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How can we use Hardy-Weinberg equilibrium to calculate carrier frequencies of recessive diseases if we know the proportion of people who are affected?. Helen Stuart, Cardiff. Essay plan. Description of Hardy-Weinberg principle (HWP) Allele frequencies: p+q=1

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helen stuart cardiff

How can we use Hardy-Weinberg equilibrium to calculate carrier frequencies of recessive diseases if we know the proportion of people who are affected?

Helen Stuart, Cardiff

essay plan
Essay plan
  • Description of Hardy-Weinberg principle (HWP)
  • Allele frequencies: p+q=1
  • Genotype frequencies: 2pq + q2 + p2
  • Assumptions of HWP including single locus with 2 alleles, random mating, no selection, limitless population
  • Know proportion of people affected = q2
  • Deduce q value
  • Use HWP (q+p=1) to calculate p value
  • Use HWP to calculate carrier frequency = 2pq
  • Give autosomal (Tay Sachs or CF) and X-linked (red-green colour blindness) HW calculation examples
hardy weinberg equilibrium
Hardy-Weinberg equilibrium
  • Hardy-Weinberg equilibrium states that both allele and genotype frequencies in a population remain constant (i.e. they are in equilibrium) from generation to generation unless specific disturbing influences are introduced. wikipedia
simplest scenario
Simplest scenario
  • In the simplest case of a single locus with two alleles: the dominant allele is denoted A and the recessive a and their frequencies are denoted by p and q
  • freq(A) = p and freq(a) = q
  • So, p + q = 1
  • If the population is in equilibrium, then we will have:
  • freq(AA) = p2 for the AA homozygotes in the population
  • freq(aa) =  q2 for the aa homozygotes
  • and freq(Aa) = 2pq for the heterozygotes.
how to calculate carrier frequency of a recessive disorder
How to calculate carrier frequency of a recessive disorder….
  • If you know the proportion of people who are affected with an autosomal recessive condition, you know q2
  • Remember: q2 is the genotype frequency of aa homozygotes (i.e. affected individuals)
  • Use this value to calculate q,

i.e. square root of q2

  • Use HWP to calculate p (p+q=1)
  • Use HWP to calculate carrier frequency = 2pq
example 1 autosomal recessive use of hardy weinberg principle
Example 1: Autosomal recessive use of Hardy-Weinberg principle

Tay Sachs disease affects 1 in 3,900 Ashkenazi Jews. What is the expected frequency of carriers?

q2 = 1/3,900

q = square root of 1/3,900 = 1/62

p+q=1 so: p+1/62=1 so: p=61/62

Carrier frequency (2pq) = 2 x 61/62 x 1/62

= approx 1/31 in Ashkenazi Jewish population

example 2 x linked use of hardy weinberg principle
Example 2: X-linked use of Hardy-Weinberg principle

Red-green colour blindness has an incidence among males of 1/12 (8%). What is the expected frequency of female carriers?

For X-linked disorders, the affected genotype frequency is q (not q2 as for recessive conditions).

So, q= 1/12

p+q=1 so: p+1/12=1 so: p=11/12

Female carrier frequency (2pq) = 2 x 11/12 x 1/12

= approx 22/144 (approx 1/8 or 15%)

example 3 autosomal recessive familial case
Example 3: autosomal recessive familial case

A pregnant African-American couple presents concerned about their risk of having a child with sickle cell anemia (SSA). The husband has a sister with SSA, and the wife has no family history for SSA. Neither have been tested for SS-trait (SST). The disease occurs in 1 in 576 live born African-American children. Calculate this couple’s risk of delivering a baby with SSA. Hint: The square root of 576 = 24

example 3 autosomal recessive familial case2
Example 3: autosomal recessive familial case
  • Calculate wife’s SST carrier risk using Hardy-Weinberg equilibrium calculation:
  • q2 = 1/576
  • So, q = 1/24
  • p+q=1 so: p+1/24=1 so: p=23/24
  • Carrier frequency (2pq) = 2 x 1/24 x 23/24 = approx 1/12
  • Couple’s risk of SSA = 2/3 x 1/12 /1/4 = 2/144 = 1/72

http://www.medschool.lsuhsc.edu/ob_gyn/study_guide/D%20Basic%20genetics%20review.doc

references
References
  • Strachan and Read chapter 3
  • http://www.medschool.lsuhsc.edu/ob_gyn/study_guide/D%20Basic%20genetics%20review.doc