Consider a cross between a plant heterozygous for the dominant traits of red flowers and wrinkled seeds (RrWw) and a plant homozygous for the recessive traits of white flowers and smooth seeds (rrww). We see the following phenotypic distribution in the offspring: - 43 with red flowers and wrinkled seeds - 7 with red flowers and smooth seeds - 9 with white flowers and wrinkled seeds - 41 with white flowers and smooth seeds The recombinant offspring are those exhibiting a combination of traits not found in either parent. This would be the 7 offspring with red flowers and smooth seeds (Rrww) and the 9 with white flowers and wrinkled seeds (rrWw). We identify these as recombinants because they display a mix of the dominant and recessive phenotypes for flower color and seed texture, which must result from crossing-over during meiosis in the heterozygous parent that leads to a new combination of alleles. Prior to crossing-over during meiosis, the heterozygous parent’s chromosomes would carry alleles configured as: - One chromosome with R (red flowers) and W (wrinkled seeds) - The homologous chromosome with r (white flowers) and w (smooth seeds) After crossing-over, the chromosomes could have segments swapped, leading to new combinations, such as: - One chromosome with R (red flowers) and w (smooth seeds) - The homologous chromosome with r (white flowers) and W (wrinkled seeds) The recombination frequency is calculated by adding the number of recombinant offspring and dividing it by the total number of offspring, then multiplying by 100 to get a percentage: Recombination frequency = (Number of recombinant offspring / Total number of offspring) × 100 Recombination frequency = ((7 + 9) / (43 + 7 + 9 + 41)) × 100 Recombination frequency = (16 / 100) × 100 Recombination frequency = 16% Since 1 map unit (m.u.) is equivalent to a 1% recombination frequency, the distance between the genes for flower color and seed shape is approximately 16 map units.

The recombinant offspring are those that display trait combinations not present in either parent, specifically the 7 red flowers, smooth seeds (Rrww) and the 9 white flowers, wrinkled seeds (rrWw) in this cross. These combinations are due to crossing-over during meiosis in the heterozygous parent (RrWw), which produces gametes with new allele combinations.

Let's calculate the recombination frequency using the provided numbers:

- Total recombinants (red flowers, smooth seeds + white flowers, wrinkled seeds): 7 + 9 = 16 - Total offspring: 43 + 7 + 9 + 41 = 100

Now, to get the recombination frequency, use the formula:

Recombination frequency = (Number of recombinant offspring / Total number of offspring) × 100

Using the numbers:

Recombination frequency = (16 / 100) × 100 = 16%

If we use map units (m.u.) to express genetic distance, where 1 map unit is equivalent to a 1% recombination frequency, the genetic distance between the genes for flower color and seed shape would be approximately 16 map units.

Extra: In genetics, the term "recombinant" refers to an offspring whose combination of traits is different from that of the parents due to the exchange of genetic material during the process of sexual reproduction. This can occur during meiosis, when homologous chromosomes exchange parts with one another in a process known as crossing-over. In the case of a dihybrid cross (cross involving two traits), like the one between a plant with the genotype RrWw and another with the genotype rrww, the recombinant offspring occur due to such crossing-over events, resulting in non-parental allele combinations.

The study of recombination frequency helps geneticists to map the location of genes on chromosomes. The closer two genes are to each other, the less likely they are to be separated by crossing-over, and thus, they have a lower recombination frequency. Conversely, genes that are far apart on a chromosome are more likely to be separated by crossing-over, resulting in a higher recombination frequency. Genetic maps are constructed based on these frequencies, and they are measured in map units, where 1% recombination is equivalent to 1 map unit.

Understanding genetic linkage and recombination is crucial in various fields, including plant and animal breeding, where the goal is to combine desirable traits from different varieties or breeds. It also plays a significant role in human genetics and is instrumental in identifying genes associated with inherited diseases.