12.8
Leis de Probabilidade
Visão Geral
A probabilidade de herdar uma característica pode ser calculada usando as regras da soma e do produto. A regra da soma é usada para calcul…
A soma e as regras de probabilidade do produto são usados para determinar a probabilidade de alguém exibir um traço. Por exemplo, se uma árvore da família de uma mulher gestante demonstrarem uma doença como a deficiência de biotinidase, a probabilidade de ela ou do seu parceiro de ser portadores do alelo recessivo de deficiência da biotinidase determina o risco da criança de ter essa desordem. Aqui a linhagem da mulher mostra um irmão afetado mas pais não afetados que devem ser heterozigotos.
Um quadrado Punnett mostra que a mulher poderia ser homozigótica para o alelo normal ou ter herdado o alelo doente de sua mãe ou pai. A opção homozigoto recessiva é descontada. Uma vez que existem duas maneiras que ela poderia ser uma portadora, ambas com probabilidades de um em três, a soma das suas probabilidades é a probabilidade que ela seja heterozigota, a regra da soma.
Por outro lado, no pai a probabilidade é de um em 120 pois esta é a probabilidade de um indivíduo aleatório ser heterozigoto. Ambos os futuros pais devem ser portadores, probabilidades de dois de três e um de 120 e para passar adiante o alelo doente, uma probabilidade de um em quatro então a probabilidade do seu filho ter deficiência de biotinidase é o produto dessas probabilidades, aproximadamente 0, 14%a regra do produto. Esta é a probabilidade teórica calculada.
No entanto, alguns casais podem ter apenas filhos com Deficiência de Biotinidase e se observado a probabilidade empírica de 100%No entanto, se muitos pedigrees fossem estudados, essas probabilidades corresponderiam.
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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.