Name: inheritance risk with sum and product rules
Uploaded: 2019-03-11T09:21:16.000Z
Duration: 1 min 49 s
Channel: JoVE

K12 Standards

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North Carolina K-12 Science Standard Course of Study

9-12

Biology

heredity-inheritance-and-variation-of-traits

Heredity- Inheritance and Variation of Traits

LS.Bio.7.2

Probability Laws

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.

Griffiths, Anthony J.F., Jeffrey H. Miller, David T. Suzuki, Richard C. Lewontin und William M. Gelbart. 2000. "Verwendung genetischer Verhältnisse." In einer Einführung in die genetische Analyse. 7. Auflage. New York: W. H. Freeman und Company. [<a href="https://www.ncbi.nlm.nih.gov/books/NBK21812/" target="__blank">Quelltext</a>]

wahrscheinlichkeitsgesetze

<h4>Überblick</h4>
 
 Die Wahrscheinlichkeit der Vererbung eines Merkmals kann mit Hilfe der Summen -und Produktregeln berechnet werden. Die Summenregel wird zur Berechnung der Wahrscheinlichkeit sich gegenseitig ausschließender Ereignisse verwendet. Die Produktregel sagt die Wahrscheinlichkeit mehrerer unabhängiger Ereignisse voraus. Diese Wahrscheinlichkeitsregeln bestimmen die theoretische Wahrscheinlichkeit. Es handelt sich um die Wahrscheinlichkeit, dass Ereignisse eintreten, bevor sie geschehen. Die empirische Wahrscheinlichkeit dagegen wird auf der Basis bereits eingetretener Ereignisse errechnet.
 
 <h4>Die Summen- und Produktregeln werden zur Berechnung von Erbwahrscheinlichkeiten genutzt</h4>
 
 Obwohl Punnett-Quadrate nützlich sind, um die Vererbung von ein oder zwei Merkmalen zu visualisieren, ist ihre Nutzung in komplexen Szenarien umständlich. Ein Punnett-Quadrat mit nur drei Eigenschaften enthält bereits 64 mögliche Kreuzungen. Wahrscheinlichkeitsgesetze ermöglichen eine viel effizientere Berechnung der Erbwahrscheinlichkeiten von Merkmalen.
 
 Zum Beispiel möchte eine schwangere Frau das Risiko ihres Kindes verstehen einen Biotinidasemangel (BTD) zu erben. Dabei handelt es sich um eine autosomal rezessive Krankheit, die in ihrer Familie vorkommt. Säuglinge mit unbehandelter BTD haben Entwicklungsverzögerungen, einen schlechten Muskeltonus, Hautausschläge und Haarausfall auf. Schwere Fälle sind u.a. mit Krampfanfällen und Verlust von Seh- und Hörvermögen verbunden. Weder die Frau noch ihre Eltern haben BTD, ihr Bruder ist jedoch betroffen. Beide Elternteile müssen also eine kausale Genvariante haben (d.h. beide Eltern sind heterozygot oder Träger).
 
 Die Wahrscheinlichkeit, dass das Kind dieser Frau BTD erbt, hängt davon ab, ob die Frau Trägerin ist und ein kausales Allel besitzt. Da BTD autosomal rezessiv ist und sie nicht betroffen ist, kann sie nicht zwei kausale Allele haben. Sie kann jedoch ein kausales Allel tragen, das auf ihr Kind übertragen werden könnte.
 
 Der erste Schritt zur Feststellung des Risikos für das Kinds ist es, die Wahrscheinlichkeit zu bestimmen, dass die Mutter ein Träger ist. Dies wird durch die Summenregel der Wahrscheinlichkeit erreicht. Die Summenregel besagt, dass die Wahrscheinlichkeit von sich gegenseitig ausschließenden Ereignissen die Summe ihrer Einzelwahrscheinlichkeiten ist. In diesem Fall sind die sich gegenseitig ausschließenden Ereignisse, die möglichen Kombination der elterlichen Allele, die die schwangere Frau geerbt haben könnte. Da beide Elternteile heterozygot sind (Bb Genotyp), hat sie einen von vier möglichen Genotypen: väterlich B und mütterlich B (BB), väterlich B und mütterlich b (Bb), mütterlich B und väterlich b (Bb), oder väterlich b und mütterlich b (bb). Da sie nicht BTD hat, kann der bb Genotyp ausgeschlossen werden. Es gibt also drei mögliche Genotypen mit jeweils einer gleichen Wahrscheinlichkeit von 1/3, und zwei davon resultieren in einen Träger (Bb). Nach der Summenregel beträgt ihre Wahrscheinlichkeit ein Träger zu sein 2/3 (1/3 + 1/3).
 
 Ein weiterer wichtiger Faktor in der Berechnung der Wahrscheinlichkeit, ob das Kind BTD entwickelt oder nicht, ist die Wahrscheinlichkeit des Vaters ein Träger zu sein. Hier kommt die Produktregel ins Spiel. Die Produktregel besagt, dass die Wahrscheinlichkeit mehrerer unabhängiger Ereignisse das Produkt der Ereignisse (individuelle Wahrscheinlichkeiten) ist. Wenn die Mutter ein Träger ist, hat das keinen Einfluss darauf, ob der Vater ein Träger ist. Es sind also unabhängige Ereignisse.
 
 Damit das Kind BTD erbt, müssen mehrere unabhängige Ereignisse auftreten. Zunächst muss die Mutter ein Träger sein (2/3 Wahrscheinlichkeit). Zweitens muss der Vater auch ein Träger sein. Wenn der Vater nicht betroffen ist und keine familiäre Vorgeschichte von BTD hat, ist die Wahrscheinlichkeit, dass er Träger ist gleichwertig mit der der allgemeinen Bevölkerung (1/120). Drittens muss das Kind das rezessive Allel von beiden Eltern erben (1/4 Wahrscheinlichkeit, wenn beide Eltern Träger sind). Gemäß der Produktregel ist das Risiko des Kindes, BTD zu erben, das Produkt jeder dieser Wahrscheinlichkeiten: (2/3) x (1/120) x (1/4) = ~0.0014, oder etwa 0.14%.
 
 <h4>Theoretische und empirische Wahrscheinlichkeiten werden jeweils vor und nach Ereignissen berechnet</h4>
 
 Das Risiko des Kindes BTD mit 0.14 % zu erben, ist eine vor der Geburt berechnete Vorhersage, also eine theoretische Wahrscheinlichkeit. Es ist jedoch möglich, dass das Kind und seine Geschwister BTD erben werden, was eine empirische Wahrscheinlichkeit von 100% darstellt. Im Gegensatz zu theoretischen Wahrscheinlichkeiten, die vor dem Eintreten der Ereignisse berechnet werden, stützen sich die empirischen Wahrscheinlichkeiten auf Beobachtungen. Bei der Analyse von individuellen Stammbäumen können die theoretischen und empirischen Wahrscheinlichkeiten sehr unterschiedlich sein. Je mehr Stammbäume jedoch analysiert werden, desto mehr gleichen sich theoretische und empirische Wahrscheinlichkeiten an.

Wahrscheinlichkeitsgesetze

Überblick

Die Wahrscheinlichkeit, ein Merkmal zu erben, kann mit Hilfe der Summen- und Produktregeln berechnet werden. Die Summenregel wird verwendet, um die Wahrscheinlichkeit von ...

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KERNBEGRIFFE UND KONZEPTE

inheritance risk with sum and product rules

Inheritance risk can be calculated with the sum rule and the product rule. The sum rule applies to mutually exclusive events, or events that cannot happen at the same time. The product rule applies to independent events, or events that do not affect one another. These rules describe theoretical probability, which is the chance of an event before it happens. Empirical probability is different because it is based on events that have already occurred.

These probability rules are useful in genetics because Punnett squares can become too large for complex crosses. A Punnett square for three traits already has 64 possible crosses. Probability laws make it easier to estimate how a trait may be inherited. They can also be used to follow the chance of an autosomal recessive disease such as biotinidase deficiency, or BTD.

BTD can cause developmental delays, poor muscle tone, skin rashes, and hair loss if it is not treated. Severe cases can also involve seizures and loss of vision and hearing. In the example from the transcript, a pregnant woman is trying to estimate her child’s risk because her brother has BTD. Since her parents do not have the disease but have an affected child, both parents must be carriers, which means they are heterozygotes with one causal gene variant.

The first step is to find the woman’s chance of being a carrier. Because BTD is autosomal recessive and she is unaffected, she cannot have two causal alleles. Her possible genotypes from two carrier parents are BB, Bb, Bb, or bb. The bb genotype can be ruled out, so three outcomes remain, each with a probability of 1/3. Two of those outcomes make her a carrier, so the sum rule gives her a carrier probability of 2/3.

Next, the father’s carrier chance must be considered. If the father is unaffected and has no family history of BTD, his carrier probability is treated as the same as that of the general population, or 1/120. This step uses the product rule because the mother’s carrier status does not change the father’s carrier status. The child must inherit the recessive allele from both parents, which has a probability of 1/4 if both parents are carriers. Multiplying these values gives a BTD risk of about 0.14%.

That 0.14% estimate is a theoretical probability because it is calculated before birth. If a child or siblings actually inherit BTD, that is an empirical result because it is based on observation after the event. When only one pedigree is examined, theoretical and empirical probability may differ a lot. As more pedigrees are studied, the two values tend to become closer.

Inheritance Risk with Sum and Product Rules

genetic lingo

Genotype, Phenotype, and Inheritance

Genotype, phenotype, and inheritance help explain how traits and disease risk are passed from parents to offspring. In diploid organisms, including humans, most other animals, and many plants, somatic cells carry a duplicate set of chromosomes. These chromosome pairs are homologous, with similar length, centromere position, and gene locations. Diploid organisms inherit two versions of each gene, one from each parent. These versions are called alleles, and they sit at the same relative locus,...

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Gregor Mendel used pea plants to study how traits are passed from parents to offspring. His breeding experiments in the 1850s and 1860s showed that inheritance follows clear patterns. He crossed true-breeding plants that differed in one trait and found that dominant traits can hide recessive traits. Mendel focused on seven pea plant traits, and each trait had two forms controlled by a single gene locus. He noticed that true-breeding plants always produced offspring with the same phenotype, or...

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Mendel's Law of Independent Assortment

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law of segregation

Mendel’s Pea Cross Ratios

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probability laws

Inheritance risk can be calculated with the sum rule and the product rule. The sum rule applies to mutually exclusive events, or events that cannot happen at the same time. The product rule applies to independent events, or events that do not affect one another. These rules describe theoretical probability, which is the chance of an event before it happens. Empirical probability is different because it is based on events that have already occurred. These probability rules are useful in...

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epistasis

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x-linked traits

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key terms and concepts

Learn how the sum rule and product rule help estimate inherited trait risk, including carrier probability and autosomal recessive disease examples like BTD.

Inheritance Risk with Sum and Product Rules | JoVE K12

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Minnesota Academic Standards in Science

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Heredity: Inheritance and Variation of Traits

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Overview

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Inheritance Risk with Sum and Product Rules

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