Related Experiment Video
Updated: Jun 30, 2025
04:35
Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach
Published on: July 3, 2020
3.3K
The ancestral selection graph for a Λ-asymmetric Moran model
Adrián González Casanova1, Noemi Kurt2, José Luis Pérez3
1Instituto de Matematicas, Universidad Nacional Autonoma de Mexico (UNAM), Cuernavaca, Mexico; Department of Statistics, University of California at Berkeley, United States of America.
Theoretical Population Biology
|March 15, 2024
Summary
We developed a new model to study how selection impacts populations with different reproductive rates (Λ-reproduction). This model helps calculate the probability of less advantageous traits becoming fixed in a population.
Area of Science:
- Population Genetics
- Mathematical Biology
- Evolutionary Dynamics
Background:
- Understanding selective advantage is crucial for population genetics.
- Existing models often simplify reproduction mechanisms, limiting applicability to skewed reproduction scenarios.
Purpose of the Study:
- To investigate the impact of selective advantage in populations with skewed reproduction mechanisms.
- To develop a mathematical framework for analyzing competition between two types with differing reproductive success (Λ-reproduction).
Main Methods:
- Construction of a Λ-asymmetric Moran model to simulate competition between two types.
- Development of the Λ-asymmetric ancestral selection graph for pathwise duality.
- Application of the ancestral selection graph to derive scaling limits and analyze stochastic differential equations (SDEs).
Main Results:
- Established a pathwise duality between the forward Moran model and its ancestral process.
- Demonstrated that the frequency process converges to an SDE with discontinuous paths.
- Derived a Griffiths representation for the SDE generator.
Conclusions:
- The Λ-asymmetric Moran model and ancestral selection graph provide a powerful tool for studying selection in complex reproductive scenarios.
- The findings offer a semi-explicit formula for the fixation probability of less beneficial types, advancing evolutionary theory.
Related Concept Videos
01:21Frequency-dependent Selection
22.0K
When the fitness of a trait is influenced by how common it is (i.e., its frequency) relative to different traits within a population, this is referred to as frequency-dependent selection. Frequency-dependent selection may occur between species or within a single species. This type of selection can either be positive—with more common phenotypes having higher fitness—or negative, with rarer phenotypes conferring increased fitness.
22.0K
01:29Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving
53
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...
53
01:46Types of Selection
40.4K
Natural selection influences the frequencies of particular alleles and phenotypes within populations in several different ways. Primarily, natural selection can be directional, stabilizing, or disruptive. Directional selection favors one extreme trait and shifts the population towards that phenotype while selecting against individuals displaying alternate traits. Stabilizing selection favors an intermediate trait with a narrow range of variation. Deviation from the optimal phenotype towards an...
40.4K
01:26Pharmacokinetic Models: Comparison and Selection Criterion
71
Physiological and compartmental models are valuable tools used in studying biological systems. These models rely on differential equations to maintain mass balance within the system, ensuring an accurate representation of the dynamic processes at play.
Physiological models take a detailed approach by considering specific molecular processes. They can predict drug distribution, metabolism, and elimination changes, providing a comprehensive understanding of how drugs interact with the body.
Physiological models take a detailed approach by considering specific molecular processes. They can predict drug distribution, metabolism, and elimination changes, providing a comprehensive understanding of how drugs interact with the body.
71
01:24One-Compartment Open Model: Wagner-Nelson and Loo Riegelman Method for ka Estimation
491
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...
491
01:14Parametric Survival Analysis: Weibull and Exponential Methods
425
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...
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...
425