A field theoretic approach to non-equilibrium population genetics in the strong selection regime

Balick, Daniel J.

doi:10.1101/2023.01.16.524324

Cited by 3 publications

(5 citation statements)

References 83 publications

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“…Few path integrals yield exact solutions (Feynman, 1972, Chapter 3.2); however, we can conveniently approximate them using a perturbation scheme. Perturbation analyses are well known in the mathematics literature (Langouche et al, 1982;Schulman, 1996;Dickman and Vidigal, 2003) and have been widely used in quantum mechanics (Feynman, 1972(Feynman, , 2010, but are underused in population genetics (but see Rouhani and Barton, 1987;Schraiber, 2014;Balick, 2023). While transition densities may be derived without the use of path integration, we find this formulation particularly intuitive.…”

Section: Path Integral Solutionmentioning

confidence: 74%

“…N ourmohammad and E ksin (2021) used a path integral control approach to derive artificial selection strategies to guide the evolution of molecular phenotypes. S chraiber (2014) and B alick (2023) derived analytic transition probabilities for alleles under weak and strong genic selection, respectively.…”

Section: Discussionmentioning

confidence: 99%

“…A path integral expresses a transition probability, P ( y, t | x , 0), by computing the probability of a given allele frequency trajectory (or path) through time, , between the initial, z 0 = x , and final, z t = y , frequencies, and then integrating over every possible path (Appendix A.1), Few path integrals yield exact solutions (F eynman , 1972, Chapter 3.2); however, we can conveniently approximate them using a perturbation scheme. Perturbation analyses are well known in the mathematics literature (L angouche et al ., 1982; S chulman , 1996; D ickman and V idigal , 2003) and have been widely used in quantum mechanics (F eynman , 1972, 2010), but are underused in population genetics (but see R ouhani and B arton , 1987; S chraiber , 2014; B alick , 2023). While transition densities may be derived without the use of path integration, we find this formulation particularly intuitive.…”

Section: Path Integral Solutionmentioning

confidence: 99%

“…While the transition density of a neutral allele was solved by Kimura (1955b), finding solutions for the transition density under more general selection models has proved challenging. Analytic solutions have only been found in some special cases (Song and Steinrücken, 2012;Steinrücken et al, 2013;Schraiber, 2014;Živković et al, 2015;Balick, 2023). Most approaches assumed time-invariant selection, though Steinrücken et al (2016) allow for piece-wise constant selection.…”

Section: Introductionmentioning

confidence: 99%

“…This involves representing the transition probability as a path integral that is then approximated using a perturbation analysis. Recently, B alick (2023) introduced a second path integral method rooted in Langevin equations and solved for transition densities of alleles under strong selection. Our approach follows the path integral method from S chraiber (2014), applied to non-constant selection functions relevant to selection on polygenic traits.…”

Section: Introductionmentioning

confidence: 99%

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A Path Integral Approach for Allele Frequency Dynamics Under Polygenic Selection

Anderson,

Kirk,

Schraiber

et al. 2024

Preprint

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Many phenotypic traits have a polygenic genetic basis, making it challenging to learn their genetic architectures and predict individual phenotypes. One promising avenue to resolve the genetic basis of complex traits is through evolve-and-resequence experiments, in which laboratory populations are exposed to some selective pressure and trait-contributing loci are identified by extreme frequency changes over the course of the experiment. However, small laboratory populations will experience substantial random genetic drift, and it is difficult to determine whether selection played a roll in a given allele frequency change. Predicting how much allele frequencies change under drift and selection had remained an open problem well into the 21st century, even those contributing to simple, monogenic traits. Recently, there have been efforts to apply the path integral, a method borrowed from physics, to solve this problem. So far, this approach has been limited to genic selection, and is therefore inadequate to capture the complexity of quantitative, highly polygenic traits that are commonly studied. Here we extend one of these path integral methods, the perturbation approximation, to selection scenarios that are of interest to quantitative genetics. In particular, we derive analytic expressions for the transition probability (i.e., the probability that an allele will change in frequency fromx, toyin timet) of an allele contributing to a trait subject to stabilizing selection, as well as that of an allele contributing to a trait rapidly adapting to a new phenotypic optimum. We use these expressions to characterize the use of allele frequency change to test for selection, as well as explore optimal design choices for evolve-and-resequence experiments to uncover the genetic architecture of polygenic traits under selection.

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Section: Path Integral Solutionmentioning

confidence: 74%

Section: Discussionmentioning

confidence: 99%

Section: Path Integral Solutionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

A Path Integral Approach for Allele Frequency Dynamics Under Polygenic Selection

Anderson,

Kirk,

Schraiber

et al. 2024

Preprint

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A path integral approach for allele frequency dynamics under polygenic selection

Anderson,

Kirk,

Schraiber

et al. 2024

Genetics

View full text Add to dashboard Cite

Many phenotypic traits have a polygenic genetic basis, making it challenging to learn their genetic architectures and predict individual phenotypes. One promising avenue to resolve the genetic basis of complex traits is through evolve-and-resequence experiments, in which laboratory populations are exposed to some selective pressure and trait-contributing loci are identified by extreme frequency changes over the course of the experiment. However, small laboratory populations will experience substantial random genetic drift, and it is difficult to determine whether selection played a role in a given allele frequency change. Predicting allele frequency changes under drift and selection, even for alleles contributing to simple, monogenic traits, has remained a challenging problem. Recently, there have been efforts to apply the path integral, a method borrowed from physics, to solve this problem. So far, this approach has been limited to genic selection, and is therefore inadequate to capture the complexity of quantitative, highly polygenic traits that are commonly studied. Here we extend one of these path integral methods, the perturbation approximation, to selection scenarios that are of interest to quantitative genetics. We derive analytic expressions for the transition probability (i.e., the probability that an allele will change in frequency from x to y in time t) of an allele contributing to a trait subject to stabilizing selection, as well as that of an allele contributing to a trait rapidly adapting to a new phenotypic optimum. We use these expressions to characterize the use of allele frequency change to test for selection, as well as explore optimal design choices for evolve-and-resequence experiments to uncover the genetic architecture of polygenic traits under selection.

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Genetic diversity during selective sweeps in non-recombining populations

Kaushik,

Jain,

Johri

2024

Preprint

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Selective sweeps, resulting from the spread of beneficial, neutral, or deleterious mutations through a population, shape patterns of genetic variation at linked neutral sites. While many theoretical, computational, and statistical advances have been made in understanding the genomic signatures of selective sweeps in recombining populations, substantially less is understood in populations with little/no recombination. We present a mathematical framework based on diffusion theory for obtaining the site frequency spectrum (SFS) at linked neutral sites immediately post and during the fixation of moderately or strongly beneficial mutations. We find that when a single hard sweep occurs, the SFS decays as 1/xfor low derived allele frequencies (x), similar to the neutral SFS at equilibrium, whereas at higher derived allele frequencies, it follows a 1/x2power law. These power laws are universal in the sense that they are independent of the dominance and inbreeding coefficient, and also characterize the SFS during the sweep. Additionally, we find that the derived allele frequency where the SFS shifts from the 1/xto 1/x2law, is inversely proportional to the selection strength: thus under strong selection, the SFS follows the 1/x2dependence for most allele frequencies, resembling a rapidly expanding neutral population. When clonal interference is pervasive, the SFS immediately post-fixation becomes U-shaped and is better explained by the equilibrium SFS of selected sites. Our results will be important in developing statistical methods to infer the timing and strength of recent selective sweeps in asexual populations, genomic regions that lack recombination, and clonally propagating tumor populations.

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A field theoretic approach to non-equilibrium population genetics in the strong selection regime

Cited by 3 publications

References 83 publications

A Path Integral Approach for Allele Frequency Dynamics Under Polygenic Selection

A Path Integral Approach for Allele Frequency Dynamics Under Polygenic Selection

A path integral approach for allele frequency dynamics under polygenic selection

Genetic diversity during selective sweeps in non-recombining populations

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