Lesson 4 of 7 / Inheritance and genetic problems
Sex linkage and conditional probability
Is the answer a fraction of sons or a fraction of all offspring?
I can solve X-linked problems, including an independently assorting autosomal locus.
I can use genetic terminology, including locus and linkage.Syllabus
Syllabus 9477, Core 2(u). Use genetic terminology, including locus and linkage.
I can solve dihybrid problems involving dominance, codominance, multiple alleles, sex linkage, autosomal linkage and epistasis.Syllabus
Syllabus 9477, Core 2(x). Solve dihybrid problems involving dominance, codominance, multiple alleles, sex linkage, autosomal linkage and epistasis.
About 8 min
Make a guess. You are not marked.
A mother carries a recessive X-linked allele; the father is unaffected. What fraction of all their children are affected sons?
Show the answer
1/4 of all children.
Half of children are sons, and half of sons get the mother's affected X: 1/2 x 1/2 = 1/4.
The key idea
Write the allele on its sex chromosome and keep the probability denominator explicit.
Build from gametes
Separate all offspring from sons only
X^R X^r Aa x X^R Y aa
8 of 8 equally likely combinations are shown: probability 8/8.
Read every combination as text
- XR A with XR a gives XRXR Aa: Daughter
- XR A with Y a gives XRY Aa: Other son
- XR a with XR a gives XRXR aa: Daughter
- XR a with Y a gives XRY aa: Other son
- Xr A with XR a gives XRXr Aa: Daughter
- Xr A with Y a gives XrY Aa: Other son
- Xr a with XR a gives XRXr aa: Daughter
- Xr a with Y a gives XrY aa: Affected son, aa
Green = selected class. Each locus segregates normally; the two loci assort independently and offspring classes have equal viability in this model. An underscore means either allele can fill that position. IA, IB and IO name ABO alleles. XR and Xr mean an X chromosome bearing R or r; Y is a chromosome, not a recessive allele.
Explanation
In the usual XX/XY inheritance model, an X-linked locus can have two alleles in an XX individual but only one copy in an XY individual if the corresponding Y region lacks that gene. A recessive X-linked allele can therefore be expressed in an XY individual without a second recessive copy.
Write X^R and X^r to keep the allele attached to the X chromosome; do not write Y^R unless the problem specifically includes that locus on Y. For X^R X^r x X^R Y, daughters receive paternal X^R and sons receive paternal Y. Half the sons are expected to receive maternal X^r.
The probability of an affected son among all offspring is 1/2 for a son multiplied by 1/2 for X^r, giving 1/4. Among sons only, the probability is 1/2. These are different questions, not competing answers.
An independent autosomal trait can be combined with the sex-linked result. If Aa x aa gives aa with probability 1/2, the probability of an affected son who is also aa is 1/2 x 1/2 x 1/2 = 1/8 of all offspring. Always state assumptions about independence and equal gamete probabilities.
Exam questions often give a pedigree: a family tree with squares for males, circles for females, shaded symbols for affected people and half-shaded or dotted symbols for carriers. Read it with key individuals, not ratios, because families are small. Two unaffected parents with an affected child show that the allele is recessive; two affected parents with an unaffected child show that it is dominant. Then test X-linkage. An affected daughter of an unaffected father rules out X-linked recessive, because she must receive an affected X from him. Male-to-male transmission rules out any X-linked pattern, because a father gives his son a Y. If mostly males are affected through unaffected carrier mothers, X-linked recessive fits best. To find a carrier probability, use what the pedigree shows: an unaffected child of two Aa parents has a 2/3 chance of being Aa, because the aa outcome is already excluded.
Step by step
- 1
Write chromosome-labelled alleles
Keep X^R, X^r and Y distinct.
- 2
Separate offspring categories
Follow paternal X or Y contribution.
- 3
State the denominator
Multiply the sex probability only when considering all offspring.
Worked example
Work through the evidence
For X^R X^r x X^R Y, what fraction of sons is affected and what fraction of all offspring is affected sons?
One way to explain it
Half of sons are affected; affected sons are one quarter of all offspring under the stated simple model.
Why this answer works
- The conditional group of sons is already selected in the first question.
- The second question includes the probability of being a son.
Watch out for this
A student says: "A father passes his X-linked allele directly to every son." What is wrong with this?
Show the answer
In the usual XX/XY model, sons receive the father's Y, while daughters receive his X.
Check your understanding
P(affected | son) = 1/2 and P(son) = 1/2. What is P(affected son)?
Show the answer
1/4
1/2 x 1/2 = 1/4 of all offspring.
Exam-style questions
Check your understanding
In a pedigree, two unaffected parents have an affected daughter and an unaffected son. Which mode of inheritance fits this family best?
Show the answer
Autosomal recessive
Unaffected parents with an affected child show the allele is recessive. An affected daughter of an unaffected father rules out X-linked recessive, so it is autosomal.
Check your understanding
Two parents are both carriers (Aa) of an autosomal recessive condition. Their unaffected daughter is shown in the pedigree. What is the probability that she is a carrier?
Show the answer
2/3
Being unaffected excludes aa, leaving AA, Aa and aA in equal shares. Two of these three are carriers.
Quick recall
Is the answer a fraction of sons or a fraction of all offspring?