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I am currently doing some research into distributions and probabilities with Mendellian genetics. I came across this problem that I cannot seem to wrap my head around.
Given that the population has two characteristics, they are color and texture. Supposed two dihybrids reproduce (
AaBb x AaBb) and if the dominant form of the color gene is contributed, then the dominant form of the texture gene is three times as likely to be contributed as the recessive form. If the recessive color gene is contributed then the dominant and recessive genes for texture are equally likely.
From this the geneotypic distribution has to be calculated.
I know the solution is:
[9/64 6/64 1/64 3/16 1/4 1/16 1/16 2/16 1/16] AABB AABb AAbb AaBB AaBb Aabb aaBB aaBb aabb
When I performed the punnett square I got the distribution of:
[1/16 2/16 1/16 2/16 4/16 2/16 1/16 2/16 1/16] AABB AABb AAbb AaBB AaBb Aabb aaBB aaBb aabb
and did not know where to go from there.
My question is how did they incorporate the
"times as likely"condition into the solution.
You are… done. You fully answered the question; if I were you, I might just put it in ratio format instead of probability, just to be safe.
The three times thing is a bit weird, but I have seen it before. First, let's look at the phenotypic ratio of the progeny: 9:3:3:1 for Dominant Both:Dominant A Recessive B:Recessive A Dominant B: Recessive Both.
Let's find out how many dominant and recessive there are for each trait. For the dominant A trait, you add up the 9 and 3, because they are the only two types of dominant phenotypes, and find that 12 different organisms of the 16 possible are dominant for Trait A, so the probability of getting trait A is 3/4 or 75%. This means that 4 of the 16 orgamisms are recessive for Trait A, so the probability of being recessive for Trait A is 4/16, or 25%. Therefore, the ratio of Dominant Organism probability:Recessive organism probability is 75% to 25%, or 3:1. This means that it is 3 times as likely to get the dominant trait than the recessive trait. Make sense?
5 Conditions for Hardy-Weinberg Equilibrium
One of the most important principles of population genetics, the study of the genetic composition of and differences in populations, is the Hardy-Weinberg equilibrium principle. Also described as genetic equilibrium, this principle gives the genetic parameters for a population that is not evolving. In such a population, genetic variation and natural selection do not occur and the population does not experience changes in genotype and allele frequencies from generation to generation.
- Godfrey Hardy and Wilhelm Weinberg postulated the Hardy-Weinberg principle in the early 20th century. It predicts both allele and genotype frequencies in populations (non-evolving ones).
- The first condition that must be met for Hardy-Weinberg equilibrium is the lack of mutations in a population.
- The second condition that must be met for Hardy-Weinberg equilibrium is no gene flow in a population.
- The third condition that must be met is the population size must be sufficient so that there is no genetic drift.
- The fourth condition that must be met is random mating within the population.
- Finally, the fifth condition necessitates that natural selection must not occur.
Natural selection and some of the other evolutionary forces can only act on heritable traits, namely an organism’s genetic code. Because alleles are passed from parent to offspring, those that confer beneficial traits or behaviors may be selected, while deleterious alleles may not. Acquired traits, for the most part, are not heritable. For example, if an athlete works out in the gym every day, building up muscle strength, the athlete’s offspring will not necessarily grow up to be a body builder. If there is a genetic basis for the ability to run fast, on the other hand, a parent may pass this to a child.
Heritability is the fraction of phenotype variation that can be attributed to genetic differences, or genetic variance, among individuals in a population. The greater the hereditability of a population’s phenotypic variation, the more susceptible it is to the evolutionary forces that act on heritable variation.
The diversity of alleles and genotypes within a population is called genetic variance. When scientists are involved in the breeding of a species, such as with animals in zoos and nature preserves, they try to increase a population’s genetic variance to preserve as much of the phenotypic diversity as they can. This also helps reduce the risks associated with inbreeding, the mating of closely related individuals, which can have the undesirable effect of bringing together deleterious recessive mutations that can cause abnormalities and susceptibility to disease. For example, a disease that is caused by a rare, recessive allele might exist in a population, but it will only manifest itself when an individual carries two copies of the allele. Because the allele is rare in a normal, healthy population with unrestricted habitat, the chance that two carriers will mate is low, and even then, only 25 percent of their offspring will inherit the disease allele from both parents. While it is likely to happen at some point, it will not happen frequently enough for natural selection to be able to swiftly eliminate the allele from the population, and as a result, the allele will be maintained at low levels in the gene pool. However, if a family of carriers begins to interbreed with each other, this will dramatically increase the likelihood of two carriers mating and eventually producing diseased offspring, a phenomenon known as inbreeding depression.
Changes in allele frequencies that we identify in a population can shed light on how it is evolving. In addition to natural selection, there are other evolutionary forces that could be in play: genetic drift, gene flow, mutation, nonrandom mating, and environmental variances.
Consider a population of monoecious diploids, where each organism produces male and female gametes at equal frequency, and has two alleles at each gene locus. Organisms reproduce by random union of gametes (the "gene pool" population model). A locus in this population has two alleles, A and a, that occur with initial frequencies f0(A) = p and f0(a) = q , respectively. [note 1] The allele frequencies at each generation are obtained by pooling together the alleles from each genotype of the same generation according to the expected contribution from the homozygote and heterozygote genotypes, which are 1 and 1/2, respectively:
The different ways to form genotypes for the next generation can be shown in a Punnett square, where the proportion of each genotype is equal to the product of the row and column allele frequencies from the current generation.
|A (p)||a (q)|
|Males||A (p)||AA (p 2 )||Aa (pq)|
|a (q)||Aa (qp)||aa (q 2 )|
The sum of the entries is p 2 + 2pq + q 2 = 1 , as the genotype frequencies must sum to one.
Note again that as p + q = 1 , the binomial expansion of (p + q) 2 = p 2 + 2pq + q 2 = 1 gives the same relationships.
Summing the elements of the Punnett square or the binomial expansion, we obtain the expected genotype proportions among the offspring after a single generation:
These frequencies define the Hardy–Weinberg equilibrium. It should be mentioned that the genotype frequencies after the first generation need not equal the genotype frequencies from the initial generation, e.g. f1(AA) ≠ f0(AA) . However, the genotype frequencies for all future times will equal the Hardy–Weinberg frequencies, e.g. ft(AA) = f1(AA) for t > 1 . This follows since the genotype frequencies of the next generation depend only on the allele frequencies of the current generation which, as calculated by equations (1) and (2), are preserved from the initial generation:
For the more general case of dioecious diploids [organisms are either male or female] that reproduce by random mating of individuals, it is necessary to calculate the genotype frequencies from the nine possible matings between each parental genotype (AA, Aa, and aa) in either sex, weighted by the expected genotype contributions of each such mating.  Equivalently, one considers the six unique diploid-diploid combinations:
and constructs a Punnett square for each, so as to calculate its contribution to the next generation's genotypes. These contributions are weighted according to the probability of each diploid-diploid combination, which follows a multinomial distribution with k = 3 . For example, the probability of the mating combination (AA,aa) is 2 ft(AA)ft(aa) and it can only result in the Aa genotype: [0,1,0] . Overall, the resulting genotype frequencies are calculated as:
As before, one can show that the allele frequencies at time t+1 equal those at time t , and so, are constant in time. Similarly, the genotype frequencies depend only on the allele frequencies, and so, after time t=1 are also constant in time.
If in either monoecious or dioecious organisms, either the allele or genotype proportions are initially unequal in either sex, it can be shown that constant proportions are obtained after one generation of random mating. If dioecious organisms are heterogametic and the gene locus is located on the X chromosome, it can be shown that if the allele frequencies are initially unequal in the two sexes [e.g., XX females and XY males, as in humans], f ′(a) in the heterogametic sex 'chases' f (a) in the homogametic sex of the previous generation, until an equilibrium is reached at the weighted average of the two initial frequencies.
The seven assumptions underlying Hardy–Weinberg equilibrium are as follows: 
- organisms are diploid
- only sexual reproduction occurs
- generations are nonoverlapping
- mating is random
- population size is infinitely large
- allele frequencies are equal in the sexes
- there is no migration, gene flow, admixture, mutation or selection
Violations of the Hardy–Weinberg assumptions can cause deviations from expectation. How this affects the population depends on the assumptions that are violated.
- . The HWP states the population will have the given genotypic frequencies (called Hardy–Weinberg proportions) after a single generation of random mating within the population. When the random mating assumption is violated, the population will not have Hardy–Weinberg proportions. A common cause of non-random mating is inbreeding, which causes an increase in homozygosity for all genes.
If a population violates one of the following four assumptions, the population may continue to have Hardy–Weinberg proportions each generation, but the allele frequencies will change over time.
- , in general, causes allele frequencies to change, often quite rapidly. While directional selection eventually leads to the loss of all alleles except the favored one (unless one allele is dominant, in which case recessive alleles can survive at low frequencies), some forms of selection, such as balancing selection, lead to equilibrium without loss of alleles. will have a very subtle effect on allele frequencies. Mutation rates are of the order 10 −4 to 10 −8 , and the change in allele frequency will be, at most, the same order. Recurrent mutation will maintain alleles in the population, even if there is strong selection against them.
- Migration genetically links two or more populations together. In general, allele frequencies will become more homogeneous among the populations. Some models for migration inherently include nonrandom mating (Wahlund effect, for example). For those models, the Hardy–Weinberg proportions will normally not be valid. can cause a random change in allele frequencies. This is due to a sampling effect, and is called genetic drift. Sampling effects are most important when the allele is present in a small number of copies.
In real world genotype data, deviations from Hardy-Weinberg Equilibrium may be a sign of genotyping error.   
Where the A gene is sex linked, the heterogametic sex (e.g., mammalian males avian females) have only one copy of the gene (and are termed hemizygous), while the homogametic sex (e.g., human females) have two copies. The genotype frequencies at equilibrium are p and q for the heterogametic sex but p 2 , 2pq and q 2 for the homogametic sex.
For example, in humans red–green colorblindness is an X-linked recessive trait. In western European males, the trait affects about 1 in 12, (q = 0.083) whereas it affects about 1 in 200 females (0.005, compared to q 2 = 0.007), very close to Hardy–Weinberg proportions.
If a population is brought together with males and females with a different allele frequency in each subpopulation (males or females), the allele frequency of the male population in the next generation will follow that of the female population because each son receives its X chromosome from its mother. The population converges on equilibrium very quickly.
The simple derivation above can be generalized for more than two alleles and polyploidy.
Generalization for more than two alleles Edit
Consider an extra allele frequency, r. The two-allele case is the binomial expansion of (p + q) 2 , and thus the three-allele case is the trinomial expansion of (p + q + r) 2 .
More generally, consider the alleles A1, . An given by the allele frequencies p1 to pn
Generalization for polyploidy Edit
The Hardy–Weinberg principle may also be generalized to polyploid systems, that is, for organisms that have more than two copies of each chromosome. Consider again only two alleles. The diploid case is the binomial expansion of:
and therefore the polyploid case is the polynomial expansion of:
where c is the ploidy, for example with tetraploid (c = 4):
|AAAA||p 4 |
|AAAa||4 p 3 q |
|AAaa||6 p 2 q 2 |
|Aaaa||4 p q 3 |
|aaaa||q 4 |
Whether the organism is a 'true' tetraploid or an amphidiploid will determine how long it will take for the population to reach Hardy–Weinberg equilibrium.
Complete generalization Edit
Testing deviation from the HWP is generally performed using Pearson's chi-squared test, using the observed genotype frequencies obtained from the data and the expected genotype frequencies obtained using the HWP. For systems where there are large numbers of alleles, this may result in data with many empty possible genotypes and low genotype counts, because there are often not enough individuals present in the sample to adequately represent all genotype classes. If this is the case, then the asymptotic assumption of the chi-squared distribution, will no longer hold, and it may be necessary to use a form of Fisher's exact test, which requires a computer to solve. More recently a number of MCMC methods of testing for deviations from HWP have been proposed (Guo & Thompson, 1992 Wigginton et al. 2005)
Example χ 2 > test for deviation Edit
This data is from E. B. Ford (1971) on the scarlet tiger moth, for which the phenotypes of a sample of the population were recorded. Genotype-phenotype distinction is assumed to be negligibly small. The null hypothesis is that the population is in Hardy–Weinberg proportions, and the alternative hypothesis is that the population is not in Hardy–Weinberg proportions.
|Phenotype||White-spotted (AA)||Intermediate (Aa)||Little spotting (aa)||Total|
From this, allele frequencies can be calculated:
There is 1 degree of freedom (degrees of freedom for test for Hardy–Weinberg proportions are # genotypes − # alleles). The 5% significance level for 1 degree of freedom is 3.84, and since the χ 2 value is less than this, the null hypothesis that the population is in Hardy–Weinberg frequencies is not rejected.
Fisher's exact test (probability test) Edit
Fisher's exact test can be applied to testing for Hardy–Weinberg proportions. Since the test is conditional on the allele frequencies, p and q, the problem can be viewed as testing for the proper number of heterozygotes. In this way, the hypothesis of Hardy–Weinberg proportions is rejected if the number of heterozygotes is too large or too small. The conditional probabilities for the heterozygote, given the allele frequencies are given in Emigh (1980) as
where n11, n12, n22 are the observed numbers of the three genotypes, AA, Aa, and aa, respectively, and n1 is the number of A alleles, where n 1 = 2 n 11 + n 12
An example Using one of the examples from Emigh (1980),  we can consider the case where n = 100, and p = 0.34. The possible observed heterozygotes and their exact significance level is given in Table 4.
|Number of heterozygotes||Significance level|
Using this table, one must look up the significance level of the test based on the observed number of heterozygotes. For example, if one observed 20 heterozygotes, the significance level for the test is 0.007. As is typical for Fisher's exact test for small samples, the gradation of significance levels is quite coarse.
However, a table like this has to be created for every experiment, since the tables are dependent on both n and p.
The inbreeding coefficient, F (see also F-statistics), is one minus the observed frequency of heterozygotes over that expected from Hardy–Weinberg equilibrium.
where the expected value from Hardy–Weinberg equilibrium is given by
For example, for Ford's data above
For two alleles, the chi-squared goodness of fit test for Hardy–Weinberg proportions is equivalent to the test for inbreeding, F = 0.
The inbreeding coefficient is unstable as the expected value approaches zero, and thus not useful for rare and very common alleles. For: E = 0, O > 0, F = −∞ and E = 0, O = 0, F is undefined.
Mendelian genetics were rediscovered in 1900. However, it remained somewhat controversial for several years as it was not then known how it could cause continuous characteristics. Udny Yule (1902) argued against Mendelism because he thought that dominant alleles would increase in the population.  The American William E. Castle (1903) showed that without selection, the genotype frequencies would remain stable.  Karl Pearson (1903) found one equilibrium position with values of p = q = 0.5.  Reginald Punnett, unable to counter Yule's point, introduced the problem to G. H. Hardy, a British mathematician, with whom he played cricket. Hardy was a pure mathematician and held applied mathematics in some contempt his view of biologists' use of mathematics comes across in his 1908 paper where he describes this as "very simple": 
To the Editor of Science: I am reluctant to intrude in a discussion concerning matters of which I have no expert knowledge, and I should have expected the very simple point which I wish to make to have been familiar to biologists. However, some remarks of Mr. Udny Yule, to which Mr. R. C. Punnett has called my attention, suggest that it may still be worth making. Suppose that Aa is a pair of Mendelian characters, A being dominant, and that in any given generation the number of pure dominants (AA), heterozygotes (Aa), and pure recessives (aa) are as p:2q:r. Finally, suppose that the numbers are fairly large, so that mating may be regarded as random, that the sexes are evenly distributed among the three varieties, and that all are equally fertile. A little mathematics of the multiplication-table type is enough to show that in the next generation the numbers will be as (p + q) 2 :2(p + q)(q + r):(q + r) 2 , or as p1:2q1:r1, say. The interesting question is: in what circumstances will this distribution be the same as that in the generation before? It is easy to see that the condition for this is q 2 = pr. And since q1 2 = p1r1, whatever the values of p, q, and r may be, the distribution will in any case continue unchanged after the second generation
The principle was thus known as Hardy's law in the English-speaking world until 1943, when Curt Stern pointed out that it had first been formulated independently in 1908 by the German physician Wilhelm Weinberg.   William Castle in 1903 also derived the ratios for the special case of equal allele frequencies, and it is sometimes (but rarely) called the Hardy–Weinberg–Castle Law.
Derivation of Hardy's equations Edit
The same reasoning, applied to the other genotypes yields the two remaining recurrence relations. Equilibrium occurs when each proportion is constant between subsequent generations. More formally, a population is at equilibrium at generation t
By solving these equations necessary and sufficient conditions for equilibrium to occur can be determined. Again, consider the frequency of homozygous dominant animals. Equilibrium implies
Numerical example Edit
Estimation of genotype distribution Edit
An example computation of the genotype distribution given by Hardy's original equations is instructive. The phenotype distribution from Table 3 above will be used to compute Hardy's initial genotype distribution. Note that the p and q values used by Hardy are not the same as those used above.
As checks on the distribution, compute
p + 2 q + r = 0.83943 + 0.15771 + 0.00286 = 1.00000
For the next generation, Hardy's equations give
Again as checks on the distribution, compute
which are the expected values. The reader may demonstrate that subsequent use of the second-generation values for a third generation will yield identical results.
Estimation of carrier frequency Edit
The Hardy–Weinberg principle can also be used to estimate the frequency of carriers of an autosomal recessive condition in a population based on the frequency of suffers.
Let us assume an estimated 1 2500
This can be simplified to the carrier frequency being about twice the square root of the birth frequency.
It is possible to represent the distribution of genotype frequencies for a bi-allelic locus within a population graphically using a de Finetti diagram. This uses a triangular plot (also known as trilinear, triaxial or ternary plot) to represent the distribution of the three genotype frequencies in relation to each other. It differs from many other such plots in that the direction of one of the axes has been reversed.  The curved line in the diagram is the Hardy–Weinberg parabola and represents the state where alleles are in Hardy–Weinberg equilibrium. It is possible to represent the effects of natural selection and its effect on allele frequency on such graphs.  The de Finetti diagram was developed and used extensively by A. W. F. Edwards in his book Foundations of Mathematical Genetics. 
Unit 7 biology
(2) A modification in structure, form or function in an organism, deviating from other organisms of the same species or group.
A group of organisms of one species that interbreed and live in the same place at the same time (e.g. deer population).
A low-level taxonomic rank.
A large gene pool indicates high genetic diversity, increased chances of biological fitness, and survival. A small gene pool indicates low genetic diversity, reduced chances of acquiring biological fitness, and increased possibility of extinction.
Gene pool increases when mutation occurs and survives. Gene pool decreases when the population size is significantly reduced (e.g. famine, genetic disease, etc.). Some of the consequences when gene pool is small are low fertility, and increased probability of acquiring genetic diseases and deformities.
2. Gene Flow: The movement of alleles into and out of a gene pool. Migration of an organism into different areas can cause the allelic frequencies of that population to increase. Most populations are not isolated, which is contrary to the Hardy-Weinberg Theorem.
3. Mutations: These changes in the genome of an organism are an important source of natural selection.
4. Nonrandom mating: Inbreeding is a popular form of nonrandom mating. Individuals will mate more frequently with close individuals than more distant ones. Assortive mating, is another form of nonrandom mating. Here the individuals will mate with partners that closely resemble themselves in certain characteristics.
This is the first genetic analysis of domestication traits in yellow lupin. We found that the domestication traits vernalisation response, alkaloid content, flower and seed colour are controlled by single genes (Table 2 Table S2), which were positioned on the genetic map of yellow lupin (Fig. 4 Table S3). This study also provided clear evidence of dominance suppression epistasis (Pooni and Treharne 1994) governing the genetic control of plant growth habit, seed permeability and pod dehiscence in yellow lupin. A genome comparison among yellow vs narrow-leafed lupins and white lupins showed well-conserved synteny between these sister species despite their difference in chromosome numbers. The linkage group containing vernalisation-responsive flowering time locus in yellow lupin showed conserved synteny with the narrow-leafed lupin linkage group containing the equivalent Ku locus, which is controlled by an FT homologue (Nelson et al. 2017 Taylor et al. 2019).
Vernalisation response in yellow lupin
A varying vernalisation response was observed among the parents and RIL population. The vernalisation response was moderate in domesticated parent Wodjil (accelerating flowering by 14 days) compared to very strong in the wild parent P28213 (accelerating flowering by 27 days). These findings suggest that vernalisation accelerates flowering in both wild and domesticated germplasm but to different degrees. The yellow lupin domesticated × wild RIL population shows less extreme variation in vernalisation responsiveness compared to the narrow-leafed lupin wild × domesticated RIL population, where the earlier parent has no vernalisation response (Nelson et al. 2017). Nevertheless, the bimodal distribution in the yellow lupin RIL population distribution (Fig. 2) allowed separation into two contrasting response types: high and low, which segregated in a 1:1 ratio and were mapped to a discrete Mendelian locus on linkage group YL-21 (Fig. 4). The mapping to one locus confirmed the one-gene control of this trait in yellow lupin rather than the alternate gene model of duplicate recessive gene action.
Despite the less extreme variation in vernalisation response in the yellow lupin RIL population than narrow-leafed lupin, the vernalisation response locus mapped to the same syntenic position as the vernalisation response locus (Ku) in narrow-leafed lupin (Fig. 6). This early Ku allele in the narrow-leafed lupin genome is derived by a spontaneous 1.4 kb deletion in the 5′ regulatory region of LanFTc1, one of four FT homologues (Nelson et al. 2017). The deletion appears to have derepressed the expression of LanFTc1 in Ku types. Taylor et al. (2019) recently reported a second deletion allele at LanFTc1, which gives an intermediate vernalisation response. It would be fascinating to explore if a similar mutation has reduced vernalisation responsiveness in yellow lupin also. Rychel et al. (2019) recently reported a similar comparative analysis between white lupin and narrow-leafed lupin, although this was rather complex due to multigenic control of vernalisation response in white lupin. Thus, yellow lupin may serve as a simpler model for comparative analysis of vernalisation response in lupins.
A greater understanding of the molecular control of vernalisation response in yellow lupin would also open avenues of research to explore species-wide variation for phenological variation. Like other Mediterranean legumes, the strong vernalisation response in wild yellow lupin germplasm effectively adapts the plant to the areas with freezing winter temperatures where the crop originated. It protects wild genotypes from frost damage by keeping them in the frost tolerant vegetative phase of growth until a strong cool temperature influx triggers the transition to the more frost-sensitive flowering phase. Similarly, a moderate vernalisation requirement allows the yellow lupin crop to flower late in long growth environments with abundant moisture supply throughout the growing season and enables them to maximise vegetative growth and resource capture, ultimately resulting in higher seed yield. A weak level of vernalisation is beneficial in shorter season growth environments with terminal water-deficit conditions, where it allows plants to flower earlier and complete their life cycle earlier in order to escape the damaging effects of terminal drought (Berger et al. 2012 Berger and Ludwig 2014). This phenomenon of drought escape was clearly exhibited by this RIL population as it was revealed by time to maturity that all the genotypes under both treatments completed their life cycle at same time as the temperature rose above 25 °C to create terminal water-deficit-type conditions (Table S4). The temperatures above 25 °C result in flower and seed loss in lupins, thus in the total yield reduction (Kelleher 2003).
In this population, we observed segregation distortion pointing towards a duplicate recessive gene action for alkaloid content. But we tentatively attribute this segregation distortion to selection for bitter types as a result of inadvertent insect herbivory during RIL development in which 98 lines were lost between F2 and F9 (Iqbal et al. 2019). Nevertheless, the segregation distortion did not prevent accurate mapping. The same patterns appeared during the phenotypic and molecular characterisation of this trait in narrow-leafed lupin where the recessive iucundus allele confers sweetness or low alkaloid content in domesticated types (Gladstones 1977 Nelson et al. 2006). Recently, Kroc et al. (2019) identified an APETALA2/ethylene response transcription factor gene, RAP2-7, as a strong candidate gene for iucundus. However, since alkaloid content in yellow lupin maps to a different syntenic region in narrow-leafed lupin (chromosome NLL-20 rather than NLL-07 where iucundus is located), in yellow lupin alkaloid content is likely conferred by mutation in a different gene. Early efforts to develop low alkaloid narrow-leafed lupin and yellow lupin lupins identified three independent low alkaloid mutant genes: dulcus, amoenus and liber (Hackbarth and Sengbusch 1934 Hackbarth and Troll 1941). As it is unclear which (if any) of these low alkaloid mutants were incorporated into Wodjil, a selection from the Polish variety ‘Teo’, research is still required to determine the molecular mechanism of low alkaloid content in yellow lupin.
Flower and seed colour are important morphological markers in maintaining the integrity of genotypes through the identification of heterozygosity or mixing. The yellow lupin RIL population segregated in the expected 1:1 ratio for both flower and seed colour independently. The linkage mapping of each of these traits to one major locus confirmed the single-gene control of these traits in yellow lupin and not the duplicate recessive gene action model. By contrast, in narrow-leafed lupin flower and seed colour are both controlled by the single leucospermus locus (Nelson et al. 2006, 2010b). The wild narrow-leafed lupin has blue flowers and dark colour seeds, while domesticated narrow-leafed lupin has white flowers and white seeds (Nelson et al. 2006). The genome comparison of yellow lupin with narrow-leafed lupin and white lupin did not show any conserved synteny for flower and seed colour—unsurprising perhaps given their contrasting colours.
Phenotyping the RIL population showed that indehiscence, plant growth habit and seed permeability are each controlled by two loci. In narrow-leafed lupin, pod indehiscence is also under two-gene control (tardus and lentus) (Gladstones 1967). Unlike the two-gene control for seed permeability in yellow lupin, in narrow-leafed lupin seed permeability is controlled by the single recessive gene, mollis (Mikolajczyk 1966). The genetic control of growth habit has not been reported in narrow-leafed lupin. In chickpea, plant growth habit is controlled by a single gene with prostrate/rosette type growth habit dominant over erect/upright (Aryamanesh et al. 2010). The rosette type habit could be beneficial to retain soil moisture for extended periods through reducing evaporation of moisture by improved soil cover and competitive ability with weeds for available resources. By contrast, an erect/upright crop architecture aids agronomic management and harvesting. Yellow lupin types with intermediate growth habit may combine advantages of both extremes.
The map used is incomplete (Iqbal et al. 2019), as indicated by the excess of linkage groups (40 linkage groups rather than the target of 26 representing 26 chromosome pairs). This may be a factor in the lack of QTLs detected for time to maturity or length of reproductive phase (Fig. 4). Future mapping efforts should focus on alternative marker technologies such as targeted amplicon sequencing using transcriptome resources (unpublished data) for primer design.
Genome-wide comparison between yellow lupin and narrow-leafed lupin
This is the first genome-wide comparison of three lupin genomes, building on a previous pairwise comparison between narrow-leafed lupin and white lupin (Hufnagel et al. 2020 Ksiazkiewicz et al. 2017). We found that yellow lupin has a more similar chromosome structure to white lupin than to narrow-leafed lupin consistent with their closer number of chromosomes, contrary to the supposed closer phylogenetic relationship between yellow lupin and narrow-leafed lupin (Naganowska et al. 2003). For example, most of the yellow lupin groups aligned to white lupin groups along more of their lengths than they did with narrow-leafed lupin groups. Additionally, there were more inversions and translocations in yellow lupin linkage groups compared to narrow-leafed lupin than comparing yellow lupin groups versus white lupin groups (Supplementary Table 2). The large number of chromosomal rearrangements between yellow lupin and narrow-leafed lupin may in part explain why crosses between these two species are difficult despite their apparent close phenotypic relationship (Kasten et al. 1991). However, progress has been made in crossing methodology that could potentially lead to the transfer of useful traits between these two species such as higher seed protein content and quality from yellow lupin into narrow-leafed lupin (Clements et al. 2009).
The sequence of chromosome rearrangement events remains unresolved so far. The picture will become clearer with current development of a reference genome for yellow lupin (J. Udall, pers. comm.) and improved reference genome for narrow-leafed lupin (K. Singh, pers. comm.). We are unaware of genetic mapping or reference genome development in other lupin species however, transcriptome-based projects offer promise of improved resolution of lupin evolutionary history of New World (Nevado et al. 2016) and Old World (K. Susek, pers. comm.) lupins. The sequence tags available for GBS (100 bp) and DArTseq (69 bp) markers used to generate the yellow lupin map were too short to reliably detect orthologous sequences in the reference legume genome of M. truncatula (data not presented). A reference genome for yellow lupin would enable easier comparison to M. truncatula and other sequenced legume genomes, enabling more effective leveraging of functional genomic information generated in those model systems.
The reason for translocations observed at many genomic positions during comparative genomics of yellow lupin and narrow-leafed lupin may be because of cytogenetic differences among both species as yellow lupin contains 26 chromosome pairs (2n = 52) as compared to 20 chromosome pairs (2n = 40) in narrow-leafed lupin (Susek et al. 2016). These translocations were also observed between yellow lupin and white lupin, albeit to a lesser extent. The first 15 linkage groups of yellow lupin appear normal in that they each primarily align to one or two linkage groups of both narrow-leafed lupin (Fig. 5a, b), and they show a normal diagonal pattern (Supplementary Figure 2). The remaining yellow lupin groups seem to be mainly vertical indicating markers that have genetic recombination in yellow lupin but particularly, not in narrow-leafed lupin (Supplementary Figure 2). Two main conclusions could be drawn from this pattern: (1) we have marker clusters where the markers are likely physically close to each other but there are random (or systematic) genotyping errors which are creating a lot of apparent crossovers in yellow lupin, and (2) narrow-leafed lupin has many regions of suppressed recombination, whereas yellow lupin has abundant recombination in these areas. According to our overall experience with this mapping population, we consider that the former is much more likely because the narrow-leafed lupin and white lupin maps are so much better understood and more complete than this first draft of a yellow lupin map. Overall, despite yellow lupin map being less complete than the white lupin and narrow-leafed lupin maps, it provides a significant insight about the genetic control of key domestication traits in yellow lupin. The markers linked to key traits such as vernalisation response could be reliably utilised in marker-assisted selection for this trait in other species.
Genomics of major depressive disorder
Douglas F. Levinson , in Personalized Psychiatry , 2020
6 Molecular genetic methods
Four molecular genetic strategies have been employed in studies of MDD:
Linkage analysis detects the approximate genomic location of disease mutations with strong (dominant or recessive) effects on risk, using as few as several hundred “marker” sequences to study families with multiple cases. Replicable evidence for linkage in MDD was never discovered in cohorts or in single families, as reviewed previously ( Levinson, 2013 ).
Many studies of psychiatric disorders have focused on putatively functional variants in “candidate genes” encoding receptor proteins and metabolic enzymes for neurotransmitters impacted by psychotropic drugs (see the following discussion).
GWAS has been successful for MDD and other common disorders whose familial patterns suggest polygenic effects ( Visscher, Brown, McCarthy, & Yang, 2012 ). The Common Disease/Common Variant hypothesis ( Lander, 1996 Reich & Lander, 2001 ) posited that multiple common sequence variants underlie genetic risks for common diseases. These variants are ancient mutations whose high frequency (> 5% of chromosomes in a population) tells us that they do not have large effects on mortality or reproduction. The HapMap project ( Altshuler et al., 2005 ) identified millions of common single nucleotide polymorphisms (SNPs) in different populations, and promoted the commercial development of “SNP chip” assays of 200,000–5,000,000 SNPs. Only a small proportion of common SNPs have to be assayed to interrogate almost all common SNPs (and other types of common variants). This is because of linkage disequilibrium (LD), for example, a parent’s two copies of chromosome 1 wind around each other during meiosis, resulting in a merger of large segments (millions of nucleic acids) of each copy into a single new chromosome for the sperm or egg cell. Over many generations, these segments are broken into smaller pieces of the “ancestral” chromosome containing a set of the ancestral SNP alleles. Typically, there are several common ancient “haplotypes” in each LD “block,” so that genotypes of SNPs within each block are highly correlated, and assaying one or two of them will “tag” the entire haplotype. Genotypes for most other common SNPs can be “imputed” statistically based on knowledge of LD block haplotypes in a reference cohort ( McCarthy et al., 2016 ).
The online GWAS Catalogue (5/6/2018) lists 61,173 unique SNP-trait associations ( http://www.ebi.ac.uk/gwas/ ), including many neuropsychiatric findings. Because common variants have individually small effects on harmful traits, large samples are needed for GWAS. Multiple cohorts of cases and controls with similar geographical ancestry are usually genotyped and meta-analyzed, using extensive quality control procedures prior to association analysis ( Purcell et al., 2014 ) (and see https://gigascience.biomedcentral.com/articles/10.1186/s13742-015-0047-8 https://www.cog-genomics.org/plink2 ).
GWAS data are typically analyzed in three ways:
Association of individual SNPs or genes. Binary logistic regression is generally used to test case-control difference (0, 1, or 2 of a specified allele, for each subject) for each SNP (or common insertion-deletion), correcting for covariates reflecting ancestry differences (principal components or similar scores from a set of genome-wide SNP genotypes). Based on estimates of the number of “independent” tests among common SNPs based on LD patterns, P < 5 × 10 − 8 is considered “genome-wide significant” for each test ( Dudbridge & Gusnanto, 2008 ). Sometimes “gene-wise” tests are also used to test whether SNPs in or near each gene are more significant than expected by chance ( de Leeuw, Mooij, Heskes, & Posthuma, 2015 ).
For a given trait, underpowered cohorts produce no or few significant results, but above some N (the “inflection point”), N linearly predicts “hits,” because adequate power has been achieved. The strongest associations for MDD have ORs
1.10 for schizophrenia ( Schizophrenia Working Group of the Psychiatric Genomics Consortium, 2014 ), thus much larger samples are required.
Polygenic analyses. These methods utilize genome-wide common-SNP information to learn more about the disease and its relationships with other diseases/traits ( Wray et al., 2014 ): (a)
Polygenic risk scores (PRS or genetic risk scores, GRS) ( Purcell et al., 2009 Wray et al., 2014 ) require association statistics to be used as weights (e.g., log(OR) from a large discovery sample). Then in a target sample, if, for example, SNP allele “A” has weight W, and subject 1 carries 2 A alleles, 2⁎W is added to that subject’s score, and the score is summed across a set of SNPs with little SNP-SNP LD. PRS can evaluate consistency of genetic affects across cohorts (“leave-one-out” analyses) or across cohorts with different diagnoses or traits. Larger discovery samples predict more variance in PRS, permitting the study of individual outcomes.
Total common-SNP heritability of one trait, or shared heritability across two traits or subgroups, can be estimated using genomic-relationship matrix restricted maximum likelihood (GREML) ( Wray et al., 2014 ), or the less computationally-intensive LD score regression ( Bulik-Sullivan et al., 2015 ).
Pathway analyses determine whether lower P-values than expected by chance are observed within sets of genes with related biological functions ( de Leeuw et al., 2015 ).
Gene expression can be measured genome-wide using microarrays with oligonucleotide probes, or by sequencing messenger RNA, in the blood, brain, or other tissues. Expression reflects both inherited DNA sequence variation and current physiological state, with many potentially confounding variables. Large-scale studies of white blood cells in MDD will be discussed briefly in the following section.
Participants from the UK Biobank with British/Irish ancestry were selected based on self-reported ancestry and leading principal components calculated from SNP data, resulting in a sample size of 108,035 participants with available genotypes cleaned and imputed to a combined reference panel of 1000 Genomes and UK10K [see UK Biobank documentation for details about quality control and imputation, with sample selection following Robinson et al. (2017)]. For our analyses we selected Hapmap3 SNPs, with minor allele frequency >0.01, a Hardy–Weinberg equilibrium test P-value >1.0E−6, and imputation info-score >0.3. The total sample was randomly split into two sets (n = 54,017 and n = 54,018), with no evidence for differences in demographic variables (Supplemental Material, Supplementary Table 1). This allowed us to estimate genetic and phenotypic correlations within in each set, and also allowed estimation of genetic correlations between the two independent sets.
Traits with >10,000 observations in each dataset were selected for analysis. Selection of these traits included inspecting the distribution, and traits with drastically non-normal distributions were excluded. Key covariates and exclusion variables were identified for all traits. Exclusions were handled on a trait-by-trait basis. For example, subjects were excluded from analysis for spirometry traits if they had smoked within the last hour (see Table S2). The effects of sex, age, age 2 , and testing center were regressed out of the data using a linear model. Traits relating to the cardiovascular system had the effect of blood pressure medication regressed out (medication use was taken as a binary variable). Genetically derived principal components were also used as covariates, but only when calculating genetic correlations and not phenotypic ones. This was done to emulate a situation where genetic information is not available, which is where Cheverud’s conjecture is relevant. Finally, the residuals were transformed with a rank normal transformation (Van der Waerden transformation Lehmann 1975).
Phenotypic correlations were estimated as Pearson correlations between each pair of traits, within both discovery and replication datasets (Figure 1). A GWAS analysis was performed using PLINK 1.9 (Chang et al. 2015) for each trait in discovery and replication samples separately, using a linear association model. The proportion of variance attributable to genome-wide SNPs (SNP-heritability) and the genetic correlation attributable to genome-wide SNPs was estimated from the GWAS summary statistics using an LD-score regression analysis as implemented by Bulik-Sullivan et al. (2015b) in the LDSC software package, using LD-scores estimated from the full data set. Briefly, genetic variances (or covariances) are estimated as a function of regressions of the square (or product) of association analysis z-statistics of SNPs for traits (or pairs of traits) on their LD scores, where an LD score is the sum of LD r 2 made by the SNP with all other SNPs. The method assumes that traits have a polygenic genetic architecture. LD score estimates of genetic correlations agree well with those based on mixed model analysis of full individual-level genotype data (e.g., genetic restricted maximum likelihood (GREML) in genome-wide complex trait analysis (GCTA) Yang et al. 2010 Lee et al. 2012), but are achieved at a small fraction of computing resources, albeit with higher SE (Bulik-Sullivan et al. 2015a Ni et al. 2017). Traits with estimated SNP-heritability <0.05 were removed, as the estimates of genetic correlation are unstable for traits with low SNP-heritability. Seventeen traits were used in the final analysis (Table 1), which were characterized as either morphological (n = 10) or nonmorphological (n = 7), thereby generating 45 pairwise correlations within the morphological traits, 21 between nonmorphological traits and 70 correlations between-traits for each dataset. Genetic correlations were also estimated between all pairs of traits between the two datasets.
Schematic diagram of statistical analyses performed. 108,035 British European individuals were evenly divided into discovery and replication datasets. Genetic and phenotypic correlations were calculated within group for 17 traits. Black arrows show the comparisons performed. Empty gray arrows indicate comparisons similar to the equivalent gray arrow (i.e., the within-replication, between-trait comparison is the same as the within-discovery, between-trait comparison). * Figure 3, Table 2, and † Table 3.
Pearson correlation coefficient, linear regression, and absolute disparity (Willis et al. 1991), were calculated for within-trait, between-trait, and all traits (combined) in both within-dataset and between-dataset comparisons (see Figure 1). The difference of the slope from the unity line was assessed by comparing the least squares linear regression to a linear model with a slope of one. Significance of the slope being different from one was set at P < 0.003125, with Bonferroni correction for 16 tests.
Comparisons of the environmental correlations (re) and genetic correlations were also performed, where (Supplementary Text 1). Similar analyses were performed as with the phenotypic correlation, but using the environmental correlation in its place. The results of the analysis are shown in Supplementary Figure 1 and Supplementary Table 3.
Finally, in sensitivity analyses to assess the similarity of the structure of the matrices, various matrix similarity tests were applied, as discussed by Roff et al. (2012). It is suggested that a variety of these tests should be used, as it is possible that they are not all sensitive to the same differences between matrices. The random skewers, T-test and T 2 -test, and modified Mantel test were applied to compare phenotypic and genetic correlations. The random skewers method investigates whether two matrices respond similarly to selection (Cheverud and Marroig 2007), the T-test and T 2 -test consider the equality by examining the sum of the absolute difference or squared difference between matrix elements, and the modified Mantel test looks at the correlation between the matrix elements. Results for each of the tests are shown in Supplementary Table 4.
Given the sample sizes available, phenotypic correlations were estimated with high accuracy. There is no current literature on the expected SE or power from LD score regression however, it can be compared to those expected from the linear mixed model maximum likelihood method (GREML), which estimates SNP-heritabilities and genetic correlations from GWAS genotype data (Visscher et al. 2014). Empirical comparisons have shown that the error associated with using LD score regression is ∼50% larger than that of GREML (Ni et al. 2017). Using the GCTA-GREML power calculator developed by Visscher et al. (2014), the trait with the smallest sample size (heel bone density, n = 31,254/31,174) has a power of “0.99” to detect the heritability cutoff of 0.05, with a SE of 0.0101. The pair of traits with lowest sample size (heel bone density and forced vital capacity) had a power of 0.98, and a SE of 0.0219 to detect the genetic correlation of −0.089, as estimated by LDSC. In comparison, the observed SE from LDSC was 0.051, a little more than double that predicted for bivariate GREML, although still relatively low. Hence, we conclude that the UK Biobank Pilot data are well powered for the analyses conducted.
The authors state that all data necessary for confirming the conclusions presented in the manuscript are represented fully within the manuscript. Supplemental material available at Figshare: https://doi.org/10.25386/genetics.6213968.
ANSWERS — POPULATION GENETICS PROBLEMS
1) A study on blood types in a population found the following genotypic distribution among the people sampled: 1101 were MM, 1496 were MN and 503 were NN. Calculate the allele frequencies of M and N, the expected numbers of the three genotypic classes (assuming random mating). Using X2, determine whether or not this population is in Hardy-Weinberg equilibrium.
Freq of M = p = p2 + 1/2 (2pq) = 0.356 + 1/2 (0.482) = 0.356 + 0.241 = 0.597
Freq of N = q = 1-p = 1 – 0.597 = 0.403.
EXPECTED GENOTYPE FREQUENCIES (assuming Hardy-Weinberg):
EXPECTED NUMBER OF INDIVIDUALS of EACH GENOTYPE:
X2 = (1101-1107)2 /1107 + (1496-1491)2 /1491 + (502-503)2 /503
X2 (calculated) < X2 (table) [3.841, 1 df, 0.05 ls].
Therefore, conclude that there is no statistically significant difference between what you observed and what you expected under Hardy-Weinberg. That is, you fail to reject the null hypothesis and conclude that the population is in HWE.
2) A scientist has studied the amount of polymorphism in the alleles controlling the enzyme Lactate Dehydrogenase (LDH) in a species of minnow. From one population, 1000 individuals were sampled. The scientist found the following fequencies of genotypes: AA = .080, Aa = .280 aa = .640. From these data calculate the allele frequencies of the “A” and “a” alleles in this population. Use the appropriate statistical test to help you decide whether or not this population was in Hardy-Weinberg equilibrium.
p = Freq A = 0.08 + 1/2 (0.28) = 0.08 + 0.14 = 0.22
IF population is in HWE, then you’d expect the following frequencies:
|Genotype||Expected Numbers||Observed Numbers|
|AA||0.0484 X 1000 = 48.4||0.080 X 1000 = 80|
|Aa||0.3432 X 1000 = 343.2||0.280 X 1000 = 280|
|aa||0.6084 X 1000 = 608.4||0.640 X 1000 = 640|
X2 = [(80 – 48.4)2/ 48.4] + [(280 – 343.2)2 / 343.2] + [(640 – 608.4)2/ 608.4]
X2 (Calculated) > X2 (table), therefore reject null hypothesis. Not in HWE.
3)The compound phenylthiocarbamide(PTC)tastes very bitter to most persons. The inability to taste PTC is controlled by a single recessive gene. In the American white population, about 70% can taste PTC while 30% cannot (are non-tasters). Estimate the frequencies of the Taster (T) and nontaster (t) alleles in this population as well as the frequencies of the diploid genotypes.
Estimated Freq t = q =square root of q2=square root of 0.30 = 0.5477
Freq T = p = 1 – q = 1 – 0.5477 = 0.4523
Tt = 2pq = 2(0.4523)(0.5477) = 0.4956
4) In another study of human blood groups, it was found that among a population of 400 individuals,230 were Rh+ and 170 were Rh-.. Assuming that this trait (i.e., being Rh+) is controlled by a dominant allele (D), calculate the allele frequencies of D and d. How many of the Rh+ individuals would be expected to be heterozygous?
Number of dd individuals = 170, therefore the frequency of the genotype dd (q2) is 170/400 = 0.425. From this, we can estimate q as:
q = square root of q2 = square root of 0.425 = 0.652.
The allele frequency of D is:
Assuming HWE, genotype frequencies are as follows:
Using the expected genotype frequencies, the number Dd among the Rh+ individuals is:
5) Phenylketonuria is a severe form of mental retardation due to a rare autosomal recessive allele. About 1 in 10,000 newborn Caucasians are affected with the disease. Calculate the frequency of carriers (i.e., heterozygotes).
Given the above, estimate q from q2
q = square root of q2 =square root of 1/10,000 = square root of 0.0001 = 0.01
Therefore, p = 1 – q = 1 – 0.01 = 0.99
Using Hardy-Weinberg Law, calculate the expected number of individuals of each genotype as:
Therefore, 1.98% of the population is expected to be carriers.
6) For a human blood, there are two alleles (called S and s) and three distinct phenotypes that can be identified by means of the appropriate reagents. The following data was taken from people in Britain. Among the 1000 people sampled, the following genotype frequencies were observed SS = 99, Ss = 418 and ss = 483. Calculate the frequency of S and s in this population and carry out a X2 test. Is there any reason to reject the hypothesis of Hardy-Weinberg proportions in this population?
Observed Genotype frequencies:
Frequency of S = p = p2 + 1/2 (2pq) = 0.099 + 1/2 (0.418) = 0.308
Frequency of s = q = 1 – p = 1 – 0.308 = 0.692.
Expected Genotype frequencies:
Ss = 2pq = 2 (0.308)(0.692) = 0.426
Expected number of individuals:
X2 = (99-95)2 /95 + (418-426)2 /426 + (483-479)2 /479
X2 (calculated) < X2 (table) [3.841, 1 df at 0.05 ls).
Therefore, fail to reject null hypothesis and conclude that the population is in HWE.
7) A botanist is investigating a population of plants whose petal color is controlled by a single gene whose two alleles (B & B1) are codominant. She finds 170 plants that are homozygous brown, 340 plants that are homozygous purple and 21 plants whose petals are purple-brown. Is this population in HWE (don’t forget to do the proper statistical test)? Calculate “F” (inbreeding coefficient) and explain what is happening in this population.
Freq. of brown (BB) = p2 = 170/531 = 0.32
Freq. of purple-brown (B1B) = 2pq = 21/531 = 0.04
Freq. of purple (B1 B1) = q2 = 340/531 = 0.64.
Freq of B = p = p2 + 1/2 (2pq) = 0.32 + 1/2(0.04)
Freq of B1 = q = 1- p = 1 – 0.34
Expected Genotype Frequencies:
B1B = 2 pq = 2 (0.34)(0.66) = 0.4488
X2 = (170-61.4)2 /61.4 + (21-238.3)2 /238.3 + (340-231.3)2 /231.3
X2 (Calculated) > X2 (table), therefore reject null hypothesis. Not in HWE.
Multiple Alleles: Meaning, Characteristics and Examples | Genes
The word allele is a general term to denote the alternative forms of a gene or contrasting gene pair that denote the alternative form of a gene is called allele. These alleles were previously considered by Bateson as hypothetical partner in Mendelian segregation.
In Mendelian inheritance a given locus of chromosome was occupied by 2 kinds of genes, i.e., a normal gene (for round seed shape) and other its mutant recessive gene (wrinkled seed shape). But it may be possible that normal gene may show still many mutations in pea besides the one for wrinkledness. Here the locus will be occupied by normal allele and its two or more mutant genes.
Thus, three or more kinds of genes occupying the same locus in individual chromosome are referred to as multiple alleles. In short many alleles of a single gene are called multiple alleles. The concept of multiple alleles is described under the term “multiple allelism”.
Dawson and Whitehouse in England proposed the term panallele for all the gene mutations at a given locus in a chromosome. These differ from the multiple factor in one respect that multiple factors occupy different loci while alleles occupy same locus.
“Three or more kinds of gene which occupy the same locus are referred to as multiple alleles.” Altenburg
Characteristics of Multiple Alleles:
1. The study of multiple alleles may be done in population.
2. Multiple alleles are situated on homologous chromosomes at the same locus.
3. There is no crossing over between the members of multiple alleles. Crossing over takes place between two different genes only (inter-generic recombination) and does not occur within a gene (intragenic recombination).
4. Multiple alleles influence one or the same character only.
5. Multiple alleles never show complementation with each other. By complementation test the allelic and non-allelic genes may be differentiated well. The production of wild type phenotype in a trans-heterozygote for 2 mutant alleles is known as complementation test.
6. The wild type (normal) allele is nearly always dominant while the other mutant alleles in the series may show dominance or there may be an intermediate phenotypic effect.
7. When any two of the multiple alleles are crossed, the phenotype is of a mutant type and not the wild type.
8. Further, F2 generations from such crosses show typical monohybrid ratio for the concerned character.
Examples of Multiple Alleles:
1. Wings of Drosophila:
In Drosophila wings are normally long. There occurred two mutations at the same locus in different flies, one causing vestigial (reduced) wings and other mutation causing antlered (less developed) wings. Both vestigial and antlered are alleles of the same normal gene and also of each other and are recessive to the normal gene.
Suppose vestigial is represented by the symbol ‘vg’ and antlered wing by ‘vg a ‘. The normal allele is represented by the symbol +.
Thus, there are three races of Drosophila:
(iii) Antlered vg a vg a (vg a /vg a )
A cross between a long winged normal fly and another having vestigial wings or antlered wings is represented below:
When a fly with vestigial wing is crossed with another fly having antlered wings, the F1 hybrids are intermediate in wing length showing that none of the mutated gene is dominant over the other. This hybrid is some times said as the vestigial antlered compound and contains two mutated genes at the same locus. They show Mendelian segregation and recombination.
Besides the vestigial and antlered wing described above there are several other mutations occurring at the same locus and resulting in nicked wings, strap wings or no wings etc. These are all multiple alleles.
Close Linkage Versus Allelism:
If we assume that these mutant genes, vestigial and antlered are not allelic located at different loci in place of locating at same locus in different chromosomes so closely linked that there is no crossing over between them, the mutant gene will suppress the expression of adjacent normal allele to certain extent.
These closely linked genes are called pseudo alleles and this suppression is the result of position effect. Thus, visible or apparent cases of allelism may be explained on the assumption of close linkage.
Another example of multiple alleles is the eye colour in Drosophila. The normal colour of the eye is red. Mutation changed this red eye colour to white. Other mutations at white locus took place changing the red eye colour to various lighter shades like cherry, apricot, eosin, creamy, ivory, blood etc., are also visible and are due to multiple alleles.
A cross between the two mutant forms, produces intermediate type in the F1 except white and apricot races which are not alleles but closely linked genes.
2. Coat Colour in Rabbit:
The colour of the skin in rabbits is influenced by a series of multiple alleles. The normal colour of the skin is brown. Besides it there are white races called albino and Himalayan as the mutant races. The Himalayan is similar to albino but has darker nose, ear, feet and tail. The mutant genes albino (a) and Himalayan (a h ) occupy the same locus and are allelic. Both albino and Himalayan are recessive to their normal allele (+).
A cross between an albino and Himalayan produces a Himalayan in the F1 and not intermediate as is usual in the case of other multiple alleles.
3. Self-Sterility in Plants:
Kolreuter (1764) described self- sterility in tobacco (Nicotiana longiflora). The reason was done by East. He described that self-sterility is due to series of alleles designated as s1, s2, s3 and s4 etc. The hybrids S1/S2 or S1/S3 or S3/S4 are self-sterile because pollen grains from these varieties did not develop, but pollens of S1/S2 were effective and capable of fertilization with S3/S4.
The genes causing self-sterility in plants probably produce their effects by controlling the growth rate of the pollen tubes. In compatible combinations, the pollen tube grows more and more rapidly as it approaches the ovule, but in non-suitable ones, the growth of the pollen tube slows down considerably, so that the flower withers away before fertilization can take place.
4. Blood Groups in Man:
Several genes in man produce multiple allelic series which affect an interesting and important physiological characteristic of the human red blood cells. The red blood cells have special antigens properties by which they respond to certain specific components (antibodies) of the blood serum.
The antigen-antibody relationship is one of the great specificity like that between lock and key. Each antigen and its associated antibody has a peculiear chemical configuration. Landsteiner discovered in 1900 that when the red cells of one person are placed in the blood serum of another person, the cells become clumped or agglutinated.
If blood transfusions were made between persons of two such incompatible blood groups, the transfused cells were likely to clump and shut out the capillaries in the recipient, some times resulting in death.
However, such reactions occurred only when the cells of certain individuals were placed in serum from certain other persons. It was found that all persons could be classified in to four groups with regard to the antigen property of the blood cells.
Large number of persons have been classified in to these four groups by means of the agglutination test and the distribution of blood groups in the offspring of parents of known blood groups has been studied. The evidence shows that these blood properties are determined by a series of three allelic genes I A , I B and i, as follows:
I A is a gene for the production of the anti-gin A. I B for antigen B, and i for neither antigen. The existence of these alleles in man and the case with which the blood groups can be identified have obvious practical applications in blood transfusion, cases of disputed percentage and description of human populations.
The alleles of these genes which affect a variety of biochemical properties of the blood, act in such a way that in the heterozygous compound I A I B , each allele exhibits its own characteristics and specific effect. The cells of the heterozygote contain both antigens A and B. On the other hand, I A and I B both show complete dominance over i, which lacks both antigens.
Table showing possible blood types of children from parents of various blood groups.
5. The ‘Rhesus’ Blood Group in Man:
A very interesting series of alleles affecting the antigens of human blood has been discovered through the work of Landsteiner, Wiener, Race, Levine, Sanger, Mourant & several others.
The original discovery was that the red cells are agglutinated by a serum prepared by immunizing rabbits against the blood of Rhesus monkey. The antigen responsible for this reaction was consequently called as Rhesus factor and the gene that causes this property was denoted as R-r or Rh-rh.
Interest in this factor was stimulated by Levine’s study of a characteristic form of anaemia, known as Erythroblastosis foetalis, which occurs occasionally in new born infants.
It was found that the infants suffering from this anaemia are usually Rh-positive and so are their fathers but their mothers are Rh-negative. The origin of the disease was explained as follows: The Rh + foetus developing in the uterus of an Rh – mother causes the formation of mother’s blood stream of anti Rh antibodies.
These antibodies, especially as a result of a succession of several Rh + pregnancies, gain sufficient strength in the mother’s blood so that they may attack the red blood cells of the foetus. The reaction between these antibodies of the mother and the red cells of her unborn child provokes haemolysis and anaemia this may be serious enough to cause the death of the newborn infant or abortion of the foetus.
The blood stream of a mother who has had an erythroblastotic infant is a much more potent and convenient reagent than sera of rabbits, immunized by blood of rhesus monkey’s for testing the blood of other persons to distinguish Rh + from Rh – individuals using such sera from woman who had erythroblastotic infants, it was discovered that: there exist not one but several kinds of Rh + and Rh- persons. There are several different Rh antigens which are detected by specific antisera.
Thus, an Rh – woman immunized during pregnancy by the Rh + children may have in her blood serum antibodies, that agglutinate not only Rh+ red cells but also cells from a few persons known to be Rh – .
By selective absorption two kinds of antibodies may be separated from such a serum, one known as anti-D which agglutinates (= coagulates) only Rh + cells, the other known as anti-C which agglutinates particular rare types of Rh – . Another specific antibody, known as anti-c agglutinates all cells that lack C.
With these three antisera, six types of blood can be recognized. Studies of parent and children show that persons of type Cc are heterozygous for an allele C determining C anti-gena. CC persons are homozygous for C and cc are homozygous for c. There is obviously no dominance, each allele producing its own antigen in the heterozygote as in the AB blood type.
No anti serum is available for detecting d, the alternative to D. D + persons may be heterozygous or homozygous. However, the genotypes of such persons may be diagnosis from their progeny for example D + person who has a d – child is thereby shown to be Dd.
Two other specific antibodies, anti-E and anti-c have been found. These detect the antigens E and e determined by a pair of alleles E and e. The three elementary types of antigens C-c, D and E-e, occur in fixed combinations that are always inherited together as alleles of a single gene. Wiener and Fisher showed the existence of a series of eight different alternative arrangements of these three types of Rh antigens and expressed them by means of following symbols.
The Rh System of Alleles:
Thus, allelism is determined by cross-breeding experiments. If one gene behaves as dominant to another the conclusion is that they are alleles and that they occupy identical loci in homologous chromosomes when two genes behave as dominant to other gene. They should occupy identical loci in the chromosome. When more than a pair of alleles occur in respect of any character in inheritance the phenomenon is known as multiple allelism.
There is not much difference between the two theories of Wiener and Fisher. Wiener opinion is that there are multiple variations of one gene whereas according to the view of Fisher three different genes lying very close together are responsible for differences.
The opposite of polygene effect is known as pleiotropism i.e., a single gene influence or govern many characters. For example, gene for vestigial wing influence the nature of halters (modified balancers of Drosophila). The halters are not normal but reduced in flies with vestigial wings. The vestigial gene also affects position of dorsal bristles which instead of being horizontal turn out to be vertical.
This gene also affects the shape of spermatheca i.e., the shape of spermatheca is changed the number of egg strings in the ovaries is decreased compared to normal when the vestigial larvae are well fed but relatively increased when they are poorly fed length of life and fruitfulness or fertility are lowered, and there are still other differences.
Theories of Allelism:
Various theories have been put forward to explain the nature of allelism origin and occurrence.
1. Theory of Point Mutation:
According to this theory multiple alleles have developed as a result of mutations occurring at same locus but in different directions. Hence all the different wing lengths of Drosophila are necessarily the result of mutations which have occurred at same long normal wing locus in different directions.
2. Theory of Close Linkage or Positional Pseudoallelism:
According to this view the multiple alleles are not the gene mutations at same locus but they occupy different loci closely situated in the chromosome. These genes closely linked at different loci are said to as pseudo alleles and affect the expression of their normal genes i.e., position effect.
3. Heterochromatin Theory of Allelism:
Occasionally heterochromatin becomes associated with the genes as a result of chromosomal breakage and rearrangement. These heterochromatin particles suppress the nature of genes in question due to position effect.
In maize the position effect are some times due to transposition (act of changing place or order) of very minute particles of heterochromatin. There are also sign or token that particles of different kinds of heterochromatin suppress the expression of normal gene to different degrees.
In Drosophila the apricot might be a partially suppressed red (normal) and white completely suppressed red while apricot and white hybrid may give rise to red or intermediate by unequal crossing over. The above theories in some way or other do not explain clearly the particular case of allelism and it is possible that all the three theories are applicable in different cases.
Importance of Multiple Allelism:
The study of multiple alleles has increased our knowledge of heredity. According to T.H. Morgan a great knowledge of the nature of gene has come from multiple alleles. These alleles suggest that a gene can mutate in different ways causing different effects. Multiple allelism also put forward the idea that different amounts of heterochromatin prevent the genes to different degree or space.
1. Pseudo alleles:
Alleles are different forms of the same gene located at the corresponding loci or the same locus. Sometimes it has been found that non-homologous genes which are situated at near but different loci affect the same character in the same manner as if they are different forms or alleles of the same gene. They are said as pseudo alleles. These pseudo alleles which are closely linked show re-combinations by crossing over unlike the alleles.
2. Penetrance and Expressivity:
Simply a recessive gene produces its phenotypic effect in homozygous condition and a dominant gene produces its phenotypic effect whether in homozygous or heterozygous condition. Some genes fail to produce their phenotypic effect when they should. The ability of a gene to produce its effect is called penetrance.
The percentage of penetrance may be altered by changing the environmental conditions such as moisture, light intensity, temperature etc. A gene that always produces the expected effect is said to have 100 percent penetrance. If its phenotypic effect is produced only 60 percent of the individuals that contains it then it is said to show 60 percent penetrance.
In Gossypium a mutant gene produces crinkled leaf. While all the leaves produced in the normal season are crinkled but some of the leaves which are produced late in the season do not show this character and are normal. It represents that penetrance is zero or in other words the gene is non-penetrant. Sometimes there is great variation in the manner in which a character is expressed in different plants.
In Lima beans there is a variety named venturra where a dominant gene is responsible for tips and margins of the leaves of the seedlings to be partially deficient in chlorophyll. Sometimes only the margins are effected and sometimes only the tips. In other words, this single gene may express itself in a variety of ways that may resemble a number of characters. This gene is then to exhibit variable expressivity.
Whether a gene is expressed at all is denoted by the term penetrance whereas the term expressivity denotes the degree of its expression.
Sometimes, a dominant gene occurs in two or more forms. These multiple dominant alleles will produce the same phenotypic effect in homozygous condition but their effect will show a small difference in heterozygous state.
In Drosophila, thus, the gene for red eye colour is dominant over white. The red gene will produce dark red colour in the homozygous condition but in combination with the white allele the gene for red colour produces a dark red colour in flies from Soviet Russia but the same combination in the flies coming from the U.S.A. produces a light red colour. It does mean that dominant gene for red colour occurs in two forms. These are said as isoalleles.
Characters are the result of interaction between the genotype and the environment. When a gene mutates, its phenotypic effect also changes. Some times, a change in the environment produces a visible change in the phenotype of the normal gene which resembles the effect as already known mutant.
The effect of the normal gene under the changed environment is a mimic or imitation of the mutant gene. Such an imitation induced by environmental changes has been termed as phenocopy by Goldschmidt.
In fowls, a mutant gene is responsible for the character, ruinplessness, in which the caudal vertebrate and tail feathers do not develop. Rumplessness is also induced as a phenocopy when normal eggs which do not have the gene for rumplessness, are treated with insulin before incubation.
Phenocopies of other mutant genes are also produced in Drosophila by high temperature treatment of the larvae for short periods. It has also been found that different or non- allelic genes can produce the same phenotype. This phenomenon is said as genetic mimic or genocopy.
5. Xenia and Metaxenia:
The immediate effect of foreign pollen on visible characters of the endosperm is called xenia. The ‘xenia’ term was given by Focke (1800). This has been studied in maize plant. If a white endosperm variety is open pollinated in the field where there are also plants of the yellow endosperm variety then the cobs that develop will contain a mixture of yellow and white seeds.
The yellow colour of the endosperm in the yellow seeds is the result of fertilization by pollen from the yellow variety. The yellow colour indicates that the seeds are hybrids and the white seeds are homozygous.
The yellow colour of the endosperm is dominant over white and when the plants raised from the yellow seeds are self-pollinated, yellow and white seeds are produced in the ratio of 3:1. Another example of xenia may be exemplified. If a sweet corn (maize) is pollinated by a starchy variety, the endosperm is starchy because the starchy gene introduced by the pollen is dominant over its sugary allele.
It is the term used to describe the effect of foreign pollen on other tissues belonging to the mother plant, outside the endosperm and embryo. It is sometimes evident in the fruit and seed coats.
In cucurbitaceous fruits, the skin colour is affected by the pollen grains in oranges, the colour and flavour of the fruit is influenced by the pollen parent. The same is true of fuzziness and hair length in cotton. It has been suggested that metaxenia effects may be due to certain hormones secreted by the endosperm and embryo.