Circadian rhythms are coordinated physiological and biological changes that oscillate on an approximately 24-hour cycle. Disruptions to these rhythms in humans may affect the duration, onset, and/or quality of sleep during this cycle, resulting in familial sleep traits. These traits are not necessarily syndromes because they do not always cause distress among individuals. Instead of being disorders, familial sleep traits are variations in an individual's biological tendencies of sleep-wake times, and are only considered syndromes if affected individuals complain about life interference, in which case they may fall under the category of  Circadian Rhythm Sleep Disorders  (CRSD) that affect sleep timing and  circadian rhythms . Some of these circadian disorders include  Advanced Sleep Phase Disorder  (ASPD) and  Delayed Sleep Phase Disorder  (DSPD). Familial sleep traits are more specific than CRSD because they are  heritable  and involve a wide range of  Mendelian genes . Evidence has shown that genes significantly influence sleep schedules in mammals, including humans, and account for one-third of the variation in sleep quality and duration. [ 1 ]  Studies in human  monozygotic twins  have provided evidence that genetic factors affect "normal" sleep patterns as well, meaning ones where no individual has been diagnosed with an altered phenotypic sleep trait. [ 1 ]


Sleep timing is controlled by the  circadian clock , which can  entrain  to environmental stimuli (usually a light-dark cycle) and is regulated by a  transcription-translation feedback loop  (TTFL). In humans, there are multiple genes involved in this molecular biological clock, which when mutated may result in sleep disorders such as Familial Advanced Sleep Phase (FASP), Familial Delayed Sleep Phase (FDSP), and Familial Natural Short Sleep (FNSS). Some mutations in Mendelian genes that are involved in the TTFL have been identified as the causes of these sleep traits, including  PER2 ,  PER3 ,  CRY2 ,  CRY1 . [ 2 ] [ 3 ]  Other Mendelian genes that are not known to play a core role in the TTFL but are involved in FNSS include  DEC2  and  ADRB1 . [ 4 ] [ 5 ]


With some familial sleep traits, there may be a shift in an individual's  chronotype , which describes the time of sleep-wake behaviors that result from circadian rhythms. Chronotype may shift depending on multiple factors including gender and age. Individuals with FASP have earlier chronotypes and individuals with FDSP have later chronotypes compared to a conventional sleep period which runs from approximately 10pm to 7am. [ 6 ]  Individuals may meet the criteria for FASP or FDSP if they have Advanced Sleep Phase or Delayed Sleep Phase and at least one first degree relative with the trait. Researchers have examined the human prevalence of FASP to be 0.33-0.5% by including individuals who have a sleep onset at approximately 8:30pm and offset at 5:30am. FDSP, which includes individuals who have a delayed sleep onset and offset, has an unknown human prevalence and may vary based on location, definition, and age. [ 6 ]


Familial sleep traits have been difficult to study due to the various environmental influences (such as  entraining  daily alarms, artificial light at night, and  caffeine  or  stimulant  intake) that can contribute to different behavioral  phenotypes  in humans. Despite these potential difficulties,  Louis Ptáček  and colleagues discovered evidence of a human familial circadian rhythm variant in the 1990s. This variant resulted in a shorter period and an advance of  melatonin  and temperature rhythms and was initially termed Advanced Sleep Phase Syndrome (ASPS) in a 1999 publication. [ 7 ]  Individuals with ASPS have earlier sleep and wake onsets, meaning they both go to bed and wake up earlier compared to control groups. The first participant with this phenotype told researchers she recognized similar sleep patterns in her family. From structured interviews and family pedigree analysis, some of these individuals were identified to have ASPS as well, providing evidence that this phenotype could be genetic, resulting in Familial Advanced Sleep Phase (FASP). In this 1999 publication, researchers were also able to conclude that this trait has an  autosomal dominant  mode of inheritance with high penetrance. [ 7 ]  This means that the genes involved in FASP are passed through non-sex chromosomes, and an individual only needs one copy of the gene across   homologs  for the gene to be expressed. Since this initial 1999 FASP publication, other circadian biologists including  Phyllis Zee  and  Joseph Takahashi  have conducted further genetic analysis. They published a paper in 2001 that presented data showing a phenotypically characterized case of Advanced Sleep Phase Syndrome to provide further evidence that this trait can be hereditary. [ 8 ]  Since these studies,  Csnk1d ,  PER2 ,  PER3 , and  CRY2  have all been identified as important in hereditary FASP. [ 2 ] [ 9 ]


Another sleep trait, Delayed Sleep Phase Syndrome (DSPS) was first identified by  Elliot Weitzman  and colleagues in 1981. Individuals with DSPS typically cannot fall asleep until later and wake up later compared to control groups. They often cannot fall asleep until between 2:00-6:00am, but then have a normal sleep duration. However, DSPS was not hypothesized to have a genetic component until researchers at  University of California, San Diego  discovered a familial  pedigree  with DSPS in 2001, adding this Familial Delayed Sleep Phase (FDSP) to the list of heritable sleep traits. [ 10 ] [ 11 ]  Almost two decades later in 2017,  Michael Young  and colleagues in New York published findings that further supported delayed sleep to have a genetic component, resulting in FDSP. These scientists reported that a mutation in  CRY1 , a component of the TTFL that represses  Clock  and  Bmal1 , results in a  gain-of-function  variation that lengthens circadian period. [ 3 ]


In addition to these findings, Familial Natural Short Sleep (FNSS) is another heritable sleep trait that has been studied over the past few years. In 2009,  Ying-Hui Fu  and Ptáček discovered the first short-sleep gene by identifying a mutation in the DEC2 gene that resulted in an average of 6.25 hours of sleep a night instead of 8.06 hours, an identifying feature of FNSS. [ 12 ]  This was the first genetic discovery for this sleep trait, broadening the scope of familial sleep trait research. In 2019, Ptáček and Fu published further research about the genetic aspect of FNSS, identifying a mutation in the gene  ADRB1  that increases the activity of ADRB1+ neurons in the dorsal  pons . [ 4 ] [ 13 ]


Most of the research conducted thus far has been surrounding FASP, FDSP, and FNSS, with recent studies beginning to examine the roles of heritable sleep variability on  autism-spectrum disorder  (ASD) and  Alzheimer's disease  (AD). [ 2 ]  ASD, a  neurodevelopmental disorder , has evidence of genetic components and affected individuals have reported a high prevalence of  insomnia . Fu, Ptáček, and colleagues have hypothesized that it may be interesting to examine if sleep traits and disruptions can exacerbate the atypical neurodevelopment in ASD. [ 2 ]  Additionally, recent research about AD, a  neurodegenerative disease , has suggested that sleep disruption might contribute to the disease. A characteristic factor of AD is the accumulation of

 A
 β

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  plaques . These plaques are usually at a lower level in the brain interstitial space when an individual first wakes up and then during waking hours these levels increase. Sleep disruption can eliminate the reduction in

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 β

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  levels, which is important during disease progression. [ 2 ]  Both ASD and AD demonstrate how the heritability of sleep traits may also be involved in disorders and diseases that are not traditionally thought of as circadian, but more research must be done in this field. [ 2 ]


The functions of heritability for many sleep traits are not well known, underscoring the importance of continued research into the human genome.


Familial Advanced Sleep Phase (FASP) results in an individual having a circadian clock that is entrained to their surroundings, but gives the impression that the individual is not. [ 8 ]  This trait typically develops during middle age, and is more common in older adults. Affected individuals typically have a free-running period of about 22 hours, shorter than the average person who has a free-running period closer to 24 hours. This also means that certain physiological markers, such as body temperature and  melatonin  will be present at higher levels earlier in the day as compared to an average person. [ 8 ]


FASP is typically characterized by excessively early sleep and wake times. Additionally, individuals may experience excessive daytime sleepiness if they are forced to adhere to a schedule offset from their personal biological clock. [ 8 ]  Individuals with FASP are typically phase advanced by 4 to 6 hours as compared to the average person. [ 6 ]


FASP is traditionally treated with light therapy in the evenings, or behaviorally with  chronotherapy . Individuals with FASP typically need to have a two-hour delay per day to remain entrained, due to their 22-hour period. Pharmacological interventions are typically avoided due to risks associated with daytime drug-induced sleepiness. [ 14 ]


FASP has been mapped to  chromosome 2q . Genes that are known to influence the presentation of FASP are  CRY2 ,  PER2 ,  PER3  and  CK1∂ . [ 8 ]  TIMELESS ( hTIM ) has also been shown to cause FASP. [ 15 ]  These mutations are critical in the trait's phenotype and heritability. [ 9 ]  This trait is inherited in an autosomal dominant fashion. [ 7 ]


Familial Delayed Sleep Phase (FDSP) results in an individual having a circadian clock that is entrained to their surroundings, but gives the impression that the individual is not. The trait typically develops in adolescence. [ 16 ]  Affected individuals have a free-running period that is longer than the average 24 hours, meaning that certain physiological markers, such as body temperature and melatonin, are present in higher levels later in the day as compared to the average person.


FDSP is typically characterized by excessively late sleep times and wake times, and may include daytime sleepiness if the individual is forced to adhere to a schedule offset from their personal biological clock. Individuals with FDSP may have  comorbidities  with  depression ,  Attention Deficit Hyperactivity Disorder (ADHD) ,  obesity , and  Obsessive-Compulsive Disorder (OCD) . [ 17 ]


Treatment is usually non-pharmacological, with light therapy being a common intervention. Phase delay  chronotherapy  is also occasionally used. Melatonin taken at night will not change the individual's circadian rhythm, but may act as a temporary solution. [ 18 ]


FDSP is heritable and linked to mutations in the  PER3  and  CRY1  genes, which result in the delayed sleep phenotype. [ 3 ]


Fatal Familial Insomnia (FFI) is a disorder that results in trouble sleeping, speech and coordination problems, and eventually  dementia .  Most of those affected die within a few years, and the disorder has no cure. The disorder can manifest any time from age 18 to 60, but the average age of affected individuals is 50 years old. [ 19 ]


The disorder has a 4-stage progression, starting with individuals experiencing insomnia, progressing to seeing hallucinations, then inability to sleep and dramatic weight loss, and finally dementia, which is followed by death. Individuals have a 6-36 month prognosis after they begin experiencing symptoms. [ 19 ]


Due to the prognosis of the disorder, treatment is often minimal and  palliative  in nature. Sleeping pills and other traditional treatments are not found to be beneficial in treating FFI. [ 20 ]


The disorder is caused by a mutation of the  PRNP  gene resulting in the creation of a  prion . [ 21 ]  These prions result in  neurodegeneration , leading to FFI. This mutation can either occur spontaneously or be passed down in an  autosomal dominant  manner. [ 21 ]


Familial natural short sleep (FNSS) is a distinct category of habitual short sleep. Individuals with this trait usually get 4–6.5 hours of sleep per day but do not have daytime sleepiness and do not need catch-up sleep on the weekends. After sleep deprivation, these individuals have less of a sleep deficit than individuals without FNSS. Additionally, affected individuals have a higher behavioral drive, resulting in many holding high pressure jobs, and they may have a better ability to deal with stress. People with FNSS are commonly mistaken for having  insomnia . [ 6 ]  The prevalence of FNSS is currently unknown, however mutations in the genes  DEC2  and  ADRB1 ,  NPSR1 , and  GRM1  have been linked to FNSS. [ 6 ] [ 22 ] [ 23 ]


FNSS is unique because individuals with this sleep trait show no symptoms of shorter sleep. They are able to be active and function normally. [ 6 ]


FNSS may be seen as advantageous rather than detrimental to some individuals. Therefore, because FNSS does not negatively impact most affected individuals, treatment options for it have not been well researched or documented. [ 6 ]


Such mutations appear to reduce  Alzheimer's  pathology in mice. [ 24 ]


In 2009, Ying-Hui Fu and colleagues described how a genetic variant in DEC2 produced the short sleep phenotype. [ 6 ]  In this variant, an  arginine  residue is substituted for a  proline  residue typically present at position 384. [ 25 ]  Within the family studied, people having the DEC2 mutation had shorter sleep durations. The researchers found the same phenotype when mutating this gene in  Drosophila  and mice. [ 6 ]  Interestingly, they found that the mutant mice did not display changes in their free-running activity period. [ 25 ]  DEC2 functions as a transcriptional  repressor  and increases expression of  hypocretin , which promotes a waked state. [ 6 ]  DEC2 inhibits  CLOCK / BMAL1  activation of PER, through protein-protein interaction or competition for the  E-box  transcriptional elements. [ 25 ]  A separate study using  dizygotic twins  with a novel DEC2 mutation showed that one twin had shorter sleep duration. These results demonstrate that DEC2 is able to affect sleep length through weakened transcriptional repression. [ 6 ]


Another important gene involved in FNSS is  ADRB1 . ADRB1 neurons in mice are active they are awake and are found in the dorsal  pons . Through additional family studies, mutations in ADRB1 have shown the reduced sleep phenotype. [ 6 ]


In a more recent study done by Lijuan Xing and colleagues,  NPSR1  was linked to FNSS. In this study, researchers identified a family with a mutation in the NPSR1 gene, which caused a short sleep phenotype. NPSR1 is a  G-protein coupled receptor  that plays a role in  arousal  and sleep behaviors. This NPSR1 mutation was recreated in mice, and the researchers found the same short sleep phenotype present. [ 22 ]


In another study done by Guangsen Shi and colleagues,  GRM1  was linked to FNSS. Here, researchers identified two GRM1 mutations in two different FNSS families. They recreated these same mutations in mouse models and found that they caused the mice to sleep less. [ 23 ]


Understanding how these individuals are able to tolerate higher sleep pressure and behavioral drive will prove useful for numerous people that hold jobs which require long durations of wakefulness. [ 6 ]


Familial natural long sleep (FNLS) likely exists, however there have not been any genetic variants found that cause FNLS. People with FNLS likely need more than 8 hours of sleep per day to feel well rested. This group of individuals may be harder to detect due to  comorbidities , such as  depression . Additional research is necessary to learn more about this sleep trait. [ 6 ]


The  Kistler Prize  (1999-2011) was awarded annually to recognize original contributions "to the understanding of the connection between human heredity and human society", and was named after its benefactor, physicist and inventor  Walter Kistler . The prize was awarded by the Foundation For the Future and it included a cash award of US $100,000 and a 200-gram gold medallion. [ 1 ]


The recipients have been:


The Walter P. Kistler Book Award was established in 2003 to recognize authors of science books that "significantly increase the knowledge and understanding of the public regarding subjects that will shape the future of our species". The award includes a cash prize of US$10,000 and is formally presented in ceremonies that are open to the public.


The mission of the Foundation For the Future is to increase and diffuse knowledge concerning the long-term future of humanity. It conducts a broad range of programs and activities to promote an understanding of the factors that may affect human life in the long term. [ 2 ]


An  ADE model  is a genetic model for  twin studies  which includes  dominance  genetic effects. [ 1 ]


A  stands for  additive  genetic effects ,  D  for non-additive genetic (or  dominance ) effects, and  E  for nonshared  environment  effects. [ 2 ]


The  candidate gene  approach to conducting  genetic association  studies focuses on associations between  genetic variation  within pre-specified genes of interest, and  phenotypes  or disease states. This is in contrast to  genome-wide association studies  (GWAS), which is a hypothesis-free approach that scans the entire  genome  for associations between common genetic variants (typically  SNPs ) and traits of interest. Candidate genes are most often selected for study based on  a priori  knowledge of the gene's biological functional impact on the trait or disease in question. [ 1 ] [ 2 ]  The rationale behind focusing on allelic variation in specific, biologically relevant regions of the genome is that certain alleles within a gene may directly impact the function of the gene in question and lead to variation in the phenotype or disease state being investigated. This approach often uses the  case-control study  design to try to answer the question, "Is one allele of a candidate gene more frequently seen in subjects with the disease than in subjects without the disease?" [ 1 ]  Candidate genes hypothesized to be associated with  complex traits  have generally not been replicated by subsequent GWASs [ 3 ] [ 4 ] [ 5 ] [ 6 ]  or highly powered replication attempts. [ 7 ] [ 8 ]  The failure of candidate gene studies to shed light on the specific genes underlying such traits has been ascribed to insufficient  statistical power , low  prior probability  that scientists can correctly guess a specific allele within a specific gene that is related to a trait, poor methodological practices, and  data dredging . [ 9 ] [ 6 ] [ 10 ]


Suitable candidate genes are generally selected based on known biological, physiological, or functional relevance to the disease in question. This approach is limited by its reliance on existing knowledge about known or theoretical biology of disease. However, molecular tools are allowing insight into disease mechanisms and pinpointing potential regions of interest in the genome.  Genome-wide association studies  (GWAS) and  quantitative trait locus  (QTL) mapping examine common variation across the entire genome, and as such can detect a new region of interest that is in or near a potential candidate gene.  Microarray  data allow researchers to examine differential gene expression between cases and controls, and can help pinpoint new potential genes of interest. [ 11 ]


The great variability between organisms can sometimes make it difficult to distinguish normal variation in  single-nucleotide polymorphisms  (SNP) from a candidate gene with disease-associated variation. [ 12 ]  In analyzing large amounts of data, there are several other factors that can help lead to the most probable variant. These factors include priorities in SNPs, relative risk of functional change in genes, and  linkage disequilibrium  among SNPs. [ 13 ]


In addition, the availability of genetic information through online databases enables researchers to mine existing data and web-based resources for new candidate gene targets. [ 14 ]  Many online databases are available to research genes across species.


Before the candidate-gene approach was fully developed, various other methods were used to identify genes linked to disease-states. These methods studied  genetic linkage  and  positional cloning  through the use of a  genetic screen , and were effective at identifying relative risk genes in  Mendelian diseases . [ 13 ] [ 19 ]  However, these methods are not as beneficial when studying complex diseases for several reasons: [ 13 ]


A study of candidate genes seeks to balance the use of data while attempting to minimize the chance of creating false positive or negative results. [ 13 ]  Because this balance can often be difficult, there are several criticisms of the candidate gene approach that are important to understand before beginning such a study. For instance, the candidate-gene approach has been shown to produce a high rate of false positives, [ 22 ]  which requires that the findings of single genetic associations be treated with great caution. [ 23 ]


One critique is that findings of association within candidate-gene studies have not been easily replicated in follow up studies. [ 24 ]  For instance, a recent investigation on 18 well-studied candidate genes for depression (10 publications or more each) failed to identify any significant association with depression, despite using samples orders of magnitude larger than those from the original publications. [ 25 ]  In addition to statistical issues (e.g. underpowered studies),  population stratification  has often been blamed for this inconsistency; therefore caution must also be taken in regards to what criteria define a certain phenotype, as well as other variations in design study. [ 13 ]


Additionally, because these studies incorporate  a priori  knowledge, some critics argue that our knowledge is not sufficient to make valid predictions. Therefore, results gained from these 'hypothesis-driven' approaches are dependent on the ability to select plausible candidates from the genome, rather than use a hypothesis-free approach.


One of the earliest successes using the candidate gene approach was finding a single base mutation in the  non-coding region  of the  APOC3  (apolipoprotein C3 gene) that associated with  higher risks of  hypertriglyceridemia  and  atherosclerosis . [ 26 ]  In a study by Kim et al., genes linked to the obesity trait in both pigs and humans were discovered using  comparative genomics  and chromosomal heritability. [ 27 ]  By using these two methods, the researchers were able to overcome the criticism that candidate gene studies are solely focused on prior knowledge. Comparative genomics was completed by examining both human and pig  quantitative trait loci  through a method known as  genome-wide complex trait analysis  (GCTA), which allowed the researchers to then map genetic variance to specific chromosomes. This allowed the parameter of heritability to provide understanding of where phenotypic variation was on specific chromosomal regions, thus extending to candidate markers and genes within these regions.  Other studies may also use computational methods to find candidate genes in a widespread, complementary way, such as one study by Tiffin et al. studying genes linked to  type 2 diabetes . [ 12 ]


Many studies have similarly used candidate genes as part of a multi-disciplinary approach to examining a trait or phenotype. One example of manipulating candidate genes can be seen in a study completed by Martin E. Feder on  heat-shock proteins  and their function in  Drosophila melanogaster . [ 28 ]  Feder designed a holistic approach to study  Hsp70 , a candidate gene that was hypothesized to play a role in how an organism adapted to stress.  D. melanogaster  is a highly useful model organism for studying this trait due to the way it can support a diverse number of genetic approaches for studying a candidate gene. The different approaches this study took included both genetically modifying the candidate gene (using site-specific  homologous recombination  and the expression of various proteins), as well as examining the natural variation of  Hsp70 . He concluded that the results of these studies gave a multi-faceted view of  Hsp70 . The manipulation of candidate genes is also seen in Caspar C. Chater's study of the origin and function of  stomata  in  Physcomitrella patens , a moss.  PpSMF1 ,  PpSMF2  and  PpSCRM1  were the three candidate genes that were knocked down by homologous recombination to see any changes in the development of stomata. With the knock down experiment, Chater observed that  PpSMF1  and  PpSCRM1  were responsible for stomata development in  P. patens. [ 29 ]  By engineering and modifying these candidate genes, they were able to confirm the ways in which this gene was linked to a change phenotype. Understanding the natural and historical context in which these phenotypes operate by examining the natural genome structure complemented this.


Complex traits are phenotypes that are controlled by two or more genes and do not follow  Mendel's Law  of Dominance. They may have a range of  expression  which is typically continuous. Both environmental and genetic factors often impact the variation in expression.  Human height  is a continuous trait meaning that there is a wide range of heights. There are an estimated 50 genes that affect the height of a human. Environmental factors, like nutrition, also play a role in a human's height. Other examples of complex traits include: crop yield, plant color, and many diseases including diabetes and  Parkinson's disease . One major goal of genetic research today is to better understand the molecular mechanisms through which genetic variants act to influence complex traits. Complex traits are also known as  polygenic traits  and  multigenic traits .  [ 1 ] [ 2 ]


The existence of complex traits, which are far more common than Mendelian traits, represented a significant challenge to the acceptance of Mendel's work. Modern understanding has 3 categories of complex traits: quantitative, meristic, and threshold. These traits have been studied on a small scale with observational techniques like twin studies. They are also studied with statistical techniques like  quantitative trait loci  (QTL) mapping, and  genome-wide association studies  (GWAS) on a large scale. The overall goal of figuring out how genes interact with each other and the environment and how those interactions can lead to variation in a trait is called genetic architecture.


When  Mendel 's work on inheritance was rediscovered in 1900, scientists debated whether Mendel's laws could account for the continuous variation observed for many traits. [ citation needed ]  One group known as the biometricians argued that continuous traits such as height were largely  heritable , but could not be explained by the inheritance of single Mendelian genetic factors. Work published by  Ronald Fisher  in 1919 mostly resolved debate by demonstrating that the variation in continuous traits could be accounted for if multiple such factors contributed additively to each trait. [ 1 ]  However, the number of genes involved in such traits remained undetermined; until recently,  genetic loci  were expected to have moderate effect sizes and each explain several percent of heritability. [ 3 ]  After the conclusion of the  Human Genome Project  in 2001, it seemed that the  sequencing  and mapping of many individuals would soon allow for a complete understanding of traits'  genetic architectures . However,  variants  discovered through  genome-wide association studies  (GWASs) accounted for only a small percentage of predicted heritability; for example, while height is estimated to be 80-90% heritable, early studies only identified variants accounting for 5% of this heritability. [ 4 ]  Later research showed that most missing heritability could be accounted for by common variants missed by GWASs because their effect sizes fell below significance thresholds; a smaller percentage is accounted for by rare variants with larger effect sizes, although in certain traits such as  autism , rare variants play a more dominant role. [ 5 ] [ 6 ] [ 7 ]  While many genetic factors involved in complex traits have been identified, determining their specific contributions to phenotypes—specifically, the molecular mechanisms through which they act—remains a major challenge. [ 8 ]


Quantitative traits have phenotypes that are expressed on  continuous ranges . [ 9 ]  They have many different genes that impact the phenotype, with differing effect sizes. [ 10 ]  Many of these traits are somewhat heritable. For example, height is estimated to be 60-80% heritable; however, other quantitative traits have varying heritability. [ 11 ]


Meristic traits have phenotypes that are described by whole numbers. An example is the rate chickens lay eggs. A chicken can lay one, two, or five eggs a week, but never half an egg. [ 9 ]  The environment can also impact expression, as chickens will not lay as many eggs depending on the time of year. [ 12 ]


Threshold traits have phenotypes that have limited expressions (usually two). It is a complex trait because multiple genetic and environmental factors impact the phenotype. [ 13 ] [ 14 ]  The phenotype before the threshold is referred to as normal or absent, and after the threshold as lethal or present. These traits are often examined in a medical context, because many diseases exhibit this pattern or similar. [ 9 ]  An example of this is  type 2 diabetes , the phenotype is  either normal/healthy or lethal/diseased. [ 15 ]


Twin studies  is an observational test using  monozygotic twins  and  dizygotic twins , preferably same sex. They are used to figure out the environmental influence on complex traits. Monozygotic twins in particular are estimated to share 100% of their DNA with each other so any phenotypic differences should be caused by environmental influences. [ 2 ]


Many complex traits are genetically determined by quantitative trait loci  (QTL) . A Quantitative Trait Loci analysis can be used to find regions on the  genome sequence  that are associated with a complex trait. [ 16 ]  To find these regions, researchers will select a trait of interest and take a group of individuals of a species with varying expressions of this trait. They will label the individuals as founding parents and attempt to measure the trait. This can be difficult as most traits do not have a direct cut off point. Researchers will then  genotype  the parents using molecular markers such as  SNPs  or  RFLPs . These act as signposts pointing to an area of where the genes associated with a trait are. From there, the parents are crossed to produce offspring. These offspring are then made to produce new offspring, but who they breed with can vary. [ 17 ]  They can either reproduce with their siblings, with themselves (different from asexual reproduction), or  backcross . [ 18 ]  After this, a new generation is produced that are more genetically diverse. This is due to  recombination . The genotype and phenotype of this new generation are measured and compared with the molecular markers to identify which  alleles  are associated with the trait. [ 19 ]  This does not mean there is a direct causal relationship between these regions and the trait, but it does give insight that there are genes that do have some relationship with the trait and reveals where to look in future research.


A  Genome-Wide Association Study  (GWAS) is a technique used to find gene variants linked to complex traits. A GWAS is done with populations that mate randomly because all the genetic variants are tested at once. Then researchers can compare the different alleles at a locus. It is similar to  QTL mapping . [ 20 ]  The most common set-up for a GWAS is a case study which creates two populations one with the trait we are looking at and one without the trait. With the two populations researchers will map every subject's genome and compare them to find different variance in the  SNPs  between the two populations. [ citation needed ]  Both populations should have similar environmental backgrounds. GWAS is only looking at the DNA and does not include differences that would be caused by environmental factors. [ 2 ]


Statistical test, such as a  chi squared  is used to find if there is association with the trait and each of the SNPs tested. The statistical test produces a  p-value  which the researcher will use to conclude if the SNP is significant. This p-value cut off can range from being a higher number or a lower number at the researcher's discretion. The data can then be visualized in a  Manhattan plot  which takes the -log (p-value) so all the significant SNPs are at the top of the graph. [ 21 ] [ 22 ]


Genetic architecture  is an overall explanation of all the genetic factors that play a role in a complex trait and exists as the core foundation of  quantitative genetics . With the use of mathematical models and statistical analysis, like GWAS, researchers can determine the number of genes affecting a trait as well as the level of influence each gene has on the trait. This is not always easy as the architecture of one trait can be different between two separate populations of the same species. [ 16 ]  This can be due to the fact that both populations live in different environments. Differing environments can lead to different interactions between genes and the environment, changing the architecture of both populations. [ 23 ]


Recently, with rapid increases in available genetic data, researchers have begun to characterize the genetic architecture of complex traits better. One surprise has been the observation that most loci identified in GWASs are found in  noncoding  regions of the genome; therefore, instead of directly altering  protein sequences , such variants likely affect  gene regulation . [ 24 ]  To understand the precise effects of these variants, QTL mapping has been employed to examine data from each step of gene regulation; for example, mapping  RNA-sequencing  data can help determine the effects of variants on  mRNA  expression levels, which then presumably affect the numbers of proteins translated. A comprehensive analysis of QTLs involved in various regulatory steps— promotor  activity,  transcription  rates, mRNA expression levels,  translation  levels, and protein expression levels—showed that high proportions of QTLs are shared, indicating that regulation behaves as a “sequential ordered cascade” with variants affecting all levels of regulation. [ 25 ]  Many of these variants act by affecting  transcription factor  binding and other processes that alter  chromatin  function—steps which occur before and during RNA transcription. [ 25 ]


To determine the functional consequences of these variants, researchers have largely focused on identifying key genes, pathways, and processes that drive complex trait behavior; an inherent assumption has been that the most statistically significant variants have the greatest impact on traits because they act by affecting these key drivers. [ 8 ] [ 26 ]   For example, one study hypothesizes that there exist rate-limiting genes pivotal to the function of  gene regulatory networks . [ 27 ]  Others studies have identified the functional impacts of key genes and mutations on disorders, including autism and  schizophrenia . [ 7 ] [ 28 ]   However, a 2017 analysis by Boyle et al. argues that while genes which directly impact complex traits do exist, regulatory networks are so interconnected that any expressed gene affects the functions of these "core" genes; this idea is called the " omnigenic " hypothesis. [ 8 ]  While these "peripheral" genes each have small effects, their combined impact far exceeds the contributions of core genes themselves. To support the hypothesis that core genes play a smaller than expected role, the authors describe three main observations: the heritability for complex traits is spread broadly, often uniformly, across the genome; genetic effects do not appear to be mediated by cell-type specific function; and genes in the relevant functional categories only modestly contribute more to heritability than other genes. [ 8 ]  One alternative to the omnigenic hypothesis is the idea that peripheral genes act not by altering core genes but by altering cellular states, such as the speed of cell division or hormone response. [ 29 ] [ 30 ]


In  genetics ,  dominance  is the phenomenon of one variant ( allele ) of a  gene  on a  chromosome  masking or overriding the  effect  of a different variant of the same gene on  the other copy of the chromosome . [ 1 ] [ 2 ]  The first variant is termed  dominant  and the second is called  recessive . This state of having  two different variants  of the same gene on each chromosome is originally caused by a  mutation  in one of the genes, either new ( de novo ) or  inherited . The terms  autosomal dominant  or  autosomal recessive  are used to describe gene variants on non-sex chromosomes ( autosomes ) and their associated traits, while those on  sex chromosomes  (allosomes) are termed  X-linked dominant ,  X-linked recessive  or  Y-linked ; these have an inheritance and presentation pattern that depends on the sex of both the parent and the child (see  Sex linkage ). Since there is only one copy of the  Y chromosome , Y-linked traits cannot be dominant or recessive. [ 3 ]  Additionally, there are other forms of dominance, such as  incomplete dominance , in which a gene variant has a partial effect compared to when it is present on both chromosomes, and  co-dominance , in which different variants on each chromosome both show their associated traits.


Dominance is a key concept in  Mendelian inheritance  and  classical genetics . Letters and  Punnett squares  are used to demonstrate the principles of dominance in teaching, and the upper-case letters are used to denote dominant alleles and lower-case letters are used for recessive alleles. An often quoted example of dominance is the inheritance of  seed  shape in  peas . Peas may be round, associated with allele  R , or wrinkled, associated with allele  r . In this case, three combinations of alleles (genotypes) are possible:  RR ,  Rr , and  rr . The  RR  ( homozygous ) individuals have round peas, and the  rr  (homozygous) individuals have wrinkled peas. In  Rr  ( heterozygous ) individuals, the  R  allele masks the presence of the  r  allele, so these individuals also have round peas. Thus, allele  R  is dominant over allele  r , and allele  r  is recessive to allele  R . [ 4 ]


Dominance is not inherent to an allele or its traits ( phenotype ). It is a strictly relative effect between two alleles of a given gene of any function; one allele can be dominant over a second allele of the same gene, recessive to a third, and  co-dominant  with a fourth. Additionally, one allele may be dominant for one trait but not others. [ 5 ]  Dominance differs from  epistasis , the phenomenon of an allele of one gene masking the effect of alleles of a  different  gene. [ 6 ]


Gregor Johann Mendel , "The Father of Genetics", promulgated the idea of dominance in the 1860s. However, it was not widely known until the early twentieth century. Mendel observed that, for a variety of traits of garden peas having to do with the appearance of seeds, seed pods, and plants, there were two discrete phenotypes, such as round versus wrinkled seeds, yellow versus green seeds, red versus white flowers or tall versus short plants. When bred separately, the plants always produced the same phenotypes, generation after generation. However, when lines with different phenotypes were crossed (interbred), one and only one of the parental phenotypes showed up in the offspring (green, round, red, or tall). However, when these  hybrid  plants were crossed, the offspring plants showed the two original phenotypes, in a characteristic 3:1 ratio, the more common phenotype being that of the parental hybrid plants. Mendel reasoned that each parent in the first cross was a homozygote for different alleles (one parent AA and the other parent aa), that each contributed one allele to the offspring, with the result that all of these hybrids were heterozygotes (Aa), and that one of the two alleles in the hybrid cross dominated expression of the other: A masked a. The final cross between two heterozygotes (Aa X Aa) would produce AA, Aa, and aa offspring in a 1:2:1 genotype ratio with the first two classes showing the (A) phenotype, and the last showing the (a) phenotype, thereby producing the 3:1 phenotype ratio.


Mendel did not use the terms gene, allele, phenotype, genotype, homozygote, and heterozygote, all of which were introduced later. He did introduce the notation of capital and lowercase letters for dominant and recessive alleles, respectively, still in use today.


In 1928, British population geneticist  Ronald Fisher  proposed that dominance acted based on natural selection through the contribution of  modifier genes . In 1929, American geneticist  Sewall Wright  responded by stating that dominance is simply a physiological consequence of metabolic pathways and the relative necessity of the gene involved. [ 7 ] [ 8 ] [ 9 ] [ 5 ]


In complete dominance, the effect of one allele in a heterozygous genotype completely masks the effect of the other. The allele that masks are considered  dominant  to the other allele, and the masked allele is considered  recessive . [ 10 ]


When we only look at one trait determined by one pair of genes, we call it  monohybrid inheritance . If the crossing is done between parents (P-generation, F0-generation) who are homozygote dominant and homozygote recessive, the offspring (F1-generation) will always have the heterozygote genotype and always present the phenotype associated with the dominant gene.


However, if the F1-generation is further crossed with the F1-generation (heterozygote crossed with heterozygote) the offspring (F2-generation) will present the phenotype associated with the dominant gene ¾ times. Although heterozygote monohybrid crossing can result in two phenotype variants, it can result in three genotype variants -  homozygote dominant, heterozygote and homozygote recessive, respectively. [ 11 ]


In  dihybrid  inheritance  we look at the inheritance of two pairs of genes simultaneous. Assuming here that the two pairs of genes are located at non-homologous chromosomes, such that they are not coupled genes (see  genetic linkage ) but instead inherited independently. Consider now the cross between parents (P-generation) of genotypes homozygote dominant and recessive, respectively. The offspring (F1-generation) will always heterozygous and present the phenotype associated with the dominant allele variant.


However, when crossing the F1-generation there are four possible phenotypic possibilities and the phenotypical  ratio  for the F2-generation will always be 9:3:3:1. [ 12 ]


Incomplete dominance (also called  partial dominance ,  semi-dominance ,  intermediate inheritance , or occasionally incorrectly  co-dominance  in reptile genetics [ 13 ] ) occurs when the phenotype of the heterozygous genotype is distinct from and often intermediate to the phenotypes of the homozygous genotypes. The phenotypic result often appears as a blended form of characteristics in the heterozygous state. For example, the  snapdragon  flower color is homozygous for either red or white. When the red homozygous flower is paired with the white homozygous flower, the result yields a pink snapdragon flower. The pink snapdragon is the result of incomplete dominance. A similar type of incomplete dominance is found in the  four o'clock plant  wherein pink color is produced when true-bred parents of white and red flowers are crossed. In  quantitative genetics , where phenotypes are measured and treated numerically, if a heterozygote's phenotype is exactly between (numerically) that of the two homozygotes, the phenotype is said to exhibit  no dominance  at all, i.e. dominance exists only when the heterozygote's phenotype measure lies closer to one homozygote than the other.


When plants of the F 1  generation are self-pollinated, the phenotypic and genotypic ratio of the F 2  generation will be 1:2:1 (Red:Pink:White). [ 14 ]


Co-dominance occurs when the contributions of both alleles are visible in the phenotype and neither allele masks another.


For example, in the  ABO blood group system , chemical modifications to a  glycoprotein  (the H antigen) on the surfaces of blood cells are controlled by three alleles, two of which are co-dominant to each other ( I A ,  I B ) and dominant over the recessive  i  at the  ABO locus . The  I A  and  I B  alleles produce different modifications. The enzyme coded for by  I A  adds an N-acetylgalactosamine to a membrane-bound H antigen. The  I B  enzyme adds a galactose. The  i  allele produces no modification. Thus the  I A  and  I B  alleles are each dominant to  i  ( I A I A  and  I A i  individuals both have type A blood, and  I B I B  and  I B i  individuals both have type B blood), but  I A I B  individuals have both modifications on their blood cells and thus have type AB blood, so the  I A  and  I B  alleles are said to be co-dominant. [ 14 ]


Another example occurs at the locus for the  beta-globin  component of  hemoglobin , where the three molecular phenotypes of  Hb A /Hb A ,  Hb A /Hb S , and  Hb S /Hb S  are all distinguishable by  protein electrophoresis . (The medical condition produced by the heterozygous genotype is called  sickle-cell trait  and is a milder condition distinguishable from  sickle-cell anemia , thus the alleles show  incomplete dominance  concerning anemia, see above). For most gene loci at the molecular level, both alleles are expressed co-dominantly, because both are  transcribed  into  RNA . [ 14 ]


Co-dominance, where allelic products co-exist in the phenotype, is different from incomplete dominance, where the quantitative interaction of allele products produces an intermediate phenotype. For example, in co-dominance, a red homozygous flower and a white homozygous flower will produce offspring that have red and white spots. When plants of the F1 generation are self-pollinated, the phenotypic and genotypic ratio of the F2 generation will be 1:2:1 (Red:Spotted:White). These ratios are the same as those for incomplete dominance. Again, this classical terminology is inappropriate – in reality, such cases should not be said to exhibit dominance at all. [ 14 ]


Dominance can be influenced by various genetic interactions and it is essential to evaluate them when determining phenotypic outcomes.  Multiple alleles ,  epistasis  and  pleiotropic  genes are some factors that might influence the phenotypic outcome. [ 15 ]


Although any individual of a diploid organism has at most two different alleles at a given locus, most genes exist in a large number of allelic versions in the population as a whole. This is called  polymorphism , and is caused by mutations. Polymorphism can have an effect on the dominance relationship and phenotype, which is observed in the  ABO blood group system . The gene responsible for human blood type have three alleles; A, B, and O, and their interactions result in different blood types based on the level of dominance the alleles expresses towards each other. [ 15 ] [ 16 ]


Pleiotropic  genes  are genes where one single gene affects two or more characters (phenotype). This means that a gene can have a dominant effect on one trait, but a more recessive effect on another trait. [ 17 ]


Epistasis is interactions between multiple alleles at different loci. Easily said, several genes for one phenotype. The dominance relationship between alleles involved in epistatic interactions can influence the observed phenotypic ratios in offspring. [ 18 ]


The  effective population size  ( N e ) is the size of an  idealised population  that would experience the same rate of  genetic drift  as the real population. [ 1 ]  Idealised populations are those following simple one- locus  models that comply with assumptions of the  neutral theory of molecular evolution . The effective population size is normally smaller than the  census population size   N , partly because chance events prevent some individuals from breeding, and partly due to  background selection  and  genetic hitchhiking .


The same real population could have a different effective population size for different properties of interest, such as genetic drift (or more precisely, the speed of  coalescence ) over one generation vs. over many generations. Within a species,  areas  of the genome that have more  genes  and/or less  genetic recombination  tend to have lower effective population sizes, because of the effects of selection at linked sites. In a population with selection at many loci and abundant  linkage disequilibrium , the coalescent effective population size may not reflect the census population size at all, or may reflect its logarithm.


The concept of effective population size was introduced in the field of  population genetics  in 1931 by the  American   geneticist   Sewall Wright . [ 2 ] [ 3 ]  Some versions of the effective population size are used in wildlife conservation.


In a rare experiment that directly measured genetic drift one generation at a time, in  Drosophila  populations of census size 16, the effective population size was 11.5. [ 4 ]  This measurement was achieved through studying changes in the frequency of a neutral allele from one generation to another in over 100 replicate populations.


More commonly, effective population size is estimated indirectly by comparing data on current within-species  genetic diversity  to theoretical expectations. According to the  neutral theory of molecular evolution , an idealised diploid population will have a pairwise  nucleotide diversity  equal to 4

 μ

 {\displaystyle \mu }

 N e , where

 μ

 {\displaystyle \mu }

  is the  mutation rate . The effective population size can therefore be estimated empirically by dividing the nucleotide diversity by 4

 μ

 {\displaystyle \mu }

 . [ 5 ]  This captures the cumulative effects of genetic drift, genetic hitchhiking, and background selection over longer timescales. More advanced methods, permitting a changing effective population size over time, have also been developed. [ 6 ]


The effective size measured to reflect these longer timescales may have little relationship to the number of individuals physically present in a population. [ 7 ]  Measured effective population sizes vary between genes in the same population, being low in genome areas of low recombination and high in genome areas of high recombination. [ 8 ] [ 9 ]  Sojourn times are proportional to N in neutral theory, but for alleles under selection, sojourn times are proportional to log(N).  Genetic hitchhiking  can cause neutral mutations to have sojourn times proportional to log(N): this may explain the relationship between measured effective population size and the local recombination rate. [ 10 ]


If the  recombination map  of  recombination frequencies  along  chromosomes  is known,  N e  can be inferred from  r P 2  = 1 / (1+4 N e   r ), where  r P  is the  Pearson correlation coefficient  between loci. [ 11 ]  This expression can be interpreted as the probability that two  lineages  coalesce before one allele on either lineage recombines onto some third lineage. [ 6 ]


A survey of publications on 102 mostly wildlife animal and plant species yielded 192  N e / N  ratios. Seven different estimation methods were used in the surveyed studies. Accordingly, the ratios ranged widely from 10 -6  for Pacific oysters to 0.994 for humans, with an average of 0.34 across the examined species. Based on these data they subsequently estimated more comprehensive ratios, accounting for fluctuations in population size, variance in family size and unequal sex-ratio. These ratios average to only 0.10-0.11. [ 12 ]


A genealogical analysis of human hunter-gatherers ( Eskimos ) determined the effective-to-census population size ratio for haploid (mitochondrial DNA, Y chromosomal DNA), and diploid (autosomal DNA) loci separately: the ratio of the effective to the census population size was estimated as 0.6–0.7 for autosomal and X-chromosomal DNA, 0.7–0.9 for mitochondrial DNA and 0.5 for Y-chromosomal DNA. [ 13 ]


In an idealised Wright-Fisher model, the fate of an allele, beginning at an intermediate frequency, is largely determined by selection if the  selection coefficient  s ≫ 1/N, and largely determined by neutral genetic drift if s ≪ 1/N. In real populations, the cutoff value of s may depend instead on local recombination rates. [ 14 ] [ 15 ]  This limit to selection in a real population may be captured in a toy Wright-Fisher simulation through the appropriate choice of Ne. Populations with different selection effective population sizes are predicted to evolve profoundly different genome architectures. [ 16 ] [ 17 ]


Ronald Fisher  and  Sewall Wright  originally defined effective population size as "the number of breeding individuals in an  idealised population  that would show the same amount of dispersion of  allele frequencies  under random  genetic drift  or the same amount of  inbreeding  as the population under consideration". This implied two potentially different effective population sizes, based either on the one-generation increase in variance across replicate populations  (variance effective population size) , or on the one-generation change in the inbreeding coefficient  (inbreeding effective population size) . These two are closely linked, and derived from  F-statistics , but they are not identical. [ 18 ]


Today, the effective population size is usually estimated empirically with respect to the amount of within-species  genetic diversity  divided by the  mutation rate , yielding a  coalescent effective population size  that reflects the cumulative effects of genetic drift, background selection, and genetic hitchhiking over longer time periods. [ 5 ]  Another important effective population size is the  selection effective population size  1/s critical , where s critical  is the critical value of the  selection coefficient  at which selection becomes more important than  genetic drift . [ 14 ]


In the  Wright-Fisher idealized population model , the  conditional variance  of the allele frequency

 p
 ′

 {\displaystyle p'}

 , given the  allele frequency

 p

 {\displaystyle p}

  in the previous generation, is


Let

 var
 ^

 (

 p
 ′

 ∣
 p
 )

 {\displaystyle {\widehat {\operatorname {var} }}(p'\mid p)}

  denote the same, typically larger, variance in the actual population under consideration.  The variance effective population size

 N

 e

 (
 v
 )

 {\displaystyle N_{e}^{(v)}}

  is defined as the size of an idealized population with the same variance.  This is found by substituting

 var
 ^

 (

 p
 ′

 ∣
 p
 )

 {\displaystyle {\widehat {\operatorname {var} }}(p'\mid p)}

  for

 var

 (

 p
 ′

 ∣
 p
 )

 {\displaystyle \operatorname {var} (p'\mid p)}

  and solving for

 N

 {\displaystyle N}

  which gives


In the following examples, one or more of the assumptions of a strictly idealised population are relaxed, while other assumptions are retained. The variance effective population size of the more relaxed population model is then calculated with respect to the strict model.


Population size varies over time.  Suppose there are  t  non-overlapping  generations , then effective population size is given by the  harmonic mean  of the population sizes: [ 19 ]


For example, say the population size was  N  = 10, 100, 50, 80, 20, 500 for six generations ( t  = 6).  Then the effective population size is the  harmonic mean  of these, giving:


Note this is less than the  arithmetic mean  of the population size, which in this example is 126.7. The harmonic mean tends to be dominated by the smallest  bottleneck  that the population goes through.


If a population is  dioecious , i.e. there is no  self-fertilisation  then


or more generally,


where  D  represents dioeciousness and may take the value 0 (for not dioecious) or 1 for dioecious.


When  N  is large,  N e  approximately equals  N , so this is usually trivial and often ignored:


If population size is to remain constant, each individual must contribute on average two  gametes  to the next generation.  An idealized population assumes that this follows a  Poisson distribution  so that the  variance  of the number of gametes contributed,  k  is equal to the  mean  number contributed, i.e. 2:


However, in natural populations the variance is often larger than this. The vast majority of individuals may have no offspring, and the next generation stems only from a small number of individuals, so


The effective population size is then smaller, and given by:


Note that if the variance of  k  is less than 2,   N e  is greater than  N .  In the extreme case of a population experiencing no variation in family size, in a laboratory population in which the number of offspring is artificially controlled,  V k  = 0 and  N e  = 2 N .


When the  sex ratio  of a population varies from the  Fisherian  1:1 ratio,  effective population size is given by:


Where  N m  is the number of males and  N f  the number of females.  For example, with 80 males and 20 females (an absolute population size of 100):


Again, this results in  N e  being less than  N .


Alternatively, the effective population size may be defined by noting how the average  inbreeding coefficient  changes from one generation to the next, and then defining  N e  as the size of the idealized population that has the same change in average inbreeding coefficient as the population under consideration.  The presentation follows Kempthorne (1957). [ 20 ]


For the idealized population, the inbreeding coefficients follow the recurrence equation


Using Panmictic Index (1 −  F ) instead of inbreeding coefficient, we get the approximate recurrence equation


The difference per generation is


The inbreeding effective size can be found by solving


This is


When organisms live longer than one breeding season, effective population sizes have to take into account the  life tables  for the species.


Assume a haploid population with discrete age structure.  An example might be an organism that can survive several discrete breeding seasons.  Further, define the following age structure characteristics:


The  generation time  is calculated as


Then, the inbreeding effective population size is [ 21 ]


Similarly, the inbreeding effective number can be calculated for a diploid population with discrete age structure.  This was first given by Johnson, [ 22 ]  but the notation more closely resembles Emigh and Pollak. [ 23 ]


Assume the same basic parameters for the life table as given for the haploid case, but distinguishing between male and female, such as  N 0 ƒ  and  N 0 m  for the number of newborn females and males, respectively (notice lower case  ƒ  for females, compared to upper case  F  for inbreeding).


The inbreeding effective number is


Genetic variance  is a concept outlined by the  English   biologist  and  statistician   Ronald Fisher  in his  fundamental theorem of natural selection . In his 1930 book  The Genetical Theory of Natural Selection , Fisher postulates that the rate of change of  biological fitness  can be calculated by the genetic variance of the fitness itself. [ 1 ]  Fisher tried to give a statistical formula about how the change of fitness in a  population  can be attributed to changes in the  allele frequency . Fisher made no restrictive assumptions in his formula concerning fitness parameters,  mate choices  or the number of  alleles  and  loci  involved. [ 2 ]


Phenotypic variance, usually combines the genotype variance with the environmental variance. Genetic variance has three major components: the additive genetic variance, dominance variance, and epistatic variance. [ 3 ]


Additive genetic variance involves the inheritance of a particular allele from your parent and this allele's independent effect on the specific phenotype, which will cause the phenotype deviation from the mean phenotype. Dominance genetic variance refers to the phenotype deviation caused by the interactions between alternative alleles that control one trait at one specific locus. Epistatic variance involves an interaction between different alleles in different loci. [ 4 ]


Heritability  refers to how much of the phenotypic variance is due to variance in genetic factors. Usually after we know the total amount of genetic variance that is responsible for a trait, we can calculate the trait heritability. Heritability can be used as an important predictor to evaluate if a population can respond to artificial or natural selection. [ 5 ]


Broad-sense heritability, H 2  = V G /V P , Involves the proportion of phenotypic variation due to the effects of additive, dominance, and epistatic variance. Narrow-sense heritability, h 2  = V A /V P , refers to the proportion of phenotypic variation that is due to additive genetic values (V A ). [ 6 ]


The phenotypic variance (V P ) in a population is influenced by genetic variance (V G ) and environmental sources (V E )


V P  = V G  + V E [ 7 ] [ 8 ]


The total amount of genetic variance can be divided into several groups, including additive variance (V A ), dominance variance (V D ), and epistatic variance (V I ).


V G  = V A  + V D  + V I [ 4 ]


1. Traditionally, using  pedigree  data in humans, plants, and livestock species to estimate additive genetic variance.


2. Using a single-nucleotide polymorphisms ( SNP ) regression method to quantify the contribution of additive, dominance, and imprinting variance to the total genetic variance. [ 9 ]


3. Genetic variance–covariance (G) matrices conveniently summarize the genetic relationships among a suite of traits and are a central parameter in the determination of the multivariate response to selection. [ 10 ]


1. The distribution of genetic variance across phenotypic space and the response to selection. [ 11 ]


Understand how empirical spectral distribution of G predicts the response to selection across phenotypic space. In particular, trait combinations that form a nearly null genetic subspace with little genetic variance respond only inconsistently to selection. They set out a framework for understanding how the empirical spectral distribution of G may differ from the random expectations that have been developed under random matrix theory (RMT). Using a data set containing a large number of gene expression traits.


2. Comparing estimates of genetic variance across different relationship models . [ 12 ]


In this research, the researchers use the different relationship models to compare estimates of genetic variance components and the heritability. However, different models may give different estimates of genetic variances. They found that expected genetic variances usually equals the estimated variance times a statistic, Dk, and for the most typical models of relationships, Dk is close to 1, which means most of these models can be used to estimate the genetic variance.


3. Estimation of Additive, Dominance, and Imprinting Genetic Variance Using Genomic Data [ 13 ]


The development of  single-nucleotide polymorphisms (SNPs) mapping helps to explore the genetic variation of complex traits at individual loci. Researchers can quantify the contribution of additive, dominance, and imprinting variance to the total genetic variance by using a SNP regression method.


Heritability  is a  statistic  used in the fields of  breeding  and  genetics  that estimates the degree of  variation  in a  phenotypic trait  in a  population  that is due to  genetic variation  between individuals in that population. [ 1 ]   The concept of heritability can be expressed in the form of the following question: "What is the proportion of the variation in a given trait within a population that is  not  explained by the environment or random chance?" [ 2 ]


Other causes of measured variation in a trait are characterized as  environmental factors , including  observational error . In human studies of heritability these are often apportioned into factors from "shared environment" and "non-shared environment" based on whether they tend to result in persons brought up in the same household being more or less similar to persons who were not.


Heritability is estimated by comparing individual phenotypic variation among related individuals in a population, by examining the association between individual phenotype and genotype data, [ 3 ] [ 4 ]  or even by modeling summary-level data from genome-wide association studies (GWAS). [ 5 ]  Heritability is an important concept in  quantitative genetics , particularly in  selective breeding  and  behavior genetics  (for instance,  twin studies ). It is the source of much confusion due to the fact that its technical definition is different from its commonly-understood folk definition. Therefore, its use conveys the incorrect impression that behavioral traits are "inherited" or specifically passed down through the genes. [ 6 ]  Behavioral geneticists also conduct heritability analyses based on the assumption that genes and environments contribute in a separate, additive manner to behavioral traits. [ 7 ]


Heritability measures the fraction of phenotype variability that can be attributed to  genetic variation . This is not the same as saying that this fraction of an individual phenotype is caused by genetics. For example, it is incorrect to say that since the heritability of personality traits is about 0.6, that means that 60% of your personality is inherited from your parents and 40% comes from the environment. In addition, heritability can change without any genetic change occurring, such as when the environment starts contributing to more variation. As a case in point, consider that both  genes  and environment have the potential to influence intelligence. Heritability could increase if genetic variation increases, causing individuals to show more phenotypic variation, like showing different levels of intelligence. On the other hand, heritability might also increase if the environmental variation decreases, causing individuals to show less phenotypic variation, like showing more similar levels of intelligence. Heritability increases when genetics are contributing more variation or because non-genetic factors are contributing less variation; what matters is the relative contribution. Heritability is specific to a particular population in a particular environment. High heritability of a trait, consequently, does not necessarily mean that the trait is not very susceptible to environmental influences. [ 8 ]  Heritability can also change as a result of changes in the environment, migration,  inbreeding , or how heritability itself is measured in the population under study. [ 9 ]  The heritability of a trait should not be interpreted as a measure of the extent to which said trait is genetically determined in an individual. [ 10 ] [ 11 ]


The extent of dependence of phenotype on environment can also be a function of the genes involved. Matters of heritability are complicated because genes may  canalize  a phenotype, making its expression almost inevitable in all occurring environments. Individuals with the same genotype can also exhibit different phenotypes through a mechanism called  phenotypic plasticity , which makes heritability difficult to measure in some cases. Recent insights in molecular biology have identified changes in  transcriptional  activity of individual genes associated with environmental changes. However, there are a large number of genes whose transcription is not affected by the environment. [ 12 ]


Estimates of heritability use  statistical analyses  to help to identify the causes of differences between individuals. Since heritability is concerned with variance, it is necessarily an account of the differences between individuals in a population. Heritability can be  univariate  – examining a single trait – or multivariate – examining the genetic and environmental associations between multiple traits at once. This allows a test of the genetic overlap between different phenotypes: for instance  hair color  and  eye color . Environment and genetics may also interact, and heritability analyses can test for and examine these interactions (GxE models).


A prerequisite for heritability analyses is that there is some population variation to account for. This last point highlights the fact that heritability cannot take into account the effect of factors which are invariant in the population. Factors may be invariant if they are absent and do not exist in the population, such as no one having access to a particular  antibiotic , or because they are omnipresent, like if everyone is drinking  coffee . In practice, all human behavioral traits vary and almost all traits show some heritability. [ 13 ]


Any particular phenotype can be  modeled  as the sum of genetic and environmental effects: [ 14 ]


Likewise the phenotypic variance in the trait – Var (P) – is the sum of effects as follows:


In a planned experiment Cov( G , E ) can be controlled and held at 0. In this case, heritability,

 H

 2

 ,

 {\displaystyle H^{2},}

  is defined as [ 15 ]


H 2  is the broad-sense heritability. This reflects all the genetic contributions to a population's phenotypic variance including additive,  dominant , and  epistatic  (multi-genic interactions), as well as  maternal and paternal effects , where individuals are directly affected by their parents' phenotype, such as with  milk  production in mammals.


A particularly important component of the genetic variance is the additive variance, Var(A), which is the variance due to the average effects (additive effects) of the  alleles . Since each parent passes a single allele per  locus  to each offspring, parent-offspring resemblance depends upon the average effect of single alleles. Additive variance represents, therefore, the genetic component of variance responsible for parent-offspring resemblance. The additive genetic portion of the phenotypic variance is known as Narrow-sense heritability and is defined as


An upper case  H 2  is used to denote broad sense, and lower case  h 2  for narrow sense.


For traits which are not continuous but dichotomous such as an additional toe or certain diseases,  the contribution of the various alleles can be considered to be a sum, which past a threshold, manifests itself as the trait, giving the  liability threshold model  in which heritability can be estimated and selection modeled.


Additive variance is important for  selection . If a selective pressure such as improving livestock is exerted, the response of the trait is directly related to narrow-sense heritability. The mean of the trait will increase in the next generation as a function of how much the mean of the selected parents differs from the mean of the population from which the selected parents were chosen. The observed  response to selection  leads to an estimate of the narrow-sense heritability (called  realized heritability ). This is the principle underlying  artificial selection  or breeding.


The simplest genetic model involves a single locus with two alleles (b and B) affecting one quantitative phenotype.


The number of  B  alleles can be 0, 1, or 2. For any genotype, ( B i , B j ), where  B i  and  B j  are either 0 or 1, the expected phenotype can then be written as the sum of the overall mean, a linear effect, and a dominance deviation (one can think of the dominance term as an  interaction  between  B i  and  B j ):


P

 i
 j

 =
 μ
 +
 α

 (

 B

 i

 +

 B

 j

 )
 +
 δ

 (

 B

 i

 B

 j

 )

 =

 Population mean

 +

 Additive Effect

 (

 a

 i
 j

 =
 α
 (

 B

 i

 +

 B

 j

 )
 )
 +

 Dominance Deviation

 (

 d

 i
 j

 =
 δ
 (

 B

 i

 B

 j

 )
 )
 .

 {\displaystyle {\begin{aligned}P_{ij}&=\mu +\alpha \,(B_{i}+B_{j})+\delta \,(B_{i}B_{j})\\&={\text{Population mean}}+{\text{Additive Effect }}(a_{ij}=\alpha (B_{i}+B_{j}))+{\text{Dominance Deviation }}(d_{ij}=\delta (B_{i}B_{j})).\\\end{aligned}}}


The additive genetic variance at this locus is the  weighted average  of the squares of the additive effects:


where

 f
 (
 b
 b
 )

 a

 b
 b

 +
 f
 (
 B
 b
 )

 a

 B
 b

 +
 f
 (
 B
 B
 )

 a

 B
 B

 =
 0.

 {\displaystyle f(bb)a_{bb}+f(Bb)a_{Bb}+f(BB)a_{BB}=0.}


There is a similar relationship for the variance of dominance deviations:


where

 f
 (
 b
 b
 )

 d

 b
 b

 +
 f
 (
 B
 b
 )

 d

 B
 b

 +
 f
 (
 B
 B
 )

 d

 B
 B

 =
 0.

 {\displaystyle f(bb)d_{bb}+f(Bb)d_{Bb}+f(BB)d_{BB}=0.}


The  linear regression  of phenotype on genotype is shown in Figure 1.


Estimates of the total heritability of human traits assume the absence of epistasis, which has been called the "assumption of additivity". Although some researchers have cited such estimates in support of the existence of " missing heritability " unaccounted for by known genetic loci, the assumption of additivity may render these estimates invalid. [ 16 ]  There is also some empirical evidence that the additivity assumption is frequently violated in behavior genetic studies of adolescent intelligence and  academic achievement . [ 17 ]


Since only  P  can be observed or measured directly, heritability must be estimated from the similarities observed in subjects varying in their level of genetic or environmental similarity. The  statistical  analyses required to estimate the  genetic  and  environmental  components of variance depend on the sample characteristics. Briefly, better estimates are obtained using data from individuals with widely varying levels of genetic relationship - such as  twins , siblings, parents and offspring, rather than from more distantly related (and therefore less similar) subjects. The  standard error  for heritability estimates is improved with large sample sizes.


In non-human populations it is often possible to collect information in a controlled way. For example, among farm animals it is easy to arrange for a bull to produce offspring from a large number of cows and to control environments. Such  experimental control  is generally not possible when gathering human data, relying on naturally occurring relationships and environments.


In classical quantitative genetics, there were two schools of thought regarding estimation of heritability.


One  school of thought  was developed by  Sewall Wright  at  The University of Chicago , and further popularized by  C. C. Li  ( University of Chicago ) and  J. L. Lush  ( Iowa State University ). It is based on the analysis of correlations and, by extension, regression.  Path Analysis  was developed by  Sewall Wright  as a way of estimating heritability.


The second was originally developed by  R. A. Fisher  and expanded at  The University of Edinburgh ,  Iowa State University , and  North Carolina State University , as well as other schools. It is based on the  analysis of variance  of breeding studies, using the intraclass correlation of relatives. Various methods of estimating components of variance (and, hence, heritability) from  ANOVA  are used in these analyses.


Today, heritability can be estimated from general pedigrees using  linear mixed models  and from  genomic relatedness  estimated from genetic markers.


Studies of human heritability often utilize adoption study designs, often with  identical twins  who have been separated early in life and raised in different environments. Such individuals have identical genotypes and can be used to separate the effects of genotype and environment. A limit of this design is the common prenatal environment and the relatively low numbers of twins reared apart. A second and more common design is the  twin study  in which the similarity of identical and fraternal twins is used to estimate heritability. These studies can be limited by the fact that identical twins are  not completely genetically identical , potentially resulting in an underestimation of heritability.


In  observational studies , or because of evocative effects (where a genome evokes environments by its effect on them), G and E may covary:  gene environment correlation . Depending on the methods used to estimate heritability, correlations between genetic factors and shared or non-shared environments may or may not be confounded with heritability. [ 18 ]


The first school of estimation uses regression and correlation to estimate heritability.


In the comparison of relatives, we find that in general,


where  r  can be thought of as the  coefficient of relatedness ,  b  is the coefficient of regression and  t  is the coefficient of correlation.


Heritability may be estimated by comparing parent and offspring traits (as in Fig. 2). The slope of the line (0.57) approximates the heritability of the trait when offspring values are regressed against the average trait in the parents. If only one parent's value is used then heritability is twice the slope. (This is the source of the term " regression ," since the offspring values always tend to  regress to the mean  value for the population,  i.e. , the slope is always less than one). This regression effect also underlies the  DeFries–Fulker method  for analyzing twins selected for one member being affected. [ 19 ]


A basic approach to heritability can be taken using full-Sib designs: comparing similarity between siblings who share both a biological mother and a father. [ 20 ]  When there is only additive gene action, this sibling phenotypic correlation is an index of  familiarity  – the sum of half the additive genetic variance plus full effect of the common environment. It thus places an upper limit on additive heritability of twice the full-Sib phenotypic correlation. Half-Sib designs compare phenotypic traits of siblings that share one parent with other sibling groups.


Heritability for traits in humans is most frequently estimated by comparing resemblances between twins. "The advantage of twin studies, is that the total variance can be split up into genetic, shared or common environmental, and unique environmental components, enabling an accurate estimation of heritability". [ 21 ]  Fraternal or dizygotic (DZ) twins on average share half their genes (assuming there is no  assortative mating  for the trait), and so identical or monozygotic (MZ) twins on average are twice as genetically similar as DZ twins. A crude estimate of heritability, then, is approximately twice the difference in  correlation  between MZ and DZ twins, i.e.  Falconer's formula   H 2 =2(r(MZ)-r(DZ)).


The effect of shared environment,  c 2 , contributes to similarity between siblings due to the commonality of the environment they are raised in. Shared environment is approximated by the DZ correlation minus half heritability, which is the degree to which DZ twins share the same genes,  c 2 =DZ-1/2 h 2 . Unique environmental variance,  e 2 , reflects the degree to which identical twins raised together are dissimilar,  e 2 =1-r(MZ).


The second set of methods of estimation of heritability involves ANOVA and estimation of variance components.


We use the basic discussion of Kempthorne. [ 14 ]  Considering only the most basic of genetic models, we can look at the quantitative contribution of a single locus with genotype  G i  as


where

 g

 i

 {\displaystyle g_{i}}

  is the effect of genotype  G i  and

 e

 {\displaystyle e}

  is the environmental effect.


Consider an experiment with a group of sires and their progeny from random dams. Since the progeny get half of their genes from the father and half from their (random) mother, the progeny equation is


Consider the experiment above. We have two groups of progeny we can compare. The first is comparing the various progeny for an individual sire (called  within sire group ). The variance will include terms for genetic variance (since they did not all get the same genotype) and environmental variance. This is thought of as an  error  term.


The second group of progeny are comparisons of means of half sibs with each other (called  among sire group ). In addition to the  error term  as in the within sire groups, we have an addition term due to the differences among different means of half sibs. The intraclass correlation is


since environmental effects are independent of each other.


In an experiment with

 n

 {\displaystyle n}

  sires and

 r

 {\displaystyle r}

  progeny per sire, we can calculate the following ANOVA, using

 V

 g

 {\displaystyle V_{g}}

  as the genetic variance and

 V

 e

 {\displaystyle V_{e}}

  as the environmental variance:


The

 1
 4

 V

 g

 {\displaystyle {\frac {1}{4}}V_{g}}

  term is the  intraclass correlation  between half sibs. We can easily calculate

 H

 2

 =

 V

 g

 V

 g

 +

 V

 e

 =

 4
 (
 S
 −
 W
 )

 S
 +
 (
 r
 −
 1
 )
 W

 {\displaystyle H^{2}={\frac {V_{g}}{V_{g}+V_{e}}}={\frac {4(S-W)}{S+(r-1)W}}}

 . The expected mean square is calculated from the relationship of the individuals (progeny within a sire are all half-sibs, for example), and an understanding of intraclass correlations.


The use of ANOVA to calculate heritability often fails to account for the presence of  gene–-environment interactions , because ANOVA has a much lower  statistical power  for testing for interaction effects than for direct effects. [ 22 ]


For a model with additive and dominance terms, but not others, the equation for a single locus is


where


α

 i

 {\displaystyle \alpha _{i}}

  is the additive effect of the i th  allele,

 α

 j

 {\displaystyle \alpha _{j}}

  is the additive effect of the j th  allele,

 d

 i
 j

 {\displaystyle d_{ij}}

  is the dominance deviation for the ij th  genotype, and

 e

 {\displaystyle e}

  is the environment.


Experiments can be run with a similar setup to the one given in Table 1. Using different relationship groups, we can evaluate different intraclass correlations. Using

 V

 a

 {\displaystyle V_{a}}

  as the additive genetic variance and

 V

 d

 {\displaystyle V_{d}}

  as the dominance deviation variance, intraclass correlations become  linear functions  of these parameters. In general,


where

 r

 {\displaystyle r}

  and

 θ

 {\displaystyle \theta }

  are found as


r
 =

 {\displaystyle r=}

 P[  alleles  drawn at random from the relationship pair are  identical by descent ], and


θ
 =

 {\displaystyle \theta =}

 P[  genotypes  drawn at random from the relationship pair are  identical by descent ].


Some common relationships and their coefficients are given in Table 2.


A wide variety of approaches using linear mixed models have been reported in literature. Via these methods, phenotypic variance is partitioned into genetic, environmental and experimental design variances to estimate heritability. Environmental variance can be explicitly modeled by studying individuals across a broad range of environments, although inference of genetic variance from phenotypic and environmental variance may lead to underestimation of heritability due to the challenge of capturing the full range of environmental influence affecting a trait. Other methods for calculating heritability use data from  genome-wide association studies  to estimate the influence on a trait by genetic factors, which is reflected by the rate and influence of putatively associated genetic loci (usually  single-nucleotide polymorphisms ) on the trait. This can lead to underestimation of heritability, however. This discrepancy is referred to as "missing heritability" and reflects the challenge of accurately modeling both genetic and environmental variance in heritability models. [ 23 ]


When a large, complex pedigree or another aforementioned type of data is available, heritability and other quantitative genetic parameters can be estimated by  restricted maximum likelihood  (REML) or  Bayesian methods . The  raw data  will usually have three or more data points for each individual: a code for the sire, a code for the dam and one or several trait values. Different trait values may be for different traits or for different time points of measurement.


The currently popular methodology relies on high degrees of certainty over the identities of the sire and dam; it is not common to treat the sire identity probabilistically. This is not usually a problem, since the methodology is rarely applied to wild populations (although it has been used for several wild ungulate and bird populations), and sires are invariably known with a very high degree of certainty in breeding programmes. There are also algorithms that account for uncertain paternity.


The pedigrees can be viewed using programs such as Pedigree Viewer  [1] , and analyzed with programs such as  ASReml , VCE  [2] , WOMBAT  [3] , MCMCglmm within the R environment  [4]  or the  BLUPF90  family of programs  [5] .


Pedigree models are helpful for untangling confounds such as  reverse causality ,  maternal effects  such as the  prenatal environment , and confounding of  genetic dominance , shared environment, and maternal gene effects. [ 24 ] [ 9 ]


When genome-wide genotype data and phenotypes from large population samples are available, one can estimate the relationships between individuals based on their genotypes and use a linear mixed model to estimate the variance explained by the genetic markers. This gives a genomic heritability estimate based on the variance captured by common genetic variants. [ 4 ]  There are multiple methods that make different adjustments for allele frequency and  linkage disequilibrium . Particularly, the method called High-Definition Likelihood (HDL) can estimate genomic heritability using only GWAS summary statistics, [ 5 ]  making it easier to incorporate large sample size available in various GWAS meta-analysis.


In  selective breeding  of plants and animals, the expected response to selection of a trait with known narrow-sense heritability

 (

 h

 2

 )

 {\displaystyle (h^{2})}

  can be estimated using the  breeder's equation : [ 25 ]


In this equation, the Response to Selection (R) is defined as the realized average difference between the parent generation and the next generation, and the Selection Differential (S) is defined as the average difference between the parent generation and the selected parents. [ 14 ] : 1957  [ 26 ]


For example, imagine that a plant breeder is involved in a selective breeding project with the aim of increasing the number of kernels per ear of corn. For the sake of argument, let us assume that the average ear of corn in the parent generation has 100 kernels. Let us also assume that the selected parents produce corn with an average of 120 kernels per ear. If h 2  equals 0.5, then the next generation will produce corn with an average of 0.5(120-100) = 10 additional kernels per ear. Therefore, the total number of kernels per ear of corn will equal, on average, 110.


Observing the response to selection in an artificial selection experiment will allow calculation of realized heritability as in Fig. 4.


Heritability in the above equation is equal to the ratio

 V
 a
 r

 (
 A
 )

 /

 V
 a
 r

 (
 P
 )

 {\displaystyle \mathrm {Var} (A)/\mathrm {Var} (P)}

  only if the genotype and the environmental noise follow  Gaussian distributions .


Heritability estimates' prominent critics, such as  Steven Rose , [ 27 ]   Jay Joseph , [ 28 ]  and  Richard Bentall , focus largely on heritability estimates in  behavioral sciences  and  social sciences .  Bentall has claimed that such heritability scores are typically calculated counterintuitively to derive numerically high scores, that heritability is misinterpreted as  genetic determination , and that this alleged bias distracts from other factors that researches have found more causally important, such as childhood abuse causing later psychosis. [ 29 ] [ 30 ]  Heritability estimates are also inherently limited because they do not convey any information regarding whether genes or environment play a larger role in the development of the trait under study. For this reason,  David Moore  and  David Shenk  describe the term "heritability" in the context of behavior genetics as "...one of the most misleading in the history of science" and argue that it has no value except in very rare cases. [ 31 ]  When studying complex human traits, it is impossible to use heritability analysis to determine the relative contributions of genes and environment, as such traits result from multiple causes interacting. [ 32 ]   In particular,  Feldman  and  Lewontin  emphasize that heritability is itself a function of environmental variation. [ 33 ]   However, some researchers argue that it is possible to disentangle the two. [ 34 ]


The controversy over heritability estimates is largely via their basis in  twin studies .  The scarce success of  molecular-genetic  studies to corroborate such  population-genetic  studies' conclusions is the  missing heritability  problem . [ 35 ]  Eric Turkheimer has argued that newer molecular methods have vindicated the conventional interpretation of twin studies, [ 35 ]  although it remains mostly unclear how to explain the relations between genes and behaviors. [ 36 ]  According to Turkheimer, both genes and environment are heritable, genetic contribution varies by environment, and a focus on heritability distracts from other important factors. [ 37 ]   Overall, however,  heritability  is a concept widely applicable. [ 9 ]


Quantitative genetics  is the study of  quantitative traits , which are  phenotypes  that vary continuously—such as height or mass—as opposed to phenotypes and gene-products that are  discretely identifiable —such as eye-colour, or the presence of a particular biochemical.


Both of these branches of  genetics  use the frequencies of different  alleles  of a  gene  in breeding populations (gamodemes), and combine them with concepts from simple  Mendelian inheritance  to analyze inheritance patterns across generations and descendant lines. While  population genetics  can focus on particular genes and their subsequent metabolic products, quantitative genetics focuses more on the outward phenotypes, and makes only summaries of the underlying genetics.


Due to the continuous distribution of phenotypic values, quantitative genetics must employ many other statistical methods (such as the  effect size , the  mean  and the  variance ) to link phenotypes (attributes) to genotypes. Some phenotypes may be analyzed either as discrete categories or as continuous phenotypes, depending on the definition of cut-off points, or on the  metric  used to quantify them. [ 1 ] : 27–69   Mendel himself had to discuss this matter in his famous paper, [ 2 ]  especially with respect to his peas' attribute  tall/dwarf , which actually was derived by adding a cut-off point to "length of stem". [ 3 ] [ 4 ]  Analysis of  quantitative trait loci , or QTLs, [ 5 ] [ 6 ] [ 7 ]  is a more recent addition to quantitative genetics, linking it more directly to  molecular genetics .


In  diploid  organisms, the average  genotypic  "value" (locus value) may be defined by the allele "effect" together with a  dominance  effect, and also by how genes interact with genes at other loci ( epistasis ). The founder of quantitative genetics -  Sir Ronald Fisher  - perceived much of this when he proposed the first mathematics of this branch of genetics. [ 8 ]


Being a statistician, he defined the gene effects as deviations from a central value—enabling the use of statistical concepts such as mean and variance, which use this idea. [ 9 ]  The central value he chose for the gene was the midpoint between the two opposing homo zygotes  at the one locus. The deviation from there to the "greater" homozygous genotype can be named " +a "; and therefore it is " -a " from that same midpoint to the "lesser" homozygote genotype. This is the "allele" effect mentioned above. The heterozygote deviation from the same midpoint can be named " d ", this being the "dominance" effect referred to above. [ 10 ]  The diagram depicts the idea. However, in reality we measure phenotypes, and the figure also shows how observed phenotypes relate to the gene effects. Formal definitions of these effects recognize this phenotypic focus. [ 11 ] [ 12 ]  Epistasis has been approached statistically as interaction (i.e., inconsistencies), [ 13 ]  but  epigenetics  suggests a new approach may be needed.


If  0 < d < a , the dominance is regarded as  partial  or  incomplete —while  d = a  indicates full or  classical  dominance. Previously,  d > a  was known as "over-dominance". [ 14 ]


Mendel's pea attribute "length of stem" provides us with a good example. [ 3 ]   Mendel stated that the tall true-breeding parents ranged from 6–7 feet in stem length (183 – 213 cm), giving a median of 198 cm (= P1). The short parents ranged from 0.75 to 1.25 feet in stem length (23 – 46 cm), with a rounded median of 34 cm (= P2). Their hybrid ranged from 6–7.5 feet in length (183–229 cm), with a median of 206 cm (= F1). The mean of P1 and P2 is 116 cm, this being the phenotypic value of the homozygotes midpoint (mp). The allele affect ( a ) is [P1-mp] = 82 cm = -[P2-mp]. The dominance effect ( d ) is [F1-mp] = 90 cm. [ 15 ]   This historical example illustrates clearly how phenotype values and gene effects are linked.


To obtain means, variances and other statistics, both  quantities  and their  occurrences  are required. The gene effects (above) provide the framework for  quantities : and the  frequencies  of the contrasting alleles in the fertilization gamete-pool provide the information on  occurrences .


Commonly, the frequency of the allele causing "more" in the phenotype (including dominance) is given the symbol  p , while the frequency of the contrasting allele is  q . An initial assumption made when establishing the algebra was that the parental population was infinite and random mating, which was made simply to facilitate the derivation. The subsequent mathematical development also implied that the frequency distribution within the effective gamete-pool was uniform: there were no local perturbations where  p  and  q  varied. Looking at the diagrammatic analysis of sexual reproduction, this is the same as declaring that  p P  =  p g  =  p ; and similarly for  q . [ 14 ]  This mating system, dependent upon these assumptions, became known as "panmixia".


Panmixia rarely actually occurs in nature, [ 16 ] : 152–180  [ 17 ]  as gamete distribution may be limited, for example by dispersal restrictions or by behaviour, or by chance sampling (those local perturbations mentioned above). It is well known that there is a huge wastage of gametes in Nature, which is why the diagram depicts a  potential  gamete-pool separately to the  actual  gamete-pool. Only the latter sets the definitive frequencies for the zygotes: this is the true "gamodeme" ("gamo" refers to the gametes, and "deme" derives from Greek for "population"). But, under Fisher's assumptions, the  gamodeme  can be effectively extended back to the  potential  gamete-pool, and even back to the parental base-population (the "source" population). The random sampling arising when small "actual" gamete-pools are sampled from a large "potential" gamete-pool is known as  genetic drift , and is considered subsequently.


While panmixia may not be widely extant, the  potential  for it does occur, although it may be only ephemeral because of those local perturbations. It has been shown, for example, that the F2 derived from  random fertilization of F1 individuals  (an  allogamous  F2), following hybridization,  is an  origin  of a new  potentially  panmictic population. [ 18 ] [ 19 ]  It has also been shown that if panmictic random fertilization occurred continually, it would maintain the same allele and genotype frequencies across each successive panmictic sexual generation—this being the  Hardy Weinberg  equilibrium. [ 13 ] : 34–39  [ 20 ] [ 21 ] [ 22 ] [ 23 ]  However, as soon as genetic drift was initiated by local random sampling of gametes, the equilibrium would cease.


Male and female gametes within the actual fertilizing pool are considered usually to have the same frequencies for their corresponding alleles. (Exceptions have been considered.) This means that when  p  male gametes carrying the  A  allele randomly fertilize  p  female gametes carrying that same allele, the resulting zygote has genotype  AA , and, under random fertilization, the combination occurs with a frequency of  p  x  p  (=  p 2 ). Similarly, the zygote  aa  occurs with a frequency of  q 2 . Heterozygotes ( Aa ) can arise in two ways: when  p  male ( A  allele) randomly fertilize  q  female ( a  allele) gametes, and  vice versa . The resulting frequency for the heterozygous zygotes is thus  2pq . [ 13 ] : 32   Notice that such a population is never more than half heterozygous, this maximum occurring when  p = q = 0.5.


In summary then, under random fertilization, the zygote (genotype) frequencies are the quadratic expansion of the gametic (allelic) frequencies:

 (
 p
 +
 q

 )

 2

 =

 p

 2

 +
 2
 p
 q
 +

 q

 2

 =
 1

 {\textstyle (p+q)^{2}=p^{2}+2pq+q^{2}=1}

 . (The "=1" states that the frequencies are in fraction form, not percentages; and that there are no omissions within the framework proposed.)


Notice that "random fertilization" and "panmixia" are  not  synonyms.


Mendel's pea experiments were constructed by establishing true-breeding parents with "opposite" phenotypes for each attribute. [ 3 ]  This meant that each opposite parent was homozygous for its respective allele only. In our example, "tall  vs  dwarf", the tall parent would be genotype  TT  with  p  =  1  (and  q  =  0 ); while the dwarf parent would be genotype  tt  with  q  =  1  (and  p  =  0 ). After controlled crossing, their hybrid is  Tt , with  p  =  q  =   1 / 2  . However, the frequency of this heterozygote =  1 , because this is the F1 of an artificial cross: it has not arisen through random fertilization. [ 24 ]  The F2 generation was produced by natural self-pollination of the F1 (with monitoring against insect contamination), resulting in  p  =  q  =   1 / 2   being maintained. Such an F2 is said to be "autogamous". However, the genotype frequencies (0.25  TT , 0.5  Tt , 0.25  tt ) have arisen through a mating system very different from random fertilization, and therefore the use of the quadratic expansion has been avoided. The numerical values obtained were the same as those for random fertilization only because this is the special case of having originally crossed homozygous opposite parents. [ 25 ]  We can notice that, because of the dominance of  T-  [frequency (0.25 + 0.5)] over  tt  [frequency 0.25], the 3:1 ratio is still obtained.