“Finally,” Dr. Ciletti began, “let’s talk about cystic fibrosis. Now I mentioned that it is probably not something to worry about since neither of you has it in your family history, but there is a way to figure out the odds of being a carrier even without a past family history. Remember that in the case of a recessive autosomal disease like CF, for the disease to show up unexpectedly in your offspring both you and Greg would have to be carriers. We can estimate the probability of each of you being carriers by looking at the population as a whole.”
“You mean all the people on earth?” Olga asked.
“No. For purposes of genetics you each belong to different populations,” Dr. Ciletti began. “Now Olga, you’re of European descent, correct?”
“Yes, Swedish and German.”
“And obviously Caucasian. Now I can look up the carrier frequency, that is, the fraction of people in your population group that carry the most common cystic fibrosis allele. As it happens, one of every twenty-three Caucasians of European descent carries a recessive allele for CF.”
“That doesn’t sound very encouraging,” Olga interjected. “I have a 1 in 23 chance of having a child with cystic fibrosis.”
“Not at all. You just have a 1 in 23 chance of carrying the CF gene.” Dr. Ciletti replied. “Now Greg is Asian American and within his population group the carrier frequency is 1 out of 180. Making the odds even longer is the fact that if you are a carrier you have only a 50-50 chance of passing on your disease causing allele. So the chance of you two producing a baby with CF is actually 1/23 x 1/180 x ½ x ½ or 1 out of 16,560. So, just how big a family were you planning to have?”
“But wait,” said Greg. “If a carrier is someone who doesn’t display any of the features of a disease, how can you know how many carriers are in a population?”
“Good question, Greg. As an old professor of mine once said, ‘It all comes down to minding your P’s and Q’s.’ In a large population, the carrier frequency can be estimated by looking at the number of persons with the disease and then doing a little algebra. There are two equations we need to remember. The first describes all the alleles in the population and it just says that P + q = 1. In other words, of all the alleles in the population, a percentage of them are the healthy version, which we can call P. So if 65% of the alleles in a population are healthy, then P must be .65. The rest of the alleles must be the disease causing form, or q. If P is .65, then q must be .35, so that P + q = 1.
“But how do you know the percentage of q alleles in a population?” asked Olga. “The only people you can really identify are the people with the disease.”
“Exactly, and that brings us to the second equation we need to look at.”
Originally published at http://www.sciencecases.org/sickness_and_health/sickness_and_health5.asp
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