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{{short description|Type of biological inheritance}}
{{Use dmy dates|date=February 2016}}
{{for|a non-technical introduction to the topic|Introduction to genetics}}
{{Multiple issues|section=|
{{expert needed|biology|reason=Does not have an adequate section/referral to a page citing published research that contradicts Mendelian inheritance theory|date=October 2023}}
{{Missing information|introduction|reason=a succinct statement of the theorem|date=September 2024}}
}}

[[File:Gregor Mendel.png|thumb|[[Gregor Mendel]], the Moravian Augustinian friar who founded the modern science of [[genetics]]]]
{{Genetics sidebar}}

'''Mendelian inheritance''' (also known as '''Mendelism''') is a type of [[biology|biological]] [[Heredity|inheritance]] following the principles originally proposed by [[Gregor Mendel]] in 1865 and 1866, re-discovered in 1900 by [[Hugo de Vries]] and [[Carl Correns]], and later popularized by [[William Bateson]].<ref>[[William Bateson]]: ''[https://books.google.com/books?id=p5QDQAAACAAJ Mendel's Principles of Heredity - A Defence, with a Translation of Mendel's Original Papers on Hybridisation]'' Cambridge University Press 2009, {{ISBN|978-1-108-00613-2}}</ref> These principles were initially controversial. When Mendel's theories were integrated with the [[Boveri–Sutton chromosome theory]] of inheritance by [[Thomas Hunt Morgan]] in 1915, they became the core of [[classical genetics]]. [[Ronald Fisher]] combined these ideas with the theory of [[natural selection]] in his 1930 book ''[[The Genetical Theory of Natural Selection]]'', putting [[evolution]] onto a [[mathematics|mathematical]] footing and forming the basis for [[population genetics]] within the [[Modern synthesis (20th century)|modern evolutionary synthesis]].<ref name="grafen 69">{{cite book|title=Richard Dawkins: How A Scientist Changed the Way We Think|last=Grafen|first=Alan|author-link=Alan Grafen|author2=Ridley, Mark|year=2006|publisher=Oxford University Press|location=New York, New York|isbn=978-0-19-929116-8|page=[https://archive.org/details/richarddawkinsho00alan/page/69 69]|url=https://archive.org/details/richarddawkinsho00alan/page/69}}</ref>

==History==
{{main|History of genetics}}

The principles of Mendelian inheritance were named for and first derived by [[Gregor Johann Mendel]],<ref name="Fairbanks-2001">{{Cite journal |last1=Fairbanks |first1=Daniel J. |last2=Rytting |first2=Bryce |date=May 2001 |title=Mendelian controversies: a botanical and historical review |url=https://bsapubs.onlinelibrary.wiley.com/doi/10.2307/2657027 |journal=American Journal of Botany |language=en |volume=88 |issue=5 |pages=737–752 |doi=10.2307/2657027 |jstor=2657027 |pmid=11353700 |issn=0002-9122}}</ref> a nineteenth-century [[Moravians|Moravian]] [[monk]] who formulated his ideas after conducting simple hybridization experiments with pea plants ''([[Pisum sativum]])'' he had planted in the garden of his monastery.<ref name="Henig-2000">{{Cite book |last=Henig |first=Robin Marantz |url=http://archive.org/details/monkingardenlost00heni |title=The monk in the garden : the lost and found genius of Gregor Mendel, the father of genetics |date=2000 |publisher=Boston : Houghton Mifflin |others=Internet Archive |isbn=978-0-395-97765-1}}</ref> Between 1856 and 1863, Mendel cultivated and tested some 5,000 pea plants. From these experiments, he induced two generalizations which later became known as ''Mendel's Principles of Heredity'' or ''Mendelian inheritance''. He described his experiments in a two-part paper, ''Versuche über Pflanzen-Hybriden'' (''[[Experiments on Plant Hybridization]]''),<ref>{{Cite book |last1=Mendel |first1=Gregor |url=https://www.biodiversitylibrary.org/bibliography/61004 |title=Versuche über Pflanzen-Hybriden |last2=Mendel |first2=Gregor |date=1866 |publisher=Im Verlage des Vereines |location=Brünn}}</ref> that he presented to the Natural History Society of [[Brno]] on 8 February and 8 March 1865, and which was published in 1866.<ref name="Fairbanks-2001" /><ref>{{Cite web |title=Mendel's Paper (English - Annotated) |url=http://www.mendelweb.org/Mendel.html |access-date=2024-03-23 |website=www.mendelweb.org}}</ref><ref>{{Citation |last=Mendel |first=Gregor |chapter=Versuche über Pflanzenhybriden |date=1970 |pages=21–64 |editor-last=Mendel |editor-first=Gregor |chapter-url=https://doi.org/10.1007/978-3-663-19714-0_4 |access-date=2024-03-23 |place=Wiesbaden |publisher=Vieweg+Teubner Verlag |language=de |doi=10.1007/978-3-663-19714-0_4 |isbn=978-3-663-19714-0}}</ref><ref>{{Cite journal |last1=Mielewczik |first1=Michael |last2=Moll-Mielewczik |first2=Janine |last3=Simunek |first3=Michal V. |last4=Hossfeld |first4=Uwe |date=2022-09-01 |title="Versuche über Pflanzen-Hybriden" — neue Einsichten |url=https://doi.org/10.1007/s12268-022-1820-8 |journal=BIOspektrum |language=de |volume=28 |issue=5 |pages=565 |doi=10.1007/s12268-022-1820-8 |issn=1868-6249}}</ref>

Mendel's results were at first largely ignored. Although they were not completely unknown to biologists of the time, they were not seen as generally applicable, even by Mendel himself, who thought they only applied to certain categories of species or traits. A major roadblock to understanding their significance was the importance attached by 19th-century biologists to the [[Blending inheritance|apparent blending]] of [[Complex traits|many inherited traits]] in the overall appearance of the progeny,{{cn|date=April 2024}} now known to be due to [[Quantitative trait locus|multi-gene interactions]], in contrast to the organ-specific binary characters studied by Mendel.<ref name="Henig-2000" /> In 1900, however, his work was "re-discovered" by three European scientists, [[Hugo de Vries]], [[Carl Correns]], and [[Erich von Tschermak]]. The exact nature of the "re-discovery" has been debated: De Vries published first on the subject, mentioning Mendel in a footnote, while Correns pointed out Mendel's priority after having read De Vries' paper and realizing that he himself did not have priority. De Vries may not have acknowledged truthfully how much of his knowledge of the laws came from his own work and how much came only after reading Mendel's paper. Later scholars have accused Von Tschermak of not truly understanding the results at all.<ref>{{cite journal | doi=10.1093/oxfordjournals.jhered.a110361 | title=Tschermak: A non-discoverer of Mendelism II. A critique | date=1987 | last1=Monaghan | first1=Floyd V. | last2=Corcos | first2=Alain F. | journal=Journal of Heredity | volume=78 | issue=3 | pages=208–210 | pmid=3302014 }}</ref><ref>{{Cite book |last=Simunek |first=Michal V. |title=The Mendelian Dioskuri. Correspondence of Armin with Erich von Tschermak-Seysenegg, 1898-1951. |date=January 2011 |publisher=Pavel Mervart & Institute of Contemporary History of the AcSc Prague |year=2011 |isbn=978-80-87378-67-0}}</ref>

Regardless, the "re-discovery" made Mendelism an important but controversial theory. Its most vigorous promoter in Europe was [[William Bateson]], who coined the terms "[[genetics]]" and "[[allele]]" to describe many of its tenets.<ref name="Goldschmidt-1951">{{Cite journal |last=Goldschmidt |first=Richard B. |date=1951-01-01 |title=Chromosomes and Genes |url=http://symposium.cshlp.org/content/16/1 |journal=Cold Spring Harbor Symposia on Quantitative Biology |language=en |volume=16 |pages=1–11 |doi=10.1101/SQB.1951.016.01.003 |issn=0091-7451 |pmid=14942726}}</ref> The model of [[heredity]] was contested by other biologists because it implied that heredity was discontinuous, in opposition to the apparently continuous variation observable for many traits.<ref>{{Cite journal |last=Sumner |first=Francis B. |date=1929 |title=Is Evolution a Continuous or Discontinuous Process? |url=https://www.jstor.org/stable/14824 |journal=The Scientific Monthly |volume=29 |issue=1 |pages=72–78 |jstor=14824 |issn=0096-3771}}</ref> Many biologists also dismissed the theory because they were not sure it would apply to all species. However, later work by biologists and statisticians such as [[Ronald Fisher]] showed that if multiple Mendelian factors were involved in the expression of an individual trait, they could produce the diverse results observed, thus demonstrating that Mendelian genetics is compatible with [[natural selection]].<ref name="Fisher-1999">{{Cite book |last=Fisher |first=Sir Ronald Aylmer |url=https://books.google.com/books?id=sT4lIDk5no4C&dq=ronald+fisher+genetic+diversity&pg=PR6 |title=The Genetical Theory of Natural Selection: A Complete Variorum Edition |date=1999-10-21 |publisher=OUP Oxford |isbn=978-0-19-850440-5 |language=en}}</ref><ref name="Fisher">{{Cite journal |last1=Fisher |first1=R. A. | date=1919|title=XV.—The Correlation between Relatives on the Supposition of Mendelian Inheritance.|journal=Earth and Environmental Science Transactions of the Royal Society of Edinburgh|volume=52|issue=2|pages=399–433|doi=10.1017/S0080456800012163 |s2cid=181213898 | url=https://zenodo.org/record/1428666}}</ref> [[Thomas Hunt Morgan]] and his assistants later integrated Mendel's theoretical model with the [[chromosome]] theory of inheritance, in which the chromosomes of [[Cell (biology)|cells]] were thought to hold the actual hereditary material, and created what is now known as [[classical genetics]], a highly successful foundation which eventually cemented Mendel's place in history.<ref name="Fairbanks-2001" /><ref name="Goldschmidt-1951" />

Mendel's findings allowed scientists such as Fisher and [[J.B.S. Haldane]] to predict the expression of traits on the basis of mathematical probabilities. An important aspect of Mendel's success can be traced to his decision to start his crosses only with plants he demonstrated were [[True-breeding organism|true-breeding]].<ref name="Henig-2000" /><ref name="Fisher-1999" /> He only measured discrete (binary) characteristics, such as color, shape, and position of the seeds, rather than quantitatively variable characteristics. He expressed his results numerically and subjected them to [[Statistics#Statistical methods|statistical analysis]]. His method of data analysis and his large [[sample size]] gave credibility to his data. He had the foresight to follow several successive generations (P, F<sub>1</sub>, F<sub>2</sub>, F<sub>3</sub>) of pea plants and record their variations. Finally, he performed "test crosses" ([[backcrossing]] descendants of the initial [[Hybridization (biology)|hybridization]] to the initial true-breeding lines) to reveal the presence and proportions of [[recessive]] characters.<ref>{{Cite web |title=Gregor Mendel and the Principles of Inheritance {{!}} Learn Science at Scitable |url=http://www.nature.com/scitable/topicpage/gregor-mendel-and-the-principles-of-inheritance-593 |access-date=2024-03-23 |website=www.nature.com |language=en}}</ref>

== Inheritance tools ==

=== Punnett Squares ===
Punnett Squares are a well known genetics tool that was created by an English geneticist, Reginald Punnett, which can visually demonstrate all the possible genotypes that an offspring can receive, given the genotypes of their parents.<ref name="palomar">{{Cite web |title=Basic Principles of Genetics: Probability of Inheritance |url=https://www.palomar.edu/anthro/mendel/mendel_2.htm |access-date=2024-03-23 |website=www.palomar.edu}}</ref><ref name="Churchill-1974">{{Cite journal |last=Churchill |first=Frederick B. |date=1974 |title=William Johannsen and the Genotype Concept |url=https://www.jstor.org/stable/4330602 |journal=Journal of the History of Biology |volume=7 |issue=1 |pages=5–30 |doi=10.1007/BF00179291 |jstor=4330602 |pmid=11610096 |issn=0022-5010}}</ref><ref name="Edwards-2012">{{Cite journal |last=Edwards |first=A. W. F. |date=2012-03-01 |title=Punnett's square |url=https://www.sciencedirect.com/science/article/pii/S1369848611001373 |journal=Studies in History and Philosophy of Science Part C: Studies in History and Philosophy of Biological and Biomedical Sciences |series=Data-Driven Research in the Biological and Biomedical Sciences |volume=43 |issue=1 |pages=219–224 |doi=10.1016/j.shpsc.2011.11.011 |pmid=22326091 |issn=1369-8486}}</ref> Each parent carries two alleles, which can be shown on the top and the side of the chart, and each contribute one of them towards reproduction at a time. Each of the squares in the middle demonstrates the number of times each pairing of parental alleles could combine to make potential offspring. Using probabilities, one can then determine which genotypes the parents can create, and at what frequencies they can be created.<ref name="palomar" /><ref name="Edwards-2012" />

For example, if two parents both have a heterozygous genotype, then there would be a 50% chance for their offspring to have the same genotype, and a 50% chance they would have a homozygous genotype. Since they could possibly contribute two identical alleles, the 50% would be halved to 25% to account for each type of homozygote, whether this was a homozygous dominant genotype, or a homozygous recessive genotype.<ref name="palomar" /><ref name="Churchill-1974" /><ref name="Edwards-2012" />

=== Pedigrees ===
Pedigrees are visual tree like representations that demonstrate exactly how alleles are being passed from past generations to future ones.<ref name="Miller-2020">{{Cite journal |last=Miller |first=Christine |date=2020-09-01 |title=5.13 Mendelian Inheritance |url=https://humanbiology.pressbooks.tru.ca/chapter/5-12-mendelian-inheritance/ |language=en}}</ref> They also provide a diagram displaying each individual that carries a desired allele, and exactly which side of inheritance it was received from, whether it was from their mother's side or their father's side.<ref name="Miller-2020" /> Pedigrees can also be used to aid researchers in determining the inheritance pattern for the desired allele, because they share information such as the gender of all individuals, the phenotype, a predicted genotype, the potential sources for the alleles, and also based its history, how it could continue to spread in the future generations to come. By using pedigrees, scientists have been able to find ways to control the flow of alleles over time, so that alleles that act problematic can be resolved upon discovery.<ref>{{Cite journal |last1=Galla |first1=Stephanie J. |last2=Brown |first2=Liz |last3=Couch-Lewis (Ngāi Tahu: Te Hapū o Ngāti Wheke, Ngāti Waewae) |first3=Yvette |last4=Cubrinovska |first4=Ilina |last5=Eason |first5=Daryl |last6=Gooley |first6=Rebecca M. |last7=Hamilton |first7=Jill A. |last8=Heath |first8=Julie A. |last9=Hauser |first9=Samantha S. |date=January 2022 |title=The relevance of pedigrees in the conservation genomics era |journal=Molecular Ecology |volume=31 |issue=1 |pages=41–54 |doi=10.1111/mec.16192 |pmid=34553796 |pmc=9298073 |bibcode=2022MolEc..31...41G }}</ref>

==Mendel's genetic discoveries==
Five parts of Mendel's discoveries were an important divergence from the common theories at the time and were the prerequisite for the establishment of his rules.

# Characters are unitary, that is, they are discrete e.g.: purple ''vs''. white, tall ''vs''. dwarf. There is no medium-sized plant or light purple flower.
# Genetic characteristics have alternate forms, each inherited from one of two parents. Today these are called [[allele]]s.
# One allele is dominant over the other.  The phenotype reflects the dominant allele.
# Gametes are created by random segregation. Heterozygotic individuals produce gametes with an equal frequency of the two alleles.
# Different traits have independent assortment. In modern terms, genes are unlinked.

According to customary terminology, the principles of inheritance discovered by Gregor Mendel are here referred to as Mendelian laws, although today's geneticists also speak of ''Mendelian rules'' or ''Mendelian principles'',<ref>Science Learning Hub: ''[https://www.sciencelearn.org.nz/resources/2000-mendel-s-principles-of-inheritance Mendel's principles of inheritance]''</ref><ref>Noel Clarke: ''[https://slideplayer.com/slide/4659559/ Mendelian Genetics - An overview]''</ref> as there are many exceptions summarized under the collective term [[Non-Mendelian inheritance]]. The laws were initially formulated by the geneticist [[Thomas Hunt Morgan]] in 1916.<ref>{{cite journal |url=https://onlinelibrary.wiley.com/doi/pdf/10.1002/evan.20192 |last=Marks |first=Jonarhan |title=The Construction of Mendel's Laws |journal=Evolutionary Anthropology |volume=17 |issue=6 |doi=10.1002/evan.20192 |date=22 December 2008|pages=250–253 }}</ref>
[[File:Gregor Mendel - characteristics of pea plants - english.png|thumb|Characteristics Mendel used in his experiments<ref>Gregor Mendel: ''[http://vlp.mpiwg-berlin.mpg.de/references?id=lit26745 Versuche über Pflanzenhybriden]'' Verhandlungen des Naturforschenden Vereines in Brünn. Bd. IV. 1866, page 8</ref>]]
[[File:Dominant-recessive inheritance - flowers of pea plants.png|thumb|P-Generation and F<sub>1</sub>-Generation: The dominant allele for purple-red flower hides the phenotypic effect of the recessive allele for white flowers. F<sub>2</sub>-Generation: The recessive trait from the P-Generation phenotypically reappears in the individuals that are homozygous with the recessive genetic trait.]]
[[File:Mendel-flowers.jpg|thumb|[[Myosotis]]: Colour and distribution of colours are inherited independently.<ref>Write Work: ''[https://www.writework.com/essay/mendel-s-impact Mendel's Impact]''</ref>]]

Mendel selected for the experiment the following characters of pea plants:
* Form of the ripe seeds (round or roundish, surface shallow or wrinkled)
* Colour of the [[Seed coat|seed–coat]] (white, gray, or brown, with or without violet spotting)
* Colour of the [[seed]]s and [[cotyledon]]s (yellow or green)
* Flower colour (white or violet-red)
* Form of the ripe pods (simply inflated, not contracted, or constricted between the seeds and wrinkled)
* Colour of the unripe pods (yellow or green)
* Position of the flowers (axial or terminal)
* Length of the stem <ref>[[Gregor Mendel]]: ''[http://www.esp.org/foundations/genetics/classical/gm-65.pdf Experiments in Plant Hybridization]'' 1965, page 5</ref>

When he crossed purebred white flower and purple flower pea plants (the parental or P generation) by [[Artificiality|artificial]] pollination, the resulting flower colour was not a blend. Rather than being a mix of the two, the offspring in the first generation ([[F1 generation|F<sub>1</sub>-generation]]) were all purple-flowered. Therefore, he called this [[trait (biology)|biological trait]] dominant. When he allowed [[self-fertilization]] in the uniform looking F<sub>1</sub>-generation, he obtained both colours in the F<sub>2</sub> generation with a purple flower to white flower ratio of 3 : 1. In some of the other characters also one of the traits was dominant.

He then conceived the idea of heredity units, which he called hereditary "factors". Mendel found that there are alternative forms of factors—now called [[gene]]s—that account for variations in inherited characteristics. For example, the gene for flower color in pea plants exists in two forms, one for purple and the other for white. The alternative "forms" are now called [[allele]]s. For each trait, an organism inherits two alleles, one from each parent. These alleles may be the same or different. An organism that has two identical alleles for a gene is said to be [[homozygous]] for that gene (and is called a homozygote). An organism that has two different alleles for a gene is said to be [[heterozygous]] for that gene (and is called a heterozygote).

Mendel hypothesized that allele pairs separate randomly, or segregate, from each other during the production of the [[gametes]] in the seed plant ([[egg cell]]) and the pollen plant ([[sperm]]). Because allele pairs separate during gamete production, a [[sperm]] or [[egg]] carries only one allele for each inherited trait. When sperm and egg unite at [[fertilization]], each contributes its allele, restoring the paired condition in the offspring. Mendel also found that each pair of alleles segregates independently of the other pairs of alleles during gamete formation.

The [[genotype]] of an individual is made up of the many alleles it possesses. The [[phenotype]] is the result of the [[Genetic expression|expression]] of all characteristics that are genetically determined by its alleles as well as by its environment. The presence of an allele does not mean that the trait will be expressed in the individual that possesses it. If the two alleles of an inherited pair differ (the heterozygous condition), then one determines the organism's appearance and is called the [[Dominance (genetics)|dominant allele]]; the other has no noticeable effect on the organism's appearance and is called the [[Dominance (genetics)|recessive allele]].

==Mendel's laws of inheritance==
{| border="1" class="wikitable"
|+ Mendel's laws of inheritance
|-
! Law
! Definition
|-
| Law of dominance and uniformity
| Some alleles are dominant while others are recessive; an organism with at least one dominant allele will display the effect of the dominant allele.<ref name="Mendelian Principles">Rutgers: [http://lifesci.dls.rutgers.edu/~mcguire/Toolbox-Demo/Basic%20Genetics/Mendelian%20Principles.htm Mendelian Principles]</ref>
|-
| Law of segregation
| During gamete formation, the alleles for each gene segregate from each other so that each gamete carries only one allele for each gene.
|-
| Law of independent assortment
| Genes of different traits can segregate independently during the formation of gametes.
|}

==={{anchor|Law of Dominance and Uniformity}}Law of Dominance and Uniformity===
[[File:Dominant-recessive inheritance P - F1 - F2.png|thumb|F<sub>1</sub> generation: All individuals have the same genotype and same phenotype expressing the dominant trait (<span style="color:#990000;">red</span>).<br />F<sub>2</sub> generation: The phenotypes in the second generation show a 3 : 1 ratio.<br />In the genotype 25 % are homozygous with the dominant trait, 50 % are heterozygous  [[genetic carrier]]s of the recessive trait, 25 % are homozygous with the recessive genetic trait and [[Gene expression|expressing]] the recessive character.]]
[[File:Intermediate inheritance P - F1 - F2.png|thumb|In [[Mirabilis jalapa]] and [[Antirrhinum majus]] are examples for intermediate inheritance.<ref name="Mendelian Genetics">Biology University of Hamburg: ''[http://www1.biologie.uni-hamburg.de/b-online/e08/08a.htm Mendelian Genetics]''</ref><ref>[[Neil A. Campbell]], [[Jane B. Reece]]: Biologie. Spektrum-Verlag Heidelberg-Berlin 2003, {{ISBN|3-8274-1352-4}}, page 302–303.</ref> As seen in the F<sub>1</sub>-generation, heterozygous plants have "<span style="color:magenta;">light pink</span>" flowers—a mix of "<span style="color:#990000;">red</span>" and "white". The F<sub>2</sub>-generation shows a 1:2:1 ratio of <span style="color:#990000;">red</span>: <span style="color:magenta;">light pink</span>: <span style="color:black;">white.</span>]]
If two parents are mated with each other who differ in one [[genetic trait|genetic characteristic]] for which they are both [[homozygous]] (each pure-bred), all offspring in the first generation (F<sub>1</sub>) are equal to the examined characteristic in [[genotype]] and [[phenotype]] showing the dominant trait. This ''uniformity rule'' or ''reciprocity rule'' applies to all individuals of the F<sub>1</sub>-generation.<ref>Ulrich Weber: Biologie Gesamtband Oberstufe, 1st edition, Cornelsen Verlag Berlin 2001, {{ISBN|3-464-04279-0}}, page 170 - 171.</ref>

The principle of dominant inheritance discovered by Mendel states that in a heterozygote the dominant allele will cause the recessive allele to be "masked": that is, not expressed in the phenotype. Only if an individual is homozygous with respect to the recessive allele will the recessive trait be expressed. Therefore, a cross between a homozygous dominant and a homozygous recessive organism yields a heterozygous organism whose phenotype displays only the dominant trait.

The F<sub>1</sub> offspring of Mendel's pea crosses always looked like one of the two parental varieties. In this situation of "complete dominance", the dominant allele had the same phenotypic effect whether present in one or two copies.

But for some characteristics, the F<sub>1</sub> hybrids have an appearance ''in between'' the phenotypes of the two parental varieties. A cross between two four o'clock (''[[Mirabilis jalapa]]'') plants shows an exception to Mendel's principle, called ''incomplete dominance''. Flowers of heterozygous plants have a phenotype somewhere between the two homozygous genotypes. In cases of intermediate inheritance (incomplete dominance) in the F<sub>1</sub>-generation Mendel's principle of uniformity in genotype and phenotype applies as well. Research about intermediate inheritance was done by other scientists. The first was [[Carl Correns]] with his studies about Mirabilis jalapa.<ref name="Mendelian Genetics"/><ref>Biologie Schule - kompaktes Wissen: [http://www.biologie-schule.de/uniformitaetsregel.php Uniformitätsregel (1. Mendelsche Regel)]</ref><ref>Frustfrei Lernen: [https://www.frustfrei-lernen.de/biologie/uniformitaetsregel.html Uniformitätsregel (1. Mendelsche Regel)]</ref><ref>Spektrum Biologie: ''[http://www.spektrum.de/lexikon/biologie/unvollstaendige-dominanz/68637 Unvollständige Dominanz]''</ref><ref>Spektrum Biologie: ''[https://www.spektrum.de/lexikon/biologie/intermediaerer-erbgang/34304 Intermediärer Erbgang]''</ref>

==={{anchor|Law of Segregation}}Law of Segregation of genes===
[[File:Punnett square mendel flowers.svg|thumb|250px|left|A [[Punnett square]] for one of Mendel's pea plant experiments – [[self-fertilization]] of the F1 generation]]

The Law of Segregation of genes applies when two individuals, both heterozygous for a certain trait are crossed, for example, hybrids of the F<sub>1</sub>-generation. The offspring in the F<sub>2</sub>-generation differ in genotype and phenotype so that the characteristics of the grandparents (P-generation) regularly occur again. In a dominant-recessive inheritance, an average of 25% are homozygous with the dominant trait, 50% are heterozygous showing the dominant trait in the phenotype ([[genetic carrier]]s), 25% are homozygous with the recessive trait and therefore [[Gene expression|express]] the recessive trait in the phenotype. The genotypic ratio is 1: 2 : 1, and the phenotypic ratio is 3: 1.

In the pea plant example, the capital "B" represents the dominant allele for purple blossom and lowercase "b" represents the recessive allele for white blossom. The [[Gynoecium|pistil]] plant and the [[pollen]] plant are both F<sub>1</sub>-hybrids with genotype "B b". Each has one allele for purple and one allele for white. In the offspring, in the F<sub>2</sub>-plants in the Punnett-square, three combinations are possible. The genotypic ratio is 1 ''BB'' : 2 ''Bb'' : 1 ''bb''. But the phenotypic ratio of plants with purple blossoms to those with white blossoms is 3 : 1 due to the dominance of the allele for purple. Plants with homozygous "b b" are white flowered like one of the grandparents in the P-generation.

In cases of [[incomplete dominance]] the same segregation of alleles takes place in the F<sub>2</sub>-generation, but here also the phenotypes show a ratio of 1 : 2 : 1, as the heterozygous are different in phenotype from the homozygous because the [[Expression of genes|genetic expression]] of one allele compensates the missing expression of the other allele only partially. This results in an intermediate inheritance which was later described by other scientists.

In some literature sources, the principle of segregation is cited as the "first law". Nevertheless, Mendel did his crossing experiments with heterozygous plants after obtaining these hybrids by crossing two purebred plants, discovering the principle of dominance and uniformity first.<ref name="Neil A 2003, page 293-315">[[Neil A. Campbell]], [[Jane B. Reece]]: Biologie. Spektrum-Verlag 2003, page 293-315. {{ISBN|3-8274-1352-4}}</ref><ref name="Mendelian Principles"/>

Molecular proof of segregation of genes was subsequently found through observation of [[meiosis]] by two scientists independently, the German botanist [[Oscar Hertwig]] in 1876, and the Belgian zoologist [[Edouard Van Beneden]] in 1883. Most alleles are located in [[chromosomes]] in the [[cell nucleus]]. Paternal and maternal chromosomes get separated in meiosis because during [[spermatogenesis]] the chromosomes are segregated on the four sperm cells that arise from one mother sperm cell, and during [[oogenesis]] the chromosomes are distributed between the [[Polar body|polar bodies]] and the [[egg cell]]. Every individual organism contains two alleles for each trait. They segregate (separate) during meiosis such that each [[gamete]] contains only one of the alleles.<ref name="Bailey-2015">{{Cite web|url=http://biology.about.com/od/geneticsglossary/g/law_of_segregation.htm|title=Mendel's Law of Segregation|date=5 November 2015|access-date=2 February 2016|website=about education|publisher=About.com|last=Bailey|first=Regina}}</ref> When the gametes unite in the [[zygote]] the alleles—one from the mother one from the father—get passed on to the offspring. An offspring thus receives a pair of alleles for a trait by inheriting [[homologous chromosome]]s from the parent organisms: one allele for each trait from each parent.<ref name="Bailey-2015" /> Heterozygous individuals with the dominant trait in the phenotype are [[genetic carrier]]s of the recessive trait.

==={{anchor|Law of Independent Assortment}}Law of Independent Assortment===
[[File:Independent assortment & segregation.svg|thumb|left|Segregation and independent assortment are consistent with the [[Boveri–Sutton chromosome theory|chromosome theory of inheritance]].]]
[[File:Dihybrid inheritance pattern - cat coat.png|thumb| When the parents are homozygous for two different genetic traits ('''llSS''' and '''LL s<sub>P</sub> s<sub>P</sub>'''), their children in the F<sub>1</sub> generation are heterozygous at both loci and only show the dominant phenotypes ('''Ll S s<sub>P</sub>'''). P-Generation: Each parent possesses one dominant and one recessive trait purebred ([[homozygous]]). In this example, solid coat color is indicated by '''S''' (dominant), [[Piebald|Piebald spotting]] by '''s<sub>P</sub>''' (recessive), while fur length is indicated by '''L''' (short, dominant) or '''l''' (long, recessive). All individuals are equal in genotype and phenotype. In the F<sub>2</sub> generation all combinations of coat color and fur length occur: 9 are short haired with solid colour, 3 are short haired with spotting, 3 are long haired with solid colour and 1 is long haired with spotting. The traits are inherited independently, so that new combinations can occur. Average number ratio of phenotypes 9:3:3:1<ref>Spectrum Dictionary of Biology ''[http://www.spektrum.de/lexikon/biologie-kompakt/mendel-regeln/7470 Mendel Rules]''</ref>]]
[[File:Independent assortment.svg|thumb|For example 3 pairs of homologous chromosomes allow 8 possible combinations, all equally likely to move into the gamete during [[meiosis]]. This is the main reason for independent assortment. The equation to determine the number of possible combinations given the number of homologous pairs = 2<sup>x</sup> (x = number of homologous pairs)]]

The Law of Independent Assortment proposes alleles for separate traits are passed independently of one another.<ref>{{Cite news|url=http://biology.about.com/od/mendeliangenetics/ss/independent-assortment.htm#showall|title=Independent Assortment|access-date=24 February 2016|newspaper=Thoughtco|publisher=About.com|last=Bailey|first=Regina}}</ref><ref name="Neil A 2003, page 293-315"/> That is, the biological selection of an allele for one trait has nothing to do with the selection of an allele for any other trait. Mendel found support for this law in his dihybrid cross experiments. In his monohybrid crosses, an idealized 3:1 ratio between dominant and recessive phenotypes resulted. In dihybrid crosses, however, he found a 9:3:3:1 ratios. This shows that each of the two alleles is inherited independently from the other, with a 3:1 phenotypic ratio for each.

Independent assortment occurs in [[eukaryotic]] organisms during meiotic metaphase I, and produces a gamete with a mixture of the organism's chromosomes. The physical basis of the independent assortment of chromosomes is the random orientation of each bivalent chromosome along the metaphase plate with respect to the other bivalent chromosomes. Along with [[chromosomal crossover|crossing over]], independent assortment increases genetic diversity by producing novel genetic combinations.

There are many deviations from the principle of independent assortment due to [[genetic linkage]].

Of the 46 chromosomes in a normal [[diploid]] human cell, half are maternally derived (from the mother's [[ovum|egg]]) and half are paternally derived (from the father's [[spermatozoon|sperm]]). This occurs as [[sexual reproduction]] involves the fusion of two [[haploid]] gametes (the egg and sperm) to produce a zygote and a new organism, in which every cell has two sets of chromosomes (diploid). During [[gametogenesis]] the normal complement of 46 chromosomes needs to be halved to 23 to ensure that the resulting haploid gamete can join with another haploid gamete to produce a diploid organism.

In independent assortment, the chromosomes that result are randomly sorted from all possible maternal and paternal chromosomes. Because zygotes end up with a mix instead of a pre-defined "set" from either parent, chromosomes are therefore considered assorted independently. As such, the zygote can end up with any combination of paternal or maternal chromosomes. For human gametes, with 23 chromosomes, the number of possibilities is 2<sup>23</sup> or 8,388,608 possible combinations.<ref>{{cite web | title=Meiosis | author=Perez, Nancy | url=http://www.web-books.com/MoBio/Free/Ch8C.htm | access-date=15 February 2007 }}</ref> This contributes to the genetic variability of progeny. Generally, the recombination of genes has important implications for many evolutionary processes.<ref>{{cite journal | pmc=5698631 | year=2017 | last1=Stapley | first1=J. | last2=Feulner | first2=P. G. | last3=Johnston | first3=S. E. | last4=Santure | first4=A. W. | last5=Smadja | first5=C. M. | title=Recombination: The good, the bad and the variable | journal=Philosophical Transactions of the Royal Society of London. Series B, Biological Sciences | volume=372 | issue=1736 | doi=10.1098/rstb.2017.0279 | pmid=29109232 }}</ref><ref>{{Cite journal |doi=10.1098/rspb.2016.1243 |doi-access=free|title=The evolution of recombination rates in finite populations during ecological speciation |year=2016 |last1=Reeve |first1=James |last2=Ortiz-Barrientos |first2=Daniel |last3=Engelstädter |first3=Jan |journal=Proceedings of the Royal Society B: Biological Sciences |volume=283 |issue=1841 |pmid=27798297 |pmc=5095376 }}</ref><ref>{{Cite journal |doi=10.1016/j.jtbi.2018.01.018 |doi-access=free|title=The advantage of recombination when selection is acting at many genetic Loci |year=2018 |last1=Hickey |first1=Donal A. |last2=Golding |first2=G. Brian |journal=Journal of Theoretical Biology |volume=442 |pages=123–128 |pmid=29355539 |bibcode=2018JThBi.442..123H }}</ref>

{{anchor|Law of Dominance}}<span id="Third Law"></span>

==Mendelian trait==
A Mendelian trait is one whose inheritance follows Mendel's principles—namely, the trait depends only on a single [[locus (genetics)|locus]], whose [[allele]]s are either [[Dominance (genetics)|dominant]] or recessive. 

Many traits are inherited in a [[non-Mendelian inheritance|non-Mendelian]] fashion.<ref>{{Cite web|url=https://www.genome.gov/19016930/faq-about-genetic-disorders/|title= Genetic Disorders|date=18 May 2018|website=National Human Genome Research Institute}}</ref>

==Non-Mendelian inheritance==
{{main|Non-Mendelian inheritance}}
Mendel himself warned that care was needed in extrapolating his patterns to other organisms or traits. Indeed, many organisms have traits whose inheritance works differently from the principles he described; these traits are called non-Mendelian.<ref>{{cite journal | doi-access=free | doi=10.1016/j.crvi.2016.04.006 | title=Beyond the simplicity of Mendelian inheritance | year=2016 | last1=Schacherer | first1=Joseph | journal=Comptes Rendus Biologies | volume=339 | issue=7–8 | pages=284–288 | pmid=27344551 }}</ref><ref>Khan Academy: [https://www.khanacademy.org/science/biology/classical-genetics/variations-on-mendelian-genetics/a/variations-on-mendels-laws-overview Variations on Mendel's laws (overview)]</ref>

For example, Mendel focused on traits whose genes have only two alleles, such as "A" and "a". However, many genes have [[multiple alleles|more than two alleles.]] He also focused on traits determined by a single gene. But some traits, such as height, depend on many genes rather than just one. Traits dependent on multiple genes are called [[polygene|polygenic traits]].
==See also==
{{Portal|History of Science|Biology}}
* [[List of Mendelian traits in humans]]
* [[Simple Mendelian genetics in humans]]
* [[Mendelian disease]]s (monogenic disease)
* [[Mendelian error]]
* [[Particulate inheritance]]
* [[Punnett square]]

==References==
{{reflist|30em}}

==Notes==
* {{cite book|author=Bowler, Peter J.|author-link=Peter J. Bowler|year=1989|title=The Mendelian Revolution: The Emergence of Hereditarian Concepts in Modern Science and Society | publisher=Johns Hopkins University Press}}
* {{cite book|last=Atics|first=Jean|title=Genetics: The life of DNA|publisher=ANDRNA press}}
* {{cite book|author1=Reece, Jane B.|author2=Campbell, Neil A.|title=Mendel and the Gene Idea|work=Campbell Biology|edition=9th|publisher=Benjamin Cummings / Pearson Education |date=2011 |page=265}}

==External links==
* [http://www.khanacademy.org/video/introduction-to-heredity?playlist=Biology Khan Academy, video lecture]
* [http://anthro.palomar.edu/mendel/mendel_2.htm Probability of Inheritance]
* [http://www.biotechlearn.org.nz/themes/mendel_and_inheritance/mendel_s_principles_of_inheritance Mendel's principles of Inheritance]
* [http://www.ndsu.edu/pubweb/~mcclean/plsc431/mendel/mendel1.htm Mendelian genetics]

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