In the diploid ancestor of our modern bread wheat ( Triticum aestivum ), resista
ID: 59290 • Letter: I
Question
In the diploid ancestor of our modern bread wheat (Triticum aestivum), resistance to a particular fungal pathogen is controlled by a dominant allele at a single locus. Assume that a population of this diploid wheat is in Hardy-Weinberg equilibrium and that the frequency of the dominant (resistance) allele is 0.54.
a.Assume that all susceptible individuals in this population are eventually killed by fungal infections before they reproduce. What is the frequency of the recessive (susceptibility) allele among the survivors? (HINT: count the alleles)
b.Assume that the surviving plants cross-pollinate randomly and that each plant produces the same number of seeds. What proportion of the seeds produced will eventually become plants that are susceptible to the fungus?
Explanation / Answer
a. Hardy and Weinberg also described all the possible genotypes for a gene with two alleles. Use Hardy-Weinberg equation to solve the problem:
p2 + 2pq + q2 = 1.0; (p +q = 1)
Here,
p = frequency of the dominant allele in the population
q = frequency of the recessive allele in the population
p2 = proportion of homozygous dominant individuals
q2 = proportion of homozygous recessive individuals
2pq = proportion of heterozygotes.
Given that the dominant (resistance) allele,
p = 0.54;
So, q = 1-0.54
= 0.46.
In the given case, the resistance to a particular fungal pathogen is controlled by a dominant allele, which means the homozygous dominant and heterozygous individuals are resistant to fungal disease.
So, p2 and 2pq are resistant to disease.
p2 = 0.54* 0.54
= 0.291;
2pq = 0.496
So, 0.291+0.496
= 0.787.
The frequency of the recessive allele among the survivors is 78%.