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

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.However, realistic environmental conditions limit the number of...
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 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)...
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...
Relation between Poisson's ratio, Modulus of Elasticity and Modulus of Rigidity01:15

Relation between Poisson's ratio, Modulus of Elasticity and Modulus of Rigidity

Deformation occurs in axial and transverse directions when an axial load is applied to a slender bar. This deformation impacts the cubic element within the bar, transforming it into either a rectangular parallelepiped or a rhombus, contingent on its orientation. This transformation process induces shearing strain. Axial loading elicits both shearing and normal strains. Applying an axial load instigates equal normal and shearing stresses on elements oriented at a 45° angle to the load axis.
Estimating Population Standard Deviation01:26

Estimating Population Standard Deviation

When the population standard deviation is unknown and the sample size is large, the sample standard deviation s is commonly used as a point estimate of σ. However, it can sometimes under or overestimate the population standard deviation. To overcome this drawback, confidence intervals are determined to estimate population parameters and eliminate any calculation bias accurately. However, this only applies to random samples from normally distributed populations. Knowing the sample mean and...

You might also read

Related Articles

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

Sort by
Same author

A Disturbing View of Life History Evolution.

The American naturalist·2026
Same author

The association between adverse experiences throughout the life-course and risk of dementia in the English Longitudinal Study of Ageing.

Journal of Alzheimer's disease : JAD·2026
Same author

Analytical framework for evaluating NMPC-based robot navigation in fluid environments.

PloS one·2026
Same author

An evaluation of age-varying genetic effects underlying body-mass index and blood pressure in the UK Biobank.

PLoS genetics·2026
Same author

An instrumental variable analysis of body mass index and risk of long-term sick leave: the HUNT Study, Norway.

European journal of epidemiology·2025
Same author

The association between adverse experiences throughout the life-course and risk of dementia in the English Longitudinal Study of Ageing.

medRxiv : the preprint server for health sciences·2025

Related Experiment Video

Updated: Jun 18, 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

Patterns and rules for sensitivity and elasticity in population projection matrices.

David Carslake1, Stuart Townley, David J Hodgson

  • 1Centre for Ecology and Conservation, University of Exeter, Tremough Campus, Penryn, Cornwall TR10 9EZ, United Kingdom. D.J.Carslake@warwick.ac.uk

Ecology
|December 9, 2009
PubMed
Summary
This summary is machine-generated.

Population projection matrix (PPM) analysis reveals mathematical constraints on demographic rate impacts. Understanding these rules is crucial for accurate population modeling and conservation management.

More Related Videos

Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns
13:44

Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns

Published on: August 30, 2013

Related Experiment Videos

Last Updated: Jun 18, 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

Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns
13:44

Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns

Published on: August 30, 2013

Area of Science:

  • Ecology
  • Mathematical Biology
  • Population Dynamics

Background:

  • Sensitivity and elasticity analyses are key tools for understanding structured population dynamics.
  • Certain population projection matrix (PPM) structures exhibit inherent mathematical patterns in demographic rate contributions.

Purpose of the Study:

  • To investigate mathematical constraints on sensitivity and elasticity in various PPM models using simulations.
  • To challenge existing assumptions and identify novel constraints in population projection analysis.

Main Methods:

  • Simulation approach applied to a range of population projection matrix (PPM) models.
  • Analysis of sensitivity and elasticity patterns across different demographic rates and population structures.

Main Results:

  • Identified and challenged previously proposed mathematical constraints on sensitivity and elasticity.
  • Discovered new constraints, suggesting demographic rates of older/larger individuals have less impact on population growth.
  • Demonstrated that the validity of these rules depends on the analysis type (sensitivity vs. elasticity), population growth rate, and PPM structure.

Conclusions:

  • The study highlights the importance of selecting PPMs that accurately reflect population demographics.
  • Inaccurate model fits can lead to flawed conservation strategies.
  • The findings provide a basis for prioritizing management actions when detailed demographic data is limited, provided the model is appropriate.