= Recombination fraction
{title2=$0\le\theta\le\tfrac12$}
The recombination fraction is the <probability> that a transmitted <gamete> carries a recombinant <haplotype> between two specified <genetic loci>, relative to the parent's known <haplotype> phase. Write it as $r$ here; the symbol $\theta$ is also common in <genetic linkage> analysis. In the ordinary symmetric two-locus model, $0\le r\le1/2$, with $r=0$ for <complete genetic linkage> and $r=1/2$ for <independent assortment>.
For <phase-known genotype> $AB/ab$, fair <Mendelian segregation> and equal reciprocal <gamete> <probabilities> give
$$
P(AB)=P(ab)=\frac{1-r}{2},\qquad P(Ab)=P(aB)=\frac r2.
$$
For example, 1,000 independent informative transmissions with observed counts $400,400,100,100$ in this order have empirical <recombination fraction> $(100+100)/1000=0.2$. Those illustrative counts match the <expected values> in the toy model, but actual counts fluctuate. The <genetic linkage> diagram shows both the parental and recombinant classes, so their separate <probabilities> are not confused with the total $r$.
The <recombination fraction> measures the <probability> of an odd number of origin switches along the transmitted <chromatid>. It is neither the <expected value> of the exchange count nor the <probability> of at least one exchange: even positive counts can be invisible at the two endpoints. Converting an observed <recombination fraction> to a <genetic map> distance therefore needs an explicit model such as the <Haldane mapping function>. The distinction between transmitted-<chromatid> counts and four-<chromatid> exchange counts is discussed in https://pmc.ncbi.nlm.nih.gov/articles/PMC2704907/[Weeks, Tang and Kwon (2009), Casares' map function: No need for a 'corrected' Haldane's map function, Genetica 135, 305–307].
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