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

概率的总和和 产品规则用于 确定某人表现出特质的可能性。
 例如，如果一个准妈妈的家谱 显示出一种疾病，如生物素酶缺乏症， 她和她的伴侣成为隐性 生物素酶缺乏等位基因携带者的可能性 决定了他们孩子患这种疾病的风险。
 在这里，女人的血统显示了一个关联的兄弟， 但不受影响的父母，他们必须是杂合的 显示该女性可以通过纯合子 进行正常等位基因 或从母亲或父亲那里继承疾病等位基因。
 纯合隐性选项大打折扣。
 由于她有两种方式可以成为载体， 两者的概率均为三分之一， 他们概率的总和 是她是杂合的可能性，总和规则。
 相反，父亲的概率是120， 因为这是随机 个体杂合的可能性。
 两个准父母都必须是承运人， 120个中的两个和120个中的一个 概率通过疾病等位基因， 概率为四分之一， 所以他们的孩子患生物素酶缺乏症的可能性 是这些概率的产物， 大约0.14％，根据规则。
 这是计算出的理论概率， 但有些夫妻可能只有 生物素酶缺乏的孩子， 观察到的经验概率为100％。
 但是，如果研究了许多谱系 这些概率就会匹配。

Griffiths、Anthony J.F.、Jeffrey H. Miller、David T. Suzuki、Richard C. Lewontin 和 William M. Gelbart。2000. "使用遗传比率"。在遗传分析导论中。第 7 版。纽约:W. H. Freeman and Company。[<a href="https://www.ncbi.nlm.nih.gov/books/NBK21812/" target="__blank">来源</a>]

概率定律

“遗传一个性状的概率可以用和和积规则来计算。求和规则用于计算互斥事件的概率。积规则预测多个独立事件的概率。这些概率规则决定了理论概率，即事件发生之前发生的可能性。相反，经验概率是根据已经发生的事件计算出来的。”

<h4>利用求和规则和乘积规则来计算继承概率</h4>
 
尽管旁氏表对于可视化一个或两个特征的继承很有用，但是当应用于更复杂的场景时，它们会变得很麻烦。一个只有三个特征的旁氏表包含64个可能的杂交。概率定律可以更有效地计算性状遗传概率。
 
以一位孕妇为例，她想了解自己的孩子遗传生物素酶缺乏症（BTD）的风险，BTD是一种常染色体隐性遗传疾病，在她的家庭中普遍存在。未经治疗的BTD婴儿表现出发育迟缓、肌肉张力差、皮疹和脱发。严重的病例与癫痫发作、视力和听力丧失等症状有关。这名妇女和她的父母都没有BTD，但她的兄弟受到影响，这意味着父母双方必须有一个因果基因变体（即父母双方都是杂合子或携带者）。
 
妇女子女遗传BTD的可能性取决于妇女是否为携带者，是否具有一个因果等位基因。由于BTD是常染色体隐性遗传，而且她没有受到影响，她不能有两个因果等位基因。然而，她可能携带一个可以遗传给她的孩子的因果等位基因。
 
确定孩子风险的第一步是确定母亲成为携带者的可能性。这是用概率“和”法则来实现的。和规则指出，互斥事件的概率是它们各自的概率之和。在这种情况下，相互排斥的事件可能是孕妇可能遗传的父母等位基因组合。由于双亲均为杂合子 ( Bb基因型)，她有四种可能的基因型之一：父系 B 和母系 B ( BB )、父系 B 和母系 b ( Bb )、母系 B 和父系 b ( Bb )、或父系 b 和母系 b ( bb )。因为她没有BTD，所以可以排除 bb 基因型。因此，有三种可能的基因型，其等概率为1/3，其中两种基因型成为携带者 ( Bb )。因此，根据和规则，她成为遗传人的概率是2/3（1/3+1/3）。
 
儿童患BTD风险的另一个关键因素是父亲成为携带者的可能性。在这里，产品规则开始发挥作用。乘积规则规定，多个独立事件的概率是事件的个别概率的乘积。如果母亲是携带者，这并不影响父亲是否是携带者。因此，它们是独立的事件。
 
要使子项继承BTD，必须发生多个独立事件。首先，母亲必须是携带者（2/3概率）。其二，父亲必须是一个携带者。如果父亲未受影响且无BTD家族史，则认为其作为携带者的概率相当于一般人群的概率（1/120）。第三，孩子必须继承父母双方的隐性等位基因（如果父母双方都是携带者，则1/4的概率）。根据乘积规则，孩子继承BTD的风险是这些概率的乘积： (2/3) x (1/120) x (1/4) = ~0.0014,或约0.14%.
 
<h4>理论概率和经验概率分别在事件前后计算</h4>
 
婴儿出生前计算出的0.14%的BTD风险是一个理论概率。然而，孩子和他或她的兄弟姐妹有可能继承BTD，这代表了100%的经验概率。与理论概率（在事件发生之前计算）不同，经验概率是基于观测值的。在分析单系谱时，理论概率和经验概率可能有很大的不同。然而，随着更多的系谱被分析，理论和经验的概率变得越来越一致。

概述

可使用加法法则和乘法法则计算遗传性状的遗传概率。加法法则用于计算……的概率。

Education

教育

JoVE Core

生物学

Genetics

遗传学

Classical and Modern Genetics

经典遗传学与现代遗传学

KEY TERMS AND CONCEPTS

关键术语与概念

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系列通过300多节动画视频课简明易懂地讲解生物学中的关键概念，以及150余段视频展示科学家在现代实验室开展实际研究实验，让生物学变得平易近人。

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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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

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Inheritance Risk with Sum and Product Rules

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