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

27.5K
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.
27.5K
Exponential Equations for Modeling Growth02:33

Exponential Equations for Modeling Growth

106
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...
106
Genetic Drift03:33

Genetic Drift

42.5K
Natural selection—probably the most well-known evolutionary mechanism—increases the prevalence of traits that enhance survival and reproduction. However, evolution does not merely propagate favorable traits, nor does it always benefit populations.
42.5K
Mutation, Gene Flow, and Genetic Drift01:09

Mutation, Gene Flow, and Genetic Drift

61.3K
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).
61.3K
Diffusion01:21

Diffusion

5.9K
Diffusion is a type of passive transport. In passive transport, a substance tends to move from an area of high concentration to an area of low concentration until the concentration is equal across the space. For example, take the diffusion of substances through the air. When someone opens a perfume bottle in a room filled with people, the perfume is at its highest concentration in the bottle and is at its lowest at the edges of the room. The perfume vapor will diffuse, or spread away, from the...
5.9K
Diffusion01:12

Diffusion

214.9K
Diffusion is the passive movement of substances down their concentration gradients—requiring no expenditure of cellular energy. Substances, such as molecules or ions, diffuse from an area of high concentration to an area of low concentration in the cytosol or across membranes. Eventually, the concentration will even out, with the substance moving randomly but causing no net change in concentration. Such a state is called dynamic equilibrium, which is essential for maintaining overall...
214.9K

You might also read

Related Articles

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

Sort by
Same author

Effects of biochar application combined with different amendments on organic carbon fractions, aggregate stability, and oat yield in saline-alkali soil.

Ying yong sheng tai xue bao = The journal of applied ecology·2026
Same author

Changes in the co-occurrence patterns of negative aging perceptions and psychosocial symptoms among older adults before, during, and after the pandemic.

Journal of health psychology·2026
Same author

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 author

Empagliflozin Alleviates Osteoarthritis Progression by Attenuating Inflammation, Restoring Impaired Autophagy, and Ameliorating Chondrocyte Senescence.

Biomedicines·2026
Same author

Metabolic indicators as mediators in the relationship between lifestyle and arterial stiffness.

Nutrition, metabolism, and cardiovascular diseases : NMCD·2026
Same author

Maternal and calf diet supplementation with Saccharomyces cerevisiae fermentation-derived postbiotics: Effects on calf growth performance, health, rumen fermentation, and microbiota.

Journal of dairy science·2026
Same journal

Reaction-Diffusion Problems on Time-Periodic Domains.

Journal of dynamics and differential equations·2025
Same journal

Local Well-Posedness of the Periodic Nonlinear Schrödinger Equation with a Quadratic Nonlinearity <math> </math> in Negative Sobolev Spaces.

Journal of dynamics and differential equations·2025
Same journal

Computer-Assisted Proofs of Hopf Bubbles and Degenerate Hopf Bifurcations.

Journal of dynamics and differential equations·2024
Same journal

Regularization by Noise of an Averaged Version of the Navier-Stokes Equations.

Journal of dynamics and differential equations·2024
Same journal

Travelling Waves in a PDE-ODE Coupled Model of Cellulolytic Biofilms with Nonlinear Diffusion.

Journal of dynamics and differential equations·2024
Same journal

Well-Posedness Properties for a Stochastic Rotating Shallow Water Model.

Journal of dynamics and differential equations·2024
See all related articles

Related Experiment Video

Updated: Dec 11, 2025

Generating Controlled, Dynamic Chemical Landscapes to Study Microbial Behavior
10:07

Generating Controlled, Dynamic Chemical Landscapes to Study Microbial Behavior

Published on: January 31, 2020

6.5K

Age-Structured Population Dynamics with Nonlocal Diffusion.

Hao Kang1, Shigui Ruan1, Xiao Yu2

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

Journal of Dynamics and Differential Equations
|August 25, 2020
PubMed
Summary
This summary is machine-generated.

This study develops foundational theory for age-structured population models with nonlocal diffusion, a more realistic approach than random diffusion. We analyze spectral properties to determine the stability of population dynamics, providing insights into population persistence and structure.

Keywords:
Age structureInfinitesimal generatorNonlocal diffusionSemigroup theorySpectrum theoryStability

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

1.2K
Single-Molecule Tracking Microscopy - A Tool for Determining the Diffusive States of Cytosolic Molecules
10:20

Single-Molecule Tracking Microscopy - A Tool for Determining the Diffusive States of Cytosolic Molecules

Published on: September 5, 2019

8.6K

Related Experiment Videos

Last Updated: Dec 11, 2025

Generating Controlled, Dynamic Chemical Landscapes to Study Microbial Behavior
10:07

Generating Controlled, Dynamic Chemical Landscapes to Study Microbial Behavior

Published on: January 31, 2020

6.5K
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

1.2K
Single-Molecule Tracking Microscopy - A Tool for Determining the Diffusive States of Cytosolic Molecules
10:20

Single-Molecule Tracking Microscopy - A Tool for Determining the Diffusive States of Cytosolic Molecules

Published on: September 5, 2019

8.6K

Area of Science:

  • Mathematical Biology
  • Population Dynamics
  • Nonlocal Diffusion

Background:

  • Age-structured population models are crucial for understanding population dynamics.
  • Nonlocal diffusion models offer greater biological and physical realism than random diffusion.
  • Theoretical results for age-structured models with nonlocal diffusion are scarce.

Purpose of the Study:

  • To establish fundamental mathematical theory for age-structured population dynamics incorporating nonlocal diffusion.
  • To analyze the spectral properties of the semigroup generated by the model.
  • To determine the stability of the zero steady state in these models.

Main Methods:

  • Analysis of the semigroup of linear operators associated with the nonlocal diffusion model.
  • Utilizing spectral properties of the infinitesimal generator.
  • Investigating models with spatially independent and dependent birth/death rates.

Main Results:

  • The semigroup structure is determined by the non-diffusive model and the nonlocal operator when birth/death rates are spatially independent.
  • Asymptotic behavior is linked to the spectral bound sign when birth/death rates are spatially dependent.
  • Weak solutions and comparison principles are established for spatially and temporally dependent rates.
  • Results are generalizable to age-size structured models.

Conclusions:

  • The study provides a theoretical framework for nonlocal age-structured population models.
  • Spectral analysis is key to understanding stability and asymptotic behavior.
  • The findings extend to more complex age-size structured populations and offer comparisons to Laplacian diffusion models.