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

313
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...
313
Population Growth00:57

Population Growth

23.0K
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.
23.0K
Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving01:29

Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving

435
Mechanistic models play a crucial role in algorithms for numerical problem-solving, particularly in nonlinear mixed effects modeling (NMEM). These models aim to minimize specific objective functions by evaluating various parameter estimates, leading to the development of systematic algorithms. In some cases, linearization techniques approximate the model using linear equations.
In individual population analyses, different algorithms are employed, such as Cauchy's method, which uses a...
435
Growth Models with Integration: Problem Solving01:27

Growth Models with Integration: Problem Solving

160
In population modeling, integration provides a systematic way to determine accumulated quantities from known rates of change. One such application arises in ecology, where the total weight of a fish population in a body of water is referred to as its biomass. When the rate of growth of this biomass is known as a function of time, calculus can be used to determine the total biomass at a future date.Growth Rate and Biomass FunctionLet the growth rate of the fish population be represented by a...
160
Conservation of Declining Populations02:07

Conservation of Declining Populations

11.5K
Conservation of declining population focuses on ways of detecting, diagnosing, and halting a population decline. The approach uses methods to prevent populations from going extinct.
11.5K
What are Populations and Communities?00:30

What are Populations and Communities?

30.9K
Overview
30.9K

You might also read

Related Articles

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

Sort by
Same author

Selective sweeps in SARS-CoV-2 variant competition.

Proceedings of the National Academy of Sciences of the United States of America·2022
Same author

Spatial evolutionary games with weak selection.

Proceedings of the National Academy of Sciences of the United States of America·2017
Same author

Spatial Moran Models I. Stochastic Tunneling in the Neutral Case.

The annals of applied probability : an official journal of the Institute of Mathematical Statistics·2015
Same author

Fingering in Stochastic Growth Models.

Experimental mathematics·2015
Same author

Chemical evolutionary games.

Theoretical population biology·2014
Same author

Multiopinion coevolving voter model with infinitely many phase transitions.

Physical review. E, Statistical, nonlinear, and soft matter physics·2014
Same journal

Tau protein as a regulator of mitochondrial function and dynamics.

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

A scalable, dividing cell model for the robust propagation and quantification of human sporadic Creutzfeldt-Jakob disease prions.

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

Epigenetic regulation of mesenchymal BMP signaling directs postnatal organ innervation.

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

Single-shot wide-field biochemical imaging at 1 kHz frame rate.

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

Morphogenesis and topological evolution of a frustrated nematic liquid crystal under confinement.

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

B cell-intrinsic CXCR3 drives efficient generation of ectopic pulmonary germinal center responses to influenza A virus infection.

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

Related Experiment Video

Updated: Apr 23, 2026

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

Exact solution for a metapopulation version of Schelling's model.

Richard Durrett1, Yuan Zhang2

  • 1Department of Mathematics, Duke University, Durham, NC 27708 rtd@math.duke.edu.

Proceedings of the National Academy of Sciences of the United States of America
|September 17, 2014
PubMed
Summary
This summary is machine-generated.

This study explores Schelling

Keywords:
large deviationssegregation

More Related Videos

Spatial Multiobjective Optimization of Agricultural Conservation Practices using a SWAT Model and an Evolutionary Algorithm
11:53

Spatial Multiobjective Optimization of Agricultural Conservation Practices using a SWAT Model and an Evolutionary Algorithm

Published on: December 9, 2012

12.6K

Related Experiment Videos

Last Updated: Apr 23, 2026

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
Spatial Multiobjective Optimization of Agricultural Conservation Practices using a SWAT Model and an Evolutionary Algorithm
11:53

Spatial Multiobjective Optimization of Agricultural Conservation Practices using a SWAT Model and an Evolutionary Algorithm

Published on: December 9, 2012

12.6K

Area of Science:

  • Sociology
  • Urban Studies
  • Computational Social Science

Background:

  • Schelling's 1971 model introduced agent-based modeling for segregation.
  • The original model focused on individual household choices.
  • Metapopulation dynamics offer a broader perspective on segregation.

Purpose of the Study:

  • To analyze a metapopulation version of Schelling's segregation model.
  • To investigate the emergence of segregation in a spatially structured population.
  • To identify critical thresholds for random distribution versus segregation.

Main Methods:

  • Agent-based modeling of family movement between neighborhoods.
  • Mathematical analysis of equilibrium states in a metapopulation framework.
  • Stochastic modeling of population dynamics and spatial distribution.

Main Results:

  • Identified critical population densities (ρ(b), ρ(d), ρ(c)) influencing segregation.
  • Demonstrated a transition from random distribution to segregated equilibria.
  • Observed bistability between random and segregated states within specific density ranges.

Conclusions:

  • Neighborhood size and population density critically affect segregation patterns.
  • The metapopulation model reveals complex dynamics, including bistability and potential return to random distribution at high densities.
  • Agent movement rules based on neighborhood composition drive emergent segregation.