When two genes are on separate chromosomes, a ratio of 1:1:1:1 is expected for the nonrecombinant (parental) and recombinant (nonparental) gametic types, as described by the principle of independent assortment (Chapter 16). For two genes present in the same chromosome, we can consider two extreme situations. If they are located very far apart from each other, one or more crossovers will almost certainly occur between them, and there will be a 1:1:1:1 ratio of nonrecombinant and recombinant gametes (as shown for the case of a single crossover in Fig. 17.10a). At the other extreme, if two genes are so close together that crossing over never takes place between them, we would expect only nonrecombinant chromosomes (Fig. 17.10b).

What happens in between these extremes? In these cases, in some cells undergoing meiosis, no crossover takes place between the genes, in which case all the resulting chromosomes are nonrecombinant (Fig. 17.10b); and in other cells undergoing meiosis, a crossover occurs between the genes, in which case half the resulting chromosomes are nonrecombinant and half are recombinant (Fig. 17.10a). Since the meioses with no crossover between the genes result only in nonrecombinant chromosomes and those with a crossover result in half nonrecombinant and half recombinant chromosomes, the nonrecombinant chromosomes in the offspring will be more numerous than the recombinant chromosomes.

The actual frequency of recombinants depends on the distance between the genes. The distance between the genes is important because whether or not a crossover occurs between the genes is a matter of chance, and the closer the genes are along the chromosome, the less likely it is that a crossover will take place in the interval between them. Because the formation of recombinant chromosomes requires at least one crossover between the genes, genes that are close together (more tightly linked) show less recombination than genes that are far apart. In fact, the proportion of recombinant chromosomes observed among the total, which is called the frequency of recombination, is a measure of genetic distance between the genes along the chromosome.

In the example with the genes w and cv, the total number of chromosomes observed among the progeny is 357 + 341 + 52 + 45 = 795, and the number of recombinant chromosomes is 52 + 45 = 97. The frequency of recombination between w and cv is therefore 97/795 = 0.122, or 12.2%, and this serves as a measure of the genetic distance between the genes. In studies of genetic linkage, the distance between genes is not measured directly by physical distance between them, but rather by the frequency of recombination.

The frequency of recombination between any two genes on the same chromosome ranges from 0% (when crossing over between the genes never takes place) to 50% (when the genes are so far apart that a crossover between the genes almost always takes place). Genes that are linked have a recombination frequency somewhere between 0% and 50%. The maximum frequency of recombination is 50% because, when nonsister chromatids involved in crossovers are chosen at random, any new crossover has two equally likely consequences: It can either change a previously recombinant chromatid into a nonrecombinant chromatid, or change a previously nonrecombinant chromatid into a recombinant chromatid. The result is that however many crossovers there may be (as long as there is at least one), the maximum frequency of recombination remains 50%. A frequency of recombination of 50% yields the same ratio of gametic types as observed with independent assortment, which means that genes that are far enough apart in the same chromosome show independent assortment.

Quick Check 2 Why is the upper limit of recombination 50% rather than 100%?

Recombination plays an important role in creating new combinations of alleles in each generation and in ensuring the genetic uniqueness of each individual. If there were no recombination (that is, if all the alleles in each chromosome were completely linked), any individual human would be able to produce only 2²³ = 8.4 million types of reproductive cells. While this is a large number, the average number of sperm per ejaculate is much larger—approximately 350 million. Because recombination does occur, and because the crossovers resulting in recombination can occur at any of thousands of different positions in the genome, each of the 350 million sperm is virtually certain to carry a different combination of alleles.