Search research articles

ABOUT JoVE

Overview Leadership Blog JoVE Help Center

AUTHORS

Publishing Process Editorial Board Scope & Policies Peer Review FAQ Submit

LIBRARIANS

Testimonials Subscriptions Access Resources Library Advisory Board FAQ

RESEARCH

JoVE Journal Methods Collections JoVE Encyclopedia of Experiments Archive

EDUCATION

JoVE Core JoVE Business JoVE Science Education JoVE Lab Manual Faculty Resource Center Faculty Site

Terms & Conditions of Use

Related Concept Videos

Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving

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...

Genetic Drift

Genetic Drift

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.

Mutation, Gene Flow, and Genetic Drift

Mutation, Gene Flow, and Genetic Drift

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).

Parameters Affecting Nonlinear Elimination: Zero-Order Input, First-Order Absorption and Two-Compartment Model

Parameters Affecting Nonlinear Elimination: Zero-Order Input, First-Order Absorption and Two-Compartment Model

Drugs administered through various routes can lead to nonlinear elimination, resulting in complex pharmacokinetic behaviors crucial to understanding efficacious drug dosing.
When a drug is administered through a constant intravenous infusion and eliminated via nonlinear pharmacokinetics, it follows zero-order input. For example, oral drugs undergo first-order absorption upon administration and are eliminated through nonlinear pharmacokinetics.
In the case of subcutaneously administered drugs,...

Population Growth

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.

Modeling with Differential Equations

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...

You might also read

Related Articles

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

Sort by

Same author

Parthenogenesis, sexual conflict, and selection on fertilization rates in switching environments.

Theoretical population biology·2025

Same author

Cell size and selection for stress-induced cell fusion in unicellular eukaryotes.

PLoS computational biology·2025

Same author

Maternal transmission as a microbial symbiont sieve, and the absence of lactation in male mammals.

Nature communications·2024

Same author

Feasibility and stability in large Lotka Volterra systems with interaction structure.

Physical review. E·2023

Same author

Parthenogenesis and the Evolution of Anisogamy.

Cells·2021

Same author

Fluctuation spectra of large random dynamical systems reveal hidden structure in ecological networks.

Nature communications·2021

Search research articles

Related Experiment Video

Updated: May 1, 2026

Following the Dynamics of Structural Variants in Experimentally Evolved Populations

Following the Dynamics of Structural Variants in Experimentally Evolved Populations

Published on: February 3, 2023

Fast-mode elimination in stochastic metapopulation models.

George W A Constable¹, Alan J McKane¹

¹Theoretical Physics Division, School of Physics and Astronomy, The University of Manchester, Manchester M13 9PL, United Kingdom.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|April 16, 2014

Summary

This summary is machine-generated.

We developed a new method to simplify complex population dynamics models. This approach accurately simulates systems with migration, reproduction, and selection across multiple populations.

More Related Videos

Predicting the Effectiveness of Population Replacement Strategy Using Mathematical Modeling

Predicting the Effectiveness of Population Replacement Strategy Using Mathematical Modeling

Published on: July 4, 2007

The Use of Chemostats in Microbial Systems Biology

The Use of Chemostats in Microbial Systems Biology

Published on: October 14, 2013

Related Experiment Videos

Last Updated: May 1, 2026

Following the Dynamics of Structural Variants in Experimentally Evolved Populations

Following the Dynamics of Structural Variants in Experimentally Evolved Populations

Published on: February 3, 2023

Predicting the Effectiveness of Population Replacement Strategy Using Mathematical Modeling

Predicting the Effectiveness of Population Replacement Strategy Using Mathematical Modeling

Published on: July 4, 2007

The Use of Chemostats in Microbial Systems Biology

The Use of Chemostats in Microbial Systems Biology

Published on: October 14, 2013

Area of Science:

Mathematical Biology
Computational Biology
Population Dynamics

Background:

Stochastic dynamics models with migration, reproduction, and selection are common in biology and social sciences.
Existing models often involve intractable multidimensional Fokker-Planck equations or nonlinear stochastic differential equations.

Purpose of the Study:

To develop a general methodology for simplifying complex stochastic dynamics models.
To reduce intractable equations to a more manageable form amenable to analysis.

Main Methods:

Exploiting a separation in time scales between fast and slow variables.
Reducing multidimensional Fokker-Planck equations or coupled nonlinear stochastic differential equations.
Applying the technique to population genetics models with weak selection.

Main Results:

The developed methodology simplifies complex systems to resemble single-island models.
The technique is generally applicable across various scientific domains.
Results show excellent agreement with simulations of the full model.

Conclusions:

The new methodology provides a powerful tool for analyzing complex stochastic systems.
This approach offers a systematic and accurate way to study population dynamics.
The method is particularly useful for systems with weak selection and multiple interacting populations.