption that populations have discrete non-overlapping generations. This makes them biologically…
Interacting particle systems undergoing repeated mutation and selection steps model genetic evolution, and also describe a broad class of sequential Monte Carlo methods. The genealogical tree embedded into the system is important in both…
The variance of primes in short intervals relates to the Riemann Hypothesis, Montgomery's Pair Correlation Conjecture and the Hardy--Littlewood Conjecture. In regards to its asymptotics, very little is known unconditionally. We study the…
Compared to a neutral model, purifying selection distorts the structure of genealogies and hence alters the patterns of sampled genetic variation. Although these distortions may be common in nature, our understanding of how we expect…
We develop a family of simple rank one theories built over quite arbitrary sequences of finite hypergraphs. (This extends an idea from the recent proof that Keisler's order has continuum many classes, however, the construction does not…
In an extant population, how much information do extant individuals provide on the pedigree of their ancestors? Recent work by Kim, Mossel, Ramnarayan and Turner (2020) studied this question under a number of simplifying assumptions,…
Star-shaped branching patterns of genealogies are common in marine species. High-fecundity marine populations are characterized by low ratios of effective to actual population size, which reflect high variance in reproductive success among…
In probability theory and statistics, the IID model represents a single population, and a large, potentially infinite sample from this population. Main theorems, in particular the central limit theorem and laws of large number (LLN) assure…
The advent of modern genome sequencing techniques allows for a more stringent test of the neutrality hypothesis of Darwinian evolution, where all individuals have the same fitness. Using the individual based model of Wright and Fisher, we…
We consider real symmetric and complex Hermitian random matrices with the additional symmetry $h_{xy}=h_{N-x,N-y}$. The matrix elements are independent (up to the fourfold symmetry) and not necessarily identically distributed. This ensemble…
We consider a population of haploid individuals reproducing sexually, i.e. for which the genome of each individual is a random mixture of the genome of its two parents. We assume that initially one individual carries a mutation at one…