A planet is inhabited by creatures that reproduce with the same hereditary patterns seen in humans. Three phenotypic characters are height (T = tall, t= dwarf), head appendages (A = antennae, a = no antennae), and nose morphology (S = upturned snout, s = downturned snout). Since the creatures are not “intelligent,” Earth scientists are able to do some controlled breeding experiments using various heterozygotes in testcrosses. For tall heterozygotes with antennae, the offspring are tall antennae, 46; dwarf antennae, 7; dwarf no antennae, 42; tall no antennae, 5. For heterozygotes with antennae and an upturned snout, the offspring are antennae upturned snout 47; antennae downturned snout, 2; no antennae downturned snout, 48; no antennae upturned snout, 3. Calculate the recombination frequencies for both experiments.

Recombinant frequency measures the number of recombinant offspring obtained out of total offspring produced when parents with specific traits are crossed. It represents the crossing over that occurs between the concerned genes in a chromosome.

The recombinant frequency can be calculated by the following formula:

\({\rm{Recombination frequency}}\,{\rm{ = }}\frac{{{\rm{Number of recombinants}}}}{{{\rm{Total number of offsprings}}}}\,{\rm{ \times 100}}\)

Four types of offspring were obtained in the testcross for tall heterozygotes with antennae. These were tall antennae, dwarf antennae, dwarf no antennae, and tall no antennae. Tall antennae and dwarf no antennae were wild-type offspring, while dwarf antennae and tall no antennae were the recombinants obtained in the cross.

The total number of offspring produced in the cross is \(46\, + 7 + 42 + 5 = 100\).

The total number of recombinants is \(5 + 7 = 12\).

The recombination frequency is calculated by substituting the values into the following equation:

\({\rm{Recombination frequency}}\,{\rm{ = }}\frac{{12}}{{100}}\,{\rm{ \times 100}}\)

\({\rm{Recombination frequency}}\, = \,12\% \,\)

Thus, the recombination frequency for the genes between tall (T) and antennae (A) is 12%

Four types of offspring were obtained in the testcross for heterozygotes with antennae and an upturned snout. These were antennae upturned snout, antennae downturned snout, no antennae downturned snout, and no antennae upturned snout.

Antennae upturned snout and no antennae downturned snout were the wild type offspring, while antennae downturned snout and no antennae upturned snout were the recombinants obtained in the cross.

The total number of offspring produced in the cross is \(47 + 2 + 48 + 3 = 100\).

The total number of recombinants is \(2 + 3 = 5\).

The recombination frequency is calculated by substituting the values into the following equation:

\(\begin{aligned}{l}{\rm{Recombination frequency }}\,{\rm{ = }}\frac{5}{{100}}\,{\rm{ \times 100}}\\{\rm{Recombination frequency}}\,\, = \,\,5\% \,\,\,\,\end{aligned}\)

Thus, the recombination frequency for the genes between antennae (A) and an upturned snout is 5%.