De Finetti diagram

De Finetti Diagram

De Finetti diagram illustrating allele frequencies

The De Finetti diagram is a graphical representation used in population genetics to visualize the distribution of allele frequencies in a population. Named after the Italian statistician Bruno de Finetti, this diagram is particularly useful for illustrating the concept of Hardy-Weinberg equilibrium and the effects of genetic drift and selection on allele frequencies.

Description

The De Finetti diagram is a triangular plot that represents the frequencies of three possible genotypes in a population. These genotypes are typically denoted as $AA$, $Aa$, and $aa$, where $A$ and $a$ are two alleles of a gene. The vertices of the triangle correspond to the populations that are fixed for one of the genotypes: $AA$, $Aa$, or $aa$.

In the diagram, each point within the triangle represents a specific combination of genotype frequencies. The position of a point is determined by the relative frequencies of the three genotypes. The sum of the frequencies of the three genotypes at any point in the diagram is always equal to 1, reflecting the fact that these are the only possible genotypes in the population.

Applications

The De Finetti diagram is used to:

• Visualize Hardy-Weinberg Equilibrium: In a population at Hardy-Weinberg equilibrium, the genotype frequencies are expected to fall along a specific curve within the triangle. Deviations from this curve can indicate the presence of evolutionary forces such as selection, mutation, or genetic drift.

• Illustrate Genetic Drift: Over time, genetic drift can cause allele frequencies to fluctuate randomly. This is represented in the De Finetti diagram as a random walk of points within the triangle, potentially leading to fixation of one allele.

• Demonstrate Selection: Natural selection can shift allele frequencies in a population, moving the point within the triangle towards the vertex representing the favored genotype.

Construction

To construct a De Finetti diagram, one must first calculate the genotype frequencies in the population. These frequencies are then plotted within the triangular space. The axes of the triangle are typically labeled with the frequencies of the homozygous dominant ($AA$), heterozygous ($Aa$), and homozygous recessive ($aa$) genotypes.

Interpretation

Interpreting a De Finetti diagram requires understanding the underlying genetic principles. Points along the edges of the triangle indicate populations where one genotype is absent. Points near the center suggest a more balanced distribution of genotypes. The shape and position of the curve representing Hardy-Weinberg equilibrium can provide insights into the genetic structure of the population.

Related Pages

• Hardy-Weinberg principle
• Genetic drift
• Natural selection
• Population genetics