Understand the relationship
The reasoning behind the result
The heterozygosity ratio is a population record
FIS = 1 − Hobs/Hexp
This arithmetic compares observed heterozygosity with a declared within-population expectation. Positive values indicate a deficit relative to that denominator; negative values retain a heterozygosity excess.
Estimator choice, finite-sample correction, multiple loci and population structure remain external.
The pedigree coefficient follows ancestry paths
FX = Σ(1/2)^(n₁+n₂+1)(1+FA)
Each valid loop connects the individual's two parents through a common ancestor without visiting an individual twice. Transmission halves the path contribution at each generational step.
An ancestor's own inbreeding coefficient multiplies that path by 1+FA.
The two coefficients are not interchangeable
A pedigree coefficient concerns identity by descent in an individual under the supplied pedigree. A heterozygosity statistic compares population observations with an expectation.
Matching numerical values do not make their estimands, uncertainty or interpretation the same.
Path validity cannot be inferred from a row list
The calculator can sum valid path contributions but cannot reconstruct a pedigree, detect the same individual appearing twice in a loop or discover omitted and overlapping paths.
Pedigree completeness and parentage remain external evidence.
Follow the numbers
Sum two first-cousin common-grandparent paths
- Each parent is two generations from each shared grandparent, so n₁=n₂=2.
- Neither ancestor is entered as inbred, so 1+FA = 1.
- Each path contributes (1/2)^(2+2+1) = 1/32 = 0.03125.
- There are two distinct shared-grandparent paths.
- The individual's entered pedigree coefficient is 1/32 + 1/32 = 1/16 = 0.0625.
The sum is valid only if the two rows are complete, distinct pedigree loops under the stated path rule.
Quick guide
How to use this calculator
- Choose the coefficient definition before entering any values.
- For heterozygosity records, supply an appropriate observed and externally derived expected heterozygosity on the same locus/population basis.
- For pedigree paths, enter each valid common-ancestor loop exactly once and inspect each contribution before the sum.
Calculation method
Calculation and interpretation
Prevent two quantities commonly called an inbreeding coefficient from being treated as interchangeable measurements.
Heterozygosity record: FIS = 1 − Hobs/Hexp. Pedigree path: FX = Σ(1/2)^(n₁+n₂+1)(1+FA)
Worked example
Sum two first-cousin common-grandparent paths
The sum is valid only if the two rows are complete, distinct pedigree loops under the stated path rule.
Heterozygosity record: FIS = 1 − Hobs/Hexp. Pedigree path: FX = Σ(1/2)^(n₁+n₂+1)(1+FA)
Supported inputs
Precision and limits
Definitions remain separate
FIS heterozygosity arithmetic and an individual pedigree coefficient are never presented as the same estimator.
Expected heterozygosity is external
No allele-frequency estimator, finite-sample correction, locus weighting or population partition is supplied.
Pedigree paths are prevalidated inputs
The calculator does not reconstruct pedigrees, detect repeated individuals or identify missing/overlapping loops.
No health or reproductive interpretation
The result does not estimate disease, trait outcome, fertility, ancestry category or mating suitability.
Numerical support
Observed heterozygosity spans 0–1 and Hexp spans 10⁻¹²–1. Pedigree mode retains 1–30 paths, safe whole generation counts through 100 and ancestor FA from 0–1; total F may not exceed 1.
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