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?
In this lesson: Solve X-linked problems, including an independently assorting autosomal locus.
About 8 min
The key ideaWrite 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 in this model. 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.
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.
Is this true? "A father passes his X-linked allele directly to every son."
In the usual XX/XY model, sons receive the father's Y, while daughters receive his X.