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

K12 Standards

north-carolina-k-12-science-standard-course-of-study

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

[Instructeur] Les règles de probabilité de somme et produitservent à déterminer les chances qu'un individu présentun trait. 
Par exemple, si l'arbre généalogique d'une femme enceintemontre une maladie comme le déficit en biotinidasela probabilité qu'elle et son partenaire soient porteursd'une allèle récessive de cette maladiedétermine les risques de leur enfant d'avoir cette maladie. 
Ici, les gênes du femme montre un frère affligé maisdes parents non affectés qui doivent être hétérozygotes. 
L'échiquier de punett montre la possible homozygotiepour une allèle normal ou a héritéd'une allèle malade de sa mère ou son père. 
L'option homozygote récessive est écartéepuisqu'elle peut être porteuse de deux manière. 
Les deux avec 30 % de probabilité. 
La somme des probabilité sont les chancesqu'elle soit hétérozygote, la règle de la somme. 
Au contraire, la probabilité du père est de 1 sur 120. 
Puisque ce sont les probabilités qu'une personne moyennesoit hétérozygote. 
Les deux futur parents doivent être porteursune probabilité de 30 % et de 1 sur 120et passer l'allèle malade,une probabilité de 1 sur 4. 
Alors les chances que leurs enfants soit atteintest le produit de ces probabilité. 
Environ 0. 
14%,la règle du produit. 
C'est la probabilité théorie calculée. 
Mais certain couple n'ont que des enfantsavec la déficience biotinidase. 
Une probabilité empirique observée de 100%. 
Cependant, si de nombreux profils génétiques sont étudiésces probabilités ne correspondent pas.

Griffiths, Anthony J.F., Jeffrey H. Miller, David T. Suzuki, Richard C. Lewontin et William M. Gelbart. 2000. « Utilisation des ratios génétiques. » Dans Une introduction à l’analyse génétique. 7e éd. New York : W. H. Freeman et Cie. [<a href="https://www.ncbi.nlm.nih.gov/books/NBK21812/ » target="__blank">Source</a>]

lois de probabilité

<h4>Aperçu</h4>
 
 La probabilité d’hériter d’un trait peut être calculée à l’aide des règles de la somme et du produit. La règle de la somme est utilisée pour calculer la probabilité d’événements mutuellement exclusifs. La règle du produit prévoit la probabilité de plusieurs événements indépendants. Ces règles de probabilité déterminent la probabilité théorique — la probabilité que des événements aient lieu avant qu’ils ne se produisent. La probabilité empirique, en revanche, est calculée en fonction des événements qui se sont déjà produits.
 
 <h4>Les règles de la somme et du produit sont mises à profit pour calculer les probabilités de transmission</h4>
 
 Bien que les échiquiers de Punnett soient utiles pour visualiser la transmission d’un ou deux traits, ils deviennent encombrants lorsqu’ils sont appliqués à des cas de figure plus complexes. Un échiquier de Punnett affichant seulement trois traits contient 64 croisements possibles. Les lois sur les probabilités permettent des calculs beaucoup plus efficaces des probabilités de transmission des traits.
 
 Prenons l’exemple d’une femme enceinte qui veut comprendre le risque pour son enfant d’hériter d’un déficit en biotinidase (BTD), une maladie récessive autosomique qui affecte sa famille. Les nourrissons atteints de BTD non traités présentent des retards de développement, un faible tonus musculaire, des éruptions cutanées et une perte de cheveux. Les cas graves sont associés à des convulsions et à la perte de vision et d’audition, entre d’autres symptômes. Ni la femme ni ses parents ne sont atteints de BTD, mais son frère est affecté, ce qui signifie que les deux parents doivent avoir une variante du gène causal (c.-à-d. que les deux parents sont hétérozygotes, ou porteurs).
 
 La probabilité que l’enfant de la femme hérite de BTD dépend de si la femme est porteuse, possédant un allèle causal. Puisqu’un BTD est récessif autosomique et qu’elle n’est pas affectée, elle ne peut pas avoir deux allèles causals. Cependant, elle peut porter un allèle causal qui pourrait être transmis à son enfant.
 
 La première étape vers la détermination du risque pour l’enfant consiste à déterminer la probabilité que la mère soit porteuse. Ceci est réalisé en utilisant la règle de la somme de la probabilité. La règle de la somme stipule que la probabilité d’événements mutuellement exclusifs est la somme de leurs probabilités individuelles. Dans ce cas, les événements mutuellement exclusifs sont des combinaisons d’allèles parentales possibles que la femme enceinte peut avoir héritées. Puisque ses deux parents sont hétérozygotes (génotype Bb), elle a l’un des quatre génotypes possibles : B paternel et B maternel (BB), B paternel et b maternel (Bb), B maternel et b paternel (Bb), ou b paternel et b maternelle (bb). Comme elle n’a pas de BTD, le génotype bb peut être exclu. Il y a donc trois génotypes possibles avec des probabilités égales de 1/3, et deux d’entre eux entraînent d’être porteur (Bb). Par conséquent, selon la règle de la somme, sa probabilité d’être porteuse est de 2/3 (1/3 + 1/3).
 
 Un autre facteur crucial dans le risque de BTD de l’enfant est la probabilité que le père soit porteur. Ici, la règle du produit entre en jeu. La règle du produit stipule que la probabilité de plusieurs événements indépendants soit le produit des probabilités individuelles des événements. Si la mère est porteuse, cela n’influence pas que le père soit porteur. Ce sont donc des événements indépendants.
 
 Pour que l’enfant hérite du BTD, plusieurs événements indépendants doivent se produire. Premièrement, la mère doit être porteuse (probabilité 2/3). Deuxièmement, le père doit être porteur. Si le père n’est pas affecté et n’a pas d’antécédents familiaux de BTD, la probabilité qu’il soit porteur est considérée comme équivalente à celle de la population générale (1/120). Troisièmement, l’enfant doit hériter de l’allèle récessif des deux parents (probabilité de 1/4 si les deux parents sont porteurs). Selon la règle du produit, le risque d’hériter du BTD pour l’enfant est le produit de chacune de ces probabilités : (2/3) x (1/120) x (1/4) = ~0,0014, soit environ 0,14 %.
 
 <h4>Les probabilités théoriques et empiriques sont calculées respectivement avant et après les événements</h4>
 
 Le risque de 0,14 % que l’enfant hérite du BTD, une prévision calculée avant la naissance, est une probabilité théorique. Il est toutefois possible que l’enfant et ses frères ou sœurs héritent du BTD, ce qui représente une probabilité empirique de 100 %. Contrairement aux probabilités théoriques, qui sont calculées avant que des événements se produisent, les probabilités empiriques sont basées sur des observations. Lorsqu’on analyse des arbres généalogiques seuls, les probabilités théoriques et empiriques peuvent être très différentes. Cependant, à mesure que de plus en plus d’arbres généalogiques sont analysés, les probabilités théoriques et empiriques s’alignent de plus en plus.

Lois de probabilité

Aperçu

La probabilité d’hériter d’une caractéristique peut être calculée à l’aide des règles de somme et de produit. La règle de la somme est utilisée pour calculer la probabilité de ...

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KEY TERMS AND CONCEPTS

TERMES ET CONCEPTS CLÉS

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,...

punnett squares

Punnett Squares for Predicting Traits

Punnett squares help predict which traits offspring may inherit from two parents. They show possible genotypes, which are pairs of alleles, and can also show the chance of a phenotype, or visible trait, when the inheritance pattern is known. These grids work best for traits controlled by a single gene locus and passed on independently during meiosis. Punnett squares were developed in the early 1900s by Reginald Punnett. His work came after Gregor Mendel’s pea plant experiments revealed the...

monohybrid crosses

Mendel’s Pea Plant Inheritance Ratios

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...

dihybrid crosses

Mendel's Law of Independent Assortment

Mendel’s law of independent assortment explains how two traits can be inherited separately. Gregor Mendel tested this idea with pea plants that differed in two characteristics, such as pea color and pea shape. He used true-breeding parents that were homozygous for both traits but showed different phenotypes. In one example, Mendel crossed round, yellow peas with wrinkled, green peas. The parental generation had RRYY and rryy genotypes. Their first-generation offspring were all dihybrids,...

law of segregation

Mendel’s Pea Cross Ratios

Mendel’s pea plant crosses show how traits can disappear in one generation and return in the next. When he crossed plants, one parental trait sometimes seemed to vanish in the F1 generation and reappear in the F2 generation. Mendel used this pattern to explain why some traits are dominant and others are recessive. He proposed that traits are controlled by alleles, which are different versions of a gene. An organism inherits two copies of each gene, one from each parent. In his model, a...

law of independent assortment

Mendel’s Dihybrid Cross and Trait Ratios

Mendel’s dihybrid cross shows how two traits are inherited at the same time. A dihybrid cross is a cross in which both parents are homozygous for two distinct traits, and the F1 generation is heterozygous for both traits. Mendel used pea plants with round yellow peas and wrinkled green peas as an example. One parent had genotype YYRR, and the other had genotype yyrr. In the F1 generation, every plant showed the dominant traits, so the plants were YyRr and had yellow, round peas. The F2...

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...

test cross

Using Test Crosses to Identify Genotypes

Test crosses are used to identify the genotype of an organism with a dominant trait. A genotype is the pair of alleles inherited for a gene, and alleles are different forms of the same gene. In diploid organisms, including humans, each gene usually has two alleles, one from each parent. An allele is recessive when its effect is hidden by another allele at the same gene location. Pea plants provide a clear example with flower color. White flowers are recessive, because one copy of the purple...

polygenic traits

Polygenic Traits in Human Height

Polygenic traits are traits controlled by more than one gene. Human height is a clear example of this kind of inheritance. Because many genes work together, the final trait can vary a lot from person to person. Researchers have found hundreds of loci, or gene locations, that influence height. There are likely many more that have not yet been identified. Many of these genes affect cartilage in the growth plates of the long bones in the arms and legs, either directly or indirectly. Height is...

pedigree analysis

Reading Family Traits in Pedigrees

Pedigrees are family trees used to track how a trait passes through generations. They help scientists and students see whether a trait is dominant or recessive, whether it is autosomal or sex-linked, what genotypes family members may have, and what phenotypes may appear in future generations. For families with a history of inherited disease, this information can be important for family planning. In plants and animals, inheritance is often studied with crosses. Monohybrid crosses can show...

multiple allele traits

Blood Type and Allele Interactions

Multiple alleles can shape traits through blood type, sickle cell anemia, incomplete dominance, and codominance. Multiple allelism means a gene has three or more allelic forms. Diploid organisms, including humans, usually carry only two alleles for each gene, but many human genes exist in multiple forms in the population. Human blood type is a clear example of multiple allelism. The blood type gene has three alleles: I A , I B , and i. These alleles help determine which blood type a person has...

epistasis

Gene Masking in Rabbit Fur Color

Epistasis describes how one gene can mask or change the effect of another gene. In high school genetics, this helps explain why many traits do not follow a simple single-gene pattern. Instead, alleles at different locations can work together to shape the final phenotype. Mendel studied seven unrelated pea traits, but most traits involve multiple gene interactions. Epistasis often happens when one gene interferes with the expression of another gene. It can also occur when genes are part of the...

nature and nurture

Genes and Environment Shape Height

Genes and environment both shape human height and other traits. Genes are the inherited instructions we get from our parents. Environment includes factors such as diet, stress, and social conditions. Many phenotypes, or observable traits, reflect both influences. Some also show up later in life, including cancer and other diseases. Height is a clear example of this interaction. Scientists estimate that 70-90% of height variation comes from genetic differences among people. The remaining 10-30%...

pleiotropy

SOX10 and Multiple Traits in Pleiotropy

Pleiotropy is when one gene affects more than one trait. The SOX10 gene is a clear example because it can influence pigmentation, hearing, and intestinal movement. These traits may seem unrelated, but they can all be linked to the same gene change. In humans, a deleted region in SOX10 can cause Waardenburg Syndrome Type 4, or WS4. WS4 is an autosomal recessive disorder, which means a person usually inherits two altered copies of the gene. Common signs include a white forelock,...

sex-linked disorders

X- and Y-Linked Disorder Patterns

X- and Y-linked disorders come from mutations in genes on the sex chromosomes. These genes, like those on autosomes, are needed for normal body function. When a mutation causes a biological problem, the condition is called sex-linked. Y-linked disorders come from changes in the Y chromosome. They affect only males, because only males carry a Y chromosome. Mutations in this small chromosome can affect male sexual function and secondary sex characteristics. One example is Y-chromosome...

x-linked traits

X-Linked Inheritance in Families

X-linked inheritance explains how traits on the X chromosome are passed through families. In most mammalian species, females have two X sex chromosomes, while males have one X and one Y. A mutation on one X chromosome may be masked in females by a normal allele on the other X. In males, that same mutation is more likely to show because there is no second normal X to balance it. Traits caused by changes on the X chromosome are called X-linked traits. Color blindness is a well-studied example.

x-inactivation

Barr Bodies and X-Chromosome Balance

Barr bodies and X-chromosome balance help explain how female mammalian cells control gene activity from the X chromosome. The human X chromosome carries far more genes than the Y chromosome. Because males usually have one X chromosome and females have two, females would make twice as many of some proteins without a control system. To prevent that imbalance, female mammalian cells inactivate nearly all the genes on one X chromosome during early embryonic development. The inactive X condenses...

non-nuclear inheritance

Maternal DNA in Mitochondria and Chloroplasts

Maternal DNA in mitochondria and chloroplasts explains how some genes are inherited outside the nucleus. Most DNA is in the nucleus, but mitochondria and chloroplasts in the cell cytoplasm also carry their own DNA and can copy it independently of nuclear DNA. Mitochondria are found in both plant and animal cells. They are called the powerhouses of eukaryotic cells because they break down glucose to make energy for cellular activity. Mitochondrial DNA has about 37 genes, and many help with...

chromosomal theory of inheritance

How Genes Map to Chromosomes

Genes map to chromosomes, and this idea explains how Mendel’s inheritance patterns work. Gregor Mendel published his pea plant breeding results in 1866. He showed that physical traits follow predictable patterns. At the time, scientists did not yet know that genes existed. Mendel used the word "factors" for the hereditary units he studied. The details behind Mendel’s laws of segregation and independent assortment were still unknown for many years. In the late 1800s, better microscopes and...

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.

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Minnesota Academic Standards in Science

Life Science

2.1.1 9L.2.1.1.1

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New Jersey Student Learning Standards for Science

High School

Heredity: Inheritance and Variation of Traits

HS-LS3-3

Alabama Course of Study Science

9-12.B.3.11

Next Generation Science Standards

HS-LS3-1

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New York State Science Learning Standards

Inheritance and Variation of Traits

HS-LS3-1.

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Meiosis I

Meiosis II

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Crossing Over

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Use models to explain how DNA is passed from parents to offspring through the processes of meiosis and fertilization in sexual reproduction.

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Construct an explanation to summarize how inheritable genetic variations may result from: new genetic combinations in meiosis, mutations during replication, or mutations caused by environmental factors.

LS.Bio.6.2

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Punnett Squares

Monohybrid Crosses

Dihybrid Crosses

Trihybrid Crosses

Trihybrid Crosses
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Law of Independent Assortment

Chi-square Analysis

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Pedigree Analysis

Multiple Allele Traits

Incomplete Dominance

Gregor Mendel&#39;s work (1822 - 1884) was primarily focused on pea plants. Through his initial experiments, he determined that every gene in a diploid ...

Lethal Alleles

Agouti: A Lethal Allele
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Polygenic Traits

background-and-environment-affect-phenotype

Background and Environment Affect Phenotype

Although the genetic makeup of an organism plays a major role in determining the phenotype, there are also several environmental factors, such as ...

Use mathematics and computational thinking to predict the variation and distribution of expressed traits based on: Mendelian inheritance, co-dominance, incomplete dominance, multiple alleles, and sex-linked inheritance.

LS.Bio.7.1

Overview

A pedigree is a diagram displaying a family&#x2019;s history of a trait. Analyzing pedigrees can reveal (1) whether a trait is dominant or ...

Overview

The probability of inheriting a trait can be calculated using the sum and product rules. The sum rule is used to calculate the probability of ...

The Concept of Multiple Allelism

Multiple allelism describes genes that exist in three or more allelic forms. Although diploid organisms, like humans, ...

Analyze and interpret data to explain how polygenic traits result in a wide range of phenotypes.

Pleiotropy

Pleiotropy is the phenomenon in which a single gene impacts multiple, seemingly unrelated phenotypic traits. For example, defects in the SOX10 gene cause ...

Nature and Nurture

Many human characteristics, like height, are shaped by both nature&mdash;in other words, by our genes&mdash;and by nurture, or our environment. For ...

Construct an explanation to summarize how traits result from interactions of genetic factors (multiple genes and/or alleles) and environmental factors.

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Analyze and interpret data to compare DNA samples.

LS.Bio.8.1

Understand genetic mechanisms for variation.

Inheritance Risk with Sum and Product Rules

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