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

27.7K
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.
27.7K
Mechanistic Models: Compartment Models in Individual and Population Analysis01:23

Mechanistic Models: Compartment Models in Individual and Population Analysis

198
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...
198
Exponential Equations for Modeling Growth02:33

Exponential Equations for Modeling Growth

137
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...
137
Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving01:29

Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving

228
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...
228
Conservation of Small Populations02:04

Conservation of Small Populations

16.5K
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...
16.5K
Multicompartment Models: Overview01:14

Multicompartment Models: Overview

439
Multicompartment models are mathematical constructs that depict how drugs are distributed and eliminated within the body. They segment the body into several compartments, symbolizing various physiological or anatomical areas connected through drug transfer processes such as absorption, metabolism, distribution, and elimination.
These models offer a more comprehensive representation of drug behavior in the body than one-compartment models. They accommodate the complexity of drug distribution,...
439

You might also read

Related Articles

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

Sort by
Same author

Optimal Melanoma Treatment Protocols: a Bilinear Control Model.

Mathematical biosciences·2026
Same author

Population structure reverses selection of variants with proportionally scaled birth and death rates.

Nature communications·2025
Same author

Author Correction: Barcoded HIV-1 reveals viral persistence driven by clonal proliferation and distinct epigenetic patterns.

Nature communications·2025
Same author

Efficient mathematical methodology to determine multistep mutant burden in spatially growing cell populations.

PNAS nexus·2025
Same author

The functional form of the association between K-12 student performance and household income in U.S. school districts.

PloS one·2025
Same author

Detecting (the Absence of) Species Interactions in Microbial Ecological Systems.

Studies in applied mathematics (Cambridge, Mass.)·2025

Related Experiment Video

Updated: Dec 24, 2025

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

9.1K

Beyond the pair approximation: Modeling colonization population dynamics.

Ignacio A Rodriguez-Brenes1, Dominik Wodarz2, Natalia L Komarova1

  • 1Department of Mathematics, University of California Irvine, Irvine, California 92697, USA.

Physical Review. E
|April 16, 2020
PubMed
Summary
This summary is machine-generated.

Predicting species range expansion dynamics is now faster. New approximations using ordinary differential equations accurately model population size, spatial shape, and expansion speed, reducing computational time for colonization studies.

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

1.3K
Monitoring Spatial Segregation in Surface Colonizing Microbial Populations
07:40

Monitoring Spatial Segregation in Surface Colonizing Microbial Populations

Published on: October 29, 2016

11.4K

Related Experiment Videos

Last Updated: Dec 24, 2025

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

9.1K
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

1.3K
Monitoring Spatial Segregation in Surface Colonizing Microbial Populations
07:40

Monitoring Spatial Segregation in Surface Colonizing Microbial Populations

Published on: October 29, 2016

11.4K

Area of Science:

  • Ecology
  • Mathematical Biology
  • Computational Biology

Background:

  • Range expansion, or colonization, is a fundamental biological process where species spread into new territories.
  • Spatial dynamics of range expansion are often modeled using stochastic cellular automata.

Purpose of the Study:

  • To develop accurate approximations for predicting range expansion dynamics.
  • To reduce the computational cost associated with simulating spatial colonization models.

Main Methods:

  • Derivation of approximations for stochastic cellular automata using systems of ordinary differential equations.
  • Preservation of correlations among neighboring grid spots in the derived models.
  • Formulation of approximations for population size, spatial shape, steady-state densities, and expansion speed.

Main Results:

  • Accurate approximations for population size and spatial shape were achieved at a fraction of the simulation time.
  • Simple formulas for steady-state population densities were derived for von Neumann and Moore neighborhoods.
  • Concise approximations for range expansion speed were developed based on reproduction and death rates.

Conclusions:

  • The developed methodology provides efficient and accurate predictions of range expansion dynamics.
  • The approach is generalizable to more complex ecological scenarios, including varied interaction ranges and multi-species systems.
  • This work offers valuable tools for ecological modeling and understanding species dispersal patterns.