Genetics of X-Linked Inheritance
Many human traits (and many classic textbook traits) are X-linked, meaning the gene is located on the X chromosome.
Because males are typically XY and females are typically XX, the inheritance logic is sex-specific:
sons receive their X from the mother and their Y from the father, while daughters receive one X from each parent.
This calculator focuses on a single X-linked gene with two alleles:
XA and Xa.
The meaning of A vs a depends on the selected pattern:
in X-linked recessive, the a allele causes the trait when present without a dominant normal allele,
while in X-linked dominant, the A allele causes the trait even if only one copy is present in a female.
Key assumptions used in this calculator
The model here is the standard introductory genetics model. It assumes:
random segregation of parental X chromosomes into gametes, no selection (all zygotes survive equally),
no new mutation, and a single-gene trait with either simple dominance (dominant mode) or simple recessivity (recessive mode).
The calculator also assumes a sex ratio (default P(boy) = 0.50, P(girl) = 0.50) unless you change it.
Genotype notation
Female genotypes are written as XAXA, XAXa, or XaXa.
Male genotypes are written as XAY or XaY.
How sons and daughters inherit X chromosomes
The inheritance split is the heart of X-linked probability:
a son always receives Y from the father and the X from the mother,
so the father’s X allele does not affect the son’s genotype in an X-linked trait.
A daughter always receives the father’s X, so the father’s X allele strongly affects daughter outcomes.
X-linked recessive (most common introductory case)
For an X-linked recessive trait, assume a is the recessive allele that causes the condition:
males are affected if they inherit Xa because they have only one X chromosome,
while females must inherit Xa from both parents to be affected.
In this model:
XAXA = unaffected female,
XAXa = carrier female (typically unaffected),
XaXa = affected female,
XAY = unaffected male,
XaY = affected male.
X-linked dominant
For an X-linked dominant trait, assume A is the dominant allele that causes the trait:
a male is affected if he inherits XA,
and a female is affected if she has at least one XA.
In dominant mode, the calculator reports the probability a daughter is heterozygous (one of each allele),
which is often the more relevant “special” class than the recessive concept of a carrier.
Step-by-step probability logic
The calculator uses the same probability structure for both modes:
first determine the mother’s X gametes, then combine with the father’s sex-specific contribution.
If the mother is XAXa, she produces
XA gametes with probability 0.5 and Xa gametes with probability 0.5.
If she is homozygous, she produces only one gamete type with probability 1.
Let P(XA from mother) be the probability that the mother contributes XA in an egg,
and P(Xa from mother) be the probability she contributes Xa.
These satisfy:
\[
P(X^{A}\text{ from mother}) + P(X^{a}\text{ from mother}) = 1
\]
Probability of an affected son
Because sons receive Y from the father, the son’s X allele comes only from the mother.
Therefore, the affected-son probability depends only on the mother’s gametes and on which allele causes the trait.
For X-linked recessive (allele a causes the condition in males):
\[
P(\text{son affected}) = P(X^{a}\text{ from mother})
\]
For X-linked dominant (allele A causes the condition in males):
\[
P(\text{son affected}) = P(X^{A}\text{ from mother})
\]
Probability of affected daughters and carrier / heterozygous daughters
Daughters always inherit the father’s X chromosome, so the father’s genotype changes the daughter distribution.
The daughter genotype is formed by combining the father’s X allele with one of the mother’s X gametes.
In X-linked recessive, a daughter is affected only if she is XaXa,
and she is a carrier if she is XAXa.
In X-linked dominant, a daughter is affected if she has at least one XA,
and the calculator reports the probability of a heterozygous daughter (XAXa),
which is often a meaningful clinical/genetic class.
Overall probability of an affected child
If you assume a fixed sex ratio, you can combine the sex-specific probabilities using the law of total probability.
Let P(boy) be the probability a child is a boy and P(girl) = 1 - P(boy).
Then:
\[
P(\text{affected child}) =
P(\text{boy})\cdot P(\text{son affected}) + P(\text{girl})\cdot P(\text{daughter affected})
\]
Optional extension: probability of at least one affected child in n births
If each child is an independent birth event and P(affected child) stays the same from birth to birth,
the probability of at least one affected child among n children is found using the complement rule:
\[
P(\ge 1\ \text{affected}) = 1 - \left(1 - P(\text{affected child})\right)^{n}
\]
How to read the Punnett grid and bars
The Punnett grid in this calculator is labeled to match X-linked inheritance:
the left column corresponds to daughters (father contributes X) and the right column corresponds to sons (father contributes Y).
Within each cell, the calculator shows the genotype class and its probability,
and the stacked bars summarize the conditional outcome distribution for sons and for daughters.
Common interpretation tips
In X-linked recessive traits, a “carrier mother” (XAXa) often produces
50% affected sons if the father is unaffected, while daughters are typically unaffected but may be carriers.
In X-linked dominant traits, an affected father (XAY) passes the trait to all daughters (who inherit his X),
and to none of his sons (who inherit his Y), which is a classic diagnostic pattern.
