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

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

Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving

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...
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)...
Population Growth00:57

Population Growth

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.
Growth Models with Integration: Problem Solving01:27

Growth Models with Integration: Problem Solving

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...
Exponential Equations for Modeling Growth01:26

Exponential Equations for Modeling Growth

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 the relative...

You might also read

Related Articles

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

Sort by
Same author

How predator evolution to resist lethal or sublethal toxicant effects impact the dynamics of a discrete-time predator-prey system.

Journal of biological dynamics·2025
Same author

A SPATIALLY-EXPLICIT STOCHASTIC MODEL FOR THE GULF COAST TICK.

Ecological modelling·2025
Same author

The interplay between multiple control mechanisms in a host-parasitoid system: a discrete-time stage-structured modelling approach.

Journal of biological dynamics·2023
Same author

High resolution finite difference schemes for a size structured coagulation-fragmentation model in the space of radon measures.

Mathematical biosciences and engineering : MBE·2023
Same author

Modeling the invasion and establishment of a tick-borne pathogen.

Ecological modelling·2022
Same author

A continuous-time mathematical model and discrete approximations for the aggregation of <i>β</i>-Amyloid.

Journal of biological dynamics·2021
Same journal

Hepatitis B virus spreading via Beddington-DeAngelis incidence function and feed-forward neural network with optimal control.

Journal of biological dynamics·2026
Same journal

Optimal pest management in Moringa (<i>Moringa oleifera</i>): a mathematical model incorporating integrated pesticide use.

Journal of biological dynamics·2026
Same journal

The behavioural spillover effect: modelling behavioural interdependencies in multi-pathogen dynamics.

Journal of biological dynamics·2026
Same journal

Bistable wave speed of a diffusive three-species Lotka-Volterra competition model.

Journal of biological dynamics·2026
Same journal

A general analytic approach to predicting the best antibiotic dosing regimen.

Journal of biological dynamics·2026
Same journal

Dynamics of virus infection under the influence of antibody and cytokine.

Journal of biological dynamics·2026
See all related articles

Related Experiment Video

Updated: May 19, 2026

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

A monotone approximation for a size-structured population model with a generalized environment.

Azmy S Ackleh1, Keng Deng, Jeremy J Thibodeaux

  • 1Department of Mathematics, University of Louisiana at Lafayette, Lafayette, LA 70504-1010, USA. ackleh@louisiana.edu

Journal of Biological Dynamics
|August 11, 2012
PubMed
Summary
This summary is machine-generated.

This study presents a flexible nonlinear population model allowing size reduction. A novel numerical method ensures solution existence and uniqueness for complex ecological dynamics.

More Related Videos

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach
04:35

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach

Published on: July 3, 2020

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: May 19, 2026

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

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach
04:35

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach

Published on: July 3, 2020

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:

  • Mathematical Biology
  • Population Dynamics
  • Ecological Modeling

Background:

  • Standard population models often assume non-negative growth rates.
  • Existing models may not capture populations with size reduction.
  • Environmental hierarchies are not always incorporated.

Purpose of the Study:

  • To develop a nonlinear size-structured population model with a generalized environment.
  • To remove the constraint of non-negative growth rates, enabling modeling of size reduction.
  • To establish theoretical foundations for the model's solution and develop a numerical scheme.

Main Methods:

  • Development of a nonlinear size-structured population model.
  • Establishment of a comparison principle for existence and uniqueness proofs.
  • Construction of monotone sequences for theoretical validation.
  • Design of a fully discretized numerical scheme.

Main Results:

  • Demonstrated existence and uniqueness of solutions for the generalized model.
  • Successfully modeled populations with individuals experiencing size reduction.
  • Presented a robust numerical scheme for simulating population dynamics.

Conclusions:

  • The developed model offers a more realistic framework for population dynamics, including size reduction.
  • The theoretical and numerical methods provide a foundation for analyzing complex population systems.
  • The study advances ecological modeling by incorporating environmental hierarchies and flexible growth rates.