Subject: Risk Assessment - part 3
The next step is the calculation of risk as the genes pass from one generation in the pedigree to the next. This calculation must include both the sire's and the dam's contribution to the genotype of the offspring. To be affected the offspring must receive a defective gene from EACH parent. However, to be a carrier it must receive ONLY ONE defective gene, but it can come from either of the parents.If the sire is definitely affected, then it is certain (probability = 1) that he will pass on a defective gene to each offspring. If the sire is definitely a carrier, then there is a .5 (50%) probability that he will pass on a defective gene to the offspring. Similarly for the dam.
If the sire might be affected: designate this probability as Pa(sire), OR might be a carrier: designate this probability as Pc(sire),
Then the overall probability that he will pass on a defective gene to his offspring is Psire, where:
(a) Psire = Pa(sire) +.5 x Pc(sire)
since these events are mutually exclusive. Also,
(b) Pdam = Pa(dam) + .5 x Pc(dam)
The probability that the offspring is affected (it must get 2 defective genes to be affected, one from the sire AND the other from the dam) is
(1) Pa(offspring) = Psire x Pdam
since these events are independent.
The offspring can be a carrier by getting a normal gene from the sire and a defective gene from the dam or by getting a defective gene from the sire and a normal gene from the dam. The probability of getting a normal gene from the sire, i.e., NOT getting a defective gene from the sire is one minus the probability of getting a defective gene from the sire:
(1 - Psire)
and the probability of getting a normal gene from the dam is
(1 - Pdam)
The probability of getting a defective gene from the sire AND a normal gene from the dam is:
Psire x (1 - Pdam),
since these events are independent.
So the probability of getting one (and ONLY one) defective gene, which is the probability that the offspring is a carrier:
(2) Pc(offspring) = Psire x (1- Pdam) + Pdam x (1 - Psire)
Equations (a) and (b), and (1) and (2) are the risk transmission relationships that let us step through the pedigree one generation at a time calculating the risks for each dog.
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Jim Seltzer
Willowind Dalmatians
http://users.nbn.net/~jseltzer
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