scholarly journals Numerical complete solution for random genetic drift by energetic variational approach

2019 ◽  
Vol 53 (2) ◽  
pp. 615-634 ◽  
Author(s):  
Chenghua Duan ◽  
Chun Liu ◽  
Cheng Wang ◽  
Xingye Yue
Keyword(s):  
Genetic Drift ◽  
Variational Approach ◽  
Numerical Solutions ◽  
Complete Solution ◽  
Random Genetic Drift ◽  
Least Action Principle ◽  
Dirac Delta ◽  
Splitting Technique ◽  
Least Action ◽  
Convection Dominated

In this paper, we focus on numerical solutions for random genetic drift problem, which is governed by a degenerated convection-dominated parabolic equation. Due to the fixation phenomenon of genes, Dirac delta singularities will develop at boundary points as time evolves. Based on an energetic variational approach (EnVarA), a balance between the maximal dissipation principle (MDP) and least action principle (LAP), we obtain the trajectory equation. In turn, a numerical scheme is proposed using a convex splitting technique, with the unique solvability (on a convex set) and the energy decay property (in time) justified at a theoretical level. Numerical examples are presented for cases of pure drift and drift with semi-selection. The remarkable advantage of this method is its ability to catch the Dirac delta singularity close to machine precision over any equidistant grid.

scholarly journals Diffuse Interface Methods for Multiple Phase Materials: An Energetic Variational Approach

2015 ◽  
Vol 8 (2) ◽  
pp. 220-236 ◽  
Author(s):  
J. Brannick ◽  
C. Liu ◽  
T. Qian ◽  
H. Sun
Keyword(s):  
Contact Line ◽  
Variational Approach ◽  
Virtual Work ◽  
Dissipation Function ◽  
Force Balance ◽  
Diffuse Interface ◽  
Least Action Principle ◽  
Least Action ◽  
Interfacial Energies ◽  
The Least Action Principle

AbstractIn this paper, we introduce a diffuse interface model for describing the dynamics of mixtures involving multiple (two or more) phases. The coupled hydrodynamical system is derived through an energetic variational approach. The total energy of the system includes the kinetic energy and the mixing (interfacial) energies. The least action principle (or the principle of virtual work) is applied to derive the conservative part of the dynamics, with a focus on the reversible part of the stress tensor arising from the mixing energies. The dissipative part of the dynamics is then introduced through a dissipation function in the energy law, in line with Onsager's principle of maximum dissipation. The final system, formed by a set of coupled time-dependent partial differential equations, reflects a balance among various conservative and dissipative forces and governs the evolution of velocity and phase fields. To demonstrate the applicability of the proposed model, a few two-dimensional simulations have been carried out, including (1) the force balance at the three-phase contact line in equilibrium, (2) a rising bubble penetrating a fluid-fluid interface, and (3) a solid particle falling in a binary fluid. The effects of slip at solid surface have been examined in connection with contact line motion and a pinch-off phenomenon.

scholarly journals A least action principle for interceptive walking

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Soon Ho Kim ◽  
Jong Won Kim ◽  
Hyun Chae Chung ◽  
MooYoung Choi
Keyword(s):  
Social Systems ◽  
Equations Of Motion ◽  
Classical Mechanics ◽  
Action Principle ◽  
Lagrange Equations ◽  
Least Action Principle ◽  
Least Action ◽  
The Least Action Principle ◽  
Principle Of Least Action ◽  
Human Participants

AbstractThe principle of least effort has been widely used to explain phenomena related to human behavior ranging from topics in language to those in social systems. It has precedence in the principle of least action from the Lagrangian formulation of classical mechanics. In this study, we present a model for interceptive human walking based on the least action principle. Taking inspiration from Lagrangian mechanics, a Lagrangian is defined as effort minus security, with two different specific mathematical forms. The resulting Euler–Lagrange equations are then solved to obtain the equations of motion. The model is validated using experimental data from a virtual reality crossing simulation with human participants. We thus conclude that the least action principle provides a useful tool in the study of interceptive walking.

CYTO-NUCLEAR EPISTASIS: TWO-LOCUS RANDOM GENETIC DRIFT IN HERMAPHRODITIC AND DIOECIOUS SPECIES

Evolution ◽  
2006 ◽  
Vol 60 (4) ◽  
pp. 643 ◽  
Author(s):  
Michael J. Wade ◽  
Charles J. Goodnight
Keyword(s):  
Genetic Drift ◽  
Random Genetic Drift ◽  
Dioecious Species

scholarly journals Influence of Random Genetic Drift on Human Immunodeficiency Virus Type 1envEvolution During Chronic Infection

Genetics ◽  
2004 ◽  
Vol 166 (3) ◽  
pp. 1155-1164 ◽  
Author(s):  
Daniel Shriner ◽  
Raj Shankarappa ◽  
Mark A. Jensen ◽  
David C. Nickle ◽  
John E. Mittler ◽  
...  
Keyword(s):  
Human Immunodeficiency Virus ◽  
Human Immunodeficiency Virus Type ◽  
Virus Type ◽  
Genetic Drift ◽  
Chronic Infection ◽  
Random Genetic Drift ◽  
Immunodeficiency Virus

scholarly journals Phase reconstruction by the weighted least action principle

2006 ◽  
Vol 8 (3) ◽  
pp. 279-289 ◽  
Author(s):  
Chungmin Lee ◽  
John Lowengrub ◽  
Jacob Rubinstein ◽  
Xiaoming Zheng
Keyword(s):  
Action Principle ◽  
Phase Reconstruction ◽  
Least Action Principle ◽  
Least Action

scholarly journals A General Solution of the Wright–Fisher Model of Random Genetic Drift

2016 ◽  
Vol 27 (4) ◽  
pp. 467-492 ◽  
Author(s):  
Tat Dat Tran ◽  
Julian Hofrichter ◽  
Jürgen Jost
Keyword(s):  
General Solution ◽  
Genetic Drift ◽  
Random Genetic Drift ◽  
Fisher Model

scholarly journals Evolution of gene regulatory networks by means of selection and random genetic drift

2018 ◽  
Author(s):  
Antonios Kioukis ◽  
Pavlos Pavlidis
Keyword(s):  
Natural Selection ◽  
Positive Selection ◽  
Genetic Drift ◽  
Regulatory Networks ◽  
Fitness Landscape ◽  
Random Genetic Drift ◽  
Maturation Period ◽  
Evolutionary Forces ◽  
Gene Regulatory

The evolution of a population by means of genetic drift and natural selection operating on a gene regulatory network (GRN) of an individual has not been scrutinized in depth. Thus, the relative importance of various evolutionary forces and processes on shaping genetic variability in GRNs is understudied. Furthermore, it is not known if existing tools that identify recent and strong positive selection from genomic sequences, in simple models of evolution, can detect recent positive selection when it operates on GRNs. Here, we propose a simulation framework, called EvoNET, that simulates forward-in-time the evolution of GRNs in a population. Since the population size is finite, random genetic drift is explicitly applied. The fitness of a mutation is not constant, but we evaluate the fitness of each individual by measuring its genetic distance from an optimal genotype. Mutations and recombination may take place from generation to generation, modifying the genotypic composition of the population. Each individual goes through a maturation period, where its GRN reaches equilibrium. At the next step, individuals compete to produce the next generation. As time progresses, the beneficial genotypes push the population higher in the fitness landscape. We examine properties of the GRN evolution such as robustness against the deleterious effect of mutations and the role of genetic drift. We confirm classical results from Andreas Wagner’s work that GRNs show robustness against mutations and we provide new results regarding the interplay between random genetic drift and natural selection.

Sign in / Sign up

Export Citation Format

Share Document