At several genetic loci, a phase-known genotype specifies which alleles occur together on each chromosome, hence its two haplotypes. An unphased multilocus genotype may be compatible with several haplotype pairs. For two heterozygous loci, $AB/ab$ and $Ab/aB$ have identical unphased genotypes but different transmission probabilities when genetic linkage is present.

A haplotype is the set of alleles on one chromosome across specified genetic loci. Closely linked markers without intervening genetic recombination are transmitted as one haplotype; they are not independent observations of inheritance.

A homozygote carries two identical alleles at a locus; a heterozygote carries different alleles. Homozygosity of an observed haplotype is identity by state, and need not be identity by descent.

A heterozygote carries different alleles at a diploid locus. Under ordinary Mendelian segregation each is transmitted to an offspring with probability $1/2$. Only heterozygous parents provide a comparison between alternative transmissions in the transmission disequilibrium test.

Homozygosity means that the two allele states at a diploid genetic locus are the same; an individual with that property is a homozygote. Observed homozygosity does not by itself establish identity by descent.

Heterozygosity means that the two allele states at a diploid genetic locus differ; an individual with that property is a heterozygote. Heterozygous parental genotypes provide alternative alleles for a transmission disequilibrium test.

A genotyping error is an incorrect observed allele or genotype call. A probabilistic observation model replaces the deterministic genetic marker factor by $P(X=x\mid G=g)$, allowing nonzero probability of an observed call inconsistent with the latent genotype. Such error can bias family transmission tests and linkage likelihoods.

Genotyping determines the alleles carried at chosen genetic loci. A diploid genotype call need not identify its two haplotypes; that additionally requires a phase-known genotype or haplotype estimation.

A single-nucleotide polymorphism is variation at one nucleotide position in sampled genomes. Under an infinite sites mutation model, the number of such variable positions in a sample equals the number of mutations on the genealogy below its most recent common ancestor.

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, $0\le r\le 1/2$, 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 giveFor 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 Weeks, Tang and Kwon (2009), Casares' map function: No need for a 'corrected' Haldane's map function, Genetica 135, 305–307.

A recombination hotspot is a short region with an elevated local rate of genetic recombination. Repeated ancestral breakpoints there can separate neighboring haplotype blocks of strong linkage disequilibrium.

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Under an infinite sites mutation model, two variable sites on one unrecombined rooted tree have nested or disjoint derived-allele clades. At most three of the four biallelic haplotypes can then occur. Observation of all four haplotypes proves that the single-tree, single-mutation-per-site model cannot hold: some ancestral genetic recombination is necessary if recurrent mutation is excluded. The test gives no proof of absence of recombination when only three haplotypes occur.

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A chromosomal crossover is a reciprocal exchange of segments between nonsister chromatids of homologous chromosomes during meiosis. It can change the haplotypes inherited at selected genetic loci; whether it does so depends on the transmitted chromatid and interval.

The LOD score compares the likelihood at recombination fraction $\theta$ with independent assortment:When phenotype likelihood is independent of $\theta$, it can be computed from marker probabilities conditional on phenotype and ascertainment. Positive values support linkage; the observed marker pattern must be specified precisely because affected-only and affected-plus-unaffected observations give different likelihoods.

Homozygosity mapping searches for shared homozygous marker regions in individuals with a rare recessive condition, often in an inbred pedigree. Under a single ancestral disease copy, affected individuals inherit two copies identical by descent. Marker homozygosity alone gives identity by state, so founder haplotype frequencies matter. If a particular haplotype has founder frequency $p$ and $K$ distinct founder chromosome copies underlie all selected descendant copies, their marker-pattern probability is $E[p^K]$. For complete linkage and a single disease copy, the affected-only numerator is $p$, yielding a LOD score ${\log }_{10}(p/E[p^K])$ under linkage-equilibrium founder assumptions.

Complete linkage in a two-locus model means recombination fraction zero: only parental haplotype combinations are transmitted. Multiple genetic markers in a nonrecombining block represent one haplotype segregation observation.

Parametric linkage analysis forms a pedigree likelihood from a specified disease model, including penetrance, allele frequencies and recessive inheritance or another transmission model. It estimates or tests the recombination fraction between a disease locus and a genetic marker.

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Nonparametric linkage analysis tests excess identity by descent among relatives with a shared phenotype, without specifying its complete penetrance model or disease-allele frequency. Its null still uses Mendelian segregation and the specified pedigree.

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A genetic map turns observations of inherited haplotypes into an ordered account of genetic loci along a chromosome. Its distances describe genetic recombination, which makes the map useful for locating a genetic locus relative to known genetic markers. A genetic map measures inheritance separation; separation measured in base pairs describes positions along DNA. Recombination hotspots help explain why equal numbers of base pairs need not give equal genetic map distances. See T. A. Brown, Genomes, 2nd edition (2002), chapter 5: Mapping Genomes.

Write $d$ for the expected value of the number of chromosomal crossovers encountered along one transmitted chromatid between the chosen genetic loci, measured in morgans; $100d$ is the distance in centimorgans. This counts exchanges along that transmitted chromatid, rather than all exchanges in the four-chromatid meiotic bundle. For a short interval with very few multiple exchanges, the recombination fraction satisfies $r\approx d$: about $1\%$ recombinant gametes then corresponds to about one centimorgan.

For a longer interval, hidden even numbers of chromosomal crossovers make that approximation inaccurate. Under the Haldane mapping function, $d=0.2$ morgans gives $r\approx 0.164840$; conversely $r=0.2$ gives $d\approx 0.255413$ morgans, or $25.5413$ centimorgans. Applying the inverse formula to an already specified genetic map distance would confuse a count with a probability.

Genetic map distances add along ordered adjacent intervals because the total exchange count is the sum of its interval counts. For independent random variables describing counts in disjoint intervals of the Haldane mapping function model, the endpoint recombination fraction instead obeysExactly one interval must change parental origin. Thus $r_1=r_2=0.2$ gives $r_{12}=0.32$, although the two genetic map distances add to approximately $0.510826$ morgans. The simple composition formula requires the stated independence; crossover interference can invalidate it.