Linkage and Independent Assortment

Independent assortment: the starting point

Mendel's Law of Independent Assortment states that the alleles of different genes separate independently of one another during gamete formation. This happens in metaphase I of meiosis, when the homologous pairs line up at the equator of the cell. Each pair lines up in a random orientation, so the way one pair is separated has no effect on the others.

A plant of genotype $AaBb$, with the genes on different chromosomes, makes four types of gamete in equal numbers:

A test cross ($AaBb \times aabb$) then gives four phenotypes in a 1 : 1 : 1 : 1 ratio. A dihybrid cross ($AaBb \times AaBb$) gives 9 : 3 : 3 : 1.

Linkage

A human cell has only 46 chromosomes but around 20,000 genes. Each chromosome therefore carries hundreds or thousands of genes. Genes cannot all be on different chromosomes.

Chromosomes are passed on as whole units. Two genes on the same chromosome travel together into the same gamete, unless something breaks the chromosome between them. Linked genes do not assort independently.

We write the genotype of a linked dihybrid to show which alleles are on which chromosome. $AB/ab$ means that $A$ and $B$ are on one chromosome and $a$ and $b$ are on its homologue.

If there is no crossing over, an $AB/ab$ individual makes only two types of gamete: $AB$ and $ab$, in equal numbers. It does not make $Ab$ or $aB$.

Test crosses and linked genes

A test cross crosses an individual of unknown or heterozygous genotype with a homozygous double recessive ($ab/ab$). The double recessive can contribute only $ab$ gametes. So the phenotype of each offspring reveals exactly which gamete came from the heterozygous parent. This is why test crosses are used to investigate linkage: the offspring ratio shows directly which gametes were made, and in what proportions.

Take $AB/ab \times ab/ab$:

Crossing over and recombinants

Linkage is rarely complete. In prophase I of meiosis, homologous chromosomes pair up and non-sister chromatids can swap sections. This is crossing over. It can put $A$ and $b$ on the same chromatid.

• Parental types have the same combination of alleles as the parents ($AB$ and $ab$).

• Recombinants have a new combination ($Ab$ and $aB$), produced by crossing over.

The closer two genes are, the less likely it is that a crossover falls between them. So the recombinants are the smallest classes in a linked cross.

Recombination frequency and gene mapping

Recombination frequency is the percentage of recombinant offspring:

Crossovers happen more or less at random along a chromosome. The further apart two genes are, the more likely a crossover falls between them. So recombination frequency is a measure of distance. Geneticists use it to build linkage maps: 1% recombination is 1 map unit.

Why RF never exceeds 50%. Even if a crossover always occurred between two genes, it involves only two of the four chromatids. Half of the resulting gametes would be parental and half recombinant. So the maximum is 50%, which is the same as independent assortment. Genes with RF of 50% behave as if unlinked, even if they are on the same chromosome.

Slightly lower than the sum. In real experiments the end-to-end value can be a little less than the sum of the two shorter ones. If two crossovers occur, one in each interval, the second undoes the first and the gene combination looks parental again. These double crossovers go uncounted, so the long distance is underestimated.

For $P$ and $R$ (20%), the RF is below 50%, so they are linked and would not be expected to show independent assortment in a cross. Even $P$ and $Q$ are close enough that most gametes are parental.

Linkage, variation and breeding

Back to the farmer in Co. Meath. A dihybrid cross gave mostly the two parental phenotypes in roughly 3 : 1, with very few of the others. The two genes are linked: they are on the same chromosome, close together. The $AB/ab$ plants (the dominant alleles are on one chromosome and the recessive alleles on its homologue, called coupling phase) make mainly $AB$ and $ab$ gametes. Selfing gives mostly $A\text{-}B\text{-}$ and $aabb$ plants in roughly 3 : 1, with a few recombinant phenotypes ($A\text{-}bb$ and $aaB\text{-}$). These few unexpected phenotypes are recombinants, made when a crossover in prophase I happened between the two genes.

Linkage and variation:

• Linkage reduces variation, because favourable and unfavourable alleles on the same chromosome are inherited together as a block.

• Crossing over increases variation by creating new allele combinations that were not in the parents.

• Independent assortment also generates variation. Linkage limits how much it can do.

For a plant breeder, linkage can be a problem. A useful allele (say disease resistance) may be linked to an undesirable one (poor yield), and it takes many generations and a lot of offspring to find a rare recombinant that has one without the other. It can also be useful: if a marker gene is tightly linked to a desired gene, the marker can be used to select plants carrying it.

Summary

• Independent assortment (metaphase I) applies to genes on different chromosomes: test cross 1 : 1 : 1 : 1; dihybrid cross 9 : 3 : 3 : 1.

• Linkage: genes on the same chromosome, close together, inherited together. $AB/ab$ without crossing over gives only $AB$ and $ab$ gametes.

• In a test cross, parental types are the two large classes. Recombinants are the two small classes, made by crossing over in prophase I.

• $\text{RF} = \dfrac{\text{recombinants}}{\text{total}} \times 100$. It is at most 50%, and the further apart two genes are, the higher it is.

• Recombination frequencies give distances for linkage maps, so the order of genes can be worked out. Double crossovers make long distances slightly underestimated.

• Linkage reduces variation, crossing over restores some, and this matters to plant breeders.