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

確率の和と積の法則は，特性を発現する可能性を求めるために 使われます。例えば，妊婦の家系の中に ビオチニダーゼ欠損症のような疾患がある場合，妊婦とそのパートナーの劣性がオチニダーゼ欠損症対立遺伝子の 保因者である可能性が、障害を持つ子供の可能性を決定します。ここで、女性の家系は、異型接合でなければならない 両親ではなく，罹患している兄弟を示しています。点線の正方形は、女性が正常な対立遺伝子に対して ホモ接合性であるか、または母親または父親から 疾患対立遺伝子を受け継いでいる可能性があることを示しています。女性が罹患する場合が2通りあるので，同型接合劣性の可能性は無視されます。2通りとも3分の1の確率です。確率の合計は、和の法則を用いて，女性がヘテロ接合である可能性となります。逆に、父親の確率は120分の1です。これは，ランダムな個体がヘテロ接合である確率と 同じだからです。両親両方が，それぞれ3分の2，120分の1の確率で，罹患した対立遺伝子をもっていなければなりません。4分の1の確率です。子供がビオチニダーゼ欠乏症に なる可能性はここから計算できます。積の法則を用いて，約0.14パーセントです。これが計算された理論上の確率です。しかし，両親によってはビオチニダーゼ欠乏症の子供 のみが生まれてきます。経験的確率は100パーセントとなります。しかし，多くの家族で調べた場合，確率は一致します。

グリフィス、アンソニー J.F.、ジェフリー H. ミラー、デビッド T. スズキ、リチャード C. レウォンティン、ウィリアム M. ゲルバート。2000.「遺伝的比率の使用」 遺伝分析の紹介。第7版ニューヨーク:WHフリーマンアンドカンパニー。[<a href="https://www.ncbi.nlm.nih.gov/books/NBK21812/" target="__blank">ソース</a>]

確率の法則

<h4>概要</h4> 
 
 ある形質を受け継ぐ確率は、和の法則と積の法則を使って計算できます。和の法則は、互いに排他的な事象の確率を計算するために使われます。積の法則は、複数の独立した事象の確率を予測するものです。これらの確率則は、理論的な確率（事象が起こる前に、その事象が起こる可能性）を決定します。一方、経験的確率は、既に発生した事象に基づいて計算されます。
 
 <h4>和と積の法則を利用した継承確率の計算</h4> </h4
 
 パネットの方形は、1つまたは2つの形質の継承を視覚化するのには便利ですが、より複雑なシナリオに適用する場合には煩雑になります。たった3つの形質を表示したパネットの方形には、64の可能な交配が含まれています。確率の法則を使えば、形質の遺伝確率をより効率的に計算できます。
 
 自分の家系に起こる常染色体潜性疾患であるビオチニダーゼ欠損症(BTD)を子供が遺伝するリスクを知りたいと考えている妊婦について考えます。未治療のBTDの乳児は、発育遅延、筋力低下、皮膚の発疹、脱毛などの症状が見られます。重症の場合は、痙攣や視力・聴力の低下などの症状が見られます。この女性も両親もBTDではないですが、彼女の兄弟がBTDに罹患している場合、両親ともに原因となる遺伝子変異を持っている必要があります。つまり、両親ともにヘテロ接合体（キャリアー）です。
 
 その女性の子供がBTDを受け継ぐ確率は、その女性が原因となる対立遺伝子を1つ持っているキャリアであるかどうかにかかっています。BTDは常染色体潜性遺伝であり、女性は影響を受けていないため、原因となる対立遺伝子を2つもつことはないです。
 
 子供のリスクを確認するための最初のステップは、母親が保因者である可能性の判断です。これには確率の和の法則を用います。和の法則とは、互いに排反な事象が起こる確率は、それぞれの確率の合計（和）になるというものです。この場合、互いに排反な事象とは、妊娠中の女性が受け継ぐ可能性のある親の対立遺伝子の組み合わせです。彼女の両親はどちらもヘテロ接合体（Bb遺伝子型）であるため、彼女は4つの可能な遺伝子型のうちの1つをもちます。すなわち、父方のBと母方のB(BB)、父方のBと母方のB(Bb))、母方のBと父方のB(Bb)、または父方のBと母方のB(bb)のいずれかになります。彼女はBTDではないので、bbの遺伝子型は除外されます。したがって、1/3の等しい確率で3つの可能な遺伝子型があり、そのうちの2つが保因者（Bb）となります。したがって、和の法則によると、彼女が保因者である確率は2/3（1/3 + 1/3）となります。
 
 子供のBTDリスクのもう一つの重要な要因は、父親がキャリアである可能性です。ここで、席の法則が登場します。積の法則とは、複数の独立した事象がおこる確率は、個々の事象の確率の積で表されるというものです。母親が保因者であっても、父親が保因者であるかどうかには影響しません。したがって、両者は独立した事象になります。
 
 子供がBTDを発症するには、複数の独立した事象が発生する必要があります。まず、母親がキャリアであることです（2/3の確率）。次に、父親が保因者であることです。父親がBTDに罹患しておらず、家族歴もない場合、父親が保因者である確率は一般人の確率（1/120）と同等とみなせます。第三に、子供は両親から潜性対立遺伝子を受け継ぐ必要があります（両親が保因者の場合、確率は1/4）。積の法則によると、子供がBTDを遺伝するリスクは、これらの各確率の積となります。すなわち、(2/3) x (1/120) x (1/4) = ~0.0014、つまり約0.14%です。
 
 <h4>理論的確率と経験的確率は事象の前と後でそれぞれ計算されます</h4>。
 
 出生前に計算された子供のBTDのリスクである0.14%は、理論的な確率です。しかし、その子とその兄弟がBTDになる可能性はあり、このとき経験的確率は100％となります。事象が発生する前に計算される理論的確率とは異なり、経験的確率は観察に基づきます。単一の家系図を分析する場合、理論的確率と経験的確率は大きく異なる可能性があります。しかし、より多くの家系図を分析すると、理論的確率と経験的確率は次第に一致するようになります。

概要

特性を継承する確率は、合計ルールと積ルールを使用して計算できます。合計ルールは、...

Education

JoVE Core

生物学

Genetics

遺伝学

Classical and Modern Genetics

古典遺伝学と現代遺伝学

KEY TERMS AND CONCEPTS

主要用語と概念

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.

Inheritance Risk with Sum and Product Rules | JoVE K12

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JoVE Core シリーズは、生物学の重要な概念を説明する 300 を超える簡潔でわかりやすいアニメーション ビデオ レッスンに加え、今日の研究室で行われる実際の研究実験を示す 150 以上の科学者の活動ビデオを通じて、生物学に命を吹き込みます。

Minnesota Academic Standards in Science

Life Science

2.1.1 9L.2.1.1.1

new-jersey-student-learning-standards-for-science

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

new-york-state-science-learning-standards

New York State Science Learning Standards

Inheritance and Variation of Traits

HS-LS3-1.

HS-LS3-3.

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Meiosis I

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Monohybrid Crosses

Dihybrid Crosses

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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

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Polygenic Traits

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Background and Environment Affect Phenotype

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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

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Pleiotropy

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Nature and Nurture

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Inheritance Risk with Sum and Product Rules

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