Related papers: Non-equilibrium allele frequency spectra via spect…
We develop a global and hierarchical scheme for the forward Kolmogorov (Fokker-Planck) equation of the diffusion approximation of the Wright-Fisher model of population genetics. That model describes the random genetic drift of several…
Spectral methods for solving partial differential equations (PDEs) and stochastic partial differential equations (SPDEs) often use Fourier or polynomial spectral expansions on either uniform and non-uniform grids. However, while very widely…
In population genetic studies, the allele frequency spectrum (AFS) efficiently summarizes genome-wide polymorphism data and shapes a variety of allele frequency-based summary statistics. While existing theory typically features equilibrium…
We study the population genetics of two neutral alleles under reversible mutation in the \Lambda-processes, a population model that features a skewed offspring distribution. We describe the shape of the equilibrium allele frequency…
We develop an iterative global solution scheme for the backward Kolmogorov equation of the diffusion approximation of the Wright-Fisher model of population genetics. That model describes the random genetic drift of several alleles at the…
The diffusion approximation of the Wright-Fisher model of population genetics leads to partial differentiable equations, the so-called Kolmogorov equations, with an operator that degenerates at the boundary. Standard tools do not apply, and…
Spectral analysis in conjunction with discrete data in one and more dimensions can become a challenging task, because the methods are sometimes difficult to understand. This paper intends to provide an overview about the usage of the…
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…
Demographic models built from genetic data play important roles in illuminating prehistorical events and serving as null models in genome scans for selection. We introduce an inference method based on the joint frequency spectrum of genetic…
The investigation of allele frequency trajectories in populations evolving under controlled environmental pressures has become a popular approach to study evolutionary processes on the molecular level. Statistical models based on…
In this paper, we propose a numerical method to approximate the solution of partial differential equations in irregular domains with no-flux boundary conditions by means of spectral methods. The main features of this method are its…
We develop a general solution for the Fokker-Planck (Kolomogorov) equation representing the diffusion limit of the Wright-Fisher model of random genetic drift for an arbitrary number of alleles at a single locus. From this solution, we can…
Spectral methods have emerged as a simple yet surprisingly effective approach for extracting information from massive, noisy and incomplete data. In a nutshell, spectral methods refer to a collection of algorithms built upon the eigenvalues…
In this paper, we investigate the Hermite spectral method (HSM) to numerically solve the forward Kolmogorov equation (FKE). A useful guideline of choosing the scaling factor of the generalized Hermite functions is given in this paper. It…
Physical laws governing population dynamics are generally expressed as differential equations. Research in recent decades has incorporated fractional-order (non-integer) derivatives into differential models of natural phenomena, such as…
For multivariant Wright-Fisher models in population genetics, we introduce equilibrium states, expressed by fluctuations of probability ratio, in contrast to the traditionally used fluctuations, expressed by the difference between the…
The increased availability of time series genetic variation data from experimental evolution studies and ancient DNA samples has created new opportunities to identify genomic regions under selective pressure and to estimate their associated…
In his monograph Chebyshev and Fourier Spectral Methods, John Boyd claimed that, regarding Fourier spectral methods for solving differential equations, ``[t]he virtues of the Fast Fourier Transform will continue to improve as the relentless…
We propose spectral methods for long-term forecasting of temporal signals stemming from linear and nonlinear quasi-periodic dynamical systems. For linear signals, we introduce an algorithm with similarities to the Fourier transform but…
We introduce a multi-allele Wright-Fisher model with non-recurrent, reversible mutation and directional selection. In this setting, the allele frequencies at a single locus track the path of a hybrid jump-diffusion process with state space…