Hi could you help me with this problem as well?
The alleles for red and white coat color in cattle show absence of dominance, the heterozygote being roan.
A.In a freely breeding herd of 1000 head how many would you expect to be of each coat color if the allele for white coat has a frequency of 0.4?
B.If all the white cattle were sold for slaughter and the red and roan animals were allowed to breed freely, about what percentage of the offspring would be expected to be white?
Sure, I can help you with this problem!
A. To determine the number of each coat color, we need to consider the allele frequencies and the breeding patterns. Let's assume that the alleles for red and white coat color are represented by R and W, respectively.
Given that the allele frequency for white coat color (W) is 0.4, we can calculate the frequency of the red coat color allele (R) as follows:
Frequency of R = 1 - Frequency of W
= 1 - 0.4
= 0.6
Now, let's calculate the expected number of each coat color:
Number of red cattle = Total number of cattle * Frequency of R
= 1000 * 0.6
= 600
Number of white cattle = Total number of cattle * Frequency of W
= 1000 * 0.4
= 400
Therefore, in a freely breeding herd of 1000 head, we would expect 600 cattle to have a red coat color and 400 cattle to have a white coat color.
B. If all the white cattle are sold for slaughter and the red and roan animals are allowed to breed freely, the offspring would have the following possible genotypes:
RR: Red coat color
RW: Roan coat color
Since the roan coat is the heterozygote, any offspring resulting from the breeding of red and roan cattle would not be white. Therefore, in this scenario, we would not expect any white offspring.
I hope this helps! Let me know if you have any further questions.
Sure, I can help you with that! To answer these questions, we need to use the principles of basic genetics and the concept of allele frequencies. Let's break down each question and explain how to get the solutions.
A. In a freely breeding herd of 1000 head, we are given that the allele for white coat color has a frequency of 0.4. From this information, we can determine the expected proportion of each coat color in the population.
Let's denote the red allele as R and the white allele as W. Since the alleles show absence of dominance and the heterozygote is roan, we can assume that the red allele and white allele are co-dominant.
The possible genotypes and coat colors are:
- RR (red)
- WW (white)
- RW (roan)
Now, let's calculate the expected proportions of each genotype:
- RR: Frequency of red allele (0.6) multiplied by itself (0.6), which equals 0.36 (36%).
- WW: Frequency of white allele (0.4) multiplied by itself (0.4), which equals 0.16 (16%).
- RW: Frequency of red allele (0.6) multiplied by frequency of white allele (0.4), which equals 0.24 (24%).
To determine the expected number of each coat color in a herd of 1000 cattle, we multiply the proportions by the total population size:
- RR: 0.36 x 1000 = 360 cattle (red)
- WW: 0.16 x 1000 = 160 cattle (white)
- RW: 0.24 x 1000 = 240 cattle (roan)
Therefore, in a freely breeding herd of 1000 head, you would expect approximately 360 red cattle, 160 white cattle, and 240 roan cattle.
B. If all the white cattle were sold for slaughter and the red and roan animals were allowed to breed freely, we need to determine the expected percentage of white offspring.
Since white coat color is recessive (WW), in order for an offspring to be white, both parents (red or roan) must carry the white allele (W). Let's assume that all roan cattle are heterozygous (RW) for simplicity.
The possible parent combinations are:
- Red (RR) x Roan (RW): 50% chance of offspring being roan (RW), 50% chance of offspring being red (RR).
- Roan (RW) x Roan (RW): 25% chance of offspring being roan (RW), 25% chance of offspring being red (RR), and 50% chance of offspring being white (WW).
As we can see, for the roan x roan mating, there is a 50% chance of the offspring being white (WW).
Since RW x RW matings would account for 50% of the possible matings, we can estimate that about half of the offspring would be white (WW).
Therefore, if all the white cattle were sold for slaughter and the red and roan animals were allowed to breed freely, we could expect that approximately 50% of the offspring would be white.