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.
Parametric Survival Analysis: Weibull and Exponential Methods01:14

Parametric Survival Analysis: Weibull and Exponential Methods

Parametric survival analysis models survival data by assuming a specific probability distribution for the time until an event occurs. The Weibull and exponential distributions are two of the most commonly used methods in this context, due to their versatility and relatively straightforward application.
Weibull Distribution
The Weibull distribution is a flexible model used in parametric survival analysis. It can handle both increasing and decreasing hazard rates, depending on its shape parameter...
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 with Logarithms: Problem Solving01:29

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 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...
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...

You might also read

Related Articles

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

Sort by
Same author

Genomic prediction of wild-derived powdery mildew resistance for strawberry (Fragaria × ananassa) pre-breeding.

Heredity·2026
Same author

Opportunities and computational challenges in large-scale whole-genome sequencing data analysis.

Journal of animal science·2025
Same author

A major QTL region associated with powdery mildew resistance in leaves and fruits of the reconstructed garden strawberry.

TAG. Theoretical and applied genetics. Theoretische und angewandte Genetik·2025
Same author

A computationally efficient algorithm to leverage average information REML for (co)variance component estimation in the genomic era.

Genetics, selection, evolution : GSE·2024
Same author

Marker weighting improves single-step genomic prediction reliabilities of udder health traits in Nordic Red and Jersey dairy cattle populations.

Journal of dairy science·2024
Same author

A computationally feasible multi-trait single-step genomic prediction model with trait-specific marker weights.

Genetics, selection, evolution : GSE·2024
Same journal

The mitogenome diversity of Alpine Rendena cattle: new clues on its maternal origin and the complex substructure of haplogroup T3.

Genetics, selection, evolution : GSE·2026
Same journal

Genomic partitioning and functional dissection of inbreeding depression for stature in Brown Swiss cattle.

Genetics, selection, evolution : GSE·2026
Same journal

Modest contribution of metabolomic data to genomic prediction of breeding values for feed conversion ratio in pigs.

Genetics, selection, evolution : GSE·2026
Same journal

Determining crossover count and position in two pig lines with different selection histories.

Genetics, selection, evolution : GSE·2026
Same journal

Effect of methylation on genome mutability in cattle.

Genetics, selection, evolution : GSE·2026
Same journal

Genomic selection strategies and their potential to maintain rare alleles and de-novo mutations: a long-term assessment.

Genetics, selection, evolution : GSE·2026
See all related articles

Related Experiment Video

Updated: May 21, 2026

Precise, High-throughput Analysis of Bacterial Growth
09:00

Precise, High-throughput Analysis of Bacterial Growth

Published on: September 19, 2017

Estimation of non-linear growth models by linearization: a simulation study using a Gompertz function.

Kaarina Vuori1, Ismo Strandén, Marja-Liisa Sevón-Aimonen

  • 1MTT Agrifood Research Finland, Biotechnology and Food Research, Biometrical Genetics, FIN-31600 Jokioinen, Finland. kaarina.vuori@mtt.fi

Genetics, Selection, Evolution : GSE
|June 23, 2006
PubMed
Summary
This summary is machine-generated.

A new linearization method accurately estimates parameters in non-linear mixed effects models for animal breeding. However, truncated pig growth data can lead to unstable adult weight parameter estimation.

More Related Videos

Saccharomyces cerevisiae Exponential Growth Kinetics in Batch Culture to Analyze Respiratory and Fermentative Metabolism
07:38

Saccharomyces cerevisiae Exponential Growth Kinetics in Batch Culture to Analyze Respiratory and Fermentative Metabolism

Published on: September 30, 2018

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

Related Experiment Videos

Last Updated: May 21, 2026

Precise, High-throughput Analysis of Bacterial Growth
09:00

Precise, High-throughput Analysis of Bacterial Growth

Published on: September 19, 2017

Saccharomyces cerevisiae Exponential Growth Kinetics in Batch Culture to Analyze Respiratory and Fermentative Metabolism
07:38

Saccharomyces cerevisiae Exponential Growth Kinetics in Batch Culture to Analyze Respiratory and Fermentative Metabolism

Published on: September 30, 2018

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

Area of Science:

  • Animal breeding
  • Statistical modeling
  • Quantitative genetics

Background:

  • Non-linear mixed effects models are crucial for analyzing complex biological data, such as animal growth.
  • Accurate parameter estimation is essential for genetic improvement and breeding program decisions.
  • Existing methods for non-linear models can be computationally intensive or require specialized software.

Purpose of the Study:

  • To evaluate a Taylor series expansion-based linearization method for estimating parameters in non-linear mixed effects models.
  • To assess the method's applicability and performance in animal breeding contexts, specifically for pig growth.
  • To investigate the impact of data structure, particularly truncated trajectories, on parameter estimation accuracy.

Main Methods:

  • The study employed a Taylor series expansion to linearize non-linear mixed effects models.
  • Simulations were conducted using a Gompertz function growth model in pigs.
  • Two data scenarios were analyzed: complete growth trajectories and prematurely terminated (truncated) data.

Main Results:

  • The linearization approach provided satisfactory estimation of growth model parameters using complete data sets.
  • Parameter estimation remained stable and accurate for the full growth data across simulation replicates.
  • Estimation of parameters associated with adult weight became unstable when using truncated growth data.

Conclusions:

  • Taylor series linearization offers a computationally efficient and implementable method for non-linear mixed effects models in animal breeding.
  • The method is effective for complete animal growth data, enabling the use of existing linear model software with modifications.
  • Caution is advised when applying this linearization method to truncated data, as it can compromise the accuracy of adult weight parameter estimates.