Let’s examine how genetic crosses are analyzed to determine whether genes are linked and to determine the map distance between linked genes on a chromosome. In this cross we will look at the characters of eye shape and tooth number in MendAliens, a mythical alien species. We begin with true-breeding parental aliens. One parent is homozygous for round eyes and no tooth. The other parent is homozygous for vertical eyes and one tooth. Let’s make the cross. Note that the F1 dihybrid offspring have round eyes and no tooth. The simplest hypothesis for now is that there are two genes for these two characters, with the round-eyes allele dominant to the vertical-eyes allele and the no-tooth allele dominant to the one-tooth allele. Now, let’s see what happens when an F1 dihybrid is testcrossed with a homozygous recessive individual, an alien with vertical eyes and one tooth. Here are the results of the testcross. If the two genes showed independent assortment, we would expect a ratio of 1 to 1 to 1 to 1 in the phenotypes from the testcross. Instead, most offspring resemble the phenotypes of the parents from the original P generation; that is, the parent with round eyes and no tooth, and the parent with vertical eyes and one tooth. We can conclude that the genes for eye shape and tooth number do not assort independently. Instead, the eye-shape and tooth-number alleles are usually inherited together because the genes for these two characters are near each other on the same chromosome. Such genes are said to be linked. For linked genes, we need to include chromosomes in our genotype diagrams, as shown here. We’ll use capital R for the round-eyes allele and small r for the vertical-eyes allele, and capital N for the no-tooth allele and small n for the one-tooth allele. The parent with round eyes and no tooth has two homologous chromosomes with capital R and capital N on each chromosome. This parent can produce only one type of gamete, which has a chromosome with capital R and capital N on the same chromosome. Similarly, the parent with vertical eyes and one tooth can produce only gametes with small r and small n on the same chromosome. The F1 dihybrids inherit one chromosome with capital R and capital N from the parent with round eyes and no tooth, and one chromosome with small r and small n from the parent with vertical eyes and one tooth. These two chromosomes are homologous. Since the round-eyes allele (capital R) is dominant, the F1 dihybrids have round eyes. And since the no-tooth allele (capital N) is dominant, the F1 dihybrids have no tooth. The F1 dihybrids can produce four types of gametes during meiosis. If crossing over does not occur between the homologous chromosomes during meiosis, gametes are produced that have either the dominant alleles for both characters (capital R and capital N) or the recessive alleles for both characters (small r and small n). These gametes have the same alleles as the gametes from the original P generation. If crossing over does occur between the homologous chromosomes during gamete formation, recombinant chromosomes are produced with either capital R and small n or small r and capital N. These gametes have combinations of alleles not seen before in either the P generation or the F1 dihybrids. Now let's reexamine the testcross between an F1 dihybrid and a homozygous recessive individual, an alien with vertical eyes and one tooth. The homozygous recessive MendAlien can produce only one type of gamete, which has small r and small n on the same chromosome because even if crossing over occurred, it would just be swapping the same alleles. This Punnett square shows the genotype and phenotype of each type of offspring. Notice that there are many more parental-type offspring than recombinant offspring, indicating that these two genes did not assort independently, but instead are near each other on the same chromosome and are therefore linked. Let's look at a summary of the offspring from the testcross. We can calculate the frequency of recombinant offspring by using the following formula: recombination frequency equals number of recombinants divided by the total offspring times 100. In this example, the recombination frequency equals 25 recombinants divided by 175 total offspring times 100, which equals 14.3 percent. The recombination frequency is directly related to how far apart two genes are on a chromosome. Generally speaking, genes that are closer together, such as the eye-shape gene and the tooth-number gene, are less likely to have a crossover occur between them. Genes that are farther apart, such as the eye-shape gene and the ear-shape gene, have a greater chance of a crossover occurring between them. This tendency is reflected in a higher frequency of recombinant offspring in genes that are farther apart. Therefore, recombination frequency data are used to assign gene positions on a chromosome map. By definition, one map unit is equivalent to a 1 percent recombination frequency. Thus, the genes for eye shape and tooth number are 14.3 map units apart. In a separate experiment, it was determined that the recombination frequency for the eye-shape gene and the ear-shape gene is 21 percent. Thus, the genes for eye shape and ear shape are 21 map units apart.