Linkage, crossing over and genetic maps
Why genes on one chromosome are inherited together, how crossing over recombines them, recombination frequency and map units, and a three-point cross.
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Mendel's second law says that genes assort independently. That holds for genes on different chromosomes, but a crop has thousands of genes and only a handful of chromosomes, so most genes share a chromosome with many others. Such genes tend to be inherited together: they are linked. Linkage is broken, now and then, by crossing over during meiosis, and the frequency with which this happens between two genes is a measure of the distance between them. This simple idea gave genetics its first maps of chromosomes, and it underlies modern marker-assisted breeding.
Linkage, recombination and mapping are standard exam topics in genetics and plant breeding, nearly always with calculations.
Discovery
In 1905, W. Bateson, E. R. Saunders and R. C. Punnett found that flower colour and pollen shape in sweet pea did not assort independently; they called it "coupling" and "repulsion". In 1910–11, T. H. Morgan, working with fruit flies, explained such results by genes lying on the same chromosome, and proposed that exchange between chromosomes (crossing over) produced the occasional new combinations. In 1913, his student A. H. Sturtevant used recombination frequencies to build the first genetic map. In 1931, H. Creighton and B. McClintock in maize, and C. Stern in fruit flies, proved that genetic crossing over coincides with a physical exchange of chromosome segments.
Linkage phases
For two linked genes in a double heterozygote:
- Coupling (cis): the two dominant alleles are on one chromosome and the two recessives on the other, AB/ab.
- Repulsion (trans): each chromosome carries one dominant and one recessive, Ab/aB.
Which combinations count as "parental" or "recombinant" depends on the phase.
Crossing over
During prophase I of meiosis, homologous chromosomes pair, and non-sister chromatids exchange segments at points called chiasmata.
- A single crossover between two genes produces, from that meiosis, two parental and two recombinant chromatids. So the recombination frequency (RF) can never exceed 50 per cent, the value for unlinked genes.
- The further apart two genes are, the more likely a crossover falls between them, so RF increases with distance.
- Complete linkage (no recombination) is rare; it occurs in male fruit flies and female silkworms, which do not cross over. Most linkage is incomplete.
Recombination frequency and map units
One per cent recombination equals one map unit or centimorgan (cM), named after Morgan. The number of linkage groups equals the haploid chromosome number: 10 in maize, 12 in rice and tomato, 7 in barley, 21 in bread wheat.
A classic two-point cross in maize
In 1922, C. B. Hutchison test-crossed maize plants heterozygous in coupling for coloured (C) versus colourless (c) aleurone and full (Sh) versus shrunken (sh) endosperm:
| Progeny | Number | Type |
|---|---|---|
| coloured, full | 4,032 | parental |
| colourless, shrunken | 4,035 | parental |
| coloured, shrunken | 149 | recombinant |
| colourless, full | 152 | recombinant |
| Total | 8,368 |
RF = (149 + 152) ÷ 8,368 × 100 = 3.6 per cent, so the genes are about 3.6 cM apart. With independent assortment, each class would be about 2,092.
Three-point test cross
Mapping three genes at once finds their order and detects double crossovers, which two-point crosses miss.
Mapping three genes
A triple heterozygote is test-crossed to aabbcc, giving 1,000 progeny:
| Phenotype class | Number |
|---|---|
| A B C | 390 |
| a b c | 380 |
| A b c | 45 |
| a B C | 50 |
| A B c | 60 |
| a b C | 65 |
| A b C | 5 |
| a B c | 5 |
Step 1: parental and double-crossover classes. The two largest classes (ABC, abc) are parental; the two smallest (AbC, aBc) are double crossovers.
Step 2: gene order. Compared with the parental ABC and abc, the double crossovers have swapped only B. So B is in the middle: the order is a – b – c.
Step 3: distances.
- a–b: single crossovers in that region (Abc 45 + aBC 50) plus double crossovers (10) = 105, so RF = 10.5 cM.
- b–c: ABc 60 + abC 65 + 10 = 135, so RF = 13.5 cM.
- a–c = 10.5 + 13.5 = 24 cM.
Step 4: interference. Expected double crossovers = 0.105 × 0.135 × 1,000 ≈ 14.2; observed = 10.
- Coefficient of coincidence = 10 ÷ 14.2 = 0.70.
- Interference = 1 − 0.70 = 0.30: one crossover reduces the chance of another nearby.
Map distance and physical distance
Recombination frequencies add up only over short distances, because multiple crossovers between distant genes cancel each other out. Mapping functions correct for this; J. B. S. Haldane's function, d = −½ ln(1 − 2r), assumes no interference, and D. D. Kosambi's allows for it.
Genetic distance is not the same as physical distance in DNA base pairs. Crossovers are much more frequent in some regions, called hotspots, and rare near centromeres, so one centimorgan may correspond to tens of thousands of base pairs in one region and millions in another.
Why linkage matters in breeding
- Marker-assisted selection: a DNA marker tightly linked to a gene for disease resistance lets breeders select seedlings carrying the gene without testing for disease.
- Linkage drag: when a useful gene is transferred from a wild relative, unwanted genes linked to it come along, often reducing yield or quality; several backcross generations and tightly linked markers help break the link.
- Breaking undesirable linkages needs large populations and several generations of intermating.
- Mapping populations, such as F2, backcross, recombinant inbred lines and doubled haploids, are used to locate genes and quantitative trait loci (QTL).
Key points
- Linked genes lie on the same chromosome and tend to be inherited together; coupling AB/ab, repulsion Ab/aB.
- Crossing over between non-sister chromatids at chiasmata produces recombinants; RF cannot exceed 50 per cent.
- RF = recombinants ÷ total × 100; 1 per cent = 1 cM; linkage groups = haploid chromosome number.
- In a three-point cross, the double-crossover class identifies the middle gene; interference = 1 − coefficient of coincidence.
- Genetic and physical distances differ; mapping functions correct for multiple crossovers.
- Linkage enables marker-assisted selection and causes linkage drag.
What the exams ask
- School-leaving and entrance papers: what linkage and crossing over are, coupling and repulsion, and their significance.
- Degree and research-fellowship entrances: recombination frequency, two- and three-point test crosses, gene order, coefficient of coincidence and interference, and mapping functions.
- Research and breeding examinations: mapping populations, QTL mapping, marker-assisted selection, and linkage drag.
Described in general terms: the kind of examination, not a past paper. Laisha never reproduces exam questions.
Questions people ask
Why can recombination never exceed 50 per cent?
Each crossover involves only two of the four chromatids, so even when crossovers always occur between two genes, at most half of the products are recombinant. Genes far apart on a chromosome behave as if unlinked.
Are linked genes always close together?
Not necessarily. Genes at opposite ends of a long chromosome are physically linked but recombine so often that they appear to assort independently. They can be shown to be linked by mapping genes in between.
What is linkage disequilibrium?
The non-random association of alleles at different loci in a population. It is related to linkage but also arises from selection, mixing of populations and drift, and is used in association mapping.
Sources
- Sturtevant, A. H. "The linear arrangement of six sex-linked factors in Drosophila, as shown by their mode of association." Journal of Experimental Zoology 14, 43–59 (1913).
- Creighton, H. B. and McClintock, B. "A correlation of cytological and genetical crossing-over in Zea mays." Proceedings of the National Academy of Sciences 17, 492–497 (1931).
- Hutchison, C. B. "The linkage of certain aleurone and endosperm factors in maize, and their relation to other linkage groups." Cornell University Agricultural Experiment Station Memoir 60 (1922).
- Griffiths, A. J. F. et al. Introduction to Genetic Analysis, 12th edition. W. H. Freeman, 2020. Chapter 4.
- Collard, B. C. Y. et al. "An introduction to markers, quantitative trait loci (QTL) mapping and marker-assisted selection for crop improvement." Euphytica 142, 169–196 (2005).
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