#### Article Title

### Expected Versus Actual Random Inbreeding: A Reinterpretation of the Random/Nonrandom Inbreeding Formula

#### Document Type

Article

#### Abstract

There is some ambiguity in the usage of the terms Fst, or Fr, and FIS, or Fn, in Wright’s inbreeding formula, F = Fr(l — Fn) + Fn. Fr is generally called the random inbreeding component of the formula, and is sometimes treated as if it represents actual current random effects. However, a closer look at its derivation and calculation shows that for the current generation, Fr represents only the expected random inbreeding if there were no nonrandom inbreeding. It is suggested here that the actual random inbreeding component of the formula is Fr — FnFr, or Fr(l — Fn). An outcome of this interpretation is that each component of the inbreeding formula would equal one-quarter its corresponding component in the analogous isonymy formula, P = Pr(l ~ PJ + Pn- Furthermore, Fn is generally called the nonrandom inbreeding component of the formula, and is sometimes treated as if it represents deviation from the random-inbreeding-only expectation of Fr. It is suggested here that the remainder of F — Fr, namely Fn — FnFr, represents that deviation. Fn is also sometimes treated as if it represents the new inbreeding of a generation. It is suggested here that although Fn may represent the current inbreeding, Fn — FnF,. represents the new inbreeding. Quantitative effects of these theoretical adjustments are negligible for sexually reproducing organisms, although they may be pronounced for partial self-fertilizers.

#### Recommended Citation

Libet, Moreen L.
(1983)
"Expected Versus Actual Random Inbreeding: A Reinterpretation of the Random/Nonrandom Inbreeding Formula,"
*Human Biology*:
Vol. 55:
Iss.
2, Article 16.

Available at:
https://digitalcommons.wayne.edu/humbiol/vol55/iss2/16