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

Population Growth00:57

Population Growth

23.1K
Population size is dynamic, increasing with birth rates and immigration, and decreasing with death rates and emigration. In ideal conditions with unlimited resources, populations can increase exponentially, which plots as a J-shaped growth rate curve of population size against time. This type of curve is characteristic of newly-introduced invasive species, or populations that have suffered catastrophic declines and are rebounding.
23.1K
Modeling with Differential Equations01:25

Modeling with Differential Equations

328
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...
328
Exponential Equations for Modeling Growth01:26

Exponential Equations for Modeling Growth

458
Exponential models are essential for describing rapid, multiplicative changes in natural systems, such as population growth. When a population doubles at regular intervals, the process can be modeled using a suitable base. For instance, a bacterial culture that doubles every three hours follows the model n(t)=n0⋅2t/3, where n(t) is the population at the time t.A more general model uses the natural base e, especially for continuous growth. This takes the form n(t)=n0⋅ert, where r is...
458
Dynamic Equilibrium02:20

Dynamic Equilibrium

63.2K
A reversible chemical reaction represents a chemical process that proceeds in both forward (left to right) and reverse (right to left) directions. When the rates of the forward and reverse reactions are equal, the concentrations of the reactant and product species remain constant over time and the system is at equilibrium. A special double arrow is used to emphasize the reversible nature of the reaction. The relative concentrations of reactants and products in equilibrium systems vary greatly;...
63.2K
The Replisome03:01

The Replisome

31.1K
DNA replication is carried out by a large complex of proteins that act in a coordinated matter to achieve high-fidelity DNA replication. Together this complex is known as the DNA replication machinery or the replisome.
The synthesis of the leading and lagging strands is a highly coordinated process. To explain this, the “Trombone model” was proposed by Bruce Alberts in 1980. The DNA loop formation starts when a primer is synthesized on the parent lagging strand. The loop grows with...
31.1K
The Replisome03:01

The Replisome

9.7K
9.7K

You might also read

Related Articles

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

Sort by
Same author

Nanobubble-enabled foam fractionation to remove algogenic odorous micropollutants.

Water research·2024
Same author

Unraveling the Potential Dependence of Active Structures and Reaction Mechanism of Ni-based MOFs Electrocatalysts for Alkaline OER.

Small (Weinheim an der Bergstrasse, Germany)·2024
Same author

Search for Cosmic-Ray Boosted Sub-MeV Dark-Matter-Electron Scattering in PandaX-4T.

Physical review letters·2024
Same author

Impact of environmental stochastic fluctuations on the evolutionary stability of imitation dynamics.

Physical review. E·2024
Same author

A high cholesterol diet aggravates experimental colitis through SREBP2-modulated endocytosis and degradation of occludin and Zo-1 proteins.

The FEBS journal·2024
Same author

Plasma metabolic profiling reveals that crude and processed Polygonatum cyrtonema hua extract ameliorates myocardial ischemia-induced damage by regulating branched-chain amino acid and energy metabolism.

Journal of chromatography. B, Analytical technologies in the biomedical and life sciences·2024
Same journal

The TaMYB55-TaSnRK1α1-TabZIP9 module confers heat stress tolerance in wheat.

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

Superstatistics approach to turbulent circulation fluctuations.

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

A molecular timescale for evolution of cobamide biosynthesis.

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

Pierre Chambon, a pioneer of molecular biology and gene regulation in eukaryotes.

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

Granulosa cell glycogen fuels the avascular corpus luteum.

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

Synthetic essentiality of TRAIL/TNFSF10 in VHL-deficient renal cell carcinoma.

Proceedings of the National Academy of Sciences of the United States of America·2026
See all related articles

Related Experiment Video

Updated: Apr 27, 2026

The Collective Trust Game: An Online Group Adaptation of the Trust Game Based on the HoneyComb Paradigm
06:18

The Collective Trust Game: An Online Group Adaptation of the Trust Game Based on the HoneyComb Paradigm

Published on: October 20, 2022

2.3K

The replicator equation and other game dynamics.

Ross Cressman1, Yi Tao2

  • 1Department of Mathematics, Wilfrid Laurier University, Waterloo, ON, Canada N2L 3C5; and.

Proceedings of the National Academy of Sciences of the United States of America
|July 16, 2014
PubMed
Summary
This summary is machine-generated.

The replicator equation, a foundational concept in evolutionary game theory, models strategy evolution in games. This study explores its properties and extends it to more complex game scenarios.

Keywords:
Nash equilibriumdynamic stabilityevolutionarily stable strategy (ESS)

More Related Videos

Predicting the Effectiveness of Population Replacement Strategy Using Mathematical Modeling
20:36

Predicting the Effectiveness of Population Replacement Strategy Using Mathematical Modeling

Published on: July 4, 2007

8.2K

Related Experiment Videos

Last Updated: Apr 27, 2026

The Collective Trust Game: An Online Group Adaptation of the Trust Game Based on the HoneyComb Paradigm
06:18

The Collective Trust Game: An Online Group Adaptation of the Trust Game Based on the HoneyComb Paradigm

Published on: October 20, 2022

2.3K
Predicting the Effectiveness of Population Replacement Strategy Using Mathematical Modeling
20:36

Predicting the Effectiveness of Population Replacement Strategy Using Mathematical Modeling

Published on: July 4, 2007

8.2K

Area of Science:

  • Evolutionary Game Theory
  • Mathematical Biology
  • Game Dynamics

Background:

  • The replicator equation is a fundamental model in evolutionary game theory.
  • It was initially developed for symmetric games with a finite number of strategies.
  • Understanding its properties is crucial for analyzing strategy evolution.

Purpose of the Study:

  • To summarize the properties of the replicator equation for symmetric games.
  • To extend the theory to other game dynamics and more complex game types.
  • To illustrate the concepts with examples from existing literature.

Main Methods:

  • Analysis of the replicator equation's convergence and stability properties.
  • Extension of the replicator equation to best response dynamics and adaptive dynamics.
  • Application of the theory to multiplayer, population, and asymmetric games.

Main Results:

  • Key properties of the replicator equation in symmetric games are summarized.
  • The theory is successfully extended to various other game dynamics.
  • The extended framework is applicable to a broader range of game scenarios, including multiplayer and asymmetric games.

Conclusions:

  • The replicator equation and its extensions provide a robust framework for studying evolutionary dynamics.
  • The study highlights the versatility of game dynamics in analyzing complex strategic interactions.
  • Further research can explore applications in diverse fields using these extended models.