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I had a homework question that I could not figure out.

It states:

A woman has cystic fibrosis in her family and did not want to have a child that suffered from the disease. She and her spouse went for genetic testing and counselling. She tested positive as a carrier and her spouse tested negative, and their first child was born with cystic fibrosis. Explain how this could happen.

This doesn't make sense because the punnet square would be:

$$ \begin{array}{c|c|c} & A & A \\ \hline A & AA & AA \\ \hline a & Aa & Aa \end{array} $$

This says there are no two recessive alleles which can cause cystic fibrosis.

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Well, if the question is perfectly correct, than as per my opinion the only alternative left is MUTATION. –  Shefali Jan 31 at 2:17

2 Answers 2

If really cystic fibrose is expressed only in homozygotes, then here are some possible explanations:

  • Mutation
    • very improbable
  • Autofecundation
    • very improbable
  • False Negative when testing the father
    • Because of the test False Negative Rate. @kmm made a very interesting comment below. He said that according to this article 75% of the mutations coding for disease correspond to one pattern (3 base pair deletion). The other 25% of the mutations coding for disease might not be detected in the standard test. If so, it is very likely that a the test conducting on the father was a false negative. It would be worth further investigate the test that are usually performed to confirm this.
    • Because of human error. The laboratory operator might accidentally switch two samples or accidentally introduce stranger DNA before PCR (assuming the test is performed through sequencing)
    • I have no idea concerning the probability for such thing to occur!
  • trisomy
    • The assumes that a trisomic that have two recessive allele coding for disease and on dominant allele coding for health yield to a individual expressing the disease!
    • The gene for cystic fibrose is on chromosom 7. Trisomy 7 is extremely rare if I'm not mistaken.
  • The father is not the father!
    • According to different studies between 5% and 20% of the people are not fathered by the man they think is their dad.
    • According to this source the frequency of the disease is 1/2500 in UK. Assuming Hardy-Weinberg equilibrium the frequency of the allele coding for disease should be $p=0.02$.
    • The probability that the baby comes from another man and that the baby express the disease is $$a \cdot \left(\frac{2\cdot p\cdot (1-p)}{4} + \frac{p^2}{2}\right)$$, where $a$ is the probability that the baby was fathered by another man (let's say 10%) and $p$ is the frequency of the allele coding for the disease (0.02). The division by 2 and 4 are due to the probability that the (real) father and the mother transmit both the alleles coding for the disease. This probability equals $$0.1 \cdot \left(\frac{2\cdot 0.2\cdot (1-0.2)}{4} + \frac{0.2^2}{2}\right) = 0.01$$ This seems to be from far the most likely explanation! Note: this assumes that the mother is heterozygote (does not express the disease) otherwise, the probability would be 0.02.
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I would also add "human error" to the list, a person changing the outcome, e.g. by contaminating the sample or a spelling error while transcribing the result. This might be surprisingly likely - somebody overly tired, or having a bad day. –  jkadlubowska Jan 31 at 17:48
    
Yes, I kinda incorporated "human error" within the False Negative point. I'll make it more clear –  Remi.b Jan 31 at 23:18
    
It's probably the false negatives. According to ncbi.nlm.nih.gov/pubmed/2014829, 75% of carriers have the standard pattern. They are probably not routinely testing the other 25% (which might constitute lots of different patterns). –  kmm Feb 1 at 15:41
up vote -1 down vote accepted

I asked my Biology teacher and she said that the if the father is not a carrier, he must have the disease. So the father is aa.

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You should tell your teacher that's a terribly worded question then - "negative" definitely doesn't mean they have the disease! Not your error at all. –  Rory M Feb 2 at 22:10
    
The question came from the book we use, and she also said it was a bad question. –  user3175999 Feb 2 at 22:11
    
Well, this answer does not answer your question! It answers it assuming that the real meaning of the question was different than what was actually written! So, I am not quite sure this should be accepted as an answer and not flagged, although I agree that most likely your textbook did not expect you to perform probabilistic calculations and it actually was a very simple terribly poorly written question. –  Remi.b Feb 4 at 16:33
    
I copied the question right out of the book, and its only Grade 11 Biology. We didn't learn any calculations. –  user3175999 Feb 11 at 23:15

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