Question

In Dexter and Kerry cattle, animals may be polled (hornless) or horned. The Dexter animals have short legs, whereas the Kerry animals have long legs. When many offspring were obtained from matings between polled Kerrys and horned Dexters, half were found to be polled Dexters and half polled Kerrys. When these two types of \(\mathrm{F}_{1}\) cattle were mated to one another, the following \(\mathrm{F}_{2}\) data were obtained: \(3 / 8\) polled Dexters 3/8 polled Kerrys \(1 / 8\) horned Dexters \(1 / 8\) horned Kerrys A geneticist was puzzled by these data and interviewed farmers who had bred these cattle for decades. She learned that Kerrys were true-breeding. Dexters, on the other hand, were not truebreeding and never produced as many offspring as Kerrys. Provide a genetic explanation for these observations.

Short answer

Answer: The two traits involved are presence of horns (polled vs. horned) and leg length (short legs vs. long legs). Polled (hornless) is dominant (allele P) over horned (allele p), and short legs (allele D) are dominant over long legs (allele K). The genetics behind polled and horned Dexters and Kerrys follow Mendelian inheritance of two independent traits. The true-breeding Kerrys have a dominant homozygous genotype (KKPP), while the Dexters, not true-breeding, have a heterozygous genotype (DdPp). The F2 generation shows a ratio of 3:3:1:1 (polled Dexters, polled Kerrys, horned Dexters, horned Kerrys) following a dihybrid cross of the F1 generation.

Step-by-step solution

Identify the traits involved

There are two traits involved in this exercise: 1. Presence of horns: Polled (P) vs. horned (p) 2. Leg length: Short legs in Dexters (D) vs. long legs in Kerrys (K) We will use the letters P, p, D, and K as alleles to represent these traits in our analysis.

Interpret \(\mathrm{F}_{1}\) generation data

From the given information, when polled Kerrys (PK) are mated with horned Dexters (Dp), half of the offspring are polled Dexters (PD) and half are polled Kerrys (PK). This suggests that the dominant allele of the presence of horns (P) comes from the polled Kerry and that the allele for short legs (D) is dominant in the Dexter cattle. The genotypes of the F1 generation are thus: PD (polled Dexters) and PK (polled Kerrys)

Interpret \(\mathrm{F}_{2}\) generation data

When the \(\mathrm{F}_{1}\) generation (PD and PK) were mated, we obtained the following \(\mathrm{F}_{2}\) data: \(3 / 8\) polled Dexters, \(3 / 8\) polled Kerrys, \(1 / 8\) horned Dexters, and \(1 / 8\) horned Kerrys. This suggests that the traits are inherited independently, and we can use simple Mendelian genetics to analyze these ratios.

Determine genotypes of the parents

To proceed with the genetic analysis, we can determine the genotypes of the polled Kerry (PK) and horned Dexter (Dp) parents. Since Kerrys are true-breeding, their genotype is KKPP. Dexters have short legs, which is the dominant trait, but they are not true-breeding, so their genotype must be DdPp. Therefore, the cross between the polled Kerry and horned Dexter is: KKPP (polled Kerry) x DdPp (horned Dexter)

Perform a dihybrid cross

Now we will carry out a dihybrid cross for the two traits - presence of horns and leg length. The cross can be represented as: K(KP) x DP(dp), which gives us the following offspring genotypes: 1. K(KP) (polled Kerry) 2. K(KP) (polled Kerry) 3. D(Pp) (polled Dexter) 4. D(Pp) (polled Dexter) The ratio is thus 2:2, or 1:1, as given in the \(\mathrm{F}_{1}\) data. From the F1 generation data (PD and PK), we have two different genotypes: KDPp and DdPK. To analyse this, we will make the following cross: 1. KDPp (polled Dexter) 2. DdPK (polled Kerry) This dihybrid cross should give us the \(\mathrm{F}_{2}\) generation data, which consists of \(3 / 8\) polled Dexters, \(3 / 8\) polled Kerrys, \(1 / 8\) horned Dexters, and \(1 / 8\) horned Kerrys.

Explain the genetic observations

The F2 ratios of polled and horned Dexters and Kerrys (3:3:1:1) are consistent with the simple Mendelian inheritance of two independent traits, where the presence of horns (P) being dominant over hornless (p) and short legs (D) being dominant over long legs (K). The Kerrys, being true-breeding, only have the dominant homozygous genotype (KKPP), while the Dexters, which are not true-breeding, possess the heterozygous genotype (DdPp). The fact that Dexters do not produce as many offspring as the Kerrys could be an additional phenotypic characteristic, possibly due to survival and reproduction advantages associated with the long-legged Kerry breed.