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Ellis-van Creveld syndrome is a rare homozygous recessive disorder that affects bone growth. Individuals with this disorder are characterized by dwarfism, polydactyly, heart defects, and other symptoms. The recessive allele that causes it is extremely common in the Amish community of Lancaster County, Pennsylvania, and in the indigenous population of Western Australia. For example, the birth rate of this disorder in Lancaster County is 1 in every 5000 births ( compared to 1 in every 150,000 births worldwide). a) Approximately what percent of the Amish population are heterozygous carriers of the allele for Ellis-van Creveld syndrome? b) What percentage is homozygous dominant?

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Answer:

1.    2.8%

2.    97.1%

Explanation:

  1. If the birth rate of this disorder is 1 in every 5000 births it means that the frequency of the recessive homozygous genotype is 1/5000=0.0002

If we name the gene for the disorder with A, than the genotypes are aa (homozugous recessive), Aa (heterozygous, carrier), AA (dominant homozygous).

According to the Hardy-Weinberg equation:

frequency of AA is p2  (P)

frequency of Aa is 2pq

frequency of aa is q2 (Q) and

p2+2pq+q2=1 (P+Q=1)

Q=0.0002  P=1-0.0002=0.9998  

q= [tex]\sqrt[/tex]0.0002=0.014

p=[tex]\sqrt[/tex]0.9998=0.999

2pq=0.028=2.8%

2.  According to the Hardy-Weinberg equation:

frequency of AA is p2  (P)

frequency of Aa is 2pq

frequency of aa is q2 (Q) and

p2+2pq+q2=1 (P+Q=1)

The frequency of the recessive homozygous genotype (Q) is 1/5000=0.0002

Q=0.0002  

q2=0.0002  2pq=0.028 p2=?

p2= 1-0.0002-0.028 =0.9718=97.1%

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