Genetic linkage
= Genetic linkage
{wiki}
Why can two individually fair <allele> transmissions fail to be independent? <Genetic loci> on the same <chromosome> can travel together through <meiosis>. This tendency is <genetic linkage>; in an ordinary two-locus model, detectable <genetic linkage> means a <recombination fraction> below $1/2$. A <genetic marker> can therefore help track a neighboring <genetic locus> through a <pedigree>. See https://openstax.org/books/biology-2e/pages/13-1-chromosomal-theory-and-genetic-linkage[Clark, Douglas and Choi, Biology 2e: chromosomal theory and genetic linkage].
Take a <diploid> individual <heterozygous> at two <genetic loci>, with <phase-known genotype> $AB/ab$: one <homologous chromosome> carries <alleles> $A,B$, the other $a,b$. The parental <haplotypes> are $AB,ab$; the recombinant <haplotypes> are $Ab,aB$. Assume fair <Mendelian segregation>, equal <probabilities> within each reciprocal pair of <gametes>, and no <allele>-dependent differences in <gamete> recovery. If the <recombination fraction> is $r=0.2$, the <gamete> <probabilities> are $0.4,0.4,0.1,0.1$ in that order. Each <genetic locus> still transmits its two <alleles> equally, but $P(AB)=0.4$ exceeds $P(A)P(B)=0.25$: fairness at each <genetic locus> does not imply <independence> between <genetic loci>.
\Image[/linked-locus-gamete-probabilities.png]
{title=<Gamete> <probabilities> from the <phase-known genotype> AB/ab: parental versus recombinant <haplotypes> at three <recombination fractions>}
At $r=0$, only the parental <haplotypes> occur, each with <probability> $0.5$: this is <complete genetic linkage>. At $r=0.5$, all four <haplotypes> have <probability> $0.25$, giving <independent assortment>. A <recombination fraction> near $0.5$ alone cannot establish whether the <genetic loci> lie on different <chromosomes> or far apart on one <chromosome>.
<Genetic linkage> concerns joint transmission through <meiosis>. <Linkage disequilibrium> concerns <haplotype> frequencies in a population, while <genetic association> compares <allele> or <genotype> frequencies with a <phenotype>. These questions require different observations; <pedigrees> directly reveal co-transmission.