12.8
Wahrscheinlichkeitsgesetze
Überblick
Die Wahrscheinlichkeit der Vererbung eines Merkmals kann mit Hilfe der Summen -und Produktregeln berechnet werden. Die Summenregel wird zur…
Die Summen- und Produktwahrscheinlichkeitsregeln werden verwendet, um die Wahrscheinlichkeit zu bestimmen, dass jemand ein Merkmal aufweist. Wenn beispielsweise der Stammbaum einer werdenden Frau eine Krankheit wie Biotinidase-Mangel aufweist, bestimmt die Wahrscheinlichkeit, dass sie und ihr Partner Träger des rezessiven Biotinidase-Mangel-Allels sind, das Risiko ihres Kindes, an dieser Störung zu leiden. Hier zeigt der Stammbaum der Frau einen betroffenen Bruder, aber nicht betroffene Eltern, die heterozygot sein müssen.
Ein Punnett-Quadrat zeigt, dass die Frau für das normale Allel homozygot sein könnte oder das Krankheits-Allel von ihrer Mutter oder ihrem Vater geerbt hat. Die homozygote rezessive Option wird abgezinst, da es zwei Möglichkeiten gibt, wie sie Trägerin werden kann. Beide mit einer Wahrscheinlichkeit von eins zu drei.
Die Summe ihrer Wahrscheinlichkeiten ist die Wahrscheinlichkeit, dass sie heterozygot ist, die Summenregel. Umgekehrt ist die Wahrscheinlichkeit des Vaters eins zu 120. Da dies die Wahrscheinlichkeit ist, dass eine zufällige Person heterozygot ist.
Beide werdenden Elternteile müssen Träger einer Wahrscheinlichkeit von zwei von drei und einer von 120 sein und das erkrankte Allel weitergeben, eine Wahrscheinlichkeit von einem von vier. Die Wahrscheinlichkeit, dass ihr Kind einen Biotinidase-Mangel hat, ist das Produkt dieser Wahrscheinlichkeiten. Ungefähr 0,14 % der Produktregel.
Dies ist die berechnete theoretische Wahrscheinlichkeit. Einige Paare haben jedoch möglicherweise nur Kinder mit Biotinidase-Mangel. Und beobachtete empirische Wahrscheinlichkeit von 100 %. Wenn jedoch viele Stammbäume untersucht würden, stimmen diese Wahrscheinlichkeiten überein.
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Q1: What is the sum rule of probability and when is it used in genetics?
The sum rule calculates the probability of mutually exclusive events by adding their individual probabilities. In genetics, it determines the likelihood of a person inheriting one of several possible genotypes. For example, if a woman's parents are both heterozygous carriers, she has three possible genotypes with equal probabilities. Two result in being a carrier, so her carrier probability is 2/3 (1/3 + 1/3), calculated using the sum rule.
Q2: How does the product rule differ from the sum rule in probability calculations?
The product rule multiplies the probabilities of multiple independent events to find their combined likelihood, while the sum rule adds probabilities of mutually exclusive events. For inheritance, the product rule applies when both parents must be carriers and both must pass disease alleles to their child. If the mother's carrier probability is 2/3, the father's is 1/120, and the inheritance probability is 1/4, the child's risk is (2/3) × (1/120) × (1/4) ≈ 0.14%.
Q3: What is the difference between theoretical and empirical probability?
Theoretical probability is calculated before events occur, predicting the likelihood of outcomes. Empirical probability is based on actual observations after events have happened. A child's calculated 0.14% risk of biotinidase deficiency is theoretical, but if that child actually inherits the disease, the empirical probability becomes 100%. As more pedigrees are studied, theoretical and empirical probabilities converge and align.
Q4: How do probability laws improve genetic analysis compared to Punnett squares?
Probability laws enable efficient calculations for complex inheritance scenarios where Punnett squares become impractical. A Punnett square for three traits requires 64 possible crosses, making it cumbersome. Probability laws streamline these calculations by using the sum and product rules, allowing geneticists to quickly determine inheritance risks for autosomal recessive diseases like biotinidase deficiency without exhaustive grid construction.
Q5: Why is determining parental carrier status essential for calculating child disease risk?
A child's risk of inheriting an autosomal recessive disease depends on whether both parents carry the disease allele. If either parent is not a carrier, the child cannot inherit the disease. For biotinidase deficiency, the mother's carrier probability (2/3) and father's carrier probability (1/120) are multiplied with the inheritance probability (1/4) to calculate the child's overall risk, making parental status critical to accurate risk assessment.
Q6: What does it mean when both parents are heterozygous carriers of a recessive allele?
Heterozygous carriers possess one normal allele and one disease allele but do not express the disease phenotype. When both parents are heterozygous (Bb genotype), each has a 50% chance of passing the disease allele to their child. If both parents pass their disease alleles, the child inherits the homozygous recessive genotype (bb) and expresses the disease, such as biotinidase deficiency.
Q7: How does a pedigree help determine whether someone is likely to be a carrier?
A pedigree shows family history of disease, revealing which relatives are affected or carriers. If an unaffected woman has an affected brother but unaffected parents, both parents must be heterozygous carriers. Using the pedigree and sum rule, the woman's probability of being a carrier can be calculated. Her pedigree eliminates the homozygous recessive genotype, leaving two carrier possibilities out of three equally likely genotypes.