Related Experiment Video
Updated: Jun 21, 2026
04:35
Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach
Published on: July 3, 2020
Individual-based models for stage structured populations: formulation of "no regression" development equations.
Giuseppe Buffoni1, Sara Pasquali
1CNR-IMATI, Via Bassini 15, 20133 Milan, Italy. giuseppe.buffoni@enea.it
Journal of Mathematical Biology
|August 12, 2009
Summary
This study presents stochastic models for individual development, simulating population growth without backward steps. Analysis focuses on how variability affects these individual-based models.
Area of Science:
- Ecology
- Population Dynamics
- Mathematical Biology
Background:
- Individual-based models (IBMs) simulate population dynamics through individual life histories.
- Development, reproduction, and mortality are key individual processes.
- Physiological age tracks individual status, typically as a non-decreasing indicator.
Purpose of the Study:
- To formulate stochastic development models for IBMs.
- To specifically model development processes where regression (negative development) is forbidden.
- To analyze the behavior of these models under varying levels of stochasticity.
Main Methods:
- Utilized stochastic difference equations with discrete time for development.
- Developed models assuming a non-decreasing physiological age.
- Investigated model behavior by adjusting the stochasticity level.
Main Results:
- Presented several stochastic models for individual development.
- Demonstrated how varying stochasticity levels impact model behavior.
- Provided insights into the effects of intraspecific variability on development.
Conclusions:
- The proposed models offer a framework for simulating development in IBMs without regression.
- Stochasticity level is a critical parameter influencing population dynamics.
- Considerations for time step selection in such models are discussed.
Related Concept Videos
01:23Mechanistic 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)...
01:29Mechanistic 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...
In individual population analyses, different algorithms are employed, such as Cauchy's method, which uses a...
01:25Modeling 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...
01:24One-Compartment Open Model: Wagner-Nelson and Loo Riegelman Method for ka Estimation
This lesson introduces two critical methods in pharmacokinetics, the Wagner-Nelson and Loo-Riegelman methods, used for estimating the absorption rate constant (ka) for drugs administered via non-intravenous routes. The Wagner-Nelson method relates ka to the plasma concentration derived from the slope of a semilog percent unabsorbed time plot. However, it is limited to drugs with one-compartment kinetics and can be impacted by factors like gastrointestinal motility or enzymatic degradation.
On...
On...
01:26Exponential 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...
01:12Analysis of Population Pharmacokinetic Data
Analysis of population pharmacokinetic data involves studying the behavior of drugs within diverse populations to understand their pharmacokinetic parameters. Traditional pharmacokinetic methods typically involve collecting samples from a few individuals and estimating these parameters. While these methods are commonly used, they have limitations in capturing the variability in drug response among individuals or heterogeneous populations. Population pharmacokinetics is employed to address these...