Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Concept Videos

Modeling with Differential Equations01:25

Modeling with Differential Equations

164
Population dynamics can be described mathematically by considering the population size P(t) as a function of time. The rate of change of the population is then represented by the derivative of P(t). A simple assumption is that the rate of growth is proportional to the size of the population itself. This leads to an exponential growth model, where the population increases rapidly without bound. While this is a useful first approximation, it does not reflect realistic long-term...
164
Hardy-Weinberg Principle01:49

Hardy-Weinberg Principle

77.3K
Diploid organisms have two alleles of each gene, one from each parent, in their somatic cells. Therefore, each individual contributes two alleles to the gene pool of the population. The gene pool of a population is the sum of every allele of all genes within that population and has some degree of variation. Genetic variation is typically expressed as a relative frequency, which is the percentage of the total population that has a given allele, genotype or phenotype.
77.3K
Mechanistic Models: Compartment Models in Individual and Population Analysis01:23

Mechanistic Models: Compartment Models in Individual and Population Analysis

321
Mechanistic models are utilized in individual analysis using single-source data, but imperfections arise due to data collection errors, preventing perfect prediction of observed data. The mathematical equation involves known values (Xi), observed concentrations (Ci), measurement errors (εi), model parameters (ϕj), and the related function (ƒi) for i number of values. Different least-squares metrics quantify differences between predicted and observed values. The ordinary least...
321
Polygenic Traits01:18

Polygenic Traits

11.4K
11.4K
Polygenic Traits01:18

Polygenic Traits

70.3K
When more than one gene is responsible for a given phenotype, the trait is considered polygenic. Human height is a polygenic trait. Studies have uncovered hundreds of loci that influence height, and there are believed to be many more. Due to the high number of genes involved, as well as environmental and nutritional factors, height varies significantly within a given population. The distribution of height forms a bell-shaped curve, with relatively few individuals in the population at the...
70.3K
The Small x Assumption02:20

The Small x Assumption

50.6K
If a reaction has a small equilibrium constant, the equilibrium position favors the reactants. In such reactions, a negligible change in concentration may occur if the initial concentrations of reactants are high and the Kc value is small. In such circumstances, the equilibrium concentration is approximately equal to its initial concentration.  This estimation can be used to simplify the equilibrium calculations by assuming that some equilibrium concentrations are equal to the initial...
50.6K

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

Invariant nonequilibrium dynamics in gene regulation optimize information flow.

Proceedings of the National Academy of Sciences of the United States of America·2026
Same author

Long-term evolution of regulatory DNA sequences. Part 1: simulations on global, biophysically-realistic genotype-phenotype maps.

Current opinion in genetics & development·2026
Same author

Long-term evolution of regulatory DNA sequences. Part 2: theory and future challenges.

Current opinion in genetics & development·2026
Same author

Genealogical Analysis of Replicate Flower Colour Hybrid Zones in Antirrhinum.

Molecular ecology·2025
Same author

Joint Estimation of Paternity, Sibships and Pollen Dispersal in a Snapdragon Hybrid Zone.

Molecular ecology·2025
Same author

Invariant non-equilibrium dynamics of transcriptional regulation optimize information flow.

ArXiv·2025

Related Experiment Video

Updated: Mar 25, 2026

Why Quantification Matters: Characterization of Phenotypes at the Drosophila Larval Neuromuscular Junction
10:41

Why Quantification Matters: Characterization of Phenotypes at the Drosophila Larval Neuromuscular Junction

Published on: May 12, 2016

8.6K

A General Approximation for the Dynamics of Quantitative Traits.

Katarína Bod'ová1, Gašper Tkačik2, Nicholas H Barton2

  • 1Institute of Science and Technology Austria (IST Austria), Klosterneuburg A-3400, Austria kbodova@ist.ac.at.

Genetics
|February 19, 2016
PubMed
Summary

This study shows that a maximum-entropy approximation accurately predicts quantitative trait evolution, even with small mutation rates and changing selection pressures. This method bypasses tracking unobserved allele frequencies.

Keywords:
diffusion approximation, quasi-stationaritymaximum entropyquantitative genetics

More Related Videos

Following the Dynamics of Structural Variants in Experimentally Evolved Populations
04:52

Following the Dynamics of Structural Variants in Experimentally Evolved Populations

Published on: February 3, 2023

1.4K
Age-dependent Dynamics of Locomotion in Caenorhabditis elegans: A Lyapunov Exponent Analysis
06:44

Age-dependent Dynamics of Locomotion in Caenorhabditis elegans: A Lyapunov Exponent Analysis

Published on: September 23, 2025

686

Related Experiment Videos

Last Updated: Mar 25, 2026

Why Quantification Matters: Characterization of Phenotypes at the Drosophila Larval Neuromuscular Junction
10:41

Why Quantification Matters: Characterization of Phenotypes at the Drosophila Larval Neuromuscular Junction

Published on: May 12, 2016

8.6K
Following the Dynamics of Structural Variants in Experimentally Evolved Populations
04:52

Following the Dynamics of Structural Variants in Experimentally Evolved Populations

Published on: February 3, 2023

1.4K
Age-dependent Dynamics of Locomotion in Caenorhabditis elegans: A Lyapunov Exponent Analysis
06:44

Age-dependent Dynamics of Locomotion in Caenorhabditis elegans: A Lyapunov Exponent Analysis

Published on: September 23, 2025

686

Area of Science:

  • Population Genetics
  • Quantitative Genetics
  • Statistical Mechanics

Background:

  • Allele frequencies and their dynamics drive quantitative trait evolution.
  • Macroscopic trait dynamics are observable, but underlying allele frequencies are not.
  • Statistical mechanics analogies, using maximum entropy, have approximated allele frequency distributions.

Purpose of the Study:

  • To explore the limitations of the maximum-entropy approximation in population genetics.
  • To extend this approximation for small mutation rates (4Nmicro < 1) where populations are near fixation.
  • To investigate the accuracy of the approximation with changing mutation and selection strengths.

Main Methods:

  • Approximation of allele frequency distributions using maximum entropy.
  • Analysis of single diallelic loci under directional selection and overdominance.
  • Generalization to multiple unlinked biallelic loci with unequal effects.
  • Theoretical extension to account for varying mutation strengths.

Main Results:

  • The maximum-entropy approximation is highly accurate even when mutation is small and populations are close to fixation.
  • The approximation remains effective even with rapid changes in mutation and selection.
  • The theory was extended to handle varying mutation strengths in the near-fixation regime.

Conclusions:

  • The maximum-entropy method provides a robust framework for understanding quantitative trait evolution without direct observation of allele frequencies.
  • This approach is particularly valuable in scenarios with weak mutation and strong drift.
  • The findings support the utility of statistical mechanics principles in population genetics.