Artificial Intelligence (AI) Calculator for “Inbreeding coefficient (F) calculator”
The inbreeding coefficient (F) quantifies the probability of homozygosity due to common ancestry.
This article explores calculation methods, formulas, tables, and real-world applications of F values.
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Example User Prompts for Inbreeding Coefficient (F) Calculator
- Calculate F for offspring of first cousins.
- Determine inbreeding coefficient for a pedigree with shared grandparents.
- Find F for self-fertilizing plants after three generations.
- Compute F for offspring of half-siblings mating.
Comprehensive Tables of Common Inbreeding Coefficient (F) Values
| Relationship Type | Coefficient of Relationship (r) | Inbreeding Coefficient (F) | Interpretation |
|---|---|---|---|
| Parent-Offspring | 0.5 | 0.25 | High inbreeding; offspring shares 50% genes with parent |
| Full Siblings | 0.5 | 0.25 | High inbreeding; siblings share 50% genes |
| Half Siblings | 0.25 | 0.125 | Moderate inbreeding; share 25% genes |
| First Cousins | 0.125 | 0.0625 | Low to moderate inbreeding |
| Second Cousins | 0.03125 | 0.015625 | Minimal inbreeding |
| Unrelated Individuals | 0 | 0 | No inbreeding |
| Species / Context | Typical F Range | Notes |
|---|---|---|
| Humans (Consanguineous Marriages) | 0.0156 – 0.0625 | First cousin marriages ~0.0625 |
| Livestock (Cattle) | 0.01 – 0.10 | Selective breeding increases F |
| Dogs (Purebred) | 0.10 – 0.25 | High inbreeding due to closed gene pools |
| Plants (Self-fertilizing) | 0.50 – 1.00 | Selfing rapidly increases F |
| Wild Populations (Small Isolated) | 0.05 – 0.20 | Genetic drift and isolation increase F |
Fundamental Formulas for Calculating Inbreeding Coefficient (F)
The inbreeding coefficient (F) measures the probability that two alleles at a locus are identical by descent (IBD). It is calculated based on pedigree information and genetic relationships.
1. Basic Definition of Inbreeding Coefficient
The inbreeding coefficient of an individual (F) is defined as:
- Σ: Sum over all common ancestors
- n1: Number of generations from the individual to the common ancestor through one parent
- n2: Number of generations from the individual to the common ancestor through the other parent
- FA: Inbreeding coefficient of the common ancestor (usually 0 if unknown)
This formula accounts for all possible paths through which alleles can be inherited identically by descent.
2. Coefficient of Relationship (r)
The coefficient of relationship (r) between two individuals is the proportion of shared genes identical by descent:
- Same variables as above
- Note: F = 1/2 × r for offspring of related parents
3. Wright’s Formula for Inbreeding Coefficient
Wright’s method simplifies calculation by considering the paths of common ancestors:
- m: Number of individuals in the path connecting the parents through the common ancestor
- Used primarily in pedigree analysis
4. Inbreeding Coefficient in Self-Fertilizing Species
For self-fertilizing organisms, the inbreeding coefficient after t generations is:
- Ft: Inbreeding coefficient after t generations
- F0: Initial inbreeding coefficient (usually 0)
- Shows rapid increase of F with selfing
5. Relationship Between Inbreeding Coefficient and Heterozygosity
Inbreeding reduces heterozygosity (H) in a population:
- H: Observed heterozygosity
- H0: Expected heterozygosity without inbreeding
Detailed Real-World Examples of Inbreeding Coefficient Calculation
Example 1: Calculating F for Offspring of First Cousins
First cousins share grandparents, so the common ancestors are the grandparents. Calculate the inbreeding coefficient (F) for their offspring.
- Number of generations from offspring to common ancestor through parent 1 (n1) = 2 (offspring → parent → grandparent)
- Number of generations from offspring to common ancestor through parent 2 (n2) = 2
- Assuming grandparents are not inbred, FA = 0
Applying the formula:
Since there are two common grandparents, sum over both:
Interpretation: The offspring of first cousins has an inbreeding coefficient of 0.0625, indicating a 6.25% chance of homozygosity by descent.
Example 2: Inbreeding Coefficient for Offspring of Half-Siblings
Half-siblings share one parent. Calculate F for their offspring.
- Number of generations from offspring to common ancestor through parent 1 (n1) = 1 (offspring → parent)
- Number of generations from offspring to common ancestor through parent 2 (n2) = 1
- Assuming common parent is not inbred, FA = 0
Applying the formula:
Interpretation: The offspring of half-siblings has an inbreeding coefficient of 0.125, indicating a 12.5% chance of homozygosity by descent.
Additional Technical Insights on Inbreeding Coefficient Calculation
Calculating the inbreeding coefficient becomes increasingly complex with large pedigrees and multiple common ancestors. Modern computational tools and AI calculators simplify this process by automating path tracing and summation.
- Pedigree Depth: The number of generations considered affects accuracy; deeper pedigrees capture more distant relationships.
- Founder Inbreeding: If founders are inbred, their F values must be included in calculations.
- Multiple Common Ancestors: Summation over all common ancestors is essential to avoid underestimating F.
- Population Structure: Subpopulations with limited gene flow can have elevated F values due to genetic drift.
Inbreeding coefficients are critical in conservation genetics, animal breeding, and human genetic counseling to assess risks of recessive disorders and loss of genetic diversity.