The diagram presented appears to be a classic case of an x-linked trait that manifests in hereditary diseases such as Tay-Sachs Disease. For inherited diseases that occur as a result of a mutation on the X chromosome, most commonly, male members of the relevant population will exhibit the disease far more common than the female ones. This is because of the double-X nature of the sex chromosomes in female carriers of the disease means that there is usually a “backup copy” of the needed genetic information, so the body is able to simply override the presence of the mutated and dysfunctional or nonfunctional alleles. Only if the female individual happens to have inherited two faulty X chromosomes for the same disease or for diseases similar enough in their affected areas that the genetic blueprint is still erratic does the disease manifest. Indeed, this is exactly the pattern seen in the diagram; of those with signs and symptoms of the disease, four out of five are male. However, under this hypothesis, many of the female members of the family are carriers of the disease and likely candidates for gene therapy.
The male members of this group only have a fifty percent chance of inheriting the “bad” X chromosome from their mother, if she is a carrier. Indeed, statistics have been quite tidy in this case and have given the disease to half the male descendants of a female carrier and male person without the disease. In the case of a male individual with the disease reproducing with a female non-carrier, all the female offspring will be carriers, but all the male offspring will be disease-free since they have inherited the non-faulty Y chromosome from their male parent rather than the faulty X chromosome. Only female individuals can be carriers, so in the diagram, Martha, Leela, Donna, and Amy must all be carriers. The first three have children with the disease, so this is obvious. In the case of Amy, as stated above, the only way a female child could end up with the disease of this type is if both sides of the family brought the disease. As Amy does not have the disease, the faulty X chromosome is merely being carried. Both Liz and Sarah Jane may be carriers as well, but there is not enough information to determine this.