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

29.2K
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.
29.2K
What are Populations and Communities?00:30

What are Populations and Communities?

38.2K
Overview
38.2K
Modeling with Differential Equations01:25

Modeling with Differential Equations

129
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...
129
Mechanistic Models: Compartment Models in Individual and Population Analysis01:23

Mechanistic Models: Compartment Models in Individual and Population Analysis

310
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...
310
Growth Models with Integration: Problem Solving01:27

Growth Models with Integration: Problem Solving

81
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...
81
Conservation of Small Populations02:04

Conservation of Small Populations

17.5K
Small population sizes put a species at extreme risk of extinction due to a lack of variation, and a consequent decrease in adaptability. This weakens the chances of survival under pressures such as climate change, competition from other species, or new diseases. Large populations are more likely to survive pressures such as these, as such populations are more likely to harbor individuals that have genetic variants that are adaptive under new stresses. Small populations are much less...
17.5K

You might also read

Related Articles

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

Sort by
Same author

DYNAMICS OF STOCHASTIC MICROORGANISM FLOCCULATION MODELS.

ArXiv·2025
Same author

Population size in stochastic discrete-time ecological dynamics.

Journal of mathematical biology·2025
Same author

Long-term behavior of stochastic SIQRS epidemic models.

Journal of mathematical biology·2025
Same author

Coevolution of Patch Selection in Stochastic Environments.

The American naturalist·2023
Same author

The effects of random and seasonal environmental fluctuations on optimal harvesting and stocking.

Journal of mathematical biology·2022
Same author

Stationary distributions of persistent ecological systems.

Journal of mathematical biology·2021
Same journal

Discrete-time exploitative competition model of different stage-specific predators.

Journal of mathematical biology·2026
Same journal

Spatiotemporal SEIQR Epidemic Modeling with Optimal Control for Vaccination, Treatment, and Social Measures.

Journal of mathematical biology·2026
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
See all related articles

Related Experiment Video

Updated: Mar 3, 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

9.2K

Population size in stochastic multi-patch ecological models.

Alexandru Hening1, Siddharth Sabharwal2

  • 1Department of Mathematics, Texas A&M University, Mailstop 3368, College Station, TX, 77843-3368, United States. ahening@tamu.edu.

Journal of Mathematical Biology
|March 2, 2026
PubMed
Summary
This summary is machine-generated.

Environmental stochasticity and dispersal interact in n-patch models. Fast dispersal can prevent extinction, while stochasticity

Keywords:
DispersalPersistencePopulation sizeStationarityStochastic difference equations

More Related Videos

Modeling the Size Spectrum for Macroinvertebrates and Fishes in Stream Ecosystems
07:41

Modeling the Size Spectrum for Macroinvertebrates and Fishes in Stream Ecosystems

Published on: July 30, 2019

8.1K
Automatic Image Processing to Determine the Community Size Structure of Riverine Macroinvertebrates
08:56

Automatic Image Processing to Determine the Community Size Structure of Riverine Macroinvertebrates

Published on: January 13, 2023

2.9K

Related Experiment Videos

Last Updated: Mar 3, 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

9.2K
Modeling the Size Spectrum for Macroinvertebrates and Fishes in Stream Ecosystems
07:41

Modeling the Size Spectrum for Macroinvertebrates and Fishes in Stream Ecosystems

Published on: July 30, 2019

8.1K
Automatic Image Processing to Determine the Community Size Structure of Riverine Macroinvertebrates
08:56

Automatic Image Processing to Determine the Community Size Structure of Riverine Macroinvertebrates

Published on: January 13, 2023

2.9K

Area of Science:

  • Ecology
  • Mathematical Biology
  • Population Dynamics

Background:

  • Understanding population dynamics requires analyzing the interplay between dispersal and environmental variability.
  • Stochasticity in dispersal rates adds complexity to ecological models.

Purpose of the Study:

  • To investigate the combined effects of dispersal and environmental stochasticity on population persistence and extinction in n-patch models.
  • To derive explicit approximations for total population size under varying dispersal rates and environmental fluctuations.

Main Methods:

  • Analysis of n-patch models with stochastic dispersal rates.
  • Application of Beverton-Holt and Hassell functional responses.
  • Development of approximation methods for population size at stationarity, particularly for slow and fast dispersal scenarios.

Main Results:

  • Persistence and extinction results are proven even with stochastic dispersal rates.
  • In the Beverton-Holt model, random carrying capacity decreases population size.
  • In the Hassell model, random inverse carrying capacity increases population size.
  • Fast dispersal enhances population size and prevents extinction.
  • Covariances between random parameters significantly influence population size outcomes.

Conclusions:

  • Environmental stochasticity can be detrimental or beneficial depending on the model and parameters.
  • Both dispersal and environmental stochasticity can lead to increased population sizes.
  • Complex interactions exist between various stochastic parameters in multi-patch populations.