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Inheritance

This unit has sections which you can click on (or tap) to reveal hidden text. Watch out for a change in the mouse pointer as you pass it over spaces in the text.
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Genetics

Genetics is the study of the transfer of inherited information from one generation to another. We now know that this information is encoded in the chemical structure of DNA and RNA, and it is transferred to cells that make up the organisms of the next generation. They generally use this DNA to make RNA and then protein - perhaps enzymes.

This topic is part of a section covering genetics, populations, evolution and ecosystems. This reminds us that transfer of genetic information is essential for life, especially in the context of the maintenance of populations in the environment. Although the study of genetics is carried on in the specialised environment of the laboratory or glasshouse, the inheritance of characteristics is an important component of the evolution of different species, which has resulted in the variety of life forms in the different zones of Planet Earth.

Explanation of this transfer process involves a number of technical terms, often in pairs.



Gregor Mendel (1822-1884) worked on pea plants between 1856 and 1863. Using the results of crossing experiments he determined the rules of heredity. These are now referred to as the laws of Mendelian inheritance, and these principles have been found to apply generally to higher plants and animals.

Working as an abbot in St. Thomas' Abbey in Brno, a city now in the South Moravian Region of the Czech Republic, he and others under him took varieties of peas with different characteristics and crossed them, noting the characteristics of the resulting offspring. Generally only one variety's characteristic was seen in the first generation after the cross, but when these were left to self-pollinate and produce the second generation, both varieties could be seen. Mendel described these pairs of characteristics as either dominant or recessive. The mathematical ratio of these forms was consistently close to 3:1, which led Mendel to express his results in terms of factors operating in pairs. This established the particulate nature of inheritance and gave more predictable results than the more nebulous concept of blending inheritance which had been widely assumed.

He published his work in 1866, but he referred to his work as hybridisation and it was not widely known in the (international) scientific community of the time.

It would certainly have been helpful to Charles Darwin who was writing about evolution from 1859 but he espoused an unsupported theory - 'pangenesis' - that implied that changes to the body during an organism's life could be inherited.

Genotype and phenotype

The genotype is the makeup of an organism in terms of its genes - the units of inheritance. This may be focussed on one or two of the thousands of genes in an organism. It is generally expressed in terms of codes for the principal genes involved.

The phenotype is a description (using 'normal language') of the observable characteristic(s) of an organism as a result of its genotype, interacting with the environment. We say that the expression of an organism's genotype results in its phenotype.
Mendel's work was rediscovered in 1900 and studies on the behaviour of chromosomes in the cell cycle gave evidence for their involvement in passing on genetic information.

In 1905, William Bateson, was the first to use the word genetics to describe the study of heredity and inherited variations, and he effectively defined the term allele.

In 1909, Wilhelm Johannsen, a Danish botanist, coined the word gene to describe the units of heredity identified by Mendel. He also made the distinction between the outward appearance of an individual (its phenotype) and the internal genetic traits (genotype) which resulted in this appearance.

From 1911 onwards, Thomas Hunt Morgan and his group at Columbia University USA showed that genes are arranged on chromosomes. He made much use of the fruit fly Drosophila melanogaster.

In the 1940s George Beadle and Edward Tatum experimented on mutants produced by the action of X-rays on the red bread mould Neurospora crassa, and showed that genes act by regulating chemical activity within metabolic pathways - affirming the "one gene, one enzyme" hypothesis.

Alleles

Alleles are alternative versions of a gene, resulting from small changes in the base sequence. They are usually found at the same position (locus) on the chromosome. A single gene may have many alleles, and they can interact in a number of ways, as they exist in pairs in diploid organisms.

Certain terms are used to explain whether the pair of alleles are both the same: homozygous or different: heterozygous. A homozygote is an organism that is homozygous; a heterozygote is heterozygous. Sometimes the expression pure-breeding is used to describe homozygotes, which are normally kept as stock cultures to be used in crosses.

Origin of different varieties (and alleles)

In crop plants, different varieties are maintained by growers and suppliers. Many of these were seen to vary in some way such as flower colour, growth habit or productivity, and their seeds were kept as items of commercial value. Mendel was able to obtain a number of varieties of pea plants in this way.
The variations are mostly natural. Plants growing in the field are subject to different environmental chemicals, as well as natural radiation. Presumably these resulted in mutations and the resulting characteristics could be passed on by simple breeding processes. Most plants can self-pollinate and this would assist in the establishment of distinctively different strains.

Similarly different strains of (farm) animals have been formed as a result of selective breeding, allowing only animals with preferred characteristics to reproduce.

Within genetics laboratories different 'model organisms' have emerged. Fruit flies Drosophila melanogaster and other species are quite useful as they are small, reproduce quite well in the lab environment, have a short generation time and do not require much space (they are kept in small vials containing a soft sugary medium, inside incubators). Males and females are easy to distinguish (although much of the work requires the use of a (binocular) microscope.

Many different varieties with different wing length, eye colour, body colour and appendages such as bristles have been produced as a result of mutations following exposure of flies to X-rays, although some, e.g. vestigial wings, have been described as spontaneous mutations. Fruit flies have 3 chromosome pairs (chromosomes 2, 3 and 4), as well as X and Y sex chromosomes, similar to humans.

Types of crosses

Monohybrid crosses involve (alleles of) a single gene, at a particular locus.
Multiple alleles include a series of three or more alternative forms or alleles (all potentially at the same locus), only two of which can exist in a normal diploid individual.

Dihybrid crosses involve two genes with loci on different chromosomes. These operate independently as a result of independent assortment of genes - just as chromosomes segregate independently in meiosis.

Sex-linkage happens when the gene is found on a sex chromosome - usually the X chromosome - which females have two copies of - and males have only one X. This is usually written as an X with a (superscript?) code for the allele carried on it. Of course the Y chromosome needs to be included in the male genotype, but there should be no attached code for an allele.
These crosses are often explained using family trees or pedigrees in which males are expressed as squares, and females as circles.

Linkage occurs when (loci of) different genes are found on the same chromosome. These are often drawn as bars or lines with two different codes for the genes.
Autosomal linkage refers to genes occupying the same 'non-sex' chromosome (numbers 1-22 in humans).

Linkage can be broken due to crossing over in meiosis, and this results in recombination: new combinations of alleles. The frequency of these depends on how far apart the loci of the genes are, and crossing over can give results which depart from the fairly simple ratios of other crosses.

Epistasis is the interaction of different genes i.e. not alleles, in particular the suppression of the effect of one such gene by another.

Each of these can involve dominant, recessive and codominant alleles.

Dominant alleles are usually denoted by a capital letter, recessive alleles by a lower case version (of the same letter). Codominant alleles are often written as a letter with a superscript.

Crossing fruit flies

Male and female Drosophila Male-and-Female-Drosophila-melanogaster (104K) Males (♂) have darker tips to their abdomen.
Females (♀) are slightly larger.
Flies are tipped out of the vials (small bottles) in which they have developed, and dropped into another vial which contains ether vapour, which causes them to become inactive for a short time. There are other methods of stopping them flying whilst they are being handled.

They can then be placed on a small dish and examined under the microscope. Males and females are generally separated using a fine brush. Females may mate within 8-10 hours of emerging from their pupal cases, so cultures are routinely emptied out and euthanised in the morning, so that those emerging later in the day are virgins, and the parenthood of their offspring can be relied upon.

Selected males and females are carefully placed into a new vial containing food. Hopefully they quickly recover from the ether, then mate and lay eggs. At the next stage parents are removed and larvae hatch from the eggs. Having burrowed into the food and moulted several times, larvae grow larger and eventually leave the food medium and climb up the wall of the vial and metamorphose into pupae from which adult flies eventually emerge, to be examined and counted.

Crossing plant varieties

cross-pollination (86K)
Most flowers have both male and female parts, so self-pollination can occur. The male and female parts generally mature at different times, which encourages cross pollination.

It is normal to remove the stamens (male parts) and to cover the flower (perhaps with a paper bag) to prevent other pollen from reaching the female parts. Then when the female parts are ready, pollen can be brought from the other parent plant, perhaps using a brush, and it is dusted on the stigma (receptive female surface) before the flower is covered again and left to 'set seed'.

Seeds can be harvested later, then planted and grown to see what the offspring look like.

Genetic diagrams

These may be used to interpret and explain the results of a particular cross between different individual organisms or to predict possible outcomes.

Parental
phenotype
- × -
Parental
genotype
. . . .
Gametes . .
Offspring
genotype
. . . .
Offspring
phenotype
- : -
In these cases a systematic approach is expected, starting with the phenotypes of parental organisms, followed by their assumed genotypes and that of their gametes, followed by the possible combinations of genes passed on to their offspring, generally finishing on an interpretation of the likely phenotypes of the offspring, together with the expected ratios.

This can be done line by line on a page or using a tabular system called a Punnett Square.




A small Punnett square 2 × 2


Male gametes
. .
Female
gametes
   .    . . . .
. . . . .

Monohybrid crosses

Example crosses using fruit flies

Mutant strains of fruit flies have various modifications to parts of the body.

drosophilawtvg (62K)
The strain called vestigial has greatly reduced wing size, which would be a disadvantage in the wild, but it is not really significant when they are kept in small bottles containing food in the lab.

If a vestigial winged fly is crossed with a normal winged fly ('wild type'), all the offspring have normal wings.
See 'first cross' below
But when they are allowed to mate with one another (sib-sib mating), the resulting flies from the next generation are of two sorts: About 75% (three quarters) have normal wings, and 25% (a quarter) are vestigial winged.
See 'second cross' below

This is a classical situation; we say that normal wings are dominant, and vestigial wings are recessive.

These 2 alleles (versions of the wing size gene) are given the same letter, but the dominant form is written with a capital, and the recessive form is given a lower case version of the same letter.

It is normal to set out an explanation of a cross in the following way.

Let the allele for normal wings be N
Let the allele for vestigial wings be n


Flies are diploid, and they have two alleles of most genes in their body cells

So a pure breeding fly with long wings will have the genotype NN.
This is called homozygous, [but there are also identical looking flies that are described as heterozygous. See below]

A fly with vestigial wings will have the genotype nn, and it can only be homozygous.

Gametes (sperms and eggs) are haploid as they are formed after meiosis, and they only have one letter to describe their genotype.

Fertilised eggs (zygotes) are diploid, as they result from the fusion of the nuclei of two gametes, and their genotypes are expressed with a pair of letters. Zygotes grow into adult organisms after a large number of cell divisions by mitosis, but each cell has an identical genotype to the zygote.

First cross

Parental
phenotype
Normal wings × Vestigial wings
Parental
genotype
NN nn
Gametes N n
Offspring
genotype
All Nn
Offspring
phenotype
All normal wings

This is called the F1 - first filial - generation.

All the F1 have the same genotype Nn. They are heterozygous, and have the same phenotype as the normal-winged parent.

Second cross

Parental
phenotype
Normal wings × Normal wings
Parental
genotype
Nn Nn
Gametes N      or       n N       or       n
Offspring
genotype
NN Nn          Nn nn
Offspring
phenotype
and ratio
     3 Normal wings : 1 Vestigial wings

This is called the F2 - second filial - generation.

A 3:1 ratio of phenotypes is characteristic of a monohybrid F2 generation.

There are 3 genotypes in the F2. Of the flies with the dominant phenotype (normal long wings), two thirds are heterozygous (Nn), and one third are homozygous (NN), but they look indistinguishable, as they share the same phenotype!

The other - vestigial winged flies - have the same phenotype and genotype (nn) as their vestigial-winged grandparent.

An example of this cross has been given a chi-squared treatment below.

Test cross

This is used to see if a phenotypically normal-winged fly is heterozygous or homozygous i.e if it has the genotype Nn or NN.

The table shows the likely result if the selected normal-winged fly is heterozygous. Obviously if it is homozygous the result will be the same as the first cross above.
Click to reveal the bottom 2 lines.

Parental
phenotype
Normal wings × Vestigial wings
Parental
genotype
Nn
(assumed)
nn
Gametes N   or    n n     ONLY
Offspring
genotype
Nn     and     nn
Offspring
phenotype
and ratio
     1 Normal wings : 1 Vestigial wings

This 1:1 ratio is normally produced as a result of a test cross, if a a heterozygous individual with the dominant phenotype is crossed with an individual with the double recessive (homozygous) genotype.

The three crosses shown above are really the only alternatives with monohybrid crosses.



Example crosses using plants
- alternating with human examples

Mendel performed crosses using seven (pairs of) characteristics, and got interesting mathematical ratios in his results. It is fortunate that he chose characteristics with distinctly different (binary) forms, rather than anything based on quantitative differences, which would have given less clear-cut results.

Pea trait Dominant factor Recessive factor Numbers in F2 Ratio
Seed shape round wrinkled 5474:1850 2.96:1
Seed colour yellow green 6002:2001 2.99:1
Flower colour purple white 705:224 3.15:1
Flower position axial terminal 651:207 3.14:1
Plant height tall short 787:277 2.84:1
Pod shape inflated constricted 882:299 2.95:1
Pod colour green yellow 428:152 2.82:1
Averaging all the numbers gives a ratio of 2.98:1


These results gave Mendel the background information which he used to explain the inheritance of these traits. This has been summarised (using modern terminology) in the form of 'Mendel's laws'.

Law of dominance and uniformity: Some alleles are dominant while others are recessive; an organism with at least one dominant allele will display the effect of the dominant allele, and this is seen in all the organisms in the F1.

Law of Segregation: Individuals possess two alleles, and during gamete formation these segregate from each other so that a parent passes only one allele to his/her offspring.

There is another Mendel's law: see below

Crossing red with white

In some plant species such as peas, crossing a red-flowered variety with a white-flowered variety results in an F1 which are all red, but after self-pollination the F2 are 3/4 red and 1/4 white. So obviously red is dominant to white.

But in other species, such as the snapdragon Antirrhinum majus, carnations and 'Four-o-clocks', crossing red with white results in an F1 which are pink. So a different process takes place. This is incomplete or partial dominance.

Since the F1 is intermediate in colour, alleles for red and white flowers are each contributing to the phenotype, and neither completely dominates the other. Sometimes superscripts are used such as CR and CW, or two different capital letters - R and W are used below.

You can use this to predict the F2 phenotypes. Just click in the spaces.
Parental
phenotype
Pink
flowers
×
self-
pollination
Pink
flowers
Parental
genotype
RW RW
Gametes R or W R or W
Offspring
genotype
RR     RW    RW      WW
Offspring
phenotype
and ratio
1 red : 2 pink : 1 white
Parental
phenotype
Red
flowers
× White
flowers
Parental
genotype
RR WW
Gametes R W
Offspring
genotype
All RW
Offspring
phenotype
All pink flowers

Human blood groups

Blood transfusions

Blood of the same group can be safely given to a patient requiring a top-up after blood loss following an accident or operation.

But blood group O (from a 'universal donor') can be given to someone of blood group A, B or AB, as well as O.
And blood group AB can only be given to a patient with AB.
Rhesus positive and negative are dealt with below.

If incompatible blood is given in a transfusion, donor cells are treated as if they were foreign invaders, and the patient's immune system attacks them accordingly. The cells clump together: haemagglutination.

The ABO series

The main blood groups are determined by the presence or absence of two antigens (A and B) on the plasma membrane of the red blood cells. In blood group O there is said to be no antigen.
In fact these antigens are composed of various sugars, and the IA and IB alleles code for enzymes that link either α-N-acetyl galactosamine or α-D-galactose to a basic antigen (H-antigen) on the surface membrane of red blood cells, whereas the Io allele is a mutant that does not code for a functional enzyme.
For diagrams, see link below

Alleles IA and IB are codominant. Allele Io is recessive to both.
(Sometimes the allele for blood group O is written as i.)
So someone with blood group O will have the genotype IoIo,
someone with blood group A will have either IAIA or IAIo,
someone with blood group B will have either IBIB or IBIo, and
someone with blood group AB will have IAIB.

IA, IB, and Io are described as multiple alleles as they occupy the same locus (on chromosome 9).

Each (diploid) cell of the body will have a pair of alleles as above, but mature red blood cells do not have a nucleus. Whilst developing in the bone marrow they possess a nucleus and protein-producing machinery to produce enzymes which process the antigens on the surface membrane, before this is removed as the red blood cell matures. The ABO antigens are actually also expressed on a wide variety of human tissues and are present on most epithelial and endothelial cells.

I stands for iso(haem)agglutinogen.

The diagram below ( a 'pedigree') shows the pattern of inheritance of these blood groups in a family over three generations.
ABOpedigree (14K)

What are the genotypes of each of the numbered individuals?
Click to check your answer. Some may have more than one possibility.
1     IAIA    or    IAIo        2     IBIB    or    IBIo
3   IAIA    [or  IAIo]    4   IBIB    or    IBIo   5   IAIB      6   IAIo      7   IBIo      8   IAIA or IAIo     
9     IAIA [or IAIo]      10     IAIB      11     IAIB      12     IBIo      13     IoIo     

Squares denote males, and circles denote females, but there is no sex linkage visible above.
You might be asked about the possible phenotypes of potential offspring including sex, such as:

If individuals 6 and 7 were to have another child, what is the probability that this child would be female and blood group B? Explain your answer.
> 1 in 8 (1 in 4 for B, 1 in 2 for female) NOT 1:8
> Parents are both heterozygous (IAIo and IBIo)
> so child would get IB and X chromosome from 7 and Io and X chromosome from 6
Explain one piece of evidence from the diagram which shows that the alleles for blood group A and B are dominant to the O allele.
> 6 and 7 have a child with blood group O (13)
> They must both be heterozygous/carriers: A dominant to O in 6, B dominant to O in 7

Blood transfusions

Rh+ blood is more common than Rh-.
Rh- can be given to Rh+ patients, but Rh+ blood given to Rh- patients is inadvisable, especially in females as antigen-antibody reactions may cause disease in children.

And obviously the combination of rhesus negative with blood group O ('O negative') is vastly preferable to O positive.

Rhesus factors

Rhesus factors are distinct from the ABO series. The Rhesus blood group results from the presence or absence of another antigen (usually described as D, but there are other alternatives), which is genetically controlled. The gene for the Rhesus blood group has two alleles. The allele for Rhesus positive, R, is dominant to that for Rhesus negative, r.

Dihybrid crosses

When two different genes (each with different alleles) are involved in a cross, the number of symbols used to describe events is doubled. If these are on different chromosomes they can operate independently - which is a reflection of independent assortment of chromosomes in meiosis.

vgemale (9K)
For example:
The allele for grey body (G) is dominant to the allele for ebony body (g)

This is not the same as the allele for 'black body' which is sometimes seen in crosses.
In fact the locus of the wing genes is on chromosome 2, and the locus of the body colour gene is on chromosome 3.

The allele for normal wings (N) is dominant to the allele for vestigial wings (n).

So an individual fly that is homozygous for both genes would have the genotype GG NN. and a fly that is heterozygous for both genes would have the genotype gg nn.
The gap between the letters suggests the two genes are on different chromosomes.

First dihybrid cross

Parental
phenotype
Grey body,
Normal wings
× Ebony body,
Vestigial wings
Parental
genotype
GG NN gg nn
Gametes G N g n
Offspring
genotype
All Gg Nn
Offspring
phenotype
All grey body, normal wings

All the F1 have the same genotype Gg Nn. They are heterozygous, and have the same phenotype as the grey-bodied normal-winged parent.

Second dihybrid cross

If the F1 above are allowed to self-fertilise, there are a number of potential combinations because there are 4 possible genotypes for each gamete, so it is probably best to use a Punnett square to show the 16 possible offspring genotypes. The resulting phenotypes have been included beneath.

male gametes - sperms
G N G n g N g n
female
gametes
- eggs
G N GG NN
grey, normal
GG Nn
grey, normal
Gg NN
grey, normal
Gg Nn
grey, normal
G n GG Nn
grey, normal
GG nn
grey, vestigial
Gg Nn
grey, normal
Gg nn
grey, vestigial
g N Gg NN
grey, normal
Gg Nn
grey, normal
gg NN
ebony, normal
gg Nn
ebony, normal
g n Gg Nn
grey, normal
Gg nn
grey, vestigial
gg Nn
ebony, normal
gg nn
ebony, vestigial

Phenotypes and ratio

9 Grey, normal wings : 3 Grey, vestigial wings : 3 Ebony, normal wings : 1 Ebony, vestigial wings

A 9:3:3:1 ratio is characteristic of a dihybrid F2 generation.


The normal dominant:recessive phenotype ratio is retained for each gene: 12 grey:4 ebony and 12 normal wings: 4 vestigial wings both equate to 3:1. This underlines the independence of assortment of the alleles of these genes.

Another dihybrid cross

Vestigial-winged flies, heterozygous for grey body colour, were crossed with ebony-bodied flies, heterozygous for normal wings.

This is a little easier to display as each parent has a double recessive gene in its genotype, reducing the number of possibilities in the gametes.



Or as a Punnett square

g N g n
G n Gg Nn
Grey, normal
G g n n
Grey, vestigial
g n gg Nn
Ebony, normal
gg nn
Ebony, vestigial
Parental
phenotype
Grey body,
Vestigial wings
× Ebony body,
normal wings
Parental
genotype
Gg nn gg Nn
Gametes G n & g n g N & g n
Offspring
genotype
Gg Nn Gg nn gg Nn gg nn
Offspring
phenotype
Grey,
normal
Grey,
vestigial
Ebony,
normal
Ebony,
vestigial
Ratio 1  : 1  : 1  : 1

A 1:1:1:1 ratio is characteristic result of a cross between an individual, heterozygous for one allele and homozygous for the other recessive allele, and another individual heterozygous for the second allele and homozygous for the other recessive allele.

This is effectively the equivalent of a dihybrid test cross.


An example of this cross has been given a chi-squared treatment below.

More of Mendel's work: dihybrids

In a continuation of his work above, Mendel chose to investigate the inheritance of genes in pairs.
He crossed a pea plant that was homozygous and dominant for round (RR), yellow (YY) seeds with a pea plant that was homozygous and recessive for wrinkled (rr), green (yy) seeds, as represented by the following notation:
RR YY × rr yy

First dihybrid cross

Parental
phenotype
Round,
Yellow
× Wrinkled,
Green
Parental
genotype
RR YY rr yy
Gametes R Y r y
Offspring
genotype
All RrYy
Offspring
phenotype
All round, yellow

The F1 generation were all heterozygous plants with round, yellow seeds and the genotype Rr Yy.

This was as expected, since round seeds had been found to be dominant to wrinkled seeds, and yellow seed colour had been found to be dominant to green.

Allowing the F1 to self-pollinate gave the following results in the F2.

male gametes - pollen
R Y R y r Y r y
female
gametes
- ovules
R Y RR YY
round, yellow
RR Yy
round, yellow
Rr YY
round, yellow
Rr Yy
round, yellow
R y RR Yy
round, yellow
RR yy
round, green
Rr Yy
round, yellow
Rr yy
round, green
r Y Rr YY
round, yellow
Rr Yy
round, yellow
rr YY
wrinkled, yellow
rr Yy
wrinkled, yellow
r y Rr Yy
round, yellow
Rr yy
round, green
rr Yy
wrinkled, yellow
rr yy
wrinkled, green

In fact, these genes for seed shape and colour are now known to be on different chromosomes (peas have 7 pairs of chromosomes) so there was no linkage between them.

Phenotypes and ratio

9 round, yellow : 3 wrinkled, yellow : 3 round, green : 1 wrinkled, green

A 9:3:3:1 ratio is characteristic of a dihybrid F2 generation.

From the above, Mendel derived the following:

Law of independent assortment: Genes of different traits segregate independently during the formation of gametes.

These results and the F2 ratio have been obtained in a number of genetic crosses e.g. the fruit fly results opposite, so it transpired that the same principles applied in the inheritance of genetic characteristics in plants and animals.

Sex linkage

Like humans, fruit flies have sex determined by X and Y chromosomes. Male fruit flies have the sex chromosomes XY and the females have XX.

In the fruit fly, a gene for eye colour is carried on the X chromosome. The allele for red eyes, R, is dominant to the allele for white eyes, r.

It is normal to put the symbol for the alleles as superscripts against the letter X.

The alternative Y chromosome - only in males - does not have a locus for the eye colour gene.

A red-eyed female could have the genotype XRXR (homozygous) or XRXr (heterozygous).
A white-eyed female would have the genotype XrXr

A red-eyed male could only have the genotype XRY.
A white-eyed male could only have the genotype XrY.
Males do not exist as heterozygotes, so they cannot act as carriers for a recessive allele.

The genetic diagram shows a cross between two fruit flies.

Parental
phenotype
red-eyed female × white-eyed male
Parental
genotype
XRXR XrY
Gametes XR [and XR] Xr and Y
Offspring
genotype
XRXr XRY
Offspring
phenotype
Red-eyed females Red-eyed males
Ratio 1 : 1


Alternatively, if the female is heterozygous:

Parental
phenotype
red-eyed female × white-eyed male
Parental
genotype
XRXr XrY
Gametes XR and Xr Xr and Y
Offspring
genotype
XRXr and XrXr and XRY and XrY
Offspring
phenotype
Red-eyed & white-eyed
females
Red-eyed & white-eyed
males
Ratio 1              :              1 : 1              :             1

Colour blindness in humans

This diagram shows the inheritance of colour blindness in humans, over 4 generations. This type of colour blindness ('red-green colour blindness') is controlled by a gene carried on the X chromosome. The allele for this type of colour blindness, b, is recessive to the allele for colour vision, B. These letter codes are best used as superscripts against the chromosome symbol.
[There are other types of colour blindness, with genes not carried on the X chromosome]. colourblindpedigree (16K)

What are the genotypes of each of the numbered individuals?
Click to check your answer. Some may have more than one possibility.

1 XBY      2 XB Xb
3 XB XB OR XB Xb     4 XbY     5 XB XB     OR XB Xb     6 XB XB OR XB Xb     7 XBY
8 XB Xb     OR XB Xb     9 XBY     10 XB Xb     OR XB Xb     11 XBY    
12 XbY


Give evidence from the diagram which suggests that this colour blindness is sex-linked.
> It is only seen in males, not in females

Explain one piece of evidence from the diagram which shows that colour blindness is recessive.
Actually there are two such pieces of evidence.
> Females 2 and 10 are both carriers/heterozygous (XB Xb).
> They pass on Xb to their sons 4/12 [whereas males 1 and 11 (both XBY) only provide Y chromosome].

Other examples of sex-linked inherited conditions

Duchenne muscular dystrophy causes degeneration of muscle tissue. It is caused by a recessive allele.

Haemophilia is a genetic condition in which blood fails to clot.

Autosomal linkage

Thomas Hunt Morgan carried out crosses between fruit flies with grey bodies and long wings and fruit flies with black bodies and short wings.

The body colour gene - alleles grey (dominant): G, and black (recessive): g - was different to the one giving wrinkled body mentioned before, but the wing gene - alleles long or normal (dominant): N, and short (recessive): n - was the same one giving vestigial wings (recessive) mentioned before.

We now know that the loci of both these genes are in fact on the same chromosome (chromosome 2).

He crossed flies with grey body, long wings with flies with black body, short wings, and obtained an F1 all with grey body, long wings. In other words, he crossed a double dominant GGNN with a double recessive ggnn, and obtained an F1 that was doubly heterozygous GgNn.

Next he crossed these F1 flies with flies with black body and short wings ggnn, like one of the parents. This cross could be compared with a dihybrid test-cross, which would be expected to give a 1:1:1:1 ratio in the next generation (assuming 'independent assortment', with the body color and wing length genes on different chromosomes).

25% grey body, long wings
25% black body, short wings
25% grey body, short wings
25% black body, long wings


And if the two alleles were completely linked on the same chromosomes (GN on one chromosome and gn on the other), the resulting genotypes would be GgNn and ggnn - a simple 1:1 ratio of 1 grey body, long wings: 1 black body, short wings.

50% grey body, long wings
50% black body, short wings

In fact he obtained the following results:

42% grey body, long wings
41% black body, short wings
9% grey body, short wings
8% black body, long wings

The lower two categories were found to consistently total 17%.

Phenotypic ratios which are not simple numbers like 9:3:3:1, or 1:1:1:1 tend to point to linkage.

An example of this cross has been given a chi-squared treatment below.

This intermediate ratio can be explained by linkage, together with crossing over in meiosis.

GgNncrossover (36K)

The proportion of recombinant offspring can be used to estimate the distance between the loci of the two genes on their chromosome.

Chiasmata formation in prophase I of meiosis is a random event and exchange of genetic information may occur at any position on the chromosome, but it is more likely to happen between (loci of) two genes that are located further apart than between (loci of) two genes that are close together.

Using this information from many crosses, it is possible to create a 'chromosome map' which shows the location of the loci of genes on it.

Non-mendelian ratios

Mendelian genetics classically result in ratios like 3:1, 1:1, 9:3:3:1 and 1:1:1:1.
Other ratios of numbers can usually be explained by slight modifications . . .

Epistasis

Epistasis is the masking of the expression of one gene by another gene at a different locus. The epistatic gene does the masking; the hypostatic gene is masked. Epistatic genes can be dominant or recessive.

The inheritance of fruit colour in summer squash plants is controlled by two genes, W and Y, which are on different chromosomes (so they are not linked).
Each gene has two alleles.

Fruit colours in squashes

squash_plants_colours (217K)

The double recessive ww results in the production of an enzyme converting the colourless compound A into a green compound B, whereas genotypes WW and Ww inhibit this.

Homozygous and heterozygous dominant versions of the Y gene cause this compound B to be converted into a yellow compound C.

In a cross, the effect of the dominant gene Y is masked by the dominant gene W

Here is a cross between white and green squash plants.

Parental
phenotype
White × Green
Parental
genotype
WW YY ww yy
Gametes W Y w y
Offspring
genotype
All Ww Yy
Offspring
phenotype
All white


And allowing these plants to self-pollinate:

male gametes - pollen
W Y W y w Y w y
female
gametes
- ovules
W Y WW YY
White
WW Yy
White
Ww YY
White
Ww Yy
White
W y WW Yy
White
WW yy
White
Ww Yy
White
Ww yy
White
w Y Ww YY
White
Ww Yy
White
ww YY
Yellow
ww Yy
Yellow
w y Ww Yy
White
Ww yy
White
ww Yy
Yellow
ww yy
Green

Phenotypes and ratio

12 white : 3 yellow : 1 green

A departure from the 9:3:3:1 ratio

This one has been left for you to work out. Click to check your answer.

Test cross

Parental
phenotype
White × Green
Parental
genotype
Ww Yy ww yy
Gametes _ W Y and   W y and   w Y and   w y   _    w y
Offspring
genotype
_  Ww Yy  and   Ww yy   and ww Yy    and   ww yy
Offspring
phenotype
and ratio
_   2 white : 1 yellow   :   1 green
Another departure from the normal ratio

Lethal genes

A yellow mouse and an agouti mouse yellow_mouse (40K) The yellow mouse is heterozygous.
In mice, the yellow coat colour allele is a spontaneous mutation that shows incomplete or partial dominance over the normal brownish agouti colour.

Crossing a yellow mouse (AyA) with an agouti (AA) gives the following result:

Parental
phenotype
Yellow × Agouti
Parental
genotype
AyA AA
Gametes Ay   or    A A     ONLY
Offspring
genotype
AyA      and    AA
Offspring
phenotype
and ratio
     1 Yellow : 1 Agouti

This 1:1 ratio is what is normally produced as a result of a monohybrid test cross, confirming that the yellow colouring is a result of heterozygosity.

But if two yellow mice are mated together, the following occurs:

Parental
phenotype
Yellow × Yellow
Parental
genotype
AyA AyA
Gametes Ay   or    A Ay   or    A
Offspring
genotype
Ay Ay      and AyA   and       AyA   and     AA        
Offspring
phenotype
and ratio
[Dies before birth]      2 Yellow     : 1 Agouti
Another departure from the expected 1:2:1 ratio

Mice homozygous for the yellow allele (AyAy) die before implantation, so they are not born.
The yellow allele is a lethal allele in its homozygous form.

Heterozygotes usually become obese and infertile within a few months after birth. They are also more susceptible to several kinds of tumours than are normal mice.

Other examples of lethal genes

Manx cats (originally from the Isle of Man) come in two varieties - with a characteristically short tail (a result of malformation of the backbone in the tail region) or a normal length tail. Like yellow mice, the short-tailed cats mated together give a 2:1 ratio of short tails:normal tails. Having two copies of the gene is usually lethal in utero, resulting in miscarriage.

Chi-squared test

As a matter of fact, students will not be required to calculate values of statistical tests in a written exam paper although they should experience application of statistical tests as part of their normal learning.

The chi-squared test is a way of comparing observed and expected ratios (of phenotypes) resulting from a genetic cross, based on mathematical differences between them.
Another way of saying this is that it is used to compare the goodness of fit of observed phenotypic ratios with expected ratios.

Chi-squared is generally used in relation to genetic crosses but this statistical test may be used in a range of contexts such as comparisons of possible ratios expected in experiments.

The chi-squared test is in fact designed to analyse categorical data, i.e. data has been counted and divided into categories. Other tests are available for use with parametric or continuous data (such as body height or mass).

Calculation of chi-squared

A value for χ2 is calculated using the formula
Σ (o-e)2
e
where o = observed value, e = expected value (in each category).

This is basically the sum of the squares of the differences between observed and expected values, each divided by the expected value, for each category.
Do not say 'results' are (or are not) due to chance.
It is the 'difference' in the results that is or isn't due to chance

With a monohybrid cross, there are usually just two such fractions to be totalled, and with a dihybrid cross there are four.
The number of degrees of freedom (see below) are 1 and 3, i.e. n-1.

It is usual to propose a null hypothesis such as
'There will be no difference between observed and expected data'.

Obviously the closer to 0 (zero) the value for χ2 is, the more sure you can be that observed results match against the expected figures.

To put a numerical value for the confidence you can attach to this evidence, it is necessary to look up the value in a table for χ2 with the appropriate number of degrees of freedom and probability of 0.05, in order to obtain the 'critical value'. This p value is the widely accepted value for the level of probability that is used in Biology.

Degrees of
freedom
Probability value
0.99 0.95 0.1 0.05 0.01 0.001
1 0.0002 0.0039 2.71 3.84 6.63 10.83
2 0.020 0.103 4.61 5.99 9.21 13.82
3 0.115 0.352 6.25 7.81 11.34 16.27
4 0.297 0.711 7.78 9.49 13.28 18.47

If the calculated value for χ2 is greater than this (critical value) then you can conclude that there is a greater than 0.05/5% probability that the difference(s) (between observed and expected) occurred by chance. In other words, results differ significantly from expected.
So the null hypothesis can be rejected.

But if the calculated value for χ2 is less the critical value in the table for p=0.05 this then you can conclude that there is a less than 0.05/5% probability that the difference(s) (between observed and expected) occurred by chance, i.e. there is no significant difference.
In other words there is a greater than 95% probability that the results have a biological cause.
In this case, the null hypothesis can be accepted.
So the difference between observed and expected data is too small to be significant.

Example calculation

Monohybrid cross

The inheritance of wing length in fruit flies was investigated. Two fruit flies with normal wings were crossed. Of the offspring, 147 had normal wings and 53 had vestigial wings.

This looks like a 3:1 ratio. So there are 3 less with normal wings than expected and obviously 3 more with vestigial wings than expected.

The null hypothesis is 'There will be no difference between observed and expected data'.

Stages in the calculation of χ2

Phenotypic features O E O-E (O-E)2
(O-E)2
E
Σ (O-E)2
E
normal wings 147 150 -3 9 0.06 }0.24
vestigial wings 53 50 3 9 0.18

Interpretation

The critical value for 1 degree of freedom, p=0.05, is 3.84. See table above

The calculated value for χ2 - 0.24 - is less than this, so the null hypothesis can be accepted.

There is a less than 5% probability ( p<0.05 ) that the differences (between observed and expected) occurred by chance. So there is no significant difference between actual results and expected.

More example calculations

Dihybrid cross

In fruit flies, the allele for grey body, G, is dominant to the allele for ebony body, g, and the allele for normal wings, sN, is dominant to the allele for vestigial wings, n.

Vestigial-winged flies, heterozygous for grey body colour, were crossed with wrinkled-bodied flies, heterozygous for normal wings.

The numbers of offspring from several such crosses were

Grey body, normal wings 241
Grey body, vestigial wings 220
Ebony body, normal wings 272
Ebony body, vestigial wings 267
Total offspring 1000

This looks like a 1:1:1:1 ratio. But there are several differences from what is expected.

The null hypothesis is 'There will be no difference between observed and expected data'.

Stages in the calculation of χ2

Click in the boxes below to check your own figures
Phenotypic features O E O-E (O-E)2
(O-E)2
E
Σ (O-E)2
E
Grey body, normal wings 241 250 -9 81 0.324 > 7.016
Grey body, vestigial wings 220 250 -30 900 3.6
Ebony body, normal wings 272 250 22 484 1.936
Ebony body, vestigial wings 267 250 17 289 1.156

Interpretation

The critical value for 3 degrees of freedom, p=0.05, is 7.81. See table opposite

The calculated value for χ2 - 7.016 - is less than this, so the null hypothesis can be accepted.

There is a less than 5% probability ( p<0.05 ) that the differences (between observed and expected) occurred by chance. So there is no significant difference between actual results and expected.

Dihybrid cross- with linkage

In fruit flies, the allele for grey body, G, is dominant to the allele for black body, g, and the allele for normal long wings, N, is dominant to the allele for short wings, n.
Note: this is not the same as the cross above

Flies heterozygous to both these genes GgNn were crossed with flies with black body and short wings ggnn.

The numbers of offspring from several such crosses were

965 grey body, long wings
944 black body, short wings
205 grey body, short wings
186 black body, long wings
Total offspring 2300

If this showed independent assortment a 1:1:1:1 ratio could be expected. The null hypothesis would be 'There will be no difference between observed and expected data'.

Stages in the calculation of χ2

Click in the boxes below to check your own figures
Phenotypic features O E O-E (O-E)2
(O-E)2
E
Σ (O-E)2
E
Grey body, long wings 965 575 390 152100 264.52 > 1002.58
Black body, short wings 944 575 369 136161 236.80
Grey body, short wings 205 575 -370 136900 238.09
Black body, long wings 186 575 -389 151321 263.17

Interpretation

The critical value for 3 degrees of freedom, p=0.05, is 7.81. See table opposite

The calculated value for χ2 - 1002.58 - is greater than this, so the null hypothesis must be rejected.

There is a greater than 5% probability ( p>0.05 ) that the differences (between observed and expected) occurred by chance. So there is a significant difference between actual results and expected, and an alternative hypothesis must be formulated.

This alternative hypothesis must be based on linkage, rather than simple Mendelian inheritance.

Here is my effort:
Parental types should be in 1:1 ratio and recombinants in 1:1 ratio
Phenotypic features O E O-E (O-E)2
(O-E)2
E
Σ (O-E)2
E
Grey body, long wings 965 954.5 10.5 110.25 0.116 > 1.156
Black body, short wings 944 954.5 -10.5 110.25 0.116
Grey body, short wings 205 195.5 9.5 90.25 0.462
Black body, long wings 186 195.5 -9.5 90.25 0.462

1.156 is less than 7.81, so the hypothesis is acceptable!
Can anyone see any problems with my interpretation?

Other related topics on this site

(also accessible from the drop-down menu above)
Similar level
Genetic diversity - Mutations and meiosis
Cell recognition - For the ABO antigens see the section 'Thicker than water?' at the end of the vaccines topic

Simpler treatment
Genetics
Genetic inheritance diagrams
Genetic pedigrees("Family trees")
And others

Web references

Classical Genetics

Experiments in plant hybridisation - translation of Gregor Mendel's 1866 Versuche über Plflanzen-hybriden (Read at the February 8th, and March 8th, 1865, meetings of the Brünn Natural History Society)

Drosophila melanogaster From Wikipedia, the free encyclopedia

Drosophila melanogaster

An Introduction to Drosophila melanogaster - the Berg Lab

Linked genes, Recombination, and Chromosome Mapping

Statistics in Biology Further guidance - from AQA

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