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

Mechanistic Models: Compartment Models in Individual and Population Analysis01:23

Mechanistic Models: Compartment Models in Individual and Population Analysis

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 squares (OLS)...
Modeling with Differential Equations01:25

Modeling with Differential Equations

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...
Pharmacodynamic Models: Link Model and Systems Pharmacodynamic Model01:14

Pharmacodynamic Models: Link Model and Systems Pharmacodynamic Model

The link model is a fundamental pharmacokinetic-pharmacodynamic (PK–PD) approach to account for delayed drug responses when the observed effect does not immediately correlate with the drug's plasma concentration peak. This delay is mathematically addressed by introducing an effect compartment concentration, Ce, which is kinetically linked to the plasma concentration, Cp, via a first-order rate constant, ke0. The linkage allows for a more accurate prediction of drug effects over time. A higher...
Limits to Natural Selection01:38

Limits to Natural Selection

Organisms that are well-adapted to their environment are more likely to survive and reproduce. However, natural selection does not lead to perfectly adapted organisms. Several factors constrain natural selection.For one, natural selection can only act upon existing genetic variation. Hypothetically, redtusks may enhance elephant survival by deterring ivory-seeking poachers. However, if there are no gene variants—or alleles—for redtusks, natural selection cannot increase the prevalence of...
Evolution of New Traits in Microbes01:24

Evolution of New Traits in Microbes

Microorganisms evolve rapidly due to their large population sizes and short generation times, often exhibiting measurable changes within days under laboratory conditions. Natural selection acts on standing genetic variation, enabling the retention and amplification of beneficial traits that confer fitness advantages in changing environments.Adaptive Pigment Regulation in RhodobacterIn Rhodobacter, a genus of purple non-sulfur bacteria, light-harvesting pigments such as bacteriochlorophyll and...
Mutation, Gene Flow, and Genetic Drift01:09

Mutation, Gene Flow, and Genetic Drift

In a population that is not at Hardy-Weinberg equilibrium, the frequency of alleles changes over time. Therefore, any deviations from the five conditions of Hardy-Weinberg equilibrium can alter the genetic variation of a given population. Conditions that change the genetic variability of a population include mutations, natural selection, non-random mating, gene flow, and genetic drift (small population size).Mechanisms of Genetic VariationThe original sources of genetic variation are mutations,...

You might also read

Related Articles

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

Sort by
Same author

Evolution of noisy learning in games.

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

Reply to Sacco: Complete spaces as outcomes of evolutionary optimization.

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

Interactions between immuno-epidemiology and individual decision-making for nonpharmaceutical interventions.

Trends in microbiology·2026
Same author

Payoff equivalence and complete strategy spaces of direct reciprocity.

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

The dynamics of cooperation in asymmetric public goods games.

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

Time-Dependent Strategies in Repeated Asymmetric Public Goods Games.

Dynamic games and applications·2025

Related Experiment Video

Updated: Jun 5, 2026

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

Local replicator dynamics: a simple link between deterministic and stochastic models of evolutionary game theory.

Christian Hilbe1

  • 1Faculty of Mathematics, University of Vienna, Nordbergstrasse 15, 1090 Vienna, Austria. christian.hilbe@univie.ac.at

Bulletin of Mathematical Biology
|December 25, 2010
PubMed
Summary

This study connects evolutionary game models for infinite and finite populations. It reveals that replicator dynamics in infinite populations can model finite population processes, like the Moran process, with a modified payoff matrix.

More Related Videos

Daily Transfers, Archiving Populations, and Measuring Fitness in the Long-Term Evolution Experiment with Escherichia coli
15:00

Daily Transfers, Archiving Populations, and Measuring Fitness in the Long-Term Evolution Experiment with Escherichia coli

Published on: August 18, 2023

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

Related Experiment Videos

Last Updated: Jun 5, 2026

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

Daily Transfers, Archiving Populations, and Measuring Fitness in the Long-Term Evolution Experiment with Escherichia coli
15:00

Daily Transfers, Archiving Populations, and Measuring Fitness in the Long-Term Evolution Experiment with Escherichia coli

Published on: August 18, 2023

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

Area of Science:

  • Evolutionary Game Theory
  • Mathematical Biology
  • Population Dynamics

Background:

  • Classical replicator dynamics assumes global strategy adoption based on average payoffs.
  • Finite population models often use probabilistic processes like the Moran process for strategy selection.

Purpose of the Study:

  • To bridge evolutionary models for infinite and finite populations.
  • To demonstrate the applicability of infinite population replicator dynamics to finite populations and vice versa.

Main Methods:

  • Modeling interactions and reproduction in random groups of size N within an infinite population.
  • Deriving a modified payoff matrix for the replicator system.
  • Analyzing the resulting dynamics and comparing with finite population models.

Main Results:

  • The dynamics in randomly interacting groups simplify to the traditional replicator system with a modified payoff matrix.
  • Qualitative results align with finite population findings, including a universal one-third law.
  • The deterministic replicator equation for infinite populations can effectively study the Moran process in finite populations.

Conclusions:

  • Infinite and finite population evolutionary models are interconnected.
  • The replicator equation provides a versatile tool for analyzing evolutionary dynamics across different population structures.
  • The findings have implications for understanding cooperation, risk aversion, and strategy maintenance.