Consider the accompanying pedigree of a rare autosomal...

Consider the accompanying pedigree of a rare autosomal recessive disease, PKU. 1 ? II IV a. List the genotypes of as many of the family members as possible. b. If persons $A$ and $B$ marry, what is the probability that their first child will have PKU? c. If their first child is normal, what is the probability that their second child will have PKU? d. If their first child has the disease, what is the probability that their second child will be unaffected? (Assume that all people marrying into the pedigree lack the abnormal allele.)

Consider the accompanying pedigree of a rare autosomal recessive disease, PKU.
1
?
II
IV
a. List the genotypes of as many of the family members as possible.
b. If persons $A$ and $B$ marry, what is the probability that their first child will have PKU?
c. If their first child is normal, what is the probability that their second child will have PKU?
d. If their first child has the disease, what is the probability that their second child will be unaffected? (Assume that all people marrying into the pedigree lack the abnormal allele.)

Key Concepts

Genotype Inference

This concept involves deducing the possible genotypes of individuals by analyzing their phenotypes and the patterns of trait transmission in a family. When certain individuals display the trait, their genotype is inferred as homozygous recessive, while unaffected individuals might be either carriers or completely free of the allele, depending on their family history.

Pedigree Analysis

This is a method used to study the pattern of inheritance of traits across generations in a family. It involves analyzing family trees to infer the genotype of individuals based on their phenotypic expression of a trait, particularly when the trait is governed by a clear mode of inheritance.

Autosomal Recessive Inheritance

In autosomal recessive inheritance, an individual must inherit two copies of the mutant allele (one from each parent) to express the disease. Carriers, who possess only one mutant allele, are typically unaffected but can pass the allele to their offspring, influencing the probability of the disease appearing in a pedigree.

Probability Calculations in Genetics

Using mathematical tools like Punnett squares and probability rules, one can predict the likelihood of offspring inheriting certain genotypes and phenotypes. This involves understanding basic probability concepts such as independent events, multiplication rule, and addition rule within the context of genetic crosses.

Conditional Probability

Conditional probability is used in genetic calculations when additional information is known about the outcome, such as when an offspring is known to be unaffected. It adjusts the probability estimates for future events based on previous outcomes, thereby refining risk predictions within pedigrees.

Transcript

00:01 I rarely start questions or start answers with the pedigree already drawn or much work shown, but this is an elaborate pedigree, and i didn't want to waste a lot of time setting it up.

00:12 So what i've done is recopied the pedigree from the book, and then i've shown you what the probable genotypes of different individuals are.

00:21 And you can look at that in your leisure.

00:23 But we're interested here is a and b.

00:26 And you notice that when we get here to the parents of a and b, things start together.

00:30 Interesting.

00:31 So we're interested in trying to figure out what the probability is that a and b, we're carrying the p -ku allele.

00:39 We don't know that much about some of these individuals as much as we'd like.

00:45 But for example, this individual, a's father, right, had parents who almost certainly the father was big p, big p, and the mother would have been heterozygous, big p, little p.

00:57 So the question is, what's the probability that this person is big p, little p? well, he certainly got a big p from his father.

01:07 We don't know if he got a big p or a little b from his mother.

01:10 So there's a 50 % chance that he's big p, little p.

01:14 All right.

01:15 So when we come to a then, we can ask the same question.

01:20 What's the probability that this person is big p, little p? now, he had to have gotten a big p from his mother.

01:30 People coming from the outside won't have the disorder.

01:33 And so what's the probability that he will have the little p allel? well, there's a 50 % chance the father has it.

01:40 And if the father has it, there's a 50 % chance he would pick it up.

01:43 So the probability that a is big p, little p, is a quarter.

01:49 So a probability is one quarter that he is big p, little p, little, p.

01:58 For b, it's a somewhat similar situation.

02:04 There's a two -thirds chance that b's mother is big p, little p.

02:10 Now, we know she's not little p, little p, because she doesn't have the disorder.

02:13 So there's a one -third chance she's just homozygous dominant.

02:17 There's a two -thirds chance that she is heterozygous.

02:22 So for b, we're going to ask the probability, what's the probability? that she will inherit the little p allele.

02:35 Well, b is going to have to get the big p allel from her father.

02:40 That's this fellow right here.

02:42 And so the probability she's going to get the little p allele is simply going to be two thirds times one half, which is going to be two sixth or one third.

03:01 So there's a one third chance.

03:04 That b is big p, little p, and there's a quarter chance that a is big p, little t...

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