Solution

Past exam of the mathematics course of the University of Cambridge / 2005 / iii / Paper 45 / 4 / iv / Solution

Past exam of the mathematics course of the University of Cambridge / 2006 / iii / Paper 45 / 1 / c / Solution

Pedigree likelihood

Recombination hotspot

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Genetic recombination rearranges inherited genetic material into new combinations. In the <meiosis> example considered here, <chromosomal crossover> exchanges segments between nonsister <chromatids> of <homologous chromosomes>. A transmitted <chromatid> can consequently contain <DNA> from both parental homologues. This produces new <haplotypes> without requiring a new <mutation> at either scored <genetic locus>. See <Molecular Biology of the Cell, 4th edition by Bruce Alberts and others/Meiosis>.

For <phase-known genotype> $AB/ab$, a single <chromosomal crossover> between the selected <genetic loci> can yield $Ab$ and $aB$ on the participating <chromatids>; the other two <chromatids> can remain $AB$ and $ab$. Thus an exchange in the four-<chromatid> bundle does not mean every resulting <gamete> is recombinant. Only a <chromosomal crossover> encountered along the transmitted <chromatid> within the selected interval affects its two-locus score.

Follow parental origin along the transmitted <chromatid> from the first <genetic locus> to the second. Each exchange switches that origin. An odd number of such <chromosomal crossovers> changes the endpoint combination; an even number restores parental phase. Two exchanges can therefore leave the scored <haplotype> as $AB$ even though an internal segment came from the other parental <homologous chromosome>. Recombinant status is relative to the chosen <genetic loci>, not a complete record of exchanges along the <chromosome>.

This <integer parity> distinction connects the physical process of <genetic recombination> to the observed <recombination fraction>. It also explains why a long <genetic map> interval can accumulate many exchanges while its endpoint <recombination fraction> approaches $1/2$ in the <Haldane mapping function> model.

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 Incoming links: Genetic recombination