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

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.

Exponential Growth

Exponential Growth

Bacterial populations exhibit exponential growth when conditions such as nutrient availability and temperature are favorable. In this phase, cells reproduce through binary fission, where each cell divides into two identical daughter cells. This process causes the population to double at regular intervals, resulting in a growth rate that is directly proportional to the current number of cells. As the population increases, the number of new cells formed during each generation also grows, creating...

Growth Models with Integration: Problem Solving

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 with Logarithms: Problem Solving

Exponential Equations with Logarithms: Problem Solving

In ecological studies, exponential models are often used to predict how populations grow over time under favorable conditions. These models assume that the growth rate is proportional to the current population, leading to continuous and compounding increases.The model expresses the population as a function of time, combining the initial population with a growth factor raised to an exponent involving the growth rate and time. To estimate how long it takes for a population to reach a specific...

Exponential Equations for Modeling Growth

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...

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

Coexistence mechanisms for herbaceous plants in arid ecosystems.

Journal of plant research·2026

Same author

Longevity Hinders Evolutionary Rescue through Slower Growth but Not Necessarily Slower Adaptation.

The American naturalist·2026

Same author

Density Dependence During Evolutionary Rescue Increases Extinction Risk but Does Not Prevent Adaptation.

Ecology letters·2026

Same author

Opportunities and challenges for monitoring terrestrial biodiversity in the robotics age.

Nature ecology & evolution·2025

Same author

Biodiversity impacts of the 2019-2020 Australian megafires.

Nature·2024

Same author

Evolution is more repeatable in the introduction than range expansion phase of colonization.

Evolution letters·2024

Search research articles

Related Experiment Video

Updated: May 3, 2026

Predicting the Effectiveness of Population Replacement Strategy Using Mathematical Modeling

Predicting the Effectiveness of Population Replacement Strategy Using Mathematical Modeling

Published on: July 3, 2007

Scaling up population dynamics: integrating theory and data.

Brett A Melbourne¹, Peter Chesson

¹Center for Population Biology, University of California, Storer Hall, Davis, CA 95616, USA. bamelbourne@ucdavis.edu

|May 14, 2005

Summary

Scaling ecological dynamics requires understanding how local interactions influence regional patterns. This study presents a four-step method using scale transition theory to link local nonlinearities with spatial variation for accurate regional predictions.

More Related Videos

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

Daily Transfers, Archiving Populations, and Measuring Fitness in the Long-Term Evolution Experiment with Escherichia coli

Daily Transfers, Archiving Populations, and Measuring Fitness in the Long-Term Evolution Experiment with Escherichia coli

Published on: August 18, 2023

Related Experiment Videos

Last Updated: May 3, 2026

Predicting the Effectiveness of Population Replacement Strategy Using Mathematical Modeling

Predicting the Effectiveness of Population Replacement Strategy Using Mathematical Modeling

Published on: July 3, 2007

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

Daily Transfers, Archiving Populations, and Measuring Fitness in the Long-Term Evolution Experiment with Escherichia coli

Daily Transfers, Archiving Populations, and Measuring Fitness in the Long-Term Evolution Experiment with Escherichia coli

Published on: August 18, 2023

Area of Science:

Ecology
Ecological modeling
Population dynamics

Background:

Scaling ecological processes from local to regional levels is a significant challenge in field ecology.
Understanding how local interactions influence broader spatial dynamics is crucial for ecological management.

Purpose of the Study:

To present a systematic, four-step approach to scaling ecological dynamics using scale transition theory.
To demonstrate how local nonlinear dynamics interact with spatial variation to affect regional-scale patterns.

Main Methods:

Deriving a model to translate local dynamics to the regional scale, identifying key interactions.
Measuring local-scale nonlinearities and spatial variation in environmental factors or population density.
Combining nonlinearity and variation measures to calculate the scale transition.

Main Results:

The proposed approach effectively links local-scale nonlinear dynamics with spatial variation.
Demonstrated accurate inference of regional-scale dynamics using local-scale data in a simulated benthic stream ecology example.
The method allows for investigation of population dynamics changes across spatial scales with limited field data.

Conclusions:

Scale transition theory provides a robust framework for scaling ecological dynamics.
The four-step approach offers a practical method for ecologists to study scale-dependent processes.
This methodology can improve predictions of ecological patterns at larger spatial scales.