Related papers: Gene-Mating Dynamic Evolution Theory II: Global st…
Understanding how genes influence phenotype across species is a fundamental challenge in genetic engineering, which will facilitate advances in various fields such as crop breeding, conservation biology, and personalized medicine. However,…
We study the stable matching problem in non-bipartite graphs with incomplete but strict preference lists, where the edges have weights and the goal is to compute a stable matching of minimum or maximum weight. This problem is known to be…
We introduce a family of models incorporating random segmental substitutions and point mutations and demonstrate that such models reproduce algebraic length distributions of exact matches with the slope $-4$ observed earlier in pairwise…
We study by mean-field analysis and stochastic simulations chemical models for genetic toggle switches formed from pairs of genes that mutually repress each other. In order to determine the stability of the genetic switches, we make a…
The Weismann barrier, or the impossibility of inheritance of acquired traits, comprises a foundation of modern biology, and it has been a major obstacle in establishing the connection between evolution and ontogenesis. We propose the…
Recurrent mutations are a common phenomenon in population genetics. They may be at the origin of the fixation of a new genotype, if they give a phenotypic advantage to the carriers of the new mutation. In this paper, we are interested in…
The strong Allee effect plays an important role on the evolution of population in ecological systems. One important concept is the Allee threshold that determines the persistence or extinction of the population in a long time. In general, a…
Supergenes are genomic regions containing sets of tightly linked loci that control multi-trait phenotypic polymorphisms under balancing selection. Recent advances in genomics have uncovered significant variation in both the genomic…
We investigate the stabilization of a multidimensional system of coupled wave equations with only one Kelvin Voigt damping. Using a unique continuation result based on a Carleman estimate and a general criteria of Arendt Batty, we prove the…
We introduce a generalized version of the famous Stable Marriage problem, now based on multi-modal preference lists. The central twist herein is to allow each agent to rank its potentially matching counterparts based on more than one…
We introduce the notion of n-mating in this work, which includes the classical mating of polynomials as a special case. The new notion brings further links between the polynomial world and the rational world than the classical one, as well…
We study existence and stability of stationary solutions of a system of semilinear parabolic partial differential equations that occurs in population genetics. It describes the evolution of gamete frequencies in a geographically structured…
We propose a formalism for describing two-strand systems of a DNA type by means of soliton von Neumann equations, and illustrate how it works on a simple example exactly solvably by a Darboux transformation. The main idea behind the…
Graph neural networks (GNNs) excel in modeling relational data such as biological, social, and transportation networks, but the underpinnings of their success are not well understood. Traditional complexity measures from statistical…
The breeder's equation is a cornerstone of quantitative genetics and is widely used in evolutionary modeling. The equation which reads R=h^{2}S relates response to selection R (the mean phenotype of the progeny) to the selection…
The overarching goal of this paper is to solve the word problem for a class of idempotent commutative monoids whose elements model population haplotypes. More specifically, we design an algebraic framework in which it is possible to unravel…
New exact completely closed homogeneous Generalized Master Equations (GMEs), governing the evolution in time of equilibrium two-time correlation functions for dynamic variables of a subsystem of s particles (s<N) selected from N>>1…
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…
The classical approaches to the modeling of sex ratio evolution can be divided into two classes. The first class contains the static strategic models related to the Dusing Fisher Shaw Mohler fitness measure, based on the reproductive value…
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…