The term " wild type " allele is sometimes used to describe an allele that is thought to contribute to the typical phenotypic character as seen in "wild" populations of organisms, such as fruit flies ( Drosophila melanogaster ). Such a "wild type" allele was historically regarded as leading to a dominant (overpowering – always expressed), common, and normal phenotype, in contrast to " mutant " alleles that lead to recessive, rare, and frequently deleterious phenotypes. It was formerly thought that most individuals were homozygous for the "wild type" allele at most gene loci, and that any alternative "mutant" allele was found in homozygous form in a small minority of "affected" individuals, often as  genetic diseases , and more frequently in heterozygous form in " carriers " for the mutant allele. It is now appreciated that most or all gene loci are highly polymorphic, with multiple alleles, whose frequencies vary from population to population, and that a great deal of genetic variation is hidden in the form of alleles that do not produce obvious phenotypic differences. Wild type alleles are often denoted by a superscript plus sign ( i.e. ,  p +  for an allele  p ). [ 12 ]


A population or  species  of organisms typically includes multiple alleles at each locus among various individuals. Allelic variation at a locus is measurable as the number of alleles ( polymorphism ) present, or the proportion of heterozygotes in the population. A  null allele  is a gene variant that lacks the gene's normal function because it either is not expressed, or the expressed protein is inactive.


For example, at the gene locus for the  ABO   blood type   carbohydrate   antigens  in humans, [ 13 ]  classical genetics recognizes three alleles, I A , I B , and i, which determine compatibility of  blood transfusions . Any individual has one of six possible  genotypes  (I A I A , I A i, I B I B , I B i, I A I B , and ii) which produce one of four possible  phenotypes : "Type A" (produced by I A I A  homozygous and I A i heterozygous genotypes), "Type B" (produced by I B I B  homozygous and I B i heterozygous genotypes), "Type AB" produced by I A I B  heterozygous genotype, and "Type O" produced by ii homozygous genotype. (It is now known that each of the A, B, and O alleles is actually a class of multiple alleles with different DNA sequences that produce proteins with identical properties: more than 70 alleles are known at the ABO locus. [ 14 ]  Hence an individual with "Type A" blood may be an AO heterozygote, an AA homozygote, or an AA heterozygote with two different "A" alleles.)


The frequency of alleles in a diploid population can be used to predict the frequencies of the corresponding genotypes (see  Hardy–Weinberg principle ). For a simple model, with two alleles;


where  p  is the frequency of one allele and  q  is the frequency of the alternative allele, which necessarily sum to unity. Then,  p 2  is the fraction of the population homozygous for the first allele, 2 pq  is the fraction of heterozygotes, and  q 2  is the fraction homozygous for the alternative allele. If the first allele is dominant to the second then the fraction of the population that will show the dominant phenotype is  p 2  + 2 pq , and the fraction with the recessive phenotype is  q 2 .


With three alleles:


In the case of multiple alleles at a diploid locus, the number of possible genotypes (G) with a number of alleles (a) is given by the expression:


A number of  genetic disorders  are caused when an individual inherits two recessive alleles for a single-gene trait. Recessive genetic disorders include  albinism ,  cystic fibrosis ,  galactosemia ,  phenylketonuria  (PKU), and  Tay–Sachs disease . Other disorders are also due to recessive alleles, but because the gene locus is located on the X chromosome, so that males have only one copy (that is, they are  hemizygous ), they are more frequent in males than in females. Examples include  red–green color blindness  and  fragile X syndrome .


Other disorders, such as  Huntington's disease , occur when an individual inherits only one dominant allele.


While  heritable traits  are typically studied in terms of genetic alleles,  epigenetic  marks such as  DNA methylation  can be inherited at specific genomic regions in certain species, a process termed  transgenerational epigenetic inheritance . The term  epiallele  is used to distinguish these heritable marks from traditional alleles, which are defined by  nucleotide sequence . [ 15 ]  A specific class of epiallele, the  metastable epialleles , has been discovered in mice and in humans which is characterized by stochastic (probabilistic) establishment of epigenetic state that can be mitotically inherited. [ 16 ] [ 17 ]


The term "idiomorph", from Greek 'morphos' (form) and 'idio' (singular, unique), was introduced in 1990 in place of "allele" to denote sequences at the same locus in different strains that have no sequence similarity and probably do not share a common phylogenetic relationship. It is used mainly in the genetic research of  mycology . [ 18 ] [ 19 ]


An  amorph  is a  mutated   allele  that has lost the ability of the parent allele (whether  wild type  or any other type) to encode any functional  protein . An amorph mutation, or null, is the loss of  genetic information  for the synthesis of appropriate  mRNA . Depending on the relationships of the parent allele, an amorphous mutant can have various forms of  gene interactions . [ 1 ] [ 2 ]


The term "amorph" was used by  Hermann Joseph Muller  in 1932. [ citation needed ]


The manner in which a person folds their  arms  is a dynamic morphological demonstration of two alternative  phenotypes . Once adopted, manner of arms folding across the  chest  does not change throughout the lifetime and persons easily give up the unusual folding position, most commonly at the first attempt.


If the right arm is folded above the left  forearm , the phenotype is characterised as R (right; the right type), and in the opposite case, i.e. if the left arm is positioned above the right, it is the phenotype L (left; left-type). [ 1 ] [ 2 ] [ 3 ]


It has been shown that the phenotypes of these properties are distributed independently with left-handed and right-handed people.


Falk and Ayala (1971) found that variations in arm folding are largely inherited, but these variations are not governed by existing Mendelian models. [ 4 ]  In this regard, Ferronato et al. (1974) found no significant correlation between parents and children. [ 5 ]  Individual type of arms folding is slightly less studied than the manner of  clasping hands . In search of the main factors that determine this dimorphism, the same difficulties emerge as with clasping hands. However, utilising the findings and the views of many authors, [ 6 ] [ 7 ] [ 8 ] [ 9 ] [ 10 ] [ 11 ]  it can be concluded that the manner of arms folding is hereditary and that it inherits the model that does not fit into the genetics concept of simple Mendelian characters, although in this respect there are contradictory findings.
The main conclusion is that the manifestation of alternative phenotypes with these characteristics is irrespective of sex and age, and that it is not related to handedness.


Supporters of the assumptions that genetic factors play an important role in forming these properties are reinforced by the data of very heterogeneous frequencies of alternative phenotypes (R and L) in the explored portion of the world's population. But the point of view that basic genetics could explain the phenomena has also been put in discussion; it is not accepted by all researchers. [ 12 ]  Luria (1947/1970) proposed left-top positions in arm folding (AF) and hand clasping (HC) to be signs of "latent left-handedness". While human beings are more right-handed as animals, it is supposed that left-handedness could be latent. Experiments support Luria's proposition that a left-top preference in Arm Folding points to "latent" left-handedness, but only if associated with a right-top preference in hand clasping. [ 13 ]


The data in the following table summarize  R  distributions in various areas as concluded by the cited studies.


Auricular hypertrichosis  ( hypertrichosis lanuginosa acquisita ,  hypertrichosis pinnae auris ) is a genetic condition expressed as long and strong hairs growing from the  helix  of the  pinna . [ 1 ] [ page needed ]


Ear hair   generally refers to the  terminal hair  arising from  follicles  inside the  external auditory meatus  in humans. [ 2 ]  In its broader sense,  ear hair  may also include the fine  vellus hair  covering much of the ear, particularly at the prominent parts of the anterior ear, or even the abnormal hair growth as seen in  hypertrichosis  and  hirsutism . Medical research on the function of ear hair is currently very scarce.


Hair growth within the ear canal is often observed to increase in older men, [ 3 ]  together with increased growth of  nose hair . [ 4 ]  Excessive hair growth within or on the ear is known medically as  auricular  hypertrichosis . [ 5 ]  Some men, particularly in the male population of India, have coarse hair growth along the lower portion of the helix, a condition referred to as "having  hairy  pinnae " ( hypertrichosis lanuginosa acquisita ). [ 6 ]


The genetic basis of auricular hypertrichosis has not been settled. Some researchers have proposed a Y-linked pattern of inheritance and others have suggested an autosomal gene is responsible. A third hypothesis predicts the  phenotype  results from the interaction of two loci, one on the homologous part of the X and Y and one on the nonhomologous sequence of the Y. [ 7 ]  These hypotheses are not mutually exclusive, and there may be a variety of genetic mechanisms underlying this phenotype.


Lee et al. (2004), using Y-chromosomal DNA binary-marker haplotyping, suggested that a cohort of southern Indian hairy-eared males carried Y chromosomes from many  haplogroup . [ 8 ]  The hypothesis of Y- linkage would require multiple independent mutations within a single  population . No significant difference between the Y-haplogroup frequencies of hairy-eared males and those of a geographically matched control sample of unaffected males was established. The study concluded that auricular hypertrichosis is not Y-linked in southern India, though this result may not apply to all to all populations. [ 9 ]


In  evolutionary biology , a  balanced lethal system  is a situation where recessive  lethal alleles  are present on two  homologous chromosomes . [ 1 ]  Each of the  chromosomes  in such a pair carries a different lethal allele, which is compensated for by the functioning allele on the other chromosome. [ 1 ]  Since both these lethal alleles end up in the  gametes  in the same frequency as the functioning alleles, half of the offspring, the homozygotes, receive two copies of a lethal allele and therefore die during development. [ 1 ]  In such systems, only the heterozygotes survive. [ 1 ]


Balanced lethal systems appear to pose a challenge to  evolutionary theory , since a system so wasteful should be rapidly eliminated through  natural selection  and  recombination . [ 2 ]  Instead, it has become fixed in various species all over the tree of life. [ 1 ] [ 2 ]


The exact mechanism behind balanced lethal systems remains unknown. Prior to the availability of efficient DNA sequencing methods, it was already known that the lethality in such a system was caused by  homozygosity  of a certain chromosome pair. [ 3 ] [ 4 ]


One theory is that, in the case of the  Triturus  genus, the balanced lethal system is a remnant of an ancient  sex-determination system . [ 1 ] [ 2 ]  One of the chromosomes of the pair that contains the system is longer than the other, which is also the case for the actual sex chromosomes. [ 2 ]  In this theory, deleterious mutations accumulated on the non-recombining part of the  Y-chromosome  ( Muller’s ratchet ). [ 1 ] [ 2 ] [ 5 ]  Then, two distinct Y-chromosomes, both with different lethal mutations, co-segregated in a population. [ 1 ]  Since sex-determination in many cold-blooded vertebrates is potentially dependent on temperature, a shift away from chromosomal sex determination occurred. [ 1 ] [ 2 ]  This system favoured the  sex reversal  of females, which eventually led to the loss of the original  X-chromosome . [ 1 ] [ 2 ]  A mutation on another chromosome later restored the even sex ratio, and gave rise to a new male-heterogametic system. [ 1 ] [ 2 ]  A major restriction for this theory is that it could only evolve in species where temperature-dependent sex-reversal is possible. [ 1 ]  Since balanced lethal systems are found in many species where this is not the case, this theory does not provide a general explanation for how such a system evolved. [ 1 ]


Another theory is that balanced lethal systems are collapsed  supergenes . [ 1 ]  Supergenes are linked genes that are inherited as a single unit. [ 6 ]  Genes can only be inherited together when recombination is suppressed, for example when selection favors certain allelic combinations. [ 6 ]  The lack of recombination can lead to the accumulation of  mutations  in both supergene clusters [ 1 ] [ 6 ]  and this could generate a feedback loop: [ 1 ]  when natural selection favours heterozygotes, few homozygotes reproduce. [ 1 ]  This lack of reproduction leads to the accumulation of deleterious alleles. When lethal mutations become fixed on both supergene alleles, homozygotes are no longer viable, resulting in a balanced lethal system. [ 1 ]


A well known balanced lethal system is the one fixed in the genus  Triturus  (containing the crested and the marbled newts). [ 4 ]  Each of the homologous chromosomes of pair 1 (1A and 1B) has a different recessive deleterious allele on a non-recombining section of the chromosome. [ 2 ]  Therefore, only heterozygotes are viable since these deleterious alleles are compensated for by the functioning allele on the other homologue. As a result half of all offspring stop growing and die during early development. [ 2 ]


The offspring of  Triturus carnifex  for example, have either a viable heterozygous genotype (1A/1B) or one of the homozygous embryonic lethal genotypes: fat-tailed (1A/1A) or slim-tailed (1B/1B). [ 7 ]


Biparental inheritance  is a type of biological inheritance where the progeny inherits a maternal and a paternal  allele  for one gene. It is one of the criteria for  Mendelian inheritance .  Sexual reproduction , where offspring result from the fusion of  gametes  from two parents, is the most common form of biparental inheritance. While less common, cases of biparental inheritance in extranuclear genes have been documented, such as biparental inheritance of  mitochondrial DNA , or  chloroplast DNA  in plants. [ 1 ]  Biparental inheritance of nuclear DNA by way of sexual reproduction can allow for new combinations of alleles from each contributing parent. The production of gametes through  meiosis  can sometimes include recombination, or  crossing-over , which is a possibility for novel combinations of alleles.


Biparental inheritance is a requirement for a trait to be characterized as Mendelian. If the gene does not have alternate forms, described as alleles, which can differ in each parent and then come together in the resulting offspring, then this trait is  non-Mendelian . Part of the reason biparental inheritance is obligatory in Mendelian inheritance is because another requisite is the  fertilization  of gametes which have been produced by random segregation. Without gametes created by random segregation, fertilization (which leads to biparental inheritance through these gametes) could not result in Mendelian inheritance.


Biparental  extranuclear inheritance  occurs in the yeast  Saccharomyces cerevisiae , for example. Two  haploid  cells of opposite mating types fuse together, both of which contribute mitochondria  to the  diploid  offspring. [ 2 ]  This is contrary to the majority of  eukaryotic  mitochondrial inheritance, which is largely inherited maternally. Within mitochondrial genomes, biparental inheritance and recombination have been documented in plants, animals and fungi by Barr et al. in 2005, [ 3 ]  but the extent of these phenomena are thought to vary substantially across taxa. Occasional biparental mitochondrial transmission may benefit offspring by facilitating the removal of disadvantageous mutations from a population, while at the same time, continuing to restrict the spread of selfish genetic elements, such as genes that have a replication and transmission advantage at the expense of other genes  [ 3 ]


While uncommon among most eukaryotes, biparental inheritance of mtDNA occurs regularly in  bivalves .  Paternal mtDNA leakage  has been documented in sheep, [ 4 ]  mice, [ 5 ]  and  Drosophila . [ 6 ]  In 2018, Luo et al. documented evidence of biparental inheritance of  mitochondrial DNA  in humans, which was thought to be only transmitted maternally. [ 7 ]  Although paternal mitochondrial DNA, in addition to the typically inherited maternal mtDNA, was proven to have been inherited by 17 members in three unrelated multigenerational families, researchers are not yet sure of the mechanisms through which this occurs. Luo et al. explain that maternal transmission of mtDNA results from the active elimination of paternal mitochondria, and that the genes underlying this elimination process may have undergone certain mutations to allow mtDNA to continue through embryonic development. [ 7 ]  Mitochondrial endonuclease G relocates from the intermembrane space of paternal mitochondria to the matrix after fertilization, where it proceeds to degrade or eliminate paternal mtDNA. [ 8 ]  A defect in such an EndoG-like pathway in humans might produce a paternal contribution, thus explaining a possible mechanism for biparental inheritance.


Blending inheritance  is an  obsolete theory  in  biology  from the 19th century. The theory is that the progeny  inherits  any characteristic as the average of the parents' values of that characteristic. As an example of this, a crossing of a red flower variety with a white variety of the same  species  would yield pink-flowered offspring.


Charles Darwin 's theory of inheritance by  pangenesis , with contributions to egg or sperm from every part of the body, implied blending inheritance. His reliance on this mechanism led  Fleeming Jenkin  to attack Darwin's theory of  natural selection  on the grounds that blending inheritance would average out any novel beneficial characteristic before selection had time to act.


Blending inheritance was discarded with the general acceptance of  particulate inheritance  during the development of modern  genetics , after  c.  1900 .


Charles Darwin  developed his theory of  evolution  by  natural selection  on the basis of an understanding of  uniform processes  in  geology , acting over very long periods of time on inheritable variation within populations. One of those processes was competition for resources, as  Thomas Malthus  had indicated, leading to a struggle to survive and to reproduce. Since some individuals would by chance have traits that allowed them to leave more offspring, those traits would tend to increase in the population. Darwin assembled many lines of evidence to show that variation occurred and that  artificial selection  by animal and plant breeding had caused change. All of this demanded a reliable mechanism of  inheritance . [ 1 ]


Pangenesis  was Darwin's attempt to provide such a mechanism of inheritance. The idea was that each part of the parent's body emitted tiny particles called  gemmules , which migrated through the body to contribute to that parent's  gametes , their eggs or sperms. The theory had an intuitive appeal, as characteristics of all parts of the body, such as shape of nose, width of shoulders and length of legs are inherited from both the father and the mother. However, it had some serious weaknesses. Firstly, many characteristics can change during an individual's lifetime, and are affected by the environment:  blacksmiths  can develop strong arm muscles during their work, so the gemmules from these muscles ought to carry this acquired characteristic. That implies the  Lamarckian   inheritance of acquired characteristics . Secondly, the fact that the gemmules were supposed to mix together on  fertilisation  implies blending inheritance, namely that the offspring would all be intermediate between the father and the mother in every characteristic. That directly contradicts the observed facts of inheritance, not least that children are usually either male or female rather than all  intersex , and that traits such as flower colour often re-emerge after a generation, even when they seem to disappear when two varieties are crossed. [ 1 ] [ 2 ] [ 3 ]  Darwin was aware of both these objections, and accordingly had strong doubts about blending inheritance, as evidenced in his private correspondence. In a letter to  T.H. Huxley , dated November 12, 1857, Darwin wrote:


I have lately been inclined to speculate very crudely & indistinctly, that propagation by true fertilisation, will turn out to be a sort of mixture & not true fusion, of two distinct individuals, or rather of innumerable individuals, as each parent has its parents & ancestors:— I can understand on no other view the way in which crossed forms go back to so large an extent to ancestral forms." [ 4 ]


In a letter to  Alfred Wallace , dated February 6, 1866, Darwin mentioned conducting hybridization experiments with pea plants, not unlike those done by  Gregor Mendel , and like him obtaining  segregating  (unblended) varieties, effectively disproving his theory of pangenesis with blending:


I do not think you understand what I mean by the non-blending of certain varieties. It does not refer to fertility; an instance I will explain. I crossed the Painted Lady and Purple  sweetpeas , which are very differently coloured varieties, and got, even out of the same pod, both varieties perfect but not intermediate. Something of this kind I should think must occur at least with your butterflies & the three forms of  Lythrum ; tho’ those cases are in appearance so wonderful. I do not know that they are really more so than every female in the world producing distinct male and female offspring... [ 7 ]


Blending inheritance was also clearly incompatible with Darwin's theory of evolution by natural selection. The engineer  Fleeming Jenkin  used this to attack natural selection in his 1867 review of Darwin's  On the Origin of Species . Jenkin noted that if inheritance were by blending, any beneficial trait that might arise in a lineage would have "blended away" long before natural selection had time to act. [ 1 ] [ 5 ] [ 6 ]  The evolutionary biologist  Richard Dawkins  commented that blending inheritance was observably wrong, as it implied that every generation would be more uniform than the one before, and that Darwin should have said as much to Jenkin. The problem was not with natural selection, but with blending, and in Dawkins's view, Darwin should have settled for saying that the mechanism of inheritance was unknown, but certainly non-blending. [ 1 ]


Blending inheritance was dismissed by the eventual widespread acceptance, after his death, of  Gregor Mendel 's theory of  particulate inheritance , which he had presented in  Experiments on Plant Hybridization  (1865). [ 8 ] [ 9 ]  In 1892,  August Weismann  set out the idea of a hereditary material, which he called the  germ plasm , confined to the gonads and independent of the rest of the body (the  soma ). In Weismann's view, the germ plasm formed the body, but the body did not influence the germ plasm, except indirectly by natural selection. This contradicted both Darwin's pangenesis and Lamarckian inheritance. [ 10 ] [ 11 ]  Mendel's work was rediscovered in 1900 by the geneticist  Hugo de Vries  and others, soon confirmed that same year by experiments by  William Bateson . [ 12 ]  Mendelian inheritance with segregating, particulate  alleles  came to be understood as the explanation for both discrete and continuously varying characteristics. [ 13 ] [ 14 ] [ a ]


Complementation  refers to a  genetic  process when two  strains  of an  organism  with different homozygous recessive  mutations  that produce the same mutant  phenotype  (for example, a change in wing structure in flies) have offspring that express the  wild-type  phenotype when mated or crossed. Complementation will ordinarily occur if the mutations are in different genes (intergenic complementation). Complementation may also occur if the two mutations are at different sites within the same gene (intragenic complementation), but this effect is usually weaker than that of intergenic complementation. When the mutations are in different genes, each strain's genome supplies the wild-type  allele  to "complement" the mutated allele of the other strain's genome. Since the mutations are recessive, the offspring will display the wild-type phenotype. A  complementation test  (sometimes called a " cis-trans " test) can test whether the mutations in two strains are in different genes. Complementation is usually weaker or absent if the mutations are in the same gene. The convenience and essence of this test is that the mutations that produce a phenotype can be assigned to different genes without the exact knowledge of what the gene product is doing on a molecular level.  American geneticist  Edward B. Lewis  developed the complementation test.


For a simple example of a complementation test, suppose a geneticist is interested in studying two strains of white-eyed flies of the species  Drosophila melanogaster , more commonly known as the common fruit fly. In this species,  wild-type  flies have red eyes, and eye color is known to be related to two genes, A and B. Each of these genes has two alleles, a  dominant  one that codes for a working protein ( A  and  B  respectively) and a  recessive  one that codes for a malfunctioning protein ( a  and  b  respectively). Since both proteins are necessary for the synthesis of red pigmentation in the eyes, if a given fly is  homozygous  for either  a  or  b , it will have white eyes.


In genetics, a complementation test can be conducted to understand the interaction between different genetic strains. This test often involves crossing two pure-breeding strains, such as white-eyed flies, from separate origins. The process entails mating two flies, each from a different strain. The eye color of the resulting progeny determines the outcome of the test. If the progeny exhibit red eyes, it indicates that the two strains complement each other. Conversely, if the progeny have white eyes, it suggests non-complementation.


Complementation occurs when each strain possesses a different homozygous mutation (for example, one strain having the genotype 'aa BB' and the other 'AA bb'), resulting in a heterozygous genotype ('AaBb') in the progeny that produces a different phenotype from the parents. Non-complementation is observed when both strains share the same homozygous mutation, such as 'aaBB', 'AAbb', or 'aabb', leading to progeny with a phenotype identical to the parent strains.


Complementation tests can also be carried out with  haploid   eukaryotes  such as  fungi , with bacteria, and with viruses such as  bacteriophage . [ 1 ]   Research on the fungus  Neurospora crassa  led to the development of the one-gene-one-enzyme concept that provided the foundation for the subsequent development of molecular genetics. [ 2 ] [ 3 ]  The complementation test was one of the main tools used in the early Neurospora work, because it was easy to do, and allowed the investigator to determine whether any two nutritional mutants were defective in the same or different genes.


The complementation test was also used in the early development of molecular genetics when bacteriophage T4 was one of the main objects of study. [ 4 ]  In this case the test depends on mixed infections of host bacterial cells with two different bacteriophage mutant types. Its use was key to defining most of the genes of the virus, and provided the foundation for the study of such fundamental processes as DNA replication and repair, and how  molecular machines  are constructed.


Heterosis  is the tendency for hybrid individuals to exceed their purebred parents in size and vigor. The phenomenon has long been known in animals and plants. Heterosis appears to be largely due to genetic complementation, that is the masking of deleterious recessive alleles in hybrid individuals.


In general, the two fundamental aspects of sexual reproduction in eukaryotes are  meiosis  and  outcrossing . These two aspects have been proposed to have two natural selective advantages, respectively.  Meiosis is proposed to be adaptive because it facilitates recombinational  repair of DNA damages  that are otherwise difficult to repair. Outcrossing is proposed to be adaptive because it facilitates complementation, that is the masking of deleterious recessive alleles  [ 5 ]  (also see  heterosis ).  The benefit of masking deleterious alleles has been proposed to be a major factor in the  maintenance of sexual reproduction  among eukaryotes.  Further, the selective advantage of complementation that arises from outcrossing may largely account for the general avoidance of inbreeding in nature (e.g. see articles  kin recognition ,  inbreeding depression , and  incest taboo ). [ 6 ]


Used by  quantitative genetics  to uncover recessive mutants. Here one takes deficiencies and crosses them to a  haplotype  that is believed to contain the recessive mutant.


These rules (patterns) are not without exceptions. Non-allelic mutants may occasionally fail to complement (this is known as "non-allelic non-complementation" or "unlinked non-complementation"). This is an uncommon occurrence that depends on the type of mutants being investigated. Two mutations, for example, could be synthetically  dominant negative .  Transvection  is another instance, in which a heterozygous combination of two alleles with mutations in distinct sections of the gene complement one other to restore a wild-type phenotype. [ 7 ]


When complementation between two mutants defective in the same gene is measured, it is generally found that there is either no complementation or the complementation phenotype is intermediate between the mutant and wild-type phenotypes. Intragenic complementation (also called inter-allelic complementation) has been demonstrated in many different genes in a variety of organisms including the fungi  Neurospora crassa ,  Saccharomyces cerevisiae ,  and  Schizosaccharomyces pombe ; the bacterium  Salmonella  typhimurium ; and the virus  bacteriophage T4 . [ 8 ]  In several such studies, numerous  mutations  defective in the same gene were isolated and mapped in a linear order based on  recombination  frequencies to form a  genetic map  of the gene. Separately, the mutants were tested in pairwise combinations to measure complementation. An analysis of the results from such studies led to the conclusion that intragenic complementation, in general, arises from the interaction of differently defective polypeptide monomers to form an aggregate called a “multimer.” [ 9 ]  Genes that encode multimer-forming polypeptides appear to be common. One interpretation of the data is that polypeptide monomers are often aligned in the multimer in such a way that mutant polypeptides defective at nearby sites in the genetic map tend to form a mixed multimer that functions poorly, whereas mutant polypeptides defective at distant sites tend to form a mixed multimer that functions more effectively. The intermolecular forces likely responsible for self-recognition and multimer formation were discussed by Jehle. [ 10 ]


In  genetics ,  complete  (or  absolute )  linkage [ 1 ]  is defined as the state in which two  loci  are so close together that  alleles  of these loci are virtually never separated by  crossing over . The closer the physical location of two genes on the DNA, the less likely they are to be separated by a crossing-over event. In the case of male  Drosophila  there is complete absence of recombinant types due to absence of crossing over.  This means that all of the genes that start out on a single chromosome, will end up on that same chromosome in their original configuration. In the absence of recombination, only parental phenotypes are expected. [ 2 ]


Genetic Linkage  is the tendency of alleles, which are located closely together on a chromosome, to be inherited together during the process of  meiosis  in sexually reproducing organisms.  During the process of meiosis, homologous chromosomes pair up, and can exchange corresponding sections of DNA. As a result, genes that were originally on the same chromosome can finish up on different chromosomes. This process is known as  genetic recombination . The rate of recombination of two discrete loci corresponds to their physical proximity. Alleles that are closer together have lower rates of recombination than those that are located far apart. The distance between two alleles on a chromosome can be determined by calculating the percentage or recombination between two loci. These probabilities of recombination can be used to construct a  linkage map , or a graphical representation of the location of genes and gene in respect to one another. If linkage is complete, there should be no recombination events that separate the two alleles, and therefore only parental combinations of alleles should be observed in offspring. Linkage between two loci can have significant implications regarding the inheritance of certain types of diseases. [ 3 ]


Gene maps or Qualitative Trait Loci (QTL) maps can be produced using two separate methods. One way uses the frequency of marker alleles and compares them to individuals selected from the two tails of the trait distribution. This is called the Trait-Based approach and strictly uses phenotypic information only to select the individuals for a sample. The other approach is called the Marker-Base approach (MB), and uses both the difference in marker allele frequencies and the phenotypic values of each marker genotype when selecting samples. [ 4 ]


(Click here for more information on Linkage Maps  [1] )


In diploid eukaryotic cells, recombination can occur during the process of Meiosis. Homologous chromosomes pair up during meiosis before finally splitting, resulting in two haploid daughter cells each with a single copy of every chromosome. While homologous chromosomes are lined up, they are free to exchange corresponding segments of their own DNA with that of their homolog. This results in a chromosomes that carry both maternal and paternal DNA. Through recombination, daughter cells have the greatest amount of genetic diversity. [ 5 ]


(Click Here for a video tutorial explaining genetic recombination)


One powerful tool for interpreting and graphing linkage data sets is called  Hierarchical Clustering . Clustering organizes things into groups based on similarity. In the case of linkage, similarity equates to physical proximity on a chromosome. Hierarchical clustering is a bottom-up approach to cluster analysis, in which the two closest data points are grouped together and are treated as a single data point for later clustering. In complete-linkage Hierarchical Clustering, this process of combining data points into clusters of increasing size is repeated until all date as part of a single cluster. [ 6 ]  The resulting diagram from a Hierarchical Cluster Analysis is called a  dendrogram , in which data are nested into brackets of increasing dissimilarity. Two common issues with Hierarchical Clustering include designating a specific distance of “similarity” between two data points, in order to generate meaningful associations between data points, and also how to merge data points, in a way that will be helpful for further clustering once they have been deemed similar. A cross-clustering algorithm with automatic estimation of the number of clusters has been designed, which helps resolve some of these issues. By fine tuning the number of clusters expected, the possibility of associating two unrelated clusters is minimized. [ 7 ]  Again, under this type of analysis, a single resultant cluster signifies complete-linkage, since all data points are within the range of assigned similarity.


(Click Here for an interactive Hierarchical Clustering Demo)


The idea of genetic linkage was first discovered by the British geneticists  William Bateson ,  Edith Rebecca Saunders  and  Reginald Punnett .  Thomas Hunt Morgan  expanded the idea of linkage after noticing that in some instances the observed rate of crossing-over events differed from the expected rate of crossing-over events. He attributed the depressed rates of recombination to the smaller spatial separation of genes on a chromosome; Hypothesizing that genes which are more closely positioned on a chromosome will have smaller rates of recombination than those that are spaced farther apart. [ 8 ]  The unit of measurement describing the distance between two linked genes is the  Centimorgan , and is named after Thomas Hunt Morgan. A centimorgan is equivalent to the percent of recombination. two loci with 2% recombination frequency are located 2 centimorgans apart. [ 9 ]


recombination frequency

 =

 Number Recombinant Progeny
 Total Number Progeny

 ×
 100
 %

 {\displaystyle {\text{recombination frequency}}={\frac {\text{Number Recombinant Progeny}}{\text{Total Number Progeny}}}\times 100\%}

 [ 10 ]


Being able to determine linkage between genes can also have major economic benefits. Learning about linkage of traits in sugar cane has led to more productive and lucrative growth of the crop. Sugar cane is a sustainable crop that is one of the most economically viable renewable energy sources. QTL analysis for sugarcane was used to construct a linkage map that identified gene clusters and important linked  loci  that can be used to predict the response to fungal infection in a specific line of sugar cane. [ 11 ]


Linkage mapping can also be useful in determining the inheritance patterns of traits such as psychological disease. Linkage studies of  panic disorder  and  anxiety disorders  have indicated regions of interest on specific chromosomes. Chromosomes 4q21 and 7p are being considered strong candidate regions for panic and fear-associated anxiety disorder loci. Knowing the specific location of these loci and their probability of being inherited together based on their linkage can offer insight into how these disorders are passed down, and why they often occur together in patients. [ 12 ]


Cosegregation  is the transmission to the next generation, of two or more  genes  in proximity on the same  chromosome . Their closeness means that they are  genetically linked . [ 1 ]  It may also represent an interaction estimation probability between any number of loci.


Interaction probability is determined using specified parts of a target gene ( loci ) and a group of  nuclear profiles  (NPs). [ 2 ]  The picture to the right serves to provide visual aid as to how a slice (NP) is taken from the nucleus and loci are searched for within the NP. Cosegregation used within other mathematical models (SLICE [ 3 ]  and  normalized linkage disequilibrium ) assist in rendering 3-D visualizations as a smaller process of  genome architecture mapping  (GAM). These renderings help determine genomic density and radial position.


Cosegregation in  Genome architecture mapping  (GAM) is another process being used to identify the compaction and adjacency of genomic windows. In a study from 2017, cosegregation was used to understand gene-expression-specific contacts in organizing the genome in mammalian nuclei in the larger process of GAM. [ 3 ]  The results of the study produced complex 3D structures that displayed interactions under certain regions of chromatin contacts and proved that GAM is a useful tool in the genome biologist's skill set that expands the ability to finely dissect 3D chromatin structures, cell types and valuable human samples. A study in 2021 "discovered extensive 'melting' of long genes when they are highly expressed and/or have high chromatin accessibility. The contacts most specific of neuron subtypes contain genes associated with specialized processes, such as addiction and synaptic plasticity, which harbour putative binding sites for neuronal transcription factors within accessible chromatin regions." [ 6 ]  Both of these studies used mice as models due to their anatomical, physiological, and genetic similarity to humans. [ 7 ]


Some of the earliest known studies that have used cosegregation dates back to the early 1980s. Around this time, scientists were conducting experiments on vegetative organisms to see the if there are unique sequences of  chloroplast DNA . The process of the experiment was to track the chloroplast gene in each generation by clustering the genes in  nucleoids  to reduce the number of segregated units. This study was done at the  Duke University  in the Zoology Department [ 8 ]  where Karen P. VanWinkle-Swift utilized  Pedigree Diagrams  to show how the traits and sequences were passed down from parent to child.


Cosegregation is best suited for cases where multiple factors' interactions are under consideration. It can show how different factors are linked and highlight their interactions and connections. For example, if a genetic disorder was identified as related to a certain gene, but is not always present when that gene is, then a cosegregation analysis could help identify other genes that interact with the suspect gene more often than normal. This could lead researchers to discover the combination of genes that manifest the genetic disorder. Cosegregation is being actively used in medical fields like  cancer  research. It can highlight the strongest connections between genes in cases where cancer develops. This is useful because there often isn't a single gene causing cancer. Rather, cancer can be caused by a multitude of gene combinations. Cosegregation helps to show links between genes that could be forming these combinations. [ 3 ]


An example of an application using cosegregation would be finding the  normalized   linkage disequilibrium  (NL) between two loci. Given a 2D dataset (row = genomic window slice, column = nuclear profile (NP)) a "1" was displayed if an NP existed in a window or a "0" otherwise. From this data, the NL could be found using the base

 l
 i
 n
 k
 a
 g
 e

 {\displaystyle linkage}

  disequilibrium and its theorized maximum (

 d
 m
 a
 x

 {\displaystyle dmax}

 ). The amount of NPs present in loci (genomic windows)

 A

 {\displaystyle A}

  and

 B

 {\displaystyle B}

 , is then used to find the

 d
 e
 t
 e
 c
 t
 i
 o
 n
 f
 r
 e
 q
 u
 e
 n
 c
 i
 e
 s

 {\displaystyle detectionfrequencies}

 ,

 f
 a

 {\displaystyle fa}

  and

 f
 b

 {\displaystyle fb}

  and the co-segregation which is,

 f
 a
 b

 {\displaystyle fab}

 . after the NL is found between two loci, it was then placed into another dataset to be visualized and then analyzed to determine how interconnected a loci is.
This example was executed using  python  for computation and visualization of the given data and results and in finding the NL. Using the NL further analysis can be done to place the windows into "communities". To showcase this a graph to the right will show the community of one of the windows with the highest  centrality  which uses the average of the window's NLs.


N
 L
 =
 l
 i
 n
 k
 a
 g
 e

 /

 d
 m
 a
 x

 {\displaystyle NL=linkage/dmax}


Variables "A" and "B" are the total number of nuclear profiles (NP) present in a given a detected genomic region slice, "N" is the total number of NPs and FAB is the frequency of A and B


This formula can be easily programmed into code as seen in the  pseudo-code  in the figure to the right. The code was written to satisfy the Example described above.


Given a large dataset of nuclear profiles, cosegregation is easily scalable given its simplistic mathematical formulas. The larger the data set that is provided, the more accurate the following equations will be. As depicted in the photo below, the amount of data being added to the equation merely adds linear time adjustments to the original equation.


Fortunately, not only is it able to scale dataset sizes well, it is able to take as many loci of focus that are required to determine the interaction probability. Provided that adding each loci adds a single computation to the equation, a linear time complexity is the result. The picture below shows how the amount of loci affects the detection frequency equation.


Finally, the numerical value that results can assist in drawing multiple conclusions including radial position, compaction, and the most influential contacts.


Effective cosegregation analysis depends largely on having a strong supporting dataset because even small inaccuracies can be compounded by cosegregation. A complete understanding of the material is necessary as cosegregation only provides connections between datapoints. The interpretation of those connections must be done through another method. For example, locus cosegregation can give a score of genes that commonly interact with each other, but no matter how strong those relationships are, the results of quantitative cosegregation can seem to support either a correlated, anti-correlated or independent relationships. It is important to be aware of this and follow up cosegregation analysis with another form of analysis, such as normalized linkage disequilibrium to correct for the compounding effect cosegregation can have on negligible variations in the detection frequency of the data.


For example, imagine a simple form of cancer that is trigged by a small number of genes. Here we are examining a suspect gene and three other genes that are suspected to be involved in the processes. This chart shows a hypothetical data set of 10 people and their cancer status as well as if they possess the four genes of interest. Looking at the graph, there is a clear connection between the suspect gene and Gene A. There is also a less obvious interaction between the suspect gene and Gene C that only takes place when Gene B is absent. It is entirely possible that co-segregation would have a hard time determining that relationship. Gene B is commonly present with Gene A and that combination does result in cancer. In a real data set with hundreds or even thousands of genes being examined, one could erroneously conclude that Gene B contributes to the cancer when, in reality it does not and can actually prevent it.


Another limitation of this technique is that many mapping tools measure not only specific physical interactions between genes but also random contacts, the latter being much more common between genes with smaller linear genomic distance this could lead to inflated co-segregation scores. GAM has helped to resolve this issue because in GAM the detection of genomic windows is independent of any interactions with other regions. This allows for an expected interaction value to be calculated and combining this with the co-segregation results to filter out the noise of random connections this will provide a cleaner result. [ 3 ]


Matrices  are a rectangular structured array of numbers (entries) where the entries can be summed, subtracted, multiplied, and divided using the standard math operations. In the case of co-segregation,  Graph theory  is used to see if a variable shares an edge or vertex with another variable on a network of nodes. Graph theory is the mathematical study of objects using pairwise relations that is shown through connected nodes called vertices that are connected to other nodes by edges.


The image above depicts the conversion from a cosegregation matrix to an adjacency matrix is one use of a matrix in genome architecture mapping where scientists are using cryosectioning to find  colocalization  between DNA regions, genomes, and/or alleles. In that example, cosegregation is being used to describe the linkage of data to each other in terms of the distance between specific windows in a genome. The values in the cosegregation matrix were found using the formula above. Comparing windows  A  and  B , the formula seeks to find the intersection of Nuclear Profiles between the respective windows. The genomic windows would be the nodes and the adjacency graph is the matrix depiction of the edges connecting each node.


A heat map is a visual representation of a matrix of  m  ×  n  that can show different phenomenons on a two-dimensional scale. Heat maps have a range of color intensities based on the values and scale given from the data. Coding-wise, heat maps can be created using libraries such as  plotly.express  in Python. Using co-segregation, heat maps are used to visualize a matrix that contains values of either 1 or 0 to visualize the commonalities between 2 or more variables. "The primary benefit of using heat maps is that they make otherwise dull or impenetrable data understandable. Many people understand heat maps intuitively, without even needing to be told that those warmer colors indicate a denser focus of interactions." [ 9 ]


In the limitation section, there are two heat maps (also put below for easy viewing) shown depicting the difference between normalized and un-normalized data. Showing the difference in the graphs would help the researcher identify different patterns based on the intensity of the color gradients as well as the clustering of data points. Cosegregation results as seen above can have different forms and visualizing them in heat maps can aid researchers in understanding which genomes are connected similar to matrices.


One limitation to heat maps are that some software does not allow the use of locating specific points on the graph, especially if there are many variables. There are coding libraries such as plotly.express that can create interactive heat maps where the programmer can hover over specified points on a graph and read the exact dependent variable's value. Another limitation is that heat maps do not represent real-time data. Since heat maps work by aggregating data over time, it does not show recent changes in behavior compared to the more dominant patterns already present. [ 9 ]


Developmental noise  or  stochastic  noise  is a concept within  developmental biology  in which the observable characteristics or traits ( phenotype ) varies between individuals even though both individuals share the same genetic code ( genotypes ) and the other  environmental factors  are completely the same. [ 1 ] [ 2 ]  Factors that influence the effect include  stochastic , or randomized, gene expression and other  cellular noise . [ 3 ]


Although organisms within a species share very similar genes, similar environments and similar developmental history, each individual organism can develop differences due to noise in  signaling and signal interpretation . This developmental noise may help individuals gain the ability to adapt to the environment and contribute to their unique patterns of development. [ 4 ]  Human  fingerprints  provide a well-known example; the fingerprints differ even between genetically identical human twins. [ 5 ]


Developmental noise may help individuals gain the ability to adapt to the environment.  Biological systems  display both variation and robustness. [ 6 ]  Natural variation within a population is in large part genetically determined, but variation due to noise may contribute to a rapid response by an individual to changes in the environment. This variation can have an evolutionary tuning effect that contributes to the optimal fitness of a population. In support of this idea, it has been shown that bacteria can switch  stochastically  into a "persistent" state which has slow growth coupled with an ability to survive antibiotic treatment. [ 7 ]  In another study, it has been shown that most of the noisy proteins were associated with the stress response. When proteins are expressed in small quantities, the expression of more noisy proteins will be more influenced by noises which come from the environmental context. Types of noises include extrinsic noise which is the variation in cell-to-cell expression level of protein, and intrinsic noise which is the variation of the inherent stochastic nature of protein expression. [ 8 ]  Moreover, noisy genes are associated with a distinct promoter architecture, including the prevalence of  TATA boxes , consistent with the theoretical predictions that noise is greatly influenced by the logic of the transcriptional process itself and, in particular, the transition from closed to open chromatin. [ 9 ]


The developmental noise can contribute to unique patterns of development in each individual as well. During development of a complex organ, variability in gene expression may be required to contribute to differentiation of multiple cell types from cells that have equivalent potential. For example, the patterning of the adult fly eye relies on multiple alternative choices of differentiation pathways within an apparently homogeneous field of cells. The facets ( ommatidia ) in fly eyes occur as two types, designated pale and yellow, as defined by the particular types of rhodopsin photopigments expressed in the two inner photoreceptor cells. [ 10 ] [ 11 ]  In flies carrying mutations in the gene spineless, all ommatidia show the pale fate, while over expression of spineless induces the yellow fate. The final pattern of ommatidia is determined by stochastic variation in expression of this single  transcription factor  Spineless. [ 10 ]


A comprehensive review article summarized effects of noise on cellular decisions from bacteria to mammalian cells. [ 12 ]


The majority of study on developmental noise has focused on animals, but there are also examples from plants. In one early study, Roy made thousands of observations on petal numbers as well as on leaf tooth numbers. He observed a high degree of variability in both traits. After analyzing his data, he could not conclude that the variability was caused by environmental effect. Another example of noise in plants is lateral root behavior. People found that the growth of  lateral roots  is unpredictable in genetically identical plants which grow in the same environment. One more example of seed germination may illustrate the benefit of developmental noise in plants. Stochasticity in the timing of germination ensures that at least a fraction of the progeny will survive to reproduce. [ 11 ]


Though stochastic variations in cell behaviors may be beneficial, most biological systems need to maintain a reliable output without unpredictable variations. This ability to buffer variations generated by molecular noise,  genetic polymorphism , or environmental fluctuations is termed robustness.


For example, in the development of the repeating blocks of  somites  in the  mesoderm  of vertebrate animals, even though the biological system may be subject to a noisy environment, the segmentation clock maintains periodic gene expression through coupled oscillators, in which synchronous oscillation of neighbors is maintained through mutual coupling. This mechanism enables embryos to maintain a constant segregation of somites, despite the noise imposed by the high level mitosis required for continued growth. [ 13 ]


The sources, consequences, and control of noise are major questions in study of developmental noise. Recent studies suggest that this noise has multiple sources, including the stochastic or inherently random nature of the biochemical reactions of gene expression. But the detailed mechanisms are still unclear and the contributions of factors such as  microRNAs , whose existence was first discovered in the 1990s, remain unclear. For example, one recent study showed that microRNAs can serve different roles, from using noise to throw a developmental switch to buffering the consequences of noise in order to confer robustness to environmental perturbation. [ 13 ]  Thus, much work remains to be done in understanding the significance, control and mechanisms of developmental noise.


Dihybrid cross  is a cross between two individuals with two observed  traits  that are controlled by two distinct  genes . The idea of a dihybrid cross came from Gregor Mendel when he observed pea plants that were either yellow or green and either round or wrinkled. Crossing of two heterozygous individuals will result in predictable ratios for both  genotype  and  phenotype  in the offspring. The expected phenotypic ratio of crossing heterozygous parents would be 9:3:3:1. [ 1 ]  Deviations from these expected ratios may indicate that the two traits are  linked  or that one or both traits has a  non-Mendelian  mode of inheritance.


Gregor Mendel  was an Austrian-Czech monk who bred peas plants in his monastery garden and compared the offspring to figure out inheritance of traits from 1856-1863. [ 2 ]  He first started looking at individual traits, but began to look at two distinct traits in the same plant. In his first experiment, he looked at the two distinct traits of pea color (yellow or green) and pea shape (round or wrinkled). [ 3 ]  He applied the same rules of a  monohybrid cross  to create the dihybrid cross. From these experiments, he determined the phenotypic ratio (9:3:3:1) seen in dihybrid cross for a heterozygous cross. [ 1 ]


Through these experiments, he was able to determine the basic  law of independent assortment  and  law of dominance . The law of independent assortment states that traits controlled by different genes are going to be inherited independently of each other. [ 3 ]  Mendel was able to determine this law out because in his crosses he was able to get all four possible phenotypes. The law of dominance states that if one dominant allele is inherited then the dominant phenotype will be expressed. [ 3 ]


The phenotypic ratio of a cross between two heterozygotes is 9:3:3:1, where 9/16 of the individuals possess the dominant phenotype for both traits, 3/16 of the individuals possess the dominant phenotype for one trait, 3/16 of the individuals possess the dominant phenotype for the other trait, and 1/16 are recessive for both traits. [ 1 ]  Valid only for  Angiosperms  or similar sexually reproducing organisms. This is assuming that Mendel's laws are followed.


The expected phenotypic ratio of 9:3:3:1 can be broken down into:


In the example pictured to the right, RRYY/rryy parents result in F 1  offspring that are  heterozygous  for both R and Y (RrYy). [ 4 ]


Another example is listed in the table below and illustrates the process of a dihybrid cross between pea plants with multiple traits and their phenotypic ratio patterns. Dihybrid crosses are easily visualized using a 4 x 4  Punnett square . In these squares, the  dominant traits  are  uppercase , and the  recessive traits  of the same characteristic is  lowercase .


Diploidization  is the process of converting a polyploid genome back into a diploid one.  Polyploidy  is a product of whole genome duplication (WGD) and is followed by diploidization as a result of genome shock. [ 1 ] [ 2 ] [ 3 ] [ 4 ]  The plant kingdom has undergone multiple events of polyploidization followed by diploidization in both ancient and recent lineages. [ 1 ]  It has also been hypothesized that vertebrate genomes have gone through two rounds of  paleopolyploidy . [ 5 ]  The mechanisms of diploidization are poorly understood but patterns of chromosomal loss and evolution of novel genes are observed in the process.


Upon the formation of new polyploids, large sections of DNA are rapidly lost from one genome. [ 1 ] [ 2 ] [ 3 ]  The loss of DNA effectively achieves two purposes. First, the eliminated copy restores the normal gene dosage in the diploid organism. [ 1 ]  Second, the changes in chromosomal genetic structure increase the divergence of the homoeologous chromosomes (similar chromosomes from inter-species hybrid) and promotes  homologous chromosome  pairing. [ 2 ]  Both are important in terms of adjusting to the induced genome shock.


There have been rare events in which genes that ensure proper chromosome pairing have evolved shortly after polyploidization. One such gene, Ph1, exists in hexaploid wheat. [ 6 ]  These genes keep the two sets of genomes separately by either spatially separating them or giving them a unique chromatin identity to facilitate recognition from its homologous pair. This prevents the need of rapid gene loss to speed up homeologous chromosome diversification.


Once a polyploid is made, either synthetically or naturally, the genome goes through a period of "genome shock". Genome shock can be defined as a stage in which the genome experiences massive reorganization and structural changes to deal with the external stress (X-ray damage, chromosome duplication, etc.) imposed upon the genome. [ 7 ]  Such changes are termed  revolutionary changes  and occur early in the process of diploidization. [ 2 ]  Revolutionary changes ensure that the organism has a stable genome that can be passed to its progeny.


At the end of this process, certain duplicated genes may be preserved thus allowing evolution to shape them into novel functions. This is commonly termed as neofunctionalization. The mechanism of retaining duplicated genes is poorly understood. It has been hypothesized that dosage balance may play a key role in shaping the evolutionary fates of duplicated genes. [ 1 ]  Evolutionary changes refer to the long process of converting duplicated genes into diverse, functional gene derivatives. [ 2 ]


There are many ways in which a polyploid organism can convert back to a diploid status. This is usually achieved by elimination of duplicated genes. The main goals of diploidization are: (1) To ensure proper gene dosage; and (2) to maintain stable cellular division processes. This process does not need to occur rapidly for all chromosomes in one or few steps. In recent polyploid events, segments of the genome may still remain in a tetraploid status. In other words, diploidization is a long ongoing process that is shaped by both intrinsic and evolutionary drives. [ 8 ]


Normally, homologous chromosomes pair up in bivalents during meiosis and separate into different daughter cells. However, when multiple copies of similar chromosomes are present in the nucleus, homeologous chromosomes can also pair with homologous chromosomes resulting in the formation of trivalents or multivalents. [ 3 ]  The formation of multivalents results in unequal division of the chromosomes and lead to daughter cells lacking one or few chromosomes.


When homeologous chromosomes pair up though bivalents or multivalents, illegitimate genetic crossovers may occur. [ 3 ]  Since the chromosomes may differ in genetic structure and content, segments of the chromosome may be shuffled around resulting in massive gene loss. Additionally,  illegitimate recombinations  may also result in dicentric chromosomes lead to chromosome breakage during anaphase. [ 3 ]  This further contributes to gene loss on duplicated chromosomes.


The duplicated copies of a gene are commonly non-essential to the plant's ability to maintain normal growth and development. Therefore, one copy is generally free to mutate/be lost from the genome. [ 2 ] [ 4 ]  This contributes to gene loss through the massive chromosome reorganization events during genome shock.


As mentioned earlier, duplicated genes are under relaxed selective pressure. Thus it may also be subject to  neofunctionalization , the process in which a duplicated gene obtains a novel function.


Epistasis  is a phenomenon in  genetics  in which the effect of a  gene   mutation  is dependent on the presence or absence of mutations in one or more other genes, respectively termed  modifier genes . In other words, the effect of the mutation is dependent on the genetic background in which it appears. [ 2 ]  Epistatic mutations therefore have different effects on their own than when they occur together. Originally, the term  epistasis  specifically meant that the effect of a gene variant is masked by that of different gene. [ 3 ]


The concept of  epistasis  originated in genetics in 1907 [ 4 ]  but is now used in  biochemistry ,  computational biology  and  evolutionary biology . The phenomenon arises due to interactions, either between genes (such as mutations also being needed in  regulators of gene expression ) or within them (multiple mutations being needed before the gene loses function), leading to non-linear effects. Epistasis has a great influence on the shape of  evolutionary landscapes , which leads to profound consequences for  evolution  and for the  evolvability  of  phenotypic  traits.


Understanding of epistasis has changed considerably through the  history of genetics  and so too has the use of the term. The term was first used by  William Bateson  and his collaborators  Florence Durham  and  Muriel Wheldale Onslow . [ 4 ]  In early models of  natural selection  devised in the early 20th century, each gene was considered to make its own characteristic contribution to fitness, against an average background of other genes. Some introductory courses still teach  population genetics  this way. Because of the way that the science of  population genetics  was developed,  evolutionary geneticists  have tended to think of epistasis as the exception. However, in general, the expression of any one allele depends in a complicated way on many other alleles.


In  classical genetics , if genes A and B are mutated, and each mutation by itself produces a unique phenotype but the two mutations together show the same phenotype as the gene A mutation, then gene A is epistatic and gene B is  hypostatic . For example, the gene for  total baldness  is epistatic to the gene for  brown hair . In this sense, epistasis can be contrasted with  genetic dominance , which is an interaction between alleles at the same  gene   locus . As the study of genetics developed, and with the advent of  molecular biology , epistasis started to be studied in relation to  quantitative trait loci  (QTL) and  polygenic inheritance .


The effects of genes are now commonly quantifiable by assaying the magnitude of a phenotype (e.g.  height ,  pigmentation  or  growth rate ) or by  biochemically  assaying protein activity (e.g.  binding  or  catalysis ). Increasingly sophisticated  computational  and  evolutionary biology  models aim to describe the effects of epistasis on a  genome -wide scale and the consequences of this for  evolution . [ 5 ] [ 6 ] [ 7 ]  Since identification of epistatic pairs is challenging both computationally and statistically, some studies try to prioritize epistatic pairs. [ 8 ] [ 9 ]


Terminology about epistasis can vary between scientific fields.  Geneticists  often refer to  wild type  and mutant  alleles  where the mutation is implicitly deleterious and may talk in terms of genetic enhancement,  synthetic lethality  and genetic suppressors. Conversely, a  biochemist  may more frequently focus on beneficial mutations and so explicitly state the effect of a mutation and use terms such as reciprocal sign epistasis and compensatory mutation. [ 16 ]  Additionally, there are differences when looking at epistasis within a single gene (biochemistry) and epistasis within a  haploid  or  diploid  genome (genetics). In general, epistasis is used to denote the departure from 'independence' of the effects of different genetic loci. Confusion often arises due to the varied interpretation of 'independence' among different branches of biology. [ 17 ]  The classifications below attempt to cover the various terms and how they relate to one another.


Two mutations are considered to be purely additive if the effect of the double mutation is the sum of the effects of the single mutations. This occurs when genes do not interact with each other, for example by acting through different  metabolic pathways . Simply, additive traits were studied early on in the  history of genetics , however they are relatively rare, with most genes exhibiting at least some level of epistatic interaction. [ 18 ] [ 19 ]


When the double mutation has a fitter  phenotype  than expected from the effects of the two single mutations, it is referred to as  positive epistasis . Positive epistasis between beneficial mutations generates greater improvements in function than expected. [ 10 ] [ 11 ]  Positive epistasis between deleterious mutations protects against the negative effects to cause a less severe fitness drop. [ 13 ]


Conversely, when two mutations together lead to a less fit  phenotype  than expected from their effects when alone, it is called  negative epistasis . [ 20 ] [ 21 ]  Negative epistasis between beneficial mutations causes smaller than expected fitness improvements, whereas negative epistasis between deleterious mutations causes greater-than-additive fitness drops. [ 12 ]


Independently, when the effect on fitness of two mutations is more radical than expected from their effects when alone, it is referred to as  synergistic epistasis . The opposite situation, when the fitness difference of the double mutant from the wild type is smaller than expected from the effects of the two single mutations, it is called  antagonistic epistasis . [ 15 ]  Therefore, for deleterious mutations, negative epistasis is also synergistic, while positive epistasis is antagonistic; conversely, for advantageous mutations, positive epistasis is synergistic, while negative epistasis is antagonistic.


The term  genetic enhancement  is sometimes used when a double (deleterious) mutant has a more severe phenotype than the additive effects of the single mutants. Strong positive epistasis is sometimes referred to by  creationists  as  irreducible complexity  (although   most examples are misidentified ).


Sign epistasis [ 22 ]  occurs when one mutation has the opposite effect when in the presence of another mutation. This occurs when a mutation that is deleterious on its own can enhance the effect of a particular beneficial mutation. [ 17 ]  For example, a large and complex  brain  is a waste of energy without a range of  sense organs , but sense organs are made more useful by a large and complex brain that can better process the information. If a  fitness landscape  has no sign epistasis then it is called  smooth .


At its most extreme,  reciprocal sign epistasis [ 23 ]  occurs when two deleterious genes are beneficial when together. For example, producing a  toxin  alone can kill a  bacterium ,  and producing a  toxin exporter  alone can waste energy, but producing both can improve  fitness  by killing  competing organisms . If a fitness landscape has sign epistasis but no reciprocal sign epistasis then it is called  semismooth . [ 24 ]


Reciprocal sign epistasis also leads to  genetic suppression  whereby two deleterious mutations are less harmful together than either one on its own, i.e. one  compensates  for the other.  A clear example of genetic suppression was the demonstration that in the assembly of  bacteriophage T4  two deleterious  mutations , each causing a deficiency in the level of a different  morphogenetic  protein, could interact positively. [ 25 ]    If a mutation causes a reduction in a particular structural component, this can bring about an imbalance in morphogenesis and loss of viable virus progeny, but production of viable progeny can be restored by a second  (suppressor) mutation  in another morphogenetic component that restores the balance of protein components.


The term genetic suppression can also apply to sign epistasis where the double mutant has a phenotype intermediate between those of the single mutants, in which case the more severe single mutant phenotype is  suppressed  by the other mutation or genetic condition.  For example, in a  diploid  organism, a hypomorphic (or partial loss-of-function) mutant phenotype can be suppressed by knocking out one copy of a gene that acts oppositely in the same pathway.  In this case, the second gene is described as a "dominant suppressor" of the hypomorphic mutant;  "dominant" because the effect is seen when one wild-type copy of the suppressor gene is present (i.e. even in a heterozygote).  For most genes, the phenotype of the heterozygous suppressor mutation by itself would be wild type (because most genes are not haplo-insufficient), so that the double mutant (suppressed) phenotype is intermediate between those of the single mutants.


In non reciprocal sign epistasis, fitness of the mutant lies in the middle of that of the extreme effects seen in reciprocal sign epistasis.


When two mutations are viable alone but lethal in combination, it is called  Synthetic lethality  or  unlinked non-complementation . [ 26 ]


In a  haploid  organism with genotypes (at two  loci )  ab ,  Ab ,  aB  or  AB , we can  think of different forms of epistasis as affecting the magnitude of a phenotype upon mutation individually (Ab and aB) or in combination (AB).


Epistasis in  diploid  organisms is further complicated by the presence of two copies of each gene. Epistasis can occur between loci, but additionally, interactions can occur between the two copies of each locus in  heterozygotes . For a two  locus , two  allele  system, there are eight independent types of gene interaction. [ 27 ]


This can be the case when multiple genes act in parallel to achieve the same effect. For example, when an organism is in need of  phosphorus , multiple enzymes that break down different phosphorylated components from the  environment  may act additively to increase the amount of phosphorus available to the organism. However, there inevitably comes a point where phosphorus is no longer the limiting factor for growth and reproduction and so further improvements in phosphorus metabolism have smaller or no effect (negative epistasis). Some sets of mutations within genes have also been specifically found to be additive. [ 28 ]  It is now considered that strict additivity is the exception, rather than the rule, since most genes  interact  with hundreds or thousands of other genes. [ 18 ] [ 19 ]


Epistasis within the genomes of organisms occurs due to interactions between the genes within the genome. This interaction may be direct if the genes encode proteins that, for example, are separate components of a multi-component protein (such as the  ribosome ),  inhibit  each other's activity,  or if the protein encoded by one gene modifies the other (such as by  phosphorylation ). Alternatively the interaction may be indirect, where the genes encode components of a  metabolic pathway  or  network ,  developmental pathway ,  signalling pathway  or  transcription factor  network. For example, the gene encoding the  enzyme  that synthesizes  penicillin  is of no use to a  fungus  without the enzymes that synthesize the necessary precursors in the metabolic pathway.


Just as mutations in two separate genes can be non-additive if those genes interact, mutations in two  codons  within a gene can be non-additive. In genetics this is sometimes called  intragenic suppression  when one deleterious mutation can be compensated for by a second mutation within that gene.  Analysis of  bacteriophage T4  mutants  that were altered in the  rIIB cistron (gene)  revealed that certain pairwise combinations of mutations could mutually suppress each other; that is the double mutants had a more nearly  wild-type   phenotype  than either mutant alone. [ 29 ]   The linear map order of the mutants was established using  genetic recombination  data,  From these sources of information, the triplet nature of the  genetic code  was logically deduced for the first time in 1961, and other key features of the code were also inferred. [ 29 ]


Also intragenic suppression can occur when the  amino acids  within a protein interact. Due to the complexity of protein folding and activity, additive mutations are rare.


Proteins are held in their  tertiary structure  by a distributed, internal network of cooperative interactions ( hydrophobic ,  polar  and  covalent ). [ 30 ]  Epistatic interactions occur whenever one mutation alters the local environment of another residue (either by directly contacting it, or by inducing changes in the protein structure). [ 31 ]  For example, in a  disulphide bridge , a single  cysteine  has no effect on  protein stability  until a second is present at the correct location at which point the two cysteines form a  chemical bond  which enhances the stability of the protein. [ 32 ]  This would be observed as positive epistasis where the double-cysteine variant had a much higher stability than either of the single-cysteine variants. Conversely, when deleterious mutations are introduced, proteins often exhibit  mutational robustness  whereby as stabilising interactions are destroyed the protein still functions until it reaches some stability threshold at which point further destabilising mutations have large, detrimental effects as the protein can no longer  fold . This leads to negative epistasis whereby mutations that have little effect alone have a large, deleterious effect together. [ 33 ] [ 34 ]


In  enzymes , the protein structure orients a few, key  amino acids  into precise geometries to form an  active site  to perform  chemistry . [ 35 ]  Since these active site networks frequently require the cooperation of multiple components, mutating any one of these components massively compromises activity, and so mutating a second component has a relatively minor effect on the already inactivated enzyme. For example, removing any member of the  catalytic triad  of many enzymes will reduce activity to levels low enough that the organism is no longer viable. [ 36 ] [ 37 ] [ 38 ]


Diploid  organisms contain two copies of each gene. If these are different ( heterozygous  / heteroallelic), the two different copies of the allele may interact with each other to cause epistasis. This is sometimes called  allelic complementation , or  interallelic complementation . It may be caused by several mechanisms, for example  transvection , where an enhancer from one allele acts in  trans  to activate transcription from the promoter of the second allele. Alternately,  trans-splicing  of two non-functional RNA molecules may produce a single, functional RNA.


Similarly, at the protein level, proteins that function as  dimers  may form a  heterodimer  composed of one protein from each alternate gene and may display different properties to the  homodimer  of one or both variants.  Two bacteriophage T4 mutants defective at different locations in the same gene can undergo allelic  complementation  during a mixed infection. [ 39 ]   That is, each mutant alone upon infection cannot produce viable progeny, but upon mixed infection with two complementing mutants, viable phage are formed.  Intragenic complementation was demonstrated for several genes that encode structural proteins of the bacteriophage [ 39 ]  indicating that such proteins function as dimers or even higher order multimers. [ 40 ]


In  evolutionary genetics , the sign of epistasis is usually more significant than the magnitude of epistasis. This is because magnitude epistasis (positive and negative) simply affects how beneficial mutations are together, however sign epistasis affects whether mutation combinations are beneficial or deleterious. [ 10 ]


A  fitness landscape  is a representation of the  fitness  where all  genotypes  are arranged in 2D space and the fitness of each genotype is represented by height on a surface. It is frequently used as a visual metaphor for understanding  evolution  as the process of moving uphill from one genotype to the next, nearby, fitter genotype. [ 18 ]


If all mutations are additive, they can be acquired in any order and still give a continuous uphill trajectory. The landscape is perfectly smooth, with only one peak ( global maximum ) and all sequences can evolve uphill to it by the accumulation of beneficial mutations  in any order . Conversely, if mutations interact with one another by epistasis, the fitness landscape becomes rugged as the effect of a mutation depends on the genetic background of other mutations. [ 41 ]  At its most extreme, interactions are so complex that the fitness is 'uncorrelated' with gene sequence and the topology of the landscape is random. This is referred to as a  rugged  fitness landscape and has profound implications for the  evolutionary optimisation  of organisms. If mutations are deleterious in one combination but beneficial in another, the fittest genotypes can only be accessed by accumulating mutations  in one specific order . This makes it more likely that organisms will get stuck at  local maxima  in the fitness landscape having acquired mutations in the 'wrong' order. [ 34 ] [ 42 ]   For example, a variant of  TEM1 β-lactamase  with 5 mutations is able to cleave  cefotaxime  (a third generation  antibiotic ). [ 43 ]  However, of the 120 possible pathways to this 5-mutant variant, only 7% are accessible to evolution as the remainder passed through fitness valleys where the combination of mutations reduces activity. In contrast, changes in environment (and therefore the shape of the fitness landscape) have been shown to provide escape from local maxima. [ 34 ]  In this example, selection in changing antibiotic environments resulted in a "gateway mutation" which epistatically interacted in a positive manner with other mutations along an evolutionary pathway, effectively crossing a fitness valley. This gateway mutation alleviated the negative epistatic interactions of other individually beneficial mutations, allowing them to better function in concert. Complex environments or selections may therefore bypass local maxima found in models assuming simple positive selection.


High epistasis is usually considered a constraining factor on evolution, and improvements in a highly epistatic trait are considered to have lower  evolvability . This is because, in any given genetic background, very few mutations will be beneficial, even though many mutations may need to occur to eventually improve the trait. The lack of a smooth landscape makes it harder for evolution to access fitness peaks. In highly rugged landscapes,  fitness valleys  block access to some genes, and even if ridges exist that allow access, these may be rare or prohibitively long. [ 44 ]  Moreover, adaptation can move proteins into more precarious or rugged regions of the fitness landscape. [ 45 ]  These shifting "fitness territories" may act to decelerate evolution and could represent tradeoffs for adaptive traits.


The frustration of adaptive evolution by rugged fitness landscapes was recognized as a potential force for the evolution of  evolvability .   Michael Conrad  in 1972 was the first to propose a mechanism for the evolution of  evolvability  by noting that a mutation which smoothed the fitness landscape at other loci could facilitate the production of advantageous mutations and hitchhike along with them. [ 46 ] [ 47 ]   Rupert Riedl  in 1975 proposed that new genes which produced the same phenotypic effects with a single mutation as other loci with reciprocal sign epistasis would be a new means to attain a phenotype otherwise too unlikely to occur by mutation. [ 48 ] [ 49 ]


Rugged, epistatic fitness landscapes also affect the trajectories of evolution. When a mutation has a large number of epistatic effects, each accumulated mutation drastically changes the set of available  beneficial mutations . Therefore, the evolutionary trajectory followed depends highly on which early mutations were accepted. Thus, repeats of evolution from the same starting point tend to diverge to different local maxima rather than converge on a single global maximum as they would in a smooth, additive landscape. [ 50 ] [ 51 ]


Negative epistasis and sex are thought to be intimately correlated. Experimentally, this idea has been tested in using digital simulations of asexual and sexual populations. Over time, sexual populations move towards more negative epistasis, or the lowering of fitness by two interacting alleles. It is thought that negative epistasis allows individuals carrying the interacting deleterious mutations to be removed from the populations efficiently. This removes those alleles from the population, resulting in an overall more fit population. This hypothesis was proposed by  Alexey Kondrashov , and is sometimes known as the  deterministic mutation hypothesis [ 52 ]
and has also been tested using artificial  gene networks . [ 20 ]


However, the evidence for this hypothesis has not always been straightforward and the model proposed by Kondrashov has been criticized for assuming mutation parameters far from real world observations. [ 53 ]  In addition, in those tests which used artificial gene networks, negative epistasis is only found in more densely connected networks, [ 20 ]  whereas empirical evidence indicates that natural gene networks are sparsely connected, [ 54 ]  and theory shows that selection for robustness will favor more sparsely connected and minimally complex networks. [ 54 ]


Quantitative genetics focuses on  genetic variance  due to genetic interactions. Any two locus interactions at a particular gene frequency can be decomposed into eight independent genetic effects using a  weighted regression . In this regression, the observed two locus genetic effects are treated as dependent variables and the "pure" genetic effects are used as the independent variables.  Because the regression is weighted, the partitioning among the variance components will change as a function of gene frequency.  By analogy it is possible to expand this system to three or more loci, or to cytonuclear interactions [ 55 ]


When assaying epistasis within a gene,  site-directed mutagenesis  can be used to generate the different genes, and their  protein products  can be  assayed  (e.g. for stability or catalytic activity). This is sometimes called a double mutant cycle and involves producing and assaying the wild type protein, the two single mutants and the double mutant. Epistasis is measured as the difference between the effects of the mutations together versus the sum of their individual effects. [ 56 ]  This can be expressed as a free energy of interaction.
The same methodology can be used to investigate the interactions between larger sets of mutations but all combinations have to be produced and assayed. For example, there are 120 different combinations of 5 mutations, some or all of which may show epistasis...


Numerous computational methods have been developed for the detection and characterization of epistasis. Many of these rely on  machine learning  to detect non-additive effects that might be missed by statistical approaches such as linear regression. [ 57 ]
For example,  multifactor dimensionality reduction  (MDR) was designed specifically for nonparametric and model-free detection of combinations of genetic variants that are predictive of a phenotype such as disease status in human  populations . [ 58 ] [ 59 ]  Several of these approaches have been broadly reviewed in the literature. [ 60 ]  Even more recently, methods that utilize insights from theoretical computer science (the  Hadamard transform [ 61 ]  and  compressed sensing [ 62 ] [ 63 ] ) or maximum-likelihood inference [ 64 ]  were shown to distinguish epistatic effects from overall non-linearity in genotype–phenotype map structure, [ 65 ]  while others used patient survival analysis to identify non-linearity. [ 66 ]


Europhenome   [ 1 ] [ 2 ]  is a resource for presenting, searching and analysing mouse phenotypes that were revealed by high throughput mouse phenotyping [ 3 ]  programmes such as EUMODIC.


The EuroPhenome project provides access to raw and annotated mouse phenotyping data generated from primary pipelines such as EMPReSSlim and secondary procedures from specialist centres. Mutants of interest can be identified by searching the gene or the predicted phenotype.


EuroPhenome is an open source project to develop a software system for capturing, storing, and analysing raw phenotyping data from  standard operating procedures  contained in  EMPReSS .


EuroPhenome is primarily based in the bioinformatics group at  MRC Harwell . The development of EuroPhenome is in collaboration with the  Helmholtz Zentrum München , the  Wellcome Trust Sanger Institute , and the Clinique de la Souris (France).


Initially, EuroPhenome was developed within the EUMORPHIA (European Union Mouse Research for Public Health and Industrial Applications) programme to capture and store pilot phenotyping data obtained on four background  strains  ( C57BL/6J , C3H/HeBFeJ,  BALB/cByJ  and 129/SvPas). EUMORPHIA was a large project consisting of 18 research centres in 8 European countries, with the main focus of the project being the development of novel approaches in phenotyping, mutagenesis and informatics to improve the characterisation of mouse models for understanding human molecular physiology and pathology.


The current version of EuroPhenome is capturing data from the EUMODIC project as well as the  Wellcome Trust Sanger Institute  Mouse Genetics Programme, HMGU German Mouse Clinic pipeline, and the CMHD. EUMODIC is undertaking a primary phenotype assessment of up to 500 mouse mutant lines derived from ES cells developed in the EUCOMM project as well as other lines. Lines showing an interesting phenotype will be subject to a more in depth assessment.


EUMODIC is building upon the database of standardised phenotyping protocols, EMPReSS, developed by the EUMORPHIA project. EUMODIC has developed a selection of these screens, called EMPReSSslim, to enable comprehensive, high throughput, primary phenotyping of large numbers of mice.


Phenovariants are annotated using an automated pipeline, which assigns an MP term if the mutant data is statistically different from the baseline data. This data is shown in the Phenomap and the mine for a mutant tool. A statistically significant result and the subsequent MP annotation does not necessarily mean a true phenovariant. There are other factors that could cause this result that have not been accounted for in the analysis. It is the responsibility of the user to download the data and use their expert knowledge or further analysis to decide whether they agree or not.


F1 hybrid  (also known as  filial 1 hybrid ) is the first filial  generation  of offspring of distinctly different parental types. [ 1 ]  F1 hybrids are used in  genetics , and in  selective breeding , where the term  F1 crossbreed  may be used. The term is sometimes written with a subscript, as  F 1  hybrid . [ 2 ] [ 3 ]  Subsequent generations are called  F 2 ,  F 3 , etc.


The offspring of distinctly different parental types produce a new, uniform  phenotype  with a combination of characteristics from the parents. In fish breeding, those parents frequently are two closely related fish species, while in plant and animal breeding, the parents often are two  inbred lines .


Gregor Mendel  focused on patterns of  inheritance  and the  genetic  basis for  variation . In his  cross-pollination  experiments involving two true-breeding, or  homozygous , parents, Mendel found that the resulting F1 generation was  heterozygous  and consistent. The offspring showed a combination of the phenotypes from each parent that were genetically  dominant . Mendel's discoveries involving the F1 and F2 generations laid the foundation for modern genetics.


Crossing two genetically different plants produces a  hybrid   seed . This can happen naturally, and includes hybrids between species (for example,  peppermint  is a  sterile  F1 hybrid of  watermint  and  spearmint ). In  agronomy , the term  F1 hybrid  is usually reserved for agricultural  cultivars  derived from two-parent cultivars. These F1 hybrids are usually created by means of controlled  pollination , sometimes by  hand pollination . For  annual plants  such as tomato and  maize , F1 hybrids must be produced each season.


For mass production of F1 hybrids with uniform phenotype, the parent plants must have predictable genetic effects on the offspring.  Inbreeding  and selection for uniformity for multiple generations ensures that the parent lines are almost homozygous. The divergence between the (two) parent lines promotes improved growth and yield characteristics in offspring through the phenomenon of  heterosis  ("hybrid vigour" or "combining ability").


Two  populations  of breeding stock with desired characteristics are subjected to inbreeding until the homozygosity of the population exceeds a certain level, usually 90% or more.  Typically, this requires more than 10 generations. Thereafter, the two strains must be crossed, while avoiding  self-fertilization . Normally, this is done with plants by deactivating or removing male flowers from one population, taking advantage of time differences between male and female flowering, or hand pollinating. [ 4 ]


In 1960, 99% of all  corn , 95% of  sugar beet , 80% of  spinach , 80% of  sunflowers , 62% of  broccoli , and 60% of  onions  planted in the United States were F1 hybrids. [ citation needed ]  Beans and peas are not commercially hybridized because they are  automatic pollinators , and hand pollination is prohibitively expensive.


F2 hybrids, the result of self or cross-pollination of F1s, lack the consistency of F1s, though they may retain some desirable traits and can be produced more cheaply because hand pollination or other interventions are not required. Some seed companies offer F2 seed at less cost, particularly in  bedding plants , where consistency is less critical. [ 5 ]


F1 crosses in animals can be between two inbred lines or between two closely related species or subspecies. In fish such as  cichlids , the term F1 cross is used for crosses between two different wild-caught individuals that are assumed to be from different genetic lines. [ 6 ]


Mules  are F1 hybrids between  horses  (mares) and  donkeys  (jacks); the opposite sex cross results in  hinnies . However, such offspring are almost always sterile.


Today, certain domesticated–wild hybrid breeds, such as the  Bengal cat  and the  Savannah cat , are classified by their filial generation number. An F1 hybrid Savannah cat is the result of reproduction between an African Serval cat and a domestic cat. [ 7 ]


As explained in the International Journal of Fauna and Biological Studies, [ citation needed ]  there are four reasons for species hybridizations:


Small population size can be caused by inadequate or obliterated natural habitats that lead to species escaping to other habitats and as a result, this may lead to lesser mate availability and can cause breeding between distinct species. [ 8 ]  Habitat fragmentation and species introduction can be man-made or caused by mother nature such as deforestation,  desertification , eutrophication, urbanization, water oil extraction causing changes in the ecosystem that leads to animal migration or evading new surroundings. [ 9 ]  Third, is anthropogenic hybridization, which is "artificial or human-led hybridization" is supported for researchers to study "reproductive compatibility between species". [ 10 ]  Lastly, visual, chemical, and acoustic interferences cues are what causes species to signal sexual cues by differentiating between the same and opposite-sex leading to hybridization. [ 11 ]


The advantages of species hybridization are 1.) evolution of new interspecific breed, 2.) hybrid vigour, and 3.) enhanced longevity and immunity to diseases (Dubey, A. 2019). Dubey explains each as follows: 1.) A new interspecific breed is due to the mating of two distinguished species. 2.) Hybrid vigour is defined as a species becoming sturdier, more dynamic, and stronger than the parents. Lastly, 3.) Hybrids can have improved longevity and are "highly immune to diseases" (Dubey, A. 2019).


In contrast, the limitations can be due to genetic extinction and/or outbreeding depression. Dubey explains that genetic extinction can be caused by "hybrid swarms" noting the various degrees of hybrids. [ 12 ]  Outbreeding depression is the "cross between genetically distant populations" causing hybrids to reduce fit and isolation leading to reduced reproduction. [ 13 ]


Family aggregation , also known as  familial aggregation , is the clustering of certain  traits , behaviours, or disorders within a given family. Family aggregation may arise because of  genetic  or environmental similarities. [ 1 ]


The data from the family aggregation studies have been extensively studied to determine the mode of inheritance of  schizophrenia . Studies to date have shown that when numerous families are studied, simple modes of inheritance are not statistically supported. The majority of studies analyzing for the mode of inheritance have concluded that a multifactorial threshold mode is most likely. [ 2 ]


The most consistent and dramatic evidence of family influences on  cardiovascular disease  (CVD) is family aggregation of physiological factors. In several studies the parent-child and sibling-sibling correlations of  blood pressure  are approximately .24. Genetic determination of blood pressure is strong, but does not explain all of the variance. [ 3 ]


Familial  Parkinson's disease  (PD) exists but is infrequent. Early investigations failed to show substantial family aggregation for PD. [ 4 ]


Family resemblance  refers to physical similarities shared between close relatives, especially between  parents  and children and between  siblings . [ 1 ]  In  psychology , the similarities of  personality  are also observed.


Heritability , defined as a measure of family resemblance, causes traits to be genetically passed from parents to offspring ( heredity ), allowing evolutionarily advantageous traits to persist through generations. [ 2 ] [ 3 ] [ 4 ] [ 5 ]  Despite sharing parents, siblings do not inherit identical genes, making  studies on identical twins  (who have identical DNA) especially effective at analyzing the role genetics play in  phenotypic  similarity. [ 6 ]   Studies have found that generational resemblance of many  phenotypic traits  results from the inheritance of multiples genes that collectively influence a trait ( additive genetic variance ). [ 7 ]  There is evidence of heritability in personality traits. For example, one study found that approximately half of personality differences in high-school aged fraternal and identical twins were due to  genetic variation  - and another study suggests that no one personality trait is more heritable than another. [ 6 ] [ 8 ]