Our Methodology

How we calculate linebreeding

Genquix calculates linebreeding using Wright's path coefficient formula, first published by Sewall Wright in 1922 and the accepted standard in quantitative genetics and livestock breeding science worldwide. The coefficient F represents the probability that both alleles at any given gene locus are identical by descent — in practical terms, how likely it is that a horse has inherited the same genetic material from both its sire line and its dam line due to a shared ancestor appearing on both sides of the pedigree.

The formula

F = Σ (½)ns + nd + 1 × (1 + FA)

n_s — number of generational steps from the subject's sire to the common ancestor

n_d — number of generational steps from the subject's dam to the common ancestor

F_A — the inbreeding coefficient of the common ancestor itself, applied at the relevant generation depth

The sum runs over every valid path through every common ancestor found on both sides of the pedigree

The no-revisit rule

This is the most important and most frequently misunderstood element of Wright's formula.

When a common ancestor X sits on the path to a deeper common ancestor Y — meaning the only route from the subject to Y passes through X on both the sire side and the dam side simultaneously — counting Y as a separate contribution would double-count the genetic influence already captured by X. Wright's formula excludes these paths. This is not a simplification; it is mathematically required to avoid overstating the coefficient.

Worked example

Introduce Storm as the subject horse. Storm's pedigree contains Rose as a common ancestor — Rose appears as the paternal great-granddam (sire side, depth 3) and the maternal mat. great-granddam (dam side, depth 3). Rose contributes 3.125% to Storm's coefficient.

Now consider Henry, who is Rose's sire. Henry also appears in Storm's pedigree — but every route from Storm to Henry, on both the sire side and the dam side, passes through Rose. Counting Henry as a separate common ancestor would add his contribution on top of Rose's — but Henry's influence is already fully contained within Rose's contribution. Wright's no-revisit rule correctly excludes Henry's path.

The same applies to Grace, who is Rose's dam. Every path to Grace also passes through Rose on both sides. Grace is excluded for the same reason.

The result: Storm's coefficient reflects Rose's contribution precisely once, without inflation from ancestors whose entire influence already flows through Rose.

Why the coefficient rises with more generations

Each additional generation of pedigree data reveals more common ancestors. In breeds with a narrow genetic base — where a small number of influential foundation sires underpin a large proportion of the modern population — the coefficient rises steadily with each generation as the same bloodlines appear repeatedly on both sides. This is not an error in the calculation. It is an accurate representation of the breed's genetic structure. A coefficient calculated across 9 generations is more complete than one calculated across 4, and Genquix always displays how many generations and data points were used in each result.

Risk thresholds

The following thresholds are grounded in Wright's original framework and the standard reference Falconer & Mackay, Introduction to Quantitative Genetics:

Coefficient	Equivalent relationship	Risk level
Below 6.25%	Below first-cousin level	Low
6.25% – 12.5%	First cousin to half-sibling equivalent	Moderate
12.5% – 25%	Half-sibling to full-sibling equivalent	High
Above 25%	Exceeds full-sibling mating level	Very High

These thresholds apply to the coefficient calculated at the generation depth selected. A result at 4 generations and a result at 9 generations are not directly comparable — always compare like for like.

Ancestor linebreeding correction (F_A)

For ancestors that are themselves linebred, the (1 + F_A) factor in the formula adjusts each path's contribution upward to reflect that the shared ancestor carries a higher-than-average probability of passing identical alleles. Genquix stores these values in its database for each horse and applies them per-path at the appropriate generation depth, increasing accuracy for pedigrees that include deeply inbred foundation sires.

Data depth and completeness

Genquix calculates coefficients across up to 9 generations where pedigree records are available. Every result displays the number of generations and data points used. Where pedigree data is incomplete, the displayed coefficient will be lower than the true value — the result is always accompanied by a note indicating it is based on available data only.

Wright, S. (1922). Coefficients of inbreeding and relationship. The American Naturalist, 56(645), 330–338.

Falconer, D.S. & Mackay, T.F.C. (1996). Introduction to Quantitative Genetics (4th ed.). Longman.