Sex Determination and Inherited Disorders
Use a basic XX by XY model to explain an approximately equal chromosome-outcome ratio. Apply autosomal recessive inheritance to carrier crosses and family relationships, distinguishing a probability from a guaranteed family outcome.
What a learner can do afterwards
- Draws an XX by XY cross and calculates probabilities under stated independent, equal-chance assumptions.
- Uses family relationships recorded in a pedigree to infer carrier status under an autosomal recessive model.
- Calculates the probability that two carriers have an affected child and explains why earlier children do not change it.
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In a basic human XX/XY model, eggs carry X and sperm carry X or Y. Treat the two sperm types as equally likely. XX is typically associated with female development and XY with male development. Other chromosome patterns and differences in sex development exist, so this model does not describe every person.
Use the square method from allele crosses. For XX by XY, combine each row entry with each column entry:
| Egg / sperm | X | Y |
|---|---|---|
| X | XX | XY |
| X | XX | XY |
Half the outcomes are XX and half are XY. Each box represents a possibility, not an actual child. Under the independent, equal-chance model, earlier births do not change the next birth's probabilities.
Autosomal means the gene is not on X or Y. Here, A is a working allele and a is an allele associated with a recessive condition. In this model, AA is unaffected and not a carrier, Aa is an unaffected carrier, and aa is affected. A carrier can pass a to a child. Appearance alone cannot identify a carrier.
Cystic fibrosis is inherited as an autosomal recessive condition. For these problems, its carriers are Aa. Practise the method with a different recessive cross: P is working and p is condition-associated.
| Allele | P | p |
|---|---|---|
| p | Pp | pp |
| p | Pp | pp |
For Pp by pp, Pp is an unaffected carrier and pp is affected. Two of four outcomes are affected: 1/2. Combine each row allele with each column allele, then count. Earlier children do not change parental genotypes or the next pregnancy's probabilities.
A pedigree records biological relationships and who is affected. For these problems, assume aa always causes the condition and there are no new mutations. An unaffected child of an affected aa parent must be Aa: the parent passes a, and the child must also have A. Two unaffected parents of an affected child must both be Aa. An unaffected sibling of an affected child could be AA or Aa.
For independent events, multiply probabilities to find the chance of one specified sequence. With equal male and female probabilities, two male outcomes in order have chance 0.5 times 0.5, or 0.25. For a longer specified sequence, include one factor of 0.5 for each birth. Earlier outcomes do not use up either possibility.
For an exact count, list the different orders that fit and add their probabilities. With two independent pregnancies, exactly one XX can occur as XX then XY or XY then XX. Each order has probability 1/4, so their total is 1/2. For more pregnancies, list all fitting orders. Multiply within each order, then add the fitting orders' probabilities.
State the model, combine parental entries and count possibilities. Carrier status needs inheritance evidence. Earlier independent outcomes do not change the next probability.
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Checking an inheritance prediction
Before calculating, identify the model. An XX by XY cross predicts half XX and half XY when the two sperm types are treated as equally likely. These chromosome combinations are typically associated with female and male development, respectively. Differences in chromosomes and sex development mean that the model does not describe every person.
A recessive-condition calculation asks a separate question. Using A for a working allele and a for a condition-associated allele, Aa parents can each pass A or a. Their combined possibilities are AA, Aa, Aa and aa. Only aa is affected in this model. The two Aa possibilities count separately because either parent can supply the a allele.
Family relationships sometimes identify a carrier. An affected aa parent passes a to every child. If a child is unaffected, that child must also have A and is therefore Aa. This inference assumes that aa always causes the condition and that no new mutation occurs. An unaffected child of two carriers is less certain: either AA or Aa is possible. Appearance does not distinguish them.
Probability describes possibilities, not a required family pattern. Four children of two carriers need not include exactly one affected child. Each pregnancy has its own one-quarter affected-child probability under the model. Real family risk may require genetic testing and condition-specific information.
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