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

Правила вычисления вероятности суммы и произведения используются для определения вероятности того, что кто-то из них имеет выраженный признак. Например, семейное дерево беременной женщины демонстрирует болезнь, такую как дефицит биотинидазы;вероятность для неё и ее партнёра быть переносчиками рецессивного аллеля дефицита биотинидазы определяет риск того, что у их ребёнка проявится такое расстройство. Здесь родословная женщины показывает пострадавшего брата, но не затронутых родителей, которые в таком случае гетерозиготным Таблица Пуннета отображает, что женщина может быть гомозиготной для нормального аллеля, или унаследовать поражённый аллель от матери или отца.Рецессивная гомозиготная опция невозможна. Поскольку существует два способа для неё быть переносчиком, оба с вероятностями одного из трех, сумма их вероятностей и есть вероятность, что что она гетерозиготна, по правилу суммы. И наоборот, у отца вероятность один из 120, так как это вероятность того, что случайный человек гетерозиготен.Оба будущих родителя должны быть переносчиками, вероятности двух третей и одной сто двадцатой вероятность передать дефектный аллель, будет равна одной четвёртой, таким образом, вероятность, что их ребёнок имеет дефицит биотинидазы является произведением этих вероятностей, примерно 0.14%правило произведения. Это рассчитанное значение, теоретическая вероятность. Тем не менее, у некоторых пар могут быть только дети с дефицитом биотинидазы и наблюдаемой эмпирической вероятностью 100%Однако, если были изучены многие родословные, эти вероятности будут совпадать.

Гриффитс, Энтони Дж.Ф., Джеффри Х. Миллер, Дэвид Т. Сузуки, Ричард К. Левонтин и Уильям М. Гелбарт. 2000. "Использование генетических соотношений." Введение в генетический анализ. 7-е изд. Нью-Йорк: У. Х. Фримен и компания. [<a href="https://www.ncbi.nlm.nih.gov/books/NBK21812/" target="__blank">Источник</a>]

Законы вероятности

<h4> Обзор </h4>

 Вероятность унаследования признака можно рассчитать с помощью правил суммы и произведения. Правило сумм используется для расчета вероятности взаимоисключающих событий. Правило продукта предсказывает вероятность нескольких независимых событий. Эти правила вероятности определяют теоретическую вероятность - вероятность наступления событий до того, как они произойдут. Эмпирическая вероятность, напротив, рассчитывается на основе уже произошедших событий. 

<h4> Правила суммы и произведения используются для расчета вероятностей наследования </h4>

 Хотя квадраты Пеннета полезны для визуализации наследования одного или двух признаков, они становятся громоздкими при применении в более сложных сценариях. Квадрат Пеннета, отображающий всего три черты, содержит 64 возможных креста. Законы вероятности позволяют более эффективно вычислять вероятности наследования признаков. 

 Представьте себе беременную женщину, которая хочет понять, какой риск у своего ребенка унаследует дефицит биотинидазы (БТД), аутосомно-рецессивное заболевание, которое встречается в ее семье. Младенцы с нелеченными БТД демонстрируют задержку развития, плохой мышечный тонус, кожную сыпь и выпадение волос. Тяжелые случаи связаны, помимо других симптомов, с судорогами и потерей зрения и слуха. Ни у женщины, ни у ее родителей нет БТД, но затронут ее брат, а это означает, что оба родителя должны иметь один вариант причинного гена (т.е. оба родителя являются гетерозиготами или носителями). 

Вероятность того, что ребенок женщины наследует БТД, зависит от того, является ли женщина носителем, обладая одним причинным аллелем. Так как BTD является аутосомно-рецессивным, и она не влияет, она не может иметь два причинных аллеля. Тем не менее, она может нести один причинный аллель, который может быть передан ее ребенку.

Первым шагом на пути к установлению риска ребенка является определение вероятности того, что мать является носителем. Это достигается с использованием суммы правила вероятности. Правило суммы гласит, что вероятность взаимоисключающих событий является суммой их индивидуальных вероятностей. В этом случае, взаимоисключающие события возможны родительские аллель комбинации беременная женщина, возможно, унаследовал. Так как оба ее родителя гетерозиготы (Bb генотип), она имеет один из четырех возможных генотипов: отцовской B и материнской B (BB), отцовской B и материнской b ( Bb ),материнской B и отцовской b (Bb), или отцовской b и материнской b (bb). В виду того что она не имеет BTD, генотип bb можно исключить. Таким образом 3 по возможности генотипа с равными вероятностями 1/3, и 2 из соответствуют носителю (Bb). Таким образом, в соответствии с правилом суммы, ее вероятность быть носителем составляет 2/3 (1/3 и 1/3).

Другим критическим фактором риска БТД для ребенка является вероятность того, что отец будет носителем. Здесь вступает в силу правило произведения. Правило произведения гласит, что вероятность нескольких независимых событий является результатом индивидуальных вероятностей событий. Если мать является перевозчиком, это не влияет на то, является ли отец перевозчиком. Таким образом, это самостоятельные события.

Для того, чтобы ребенок унаследовал BTD, должно произойти несколько независимых событий. Во-первых, мать должна быть носителем (2/3 вероятности). Во-вторых, отец должен быть носителем. Если отец не пострадал и не имеет семейной истории БТД, его вероятность быть носителем считается эквивалентной вероятности для населения в целом (1/120). В-третьих, ребенок должен унаследовать рецессивный аллель от обоих родителей (1/4 вероятности, если оба родителя являются носителями). В соответствии с правилом произведения, риск ребенка наследования БТД является продуктом каждой из этих вероятностей: (2/3) x (1/120) x (1/4) - 0,0014, или около 0,14%.

<h4>Теоретические и эмпирические вероятности рассчитываются соответственно до и после событий</h4>

Риск БТД для ребенка на уровне 0,14%, прогноз, рассчитанный до рождения ребенка, является теоретической вероятностью. Вполне возможно, однако, что ребенок и его или ее братья и сестры унаследуют BTD, что представляет эмпирическую вероятность 100%. В отличие от теоретических вероятностей, которые рассчитываются до событий, эмпирические вероятности основаны на наблюдениях. При анализе отдельных родословных, теоретические и эмпирические вероятности могут быть очень разными. Однако по мере анализа более родословных теоретические и эмпирические вероятности становятся все более выровненными.

Обзор

Вероятность наследования признака может быть вычислена с помощью правил суммы и произведения. Правило суммы используется для вычисления вероятности ...

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KEY TERMS AND CONCEPTS

ОСНОВНЫЕ ТЕРМИНЫ И ПОНЯТИЯ

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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Minnesota Academic Standards in Science

Life Science

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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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What is Meiosis?

Meiosis is the process by which diploid cells divide to produce haploid daughter cells. In humans, each diploid cell contains 46 chromosomes, half from ...

Meiosis I

Meiosis II

Meiosis vs. Mitosis

Crossing Over

Crossing over is the exchange of genetic information between homologous chromosomes during prophase I of meiosis I. Genetic recombination gives rise to ...

Nondisjunction

Nondisjunction is the failure of homologous chromosomes or sister chromatids to separate correctly and move to the opposite poles of the cells. This ...

Spermatogenesis

Spermatogenesis is the process by which haploid sperm cells are produced in the male testes. It starts with stem cells located close to the outer rim of ...

Oogenesis

In human women, oogenesis produces one mature egg cell or ovum for every precursor cell that enters meiosis. This process differs in two unique ways from ...

Fertilization

During fertilization, an egg and sperm cell fuse to create a new diploid structure. In humans, the process occurs once the egg has been released from the ...

Cleavage and Blastulation

After a large-single-celled zygote is produced via fertilization, the process of cleavage occurs while zygotes travel through the uterine tube. Cleavage ...

Gastrulation

Gastrulation establishes the three primary tissues of an embryo: the ectoderm, mesoderm, and endoderm. This developmental process relies on a series of ...

Neurulation

Neurulation is the embryological process which forms the precursors of the central nervous system and occurs after gastrulation has established the three ...

Cell Migration

Cell migration, the process by which cells move from one location to another, is essential for the proper development and viability of organisms ...

Determination

During embryogenesis, cells become progressively committed to different fates through a two-step process: specification followed by determination. ...

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

LS.Bio.6.1

Mutations

Mutations are changes in the sequence of DNA. These changes can occur spontaneously or they can be induced by exposure to environmental factors. Mutations ...

genome-size-and-the-evolution-of-new-genes

Genome Size and the Evolution of New Genes

types-of-genetic-transfer-between-organisms

Types of Genetic Transfer Between Organisms

Base-pairing and DNA Repair

The DNA Replication Fork

Lagging Strand Synthesis

The Replisome

Proofreading

Synthesis of new DNA molecules is carried out by the enzyme DNA polymerase, which adds nucleotides on the daughter strand complementary to the template ...

Replication in Prokaryotes

DNA replication has three main steps: initiation, elongation, and termination. Replication in prokaryotes begins when initiator proteins bind to the ...

Replication in Eukaryotes

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Gene Conversion

Restarting Stalled Replication Forks

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

An Overview of Genetic Analysis

An organism&#8217;s physical traits, or phenotype, are a product of its genotype, which is the combination of alleles (gene variants) inherited from its ...

Genetic Crosses

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Punnett Squares

Monohybrid Crosses

Dihybrid Crosses

Trihybrid Crosses

Trihybrid Crosses
Some of Mendel&#8217;s crosses examined three pairs of contrasting characteristics. Such a cross is called a trihybrid cross. A ...

Law of Independent Assortment

Chi-square Analysis

The chi-square test is a statistical hypothesis test. It is used to check whether there is a significant difference between an expected value and an ...

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
Lucien Cu&#233;not discovered lethal alleles in 1905 while studying the inheritance of coat color in mice. The agouti gene is ...

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.

LS.Bio.7.3

PCR: The Polymerase Chain Reaction

The polymerase chain reaction, or PCR, is a technique used to amplify DNA through thermocycling &#8211; cyles of temperature changes at fixed time ...

DNA Gel Electrophoresis

DNA gel electrophoresis is a technique used for the detection and separation of DNA molecules. An electric field is applied to a gel matrix comprised of ...

DNA Isolation

DNA isolation protocols can be fast and straightforward or complex and time-consuming depending on the type and quality of DNA required for further ...

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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