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

Reguły sumy i iloczynu prawdopodobieństwa służą do określenia prawdopodobieństwa wykazania cechy przez daną osobę.

Na przykład, jeśli drzewo genealogiczne kobiety w ciąży wykazuje chorobę, taką jak niedobór biotynidazy, prawdopodobieństwo bycia nosicielką allelu recesywnego niedoboru biotynidazy przez nią i jej partnerów określa ryzyko wystąpienia tego zaburzenia u ich dziecka.

Tutaj rodowód kobiety pokazuje chorego brata, ale niedotkniętych rodziców, którzy muszą być heterozygotami

Kwadrat łubianki pokazuje, że kobieta może być homozygotyczna pod względem normalnego allelu lub odziedziczyła allel choroby od matki lub ojca. Opcja homozygotyczna recesywna jest zdyskontowana. Ponieważ istnieją dwa sposoby, w jakie może być nosicielem, oba z prawdopodobieństwem jednym do trzech, suma ich prawdopodobieństw jest prawdopodobieństwem, że jest heterozygotyczna, regułą sumy.

I odwrotnie, prawdopodobieństwo ojca wynosi jeden do 120, ponieważ jest to prawdopodobieństwo, że przypadkowy osobnik jest heterozygotyczny.

Oboje przyszli rodzice muszą być nosicielami, prawdopodobieństwo dwóch z trzech i jeden ze 120 i przekazać allel choroby, prawdopodobieństwo jeden do czterech, więc prawdopodobieństwo, że ich dziecko ma niedobór biotynidazy, jest iloczynem tych prawdopodobieństw, około 0,14%, reguła produktu.

Jest to obliczone teoretyczne prawdopodobieństwo, ale niektóre pary mogą mieć dzieci tylko z niedoborem biotynidazy, co jest obserwowane empirycznie na poziomie 100%. Gdyby jednak zbadać wiele rodowodów, prawdopodobieństwa te byłyby zgodne.

Griffithsa, Anthony'ego J.F., Jeffreya H. Millera, Davida T. Suzukiego, Richarda C. Lewontina i Williama M. Gelbarta. 2000. "Wykorzystanie proporcji genetycznych." W: Wprowadzenie do analizy genetycznej. 7 wyd. Nowy Jork: W. H. Freeman and Company. [<a href="https://www.ncbi.nlm.nih.gov/books/NBK21812/" target="__blank">Źródło</a>]

prawa prawdopodobieństwa

<h4>Przegląd</h4>

Prawdopodobieństwo odziedziczenia cechy można obliczyć za pomocą reguł sumy i iloczynu. Reguła sumy służy do obliczania prawdopodobieństwa zdarzeń wzajemnie się wykluczających. Reguła iloczynu przewiduje prawdopodobieństwo wielu niezależnych zdarzeń. Te reguły prawdopodobieństwa określają prawdopodobieństwo teoretyczne — prawdopodobieństwo wystąpienia zdarzeń, zanim one nastąpią. Natomiast prawdopodobieństwo empiryczne oblicza się na podstawie zdarzeń, które już miały miejsce.

<h4>Reguły sumy i iloczynu są wykorzystywane do obliczania prawdopodobieństwa dziedziczenia</h4>

Chociaż szachownice Punnetta są przydatne do wizualizacji dziedziczenia jednej lub dwóch cech, stają się one kłopotliwe w zastosowaniu do bardziej złożonych scenariuszy. Kwadrat Punnetta wykazujący tylko trzy cechy zawiera 64 możliwe krzyżówki. Prawa prawdopodobieństwa umożliwiają znacznie wydajniejsze obliczenia prawdopodobieństw dziedziczenia cech.

Weźmy pod uwagę kobietę w ciąży, która chce zrozumieć ryzyko odziedziczenia przez swoje dziecko niedoboru biotynidazy (BTD), choroby autosomalnej recesywnej występującej w jej rodzinie. Niemowlęta z nieleczoną BTD wykazują opóźnienia w rozwoju, słabe napięcie mięśniowe, wysypki skórne i wypadanie włosów. Ciężkie przypadki są związane między innymi z drgawkami oraz utratą wzroku i słuchu. Ani kobieta, ani jej rodzice nie chorują na BTD, ale jej brat jest nią dotknięty, co oznacza, że oboje rodzice muszą mieć jeden przyczynowy wariant genu (tj. oboje rodzice są heterozygotami, czyli nosicielami).

Prawdopodobieństwo, że dziecko kobiety odziedziczy BTD, zależy od tego, czy kobieta jest nosicielką i posiada jeden allel przyczynowy. Ponieważ BTD jest autosomalne recesywne i nie jest na nią naruszone, nie może mieć dwóch alleli przyczynowych. Może jednak posiadać jeden allel przyczynowy, który może zostać przekazany dziecku.

Pierwszym krokiem w kierunku ustalenia ryzyka dla dziecka jest określenie prawdopodobieństwa, że matka jest nosicielką. Osiąga się to za pomocą sumy reguły prawdopodobieństwa. Reguła sumy mówi, że prawdopodobieństwo zdarzeń wzajemnie się wykluczających jest sumą ich prawdopodobieństw indywidualnych. W tym przypadku zdarzeniami wzajemnie wykluczającymi się są możliwe kombinacje alleli rodzicielskich, które kobieta w ciąży mogła odziedziczyć. Ponieważ oboje jej rodzice są heterozygotami (genotyp Bb), ma jeden z czterech możliwych genotypów: B ze strony ojca i B ze strony matki (BB), B ze strony ojca i b ze strony matki (Bb), B ze strony matki i b ze strony ojca (Bb) lub b ze strony ojca i matczyne b (bb). Ponieważ nie ma BTD, można wykluczyć genotyp bb. Istnieją zatem trzy możliwe genotypy z równym prawdopodobieństwem 1/3, a dwa z nich oznaczają nosiciela (Bb). Zatem zgodnie z regułą sumy prawdopodobieństwo, że jest nosicielką wynosi 2/3 (1/3 + 1/3).

Kolejnym krytycznym czynnikiem wpływającym na ryzyko wystąpienia BTD u dziecka jest prawdopodobieństwo, że ojciec jest nosicielem. Tutaj wchodzi w grę zasada produktu. Reguła iloczynu stwierdza, że prawdopodobieństwo wielu niezależnych zdarzeń jest iloczynem prawdopodobieństw poszczególnych zdarzeń. Jeśli matka jest nosicielką, nie ma to wpływu na to, czy ojciec jest nosicielem. Są to zatem zdarzenia niezależne.

Aby dziecko odziedziczyło BTD, musi nastąpić wiele niezależnych zdarzeń. Po pierwsze, matka musi być nosicielką (prawdopodobieństwo 2/3). Po drugie, ojciec musi być nosicielem. Jeśli ojciec nie jest dotknięty chorobą i nie ma w rodzinie BTD, prawdopodobieństwo, że jest nosicielem, uważa się za równoważne prawdopodobieństwu populacji ogólnej (1/120). Po trzecie, dziecko musi odziedziczyć allel recesywny od obojga rodziców (prawdopodobieństwo 1/4, jeśli oboje rodzice są nosicielami). Zgodnie z regułą iloczynu ryzyko odziedziczenia przez dziecko BTD jest iloczynem każdego z tych prawdopodobieństw: (2/3) x (1/120) x (1/4) = ~0,0014, czyli około 0,14%.

<h4>Prawdopodobieństwa teoretyczne i empiryczne są obliczane odpowiednio przed i po zdarzeniach</h4>

Ryzyko wystąpienia BTD u dziecka wynoszące 0,14%, przewidywane przed urodzeniem, jest prawdopodobieństwem teoretycznym. Istnieje jednak możliwość, że dziecko i jego rodzeństwo odziedziczą BTD, co empirycznie wskazuje na 100%. W przeciwieństwie do prawdopodobieństw teoretycznych, które oblicza się przed wystąpieniem zdarzenia, prawdopodobieństwa empiryczne opierają się na obserwacjach. Analizując pojedyncze rodowody, prawdopodobieństwa teoretyczne i empiryczne mogą być bardzo różne. Jednak w miarę analizowania większej liczby rodowodów prawdopodobieństwa teoretyczne i empiryczne stają się coraz bardziej zbieżne.

Prawa prawdopodobieństwa

Przegląd

Prawdopodobieństwo odziedziczenia cechy można obliczyć za pomocą reguł sumy i iloczynu. Reguła sumy służy do obliczania prawdopodobieństwa ...

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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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Overview

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Inheritance Risk with Sum and Product Rules

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