Question

If you are told that the two Buckskin Dun horses come from a population where the frequency of the D allele is 0.70, for the D locus alone what is the probability of having a foal with at least one D allele from a mating of the two Buckskin Dun horses? Provide your answer to the nearest 0.001 (i.e. 3 decimal places). You may again assume that a Buckskin Dun is E_ A_ CC D_ gg ww toto rr

Expanding upon the previous question, if you are told that the two Buckskin Dun horses come from a population where the frequency of the D allele is 0.41, what is the probability of having a Buckskin Dun foal from a mating of the two Buckskin Dun horses? In other words, how likely are you to get a foal that looks like its parents? Provide your answer to the nearest 0.001 (i.e. 3 decimal places). You now need to consider all the other loci in the colour inheritance system but to make life easier, you may assume that all the other ambiguous loci have an allele frequency of 0.5 and you may assume a Buckskin Dun is still E_ A_ CC D_ gg ww toto rr

Answer 1

To find the probability of having a foal with at least one D allele from two Buckskin Dun horses, use the Hardy-Weinberg principles to calculate the genotype probabilities and sum them. To estimate the likelihood of a foal resembling its Buckskin Dun parents, apply the product and sum rules across all loci, assuming other required dominant alleles have a frequency of 0.5.

Step-by-step explanation:

When considering the probability of having a foal with at least one D allele from two Buckskin Dun horses where the frequency of the D allele (D) is 0.41, we'll use Hardy-Weinberg principles. The allele frequency of the recessive allele (d) will be 1 - 0.41 = 0.59. The chance of having at least one D allele will include genotypes DD and Dd. Using the Hardy-Weinberg equation, these genotypes have probabilities of p² (DD) and 2pq (Dd), with 'p' representing the frequency of the dominant allele and 'q' representing the recessive allele. Thus, the probability for DD is 0.41², and for Dd is 2(0.41)(0.59). To find the combined probability of having at least one D allele, we add the probabilities of DD and Dd.

Furthermore, to determine the likelihood of getting a foal that looks like its parents, a Buckskin Dun, we need to consider all loci. While we're given the frequency of allele D as 0.41, we assume that all other loci (E, A, C, g, w, t, r) have a frequency of 0.5 for the required dominant allele. Applying the product rule and the sum rule, we calculate the probability of having the dominant phenotype at each locus and then multiply them together to arrive at the final probability.