arXiv subjects

Archana Devi

Publications and source records attributed to Archana Devi.

3 recordsLinked to original sources

arXiv2026

When can fitness epistasis be ignored in a polygenic trait at equilibrium?

Although many phenotypic traits are determined by a large number of genetic variants, the behavior of allele frequencies in a polygenic trait is not completely understood. The problem is especially challenging when the quantitative trait of interest is under epistatic selection as the allele frequency at a locus is affected by those at other loci. Here, we consider a panmictic, diploid finite population evolving under stabilizing selection and symmetric mutations when the population is in linkage equilibrium. In the stationary state, using a diffusion theory, we calculate the marginal distribution of allele frequency, and find parameter regimes where fitness epistasis can not be ignored for an accurate description of the frequency distribution. For such parameters, the mean deviation in the phenotypic optimum and genic variance are, however, found to be well captured even when epistatic interactions are neglected. Thus, while the presence of epistasis may not be evident in phenotypic quantities, it can strongly affect the allele frequency distribution.We also find that the allele frequency distribution at a locus is unimodal if its effect size is below a threshold effect and bimodal otherwise; these results are the stochastic analog of the deterministic ones where the stable allele frequency becomes bistable when the effect size exceeds a threshold. Our analytical results are verified against Monte Carlo simulations and numerical integration of a Langevin equation.

q-bio.PE↗

arXiv2020

Evolutionary dynamics and eigenspectrum of confluent Heun equation

We consider a biological population evolving under the joint action of selection, mutation and random genetic drift. The evolutionary dynamics are described by a one-dimensional Fokker-Planck equation whose eigenfunctions obey a confluent Heun equation. These eigenfunctions are expanded in an infinite series of orthogonal Jacobi polynomials and the expansion coefficients are found to obey a three-term recursion equation. Using scaling ideas, we obtain an expression for the expansion coefficients and an analytical estimate of the number of terms required in the series for an accurate determination of the eigenfunction. The eigenvalue spectrum is studied using a perturbation theory for weak selection and numerically for strong selection. In the latter case, we find that the eigenvalue for the first excited state exhibits a sharp transition: for mutation rate below one, the eigenvalue increases linearly with increasing mutation rate and then remains a constant; higher eigenvalues are found to display a more complex behavior.

q-bio.PE↗

arXiv2018

Polygenic adaptation in changing environments

Although many phenotypic traits are determined by a large number of genetic variants, how a polygenic trait adapts in response to the changes in the environment is still poorly understood. Here we study the adaptation dynamics of a polygenic trait that is determined by a finite number of genetic loci in an infinitely large population which is evolving under stabilising selection and recurrent mutations. We find that in a changing environment, modeled here by a linearly moving phenotypic optimum, the mean trait also moves linearly with time. But its speed is smaller than that of the phenotypic optimum when the effect sizes of the genetic variants are small and approaches that of the environmental change for larger effect sizes. Our study thus highlights the influence of the genetic architecture of a polygenic trait on its adaptability.

q-bio.PE↗