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

Normal Distribution01:11

Normal Distribution

16.5K
The normal, a continuous distribution, is the most important of all the distributions. Its graph is a bell-shaped symmetrical curve, which is observed in almost all disciplines. Some of these include psychology, business, economics, the sciences, nursing, and, of course, mathematics. Some instructors may use the normal distribution to help determine students’ grades. Most IQ scores are normally distributed. Often real-estate prices fit a normal distribution. The normal distribution is...
16.5K
Probability Distributions01:32

Probability Distributions

11.8K
 The probability of a random variable x  is the likelihood of its occurrence. A probability distribution represents the probabilities of a random variable using a formula, graph, or table. There are two types of probability distribution– discrete probability distribution and continuous probability distribution.
A discrete probability distribution is a probability distribution of discrete random variables. It can be categorized into binomial probability distribution and Poisson...
11.8K
Estimation of the Physical Quantities01:05

Estimation of the Physical Quantities

7.2K
On many occasions, physicists, other scientists, and engineers need to make estimates of a particular quantity. These are sometimes referred to as guesstimates, order-of-magnitude approximations, back-of-the-envelope calculations, or Fermi calculations. The physicist Enrico Fermi was famous for his ability to estimate various kinds of data with surprising precision. Estimating does not mean guessing a number or a formula at random. Instead, estimation means using prior experience and sound...
7.2K
Introduction to Normal Distributions01:29

Introduction to Normal Distributions

23
Standardized test scores often follow a symmetric distribution that can be modeled with the normal distribution, a fundamental concept in statistics. This distribution is particularly useful for interpreting test performance fairly across populations, as it provides a mathematical framework for understanding variability and central tendency in large datasets.From Histogram to Frequency DistributionRaw test data are often displayed using histograms, where the height of each bar represents the...
23
Central Limit Theorem01:14

Central Limit Theorem

19.6K
The central limit theorem, abbreviated as clt, is one of the most powerful and useful ideas in all of statistics. The central limit theorem for sample means says that if you repeatedly draw samples of a given size and calculate their means, and create a histogram of those means, then the resulting histogram will tend to have an approximate normal bell shape. In other words, as sample sizes increase, the distribution of means follows the normal distribution more closely.
The sample size, n, that...
19.6K
Weighted Mean00:57

Weighted Mean

6.2K
While taking the arithmetic, geometric, or harmonic mean of a sample data set, equal importance is assigned to all the data points. However, all the values may not always be equally important in some data sets. An intrinsic bias might make it more important to give more weightage to specific values over others.
For example, consider the number of goals scored in the matches of a tournament. While computing the average number of goals scored in the tournament, it may be more important to...
6.2K

You might also read

Related Articles

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

Sort by
Same author

The Topological State Derivative: An Optimal Control Perspective on Topology Optimisation.

Journal of geometric analysis·2023
Same author

On the Allee effect and directed movement on the whole space.

Mathematical biosciences and engineering : MBE·2023
Same author

Linking mathematical models and trap data to infer the proliferation, abundance, and control of Aedes aegypti.

Acta tropica·2023
Same author

Ideal free dispersal in integrodifference models.

Journal of mathematical biology·2022
Same author

Three-patch Models for the Evolution of Dispersal in Advective Environments: Varying Drift and Network Topology.

Bulletin of mathematical biology·2021
Same author

Analysis of a mathematical model of immune response to fungal infection.

Journal of mathematical biology·2021
Same journal

Phenotypic plasticity trade-offs in an age-structured model of bacterial growth under stress.

Journal of mathematical biology·2026
Same journal

Intraspecific interactions facilitate mutualism across multilayer networks under weak selection.

Journal of mathematical biology·2026
Same journal

A two-species competition model on a compact metric graph for the invasion and competition of Aedes Aegypti and Aedes Albopictus mosquitoes in Florida.

Journal of mathematical biology·2026
Same journal

Superinfection and the hypnozoite reservoir for Plasmodium vivax: a multitype branching process approximation.

Journal of mathematical biology·2026
Same journal

Correction to: Superinfection and the hypnozoite reservoir for Plasmodium vivax: a general framework.

Journal of mathematical biology·2026
Same journal

Stoichiometric balance and sustained rhythms.

Journal of mathematical biology·2026
See all related articles

Related Experiment Video

Updated: Jan 17, 2026

The HoneyComb Paradigm for Research on Collective Human Behavior
06:48

The HoneyComb Paradigm for Research on Collective Human Behavior

Published on: January 19, 2019

9.8K

Mean Field Games and Ideal Free Distribution.

Robert Stephen Cantrell1, Chris Cosner1, King-Yeung Lam2

  • 1Department of Mathematics, University of Miami, 1365 Memorial Drive, Coral Gables, FL, 33146, USA.

Journal of Mathematical Biology
|September 18, 2025
PubMed
Summary
This summary is machine-generated.

This study models animal habitat selection using a dynamic game system. It shows population density converges to the ideal free distribution, offering a new derivation in a dynamic context.

Keywords:
Bellman equationHamilton-jacobiIdeal free distributionLong-time averageMean field gameReaction-diffusion equations

More Related Videos

WheelCon: A Wheel Control-Based Gaming Platform for Studying Human Sensorimotor Control
08:18

WheelCon: A Wheel Control-Based Gaming Platform for Studying Human Sensorimotor Control

Published on: August 15, 2020

5.4K
Measuring the Subjective Value of Risky and Ambiguous Options using Experimental Economics and Functional MRI Methods
13:04

Measuring the Subjective Value of Risky and Ambiguous Options using Experimental Economics and Functional MRI Methods

Published on: September 19, 2012

12.4K

Related Experiment Videos

Last Updated: Jan 17, 2026

The HoneyComb Paradigm for Research on Collective Human Behavior
06:48

The HoneyComb Paradigm for Research on Collective Human Behavior

Published on: January 19, 2019

9.8K
WheelCon: A Wheel Control-Based Gaming Platform for Studying Human Sensorimotor Control
08:18

WheelCon: A Wheel Control-Based Gaming Platform for Studying Human Sensorimotor Control

Published on: August 15, 2020

5.4K
Measuring the Subjective Value of Risky and Ambiguous Options using Experimental Economics and Functional MRI Methods
13:04

Measuring the Subjective Value of Risky and Ambiguous Options using Experimental Economics and Functional MRI Methods

Published on: September 19, 2012

12.4K

Area of Science:

  • Ecology
  • Mathematical Biology
  • Game Theory

Background:

  • The ideal free distribution (IFD) by Fretwell and Lucas describes habitat selection in animal populations.
  • Existing models often lack a dynamic framework for habitat selection.
  • Mean field game systems offer a powerful tool for modeling large population dynamics.

Purpose of the Study:

  • To dynamically model the habitat selection game using a mean field game system.
  • To establish the existence of classical solutions for ergodic mean field game systems.
  • To demonstrate the convergence of population density to the ideal free distribution.

Main Methods:

  • Utilizing a mean field game system with local coupling.
  • Establishing existence of classical solutions for ergodic systems.
  • Analyzing convergence as control cost approaches zero.

Main Results:

  • Existence of classical solutions for the ergodic mean field game system, including heterogeneous diffusion in 1D.
  • Population density of agents converges to the ideal free distribution.
  • Provides a derivation of IFD in a dynamical context.

Conclusions:

  • The study successfully models habitat selection dynamically using mean field games.
  • Confirms convergence to the ideal free distribution under specific conditions.
  • Offers a novel dynamical derivation of the ideal free distribution concept.