Note
Studied by 4 peopleD 3.2
D3.2.1—Production of haploid gametes in parents and their fusion to form a diploid zygote as the means of inheritance
Plants, animals and other eukaryotes that reproduce sexually pass genes to offspring in gametes. This is the basis of inheritance.
Male and female gametes have the same haploid number of chromosomes so male and female parents make an equal genetic contribution to their offspring.
As gametes are produced from diploid body cells, meiosis is required to halve the chromosome number.
Diploid body cells have two copies of each autosomal gene (genes located on a non-sex chromosome). Only one of each gene is passed on to offspring in the gamete.
The fusion of male and female gametes doubles the chromosome number, so the zygote is diploid, as are all body cells subsequently produced by mitosis.
D3.2.2—Methods for conducting genetic crosses in flowering plants
The anthers must be removed before they start to shed pollen, so the flower cannot self-pollinate.
Enclose the flower in a paper bag to prevent insects or wind from transferring
pollen to it.
When the stigma of the flower is mature, transfer pollen to it from anthers on the intended male parent.
Wait for the pollen to germinate and the male gametes to be carried down to the ovary in a pollen tube, where they will fertilise egg cells inside the ovules, resulting in seeds that can be harvested.
The parents are known to geneticists as the P generation and the offspring inside the seeds as the Fl generation. Offspring of the Fl are the F2 generation.
Crossing two plants together has been widely used to produce new varieties of crop plants and ornamental plants.
The results of genetic crosses are analysed using a table called a Punnett grid.
D3.2.3—Genotype is the combination of alleles inherited by an organism
Alleles are different versions of the same gene.
Humans and other diploid organisms have two alleles of autosomal genes, one inherited from each parent.
There could be two copies of one allele, or two different alleles. For example, for a gene with the alleles D and d, an individual could have DD, dd or Dd.
Combinations of alleles such as these are known as genotypes.
If a parent's genotype is DD, all gametes produced by them will contain a single copy of allele D.
Similarly, all the gametes produced by a parent with the genotype dd will have one allele d.
Individuals with the genotypes DD and dd are homozygous because all the gametes they produce have the same allele of this gene.
If a parent's genotype is Dd, 50% of their gametes will have allele D and 50% will have allele d.
Individuals with the genotype Dd are heterozygous because they produce gametes with different alleles of the gene.
D3.2.4—Phenotype as the observable traits of an organism resulting from genotype and environmental factors
The phenotype of an organism is its observable traits (characteristics).
Phenotype includes structural traits such as whether hair is curly or straight and functional traits such as the ability to distinguish red and green colours.
Most phenotypic traits are due to the interaction between the genotype of an organism and the environment in which it exists, but there are some determined solely by genotype and some solely by environmental factors.
D3.2.5—Effects of dominant and recessive alleles on phenotype
Dominant allele – An allele that has the same effect on the phenotype whether it is
paired with the same allele or a different one. Dominant alleles are always expressed in the phenotype.
Example: the allele ‘R’, which will lead to red petals when the genotype is either Rr or RR
Recessive allele – An allele that affects the phenotype only when present in
the homozygous state.
Example: the allele ‘r’, which will lead to white petals only when the genotype is rr
Gregor Mendel discovered a pattern of inheritance in which one allele of a gene is dominant and another allele is recessive.
Mendel crossed two pure-breeding varieties together that differed in a clear trait such as height (tall or dwarf).
Pure-breeding varieties of plants develop the same phenotype, generation after generation if self-pollinated.
With each of the traits that Mendel tested, the Fl offspring all had the same
phenotype as one of the two parents.
D3.2.6—Phenotypic plasticity is the capacity to develop traits suited to the environment experienced by an organism, by varying patterns of gene expression
Organisms can respond to their environment by varying their patterns of gene expression and therefore their traits.
This is a form of adaptation, but it is reversible because genes have only been switched on or off, not changed into new alleles.
It is known as phenotypic plasticity and is particularly useful if the environment a population inhabits is variable.
For example, a person with pale skin may become darker-skinned if there is an increase in exposure to sunlight.
A change in gene expression results in increased synthesis of the black pigment melanin in the skin.
If the sunlight stimulus diminishes, gene expression reverts to its former pattern and the skin gradually becomes paler again, as the melanin concentration reduces.
In some cases, phenotypic changes in traits cannot be reversed during the lifetime of the individual, but can when offspring are produced.
D3.2.7—Phenylketonuria as an example of a human disease due to a recessive allele
Most genetic diseases are caused by a recessive allele.
A person with one recessive allele and one dominant allele does not have symptoms of the disease but is a carrier because they can pass on the disease-causing recessive allele to offspring.
If two parents are carriers of the same recessive allele, the chance of their child inheriting the allele from both of them and therefore developing the disease is 1 in 4, or 25%.
The genetic disease phenylketonuria (PKU) is due to a recessive allele of the gene that codes for the enzyme phenylalanine hydroxylase.
This enzyme converts phenylalanine into tyrosine.
The PKU allele is recessive because a carrier with one PKU allele can still produce functioning enzymes by expressing its normal allele.
A person with two recessive PKU alleles does not produce functioning enzyme so phenylalanine accumulates in the body and there is tyrosine deficiency.
In excess, phenylalanine impairs brain development, leading to intellectual disability and mental disorders.
This can be prevented by screening for PKU at birth and giving affected children a diet low in phenylalanine.
D3.2.8—Single-nucleotide polymorphisms and multiple alleles in gene pools
A gene pool is all genes of all individuals in a sexually reproducing population.
Every new individual inherits a selection of genes from the gene pool.
Evolution is changes in the gene pool over time.
A gene is a length of DNA, with a base sequence that can be hundreds or thousands of bases long.
Alleles are different versions of a gene, that were originally generated by mutation.
The alleles of a gene differ in their base sequence.
Usually only one or a very small number of bases are different. For example, adenine might be present at a particular position in one allele and cytosine at that
position in another allele.
Positions in a gene where different bases can be present are called single nucleotide polymorphisms (abbreviated to SNPs and pronounced snips).
Even within one gene, there can be many different positions with SNPs. There can therefore be many different alleles of a gene in the gene pool.
This is known as multiple alleles.
The S-gene in apples is an example of multiple alleles. More than 30 different S-alleles have been discovered in the apple gene pool, numbered S1, S2, S3 and so on.
D3.2.9—ABO blood groups as an example of multiple alleles
ABO blood groups is an example of codominance of alleles and multiple alleles (some genes have more than two alleles);
One gene determines the ABO blood group of a person. There are three alleles of the gene. There are four different blood groups: A, B, AB and O.
The gene for the ABO blood group has three alleles- IA , IB and i;
ABO phenotypes | ABO genotypes |
A | IA IA or IA i |
B | IB IB or IB i |
AB | IA IB |
O | ii |
D3.2.10—Incomplete dominance and codominance
Incomplete dominance
In each of Mendel's crosses between varieties of pea plant, there was one dominant and one recessive allele. There are also genes where neither allele is fully dominant over the other.
Some pairs of alleles show incomplete dominance.
The phenotype of a heterozygous individual is intermediate between the phenotypes of the two types of homozygotes.
For example, if homozygous red-flowered plants of Mirabilis jalapa (four o'clock plant) are crossed with homozygous white-flowered plants, the heterozygous offspring all have pink flowers.
White flowers contain no red pigment. Pink flowers are intermediate because they contain some red pigment but less than in a red flower.
If two pink-flowered plants are crossed together, the ratio of flower colours in the
offspring is 1 red: 2 pink: 1 white.
b. Codominance
Some pairs of alleles show codominance.
Heterozygous individuals have a dual phenotype that is different to those of either of the two types of homozygotes.
The lA and IB alleles in the ABO blood group system are an example because blood group AB is a dual phenotype and is not intermediate between group A
and group B.
lA causes the production of a specific glycoprotein in the plasma membrane of red blood cells that acts as an antigen.
IB causes the production of another glycoprotein in the plasma membrane that acts as a different antigen.
Genetic disease due to codominant alleles
Autosomal codominant alleles cause Sickle Cell Anemia
HbA HbA = Normal phenotype
HbA HbS = Mild anaemia phenotype with malaria resistance
HbS HbS = Full sickle cell phenotype
D3.2.11—Sex determination in humans and inheritance of genes on sex chromosomes
Humans have 23 pairs of chromosomes in their body cells.
Sex is determined by the 23rd pair of chromosomes.
There are two types of sex chromosomes, X and Y.
Females typically have two X chromosomes, so all female gametes (eggs) have one X chromosome and all offspring inherit an X chromosome from their mother.
Males typically have one X and one Y chromosome, so male gametes (sperm) either contain an X or a Y chromosome.
The sex of offspring is therefore determined by the sperm that fertilizes the egg. A sperm with a Y chromosome makes the resulting child male, whereas an X-bearing sperm makes the child female.
The Y chromosome is small with only about 55 genes, many of which are unique to the Y chromosome and not needed in females.
One key gene on the Y chromosome causes gonads in a human embryo to develop into testes.
This gene is the testis-determining factor (TDF).
The developing testes in an embryo start to secrete testosterone, which causes the development of other organs of the male reproductive system.
The gonads develop into ovaries in an embryo without a Y chromosome and therefore no TDF gene.
The embryonic ovaries start to secrete oestradiol, causing the development of a female reproductive system.
The X chromosome is relatively large and has about 900 genes, many of which are essential in both males and females.
All humans must therefore have at least one X chromosome.
Because females have two copies of genes on the X chromosome and males only have one, the inheritance pattern differs in males and females.
Example: Drosophila ( Fruitfly)
Sex determination in Drosophila is similar to humans, with XX females and XY males. Morgan deduced that sex linkage of eye colour could be due to a gene located only on the X chromosome, with a dominant allele for red eyes and a recessive allele for white.
D3.2.12—Haemophilia as an example of a sex-linked genetic disorder
Inheritance of sex-linked traits
Sex-linked genetic disorders are due to genes located on the X chromosome.
Most sex-linked disorders are due to a recessive allele of the gene.
Males only have one copy of genes on the X chromosome, so they have the disorder if this one copy is the recessive allele.
Females are much less likely to be affected because as long as one of their two X chromosomes carries the dominant allele, they are unaffected.
a.Haemophilia is an example of sex-linked inheritance.
Haemophilia is an example of this pattern of sex-linked inheritance.
People with this disorder, usually males, either lack or have a defective form of Factor VIII.
This protein is a clotting factor that normally circulates in the blood.
Cuts and other wounds bleed for much longer than normal in people with haemophilia.
The gene for Factor VIl is located on the X chromosome.
The allele that causes haemophilia is recessive.
Females only develop haemophilia in the very rare cases where both of their X chromosomes carry the recessive allele, but much more frequently they are
carriers of the haemophilia allele.
XH for normal and Xh for haemophilia;
Females can be XHXH- is normal XH Xh is carrier and Xh Xh is hemophilic.;
Male XH Y is normal and Xh Y is hemophilic.
The alleles should always be shown as a superscript letter on the letter X to represent the X chromosome.
The Y chromosome should also be shown although it does not carry an allele of the gene.
The diagram below shows how two parents, neither of whom have haemophilia, could have a haemophilic son.
F1- Male Phenotypic ratio is 1:1 or 50%- normal , 50% hemophilic
Male genotypic ratio is 1:1 or 50%- XH Y and 50% Xh Y;
The female phenotypic ratio is 1:1, 50% normal, 50% carrier
Female genotypic ratio is 1:1, 50%- XH XH , 50%- XH Xh
b. Red-green colour blindness is an example of sex-linked inheritance.
Example: Red-green colour-blindness
Caused by a recessive allele of a gene for one of the photoreceptor proteins;
These proteins are made by cone cells in the retina of the eye and detect specific wavelength ranges of visible light;
Xb allele for colour blindness;
XB allele for the ability to distinguish colours;
Y no allele is present on the Y chromosome;
XB XB gives the phenotype of a non-affected female;
XB Xb gives the phenotype of a non-affected female who is a carrier;
Xb Xb gives the phenotype of an affected female;
XBY gives the phenotype of a non-affected male;
XbY gives the phenotype of an affected male
D3.2.13—Pedigree charts to deduce patterns of inheritance of genetic disorders
Pedigree charts (family tree diagrams) can be used to deduce how genetic disorders are inherited.
• males are shown as squares and females are shown as circles
• horizontal lines link parents and also siblings
• vertical lines link parents and offspring
• a key is used to show how phenotypes are indicated
• generations and individuals are sometimes numbered.
The two real pedigrees shown below
NOS: Scientists draw general conclusions by inductive reasoning when they base a theory on observations of some but not all cases. A pattern of inheritance may be deduced from parts of a pedigree chart and this theory may then allow genotypes of specific individuals in the pedigree to be deduced. Students should be able to distinguish between inductive and deductive reasoning.
Scientists make observations and look for patterns or trends.
They can only make observations on a limited number of particular examples or cases, but then develop a general hypothesis or theory that is intended to apply
to all cases. This is inductive reasoning.
Scientists use their general theories to explain particular cases.
This is deductive reasoning.
This process can be used to test the general hypothesis or theory to see if it is false.
Inductive reasoning can be used to develop a hypothesis for the inheritance of a genetic disorder, using observations from pedigree charts.
Deductive reasoning is based on the hypothesis that can then be used to predict the genotypes of specific individuals in pedigree charts for the disease.
For example, in the haemophilia pedigree in Section D3.2.13, we observe that only males are affected, and inductive reasoning leads to the hypothesis that the condition is sex-linked. Using this hypothesis, we can deduce all the genotypes of males in the pedigree chart and some of the females.
In the pedigree for Werner syndrome, the affected male's parents do not show the condition, leading to the hypothesis that it is due to a recessive allele.
Based on the observation that Werner syndrome is very rare, it is possible to decide whether it is more likely that the allele is sex-linked or autosomal.
The pedigree for Werner syndrome indicates the harm that can be caused by inbreeding.
The parents of the affected individuals were first cousins, making it possible
for the same recessive allele to be inherited twice from the same grandparent.
In most societies, there is a law or taboo against marriages between close relatives, which would have prevented this.
Determining Autosomal Inheritance
Dominant and recessive disease conditions may be identified only if certain patterns occur (otherwise it cannot be confirmed)
Autosomal Dominant
If both parents are affected and an offspring is unaffected, the trait must be dominant (parents are both heterozygous)
All affected individuals must have at least one affected parent
If both parents are unaffected, all offspring must be unaffected (homozygous recessive)
Autosomal Recessive
If both parents are unaffected and an offspring is affected, the trait must be recessive (parents are heterozygous carriers)
If both parents show a trait, all offspring must also exhibit the trait (homozygous recessive)
Determining X-Linked Inheritance
It is not possible to confirm sex linkage from pedigree charts, as autosomal traits could potentially generate the same results
However certain trends can be used to confirm that a trait is not X-linked dominant or recessive
X-linked Dominant
If a male shows a trait, so too must all daughters as well as his mother
An unaffected mother cannot have affected sons (or an affected father)
X-linked dominant traits tend to be more common in females (this is not sufficient evidence though)
X-linked Recessive
If a female shows a trait, so too must all sons as well as her father
An unaffected mother can have affected sons if she is a carrier (heterozygous)
X-linked recessive traits tend to be more common in males (this is not sufficient evidence though)
D3.2.14—Continuous variation due to polygenic inheritance and/or environmental factors
Variation can be discrete and continuous
Skin colour is an example of a continuous variation and ABO blood groups are an example of a discrete variation.
A. Discrete
In discrete variation, every individual fits into one of a number of non-overlapping categories.
For example, all humans are in blood groups A, B, AB or O.
In most case, discrete variation is due to one or at most a few
genes, without the environment having any influence.
B. Continuous
Continuous variation is due to the environment only in most cases, or due to both polygenic inheritance and environmental factors.
With continuous variation any level of a variable is possible ( intermediates), between the extremes.
Skin colour in humans is an example of continuous variation.
Skin colour depends on the amount of the black pigment melanin synthesized by skin cells.
Multiple genes affect this process (polygenic inheritance), with some alleles for darker skin and some for paler and many different possible combinations of alleles.
Also, sunlight stimulates the production of melanin, so pale skin becomes darker in the days following increased exposure to sunlight. This is not an all-or-nothing effect.
The combined effects of genes and environment result in continuous variation in melanin concentration, from little in the palest skin to much larger amounts in the darkest.
Skin colour is also an example of evolution in humans.
Our common ancestors living in Africa almost certainly had dark skin as an adaptation to intense sunlight and not enough body hair to give protection against ultraviolet rays.
When some humans spread out of Africa, those that migrated north evolved to have paler skins, because the sunlight was less intense and some UV penetration was needed to avoid vitamin D deficiency.
IBDP Q: Explanation of an example ( skin colour ) of how polygenic inheritance gives rise to continuous variation [4m]
human skin colour can vary from pale to very dark / amount of melanin varies;
skin colour/melanin controlled by (alleles from) at least three/several genes;
no alleles are dominant / alleles are co-dominant / incomplete dominance;
many different possible combinations of alleles;
skin colour controlled by cumulative effect/combination of genes/alleles;
IBDP Q: Description of how skin colour is determined genetically[4m]
skin colour is an example of polygenic inheritance;
many/more than two genes contribute to a person’s skin colour;
due to the amount of melanin in the skin;
combination of alleles determines the phenotype;
allows for range of skin colours / continuous variation of skin colour;
phenotypes do not follow simple Mendelian ratios of dominance and recessiveness;
the environment also affects gene expression of skin colour / sunlight/UV light stimulate melanin production;
the more recessive alleles there are, the lighter the skin colour; (vice versa)
Application of skills: Students should understand the distinction between continuous variables such as skin colour and discrete variables such as ABO blood group. They should also be able to apply measures of central tendency such as mean, median and mode.
Three different measures of central tendency are used:
Mean- is known as the average
Median-the middle value if numerical data are placed in order of increasing value. If there is an even number of values, then the median is the average of the two values in the middle.
The median may be better than the mean if there are outliers.
Mode-the most common value. The mode is useful when the data are non-numerical, such as blood type, so a mean or a median cannot be calculated.
Example: Clutch size (numbers of eggs per nest) in grey partridge (Perdix perdix). The range was 4-29 eggs.
Data in biology often follow the normal distribution.
Mean, median and mode are then all very similar.
D3.2.15—Box-and-whisker plots to represent data for a continuous variable such as student height
Application of skills: Students should use a box-and-whisker plot to display six aspects of data: outliers, minimum, first quartile, median, third quartile and maximum. A data point is categorized as an outlier if it
is more than 1.5 × IQR (interquartile range) above the third quartile or below the first quartile.
What is a box and whiskers plot?
A box and whisker plot—also called a box plot—displays the five-number summary of a set of data. The five-number summary is the minimum, first quartile, median, third quartile, and maximum.
In a box plot, we draw a box from the first quartile to the third quartile. A vertical line goes through the box at the median. The whiskers go from each quartile to the minimum or maximum.
How to determine the outliers/ anomalous data?
In addition, it allows for a quick determination of how variable the data is and whether it is skewed.
it defines a standard for identifying values as outliers.
Determine the interquartile range (IQR) by subtracting the first quartile from the third quartile.
Multiply the IQR by 1.5.
Add this value to the 3rd quartile to determine the cut-off value for an upper outlier.
Subtract this value from the 1st quartile to determine the cut-off value for a lower outlier.
Box-and-whisker plots are used to represent continuously variable data such as
human height.
The box plots show the skin pigmentation of the buttocks (left), arm (centre) and forehead (right) of a group of 12 Brazilian people.
One value for arm pigmentation is an outlier as it is more than 1.5 times the interquartile range (IQR) below the lower quartile.
ADDITIONAL HIGHER LEVEL
D3.2.16—Segregation and independent assortment of unlinked genes in meiosis
Segregation is the separation of the alleles of a gene.
Independent assortment is the segregation of the alleles of two genes so that
the outcome with each gene has no effect on the outcome with the other.
Segregation and independent assortment are the consequence of events in meiosis.
In a diploid cell, there are typically two alleles of each gene and in haploid gametes there is just one allele, so the separation of alleles into different cells must occur at some stage during gamete formation.
For example, in an individual with the genotype Dd, the alleles D and d will segregate. If the individual has the genotype Ee for a second gene, segregation could result in any of the combinations DE, De, dE and de.
Which combinations are produced will depend on the movements of chromosomes in meiosis.
Assuming that the genes are on different chromosomes, this will depend on which way homologous pairs of chromosomes (bivalents) are oriented in Metaphase | or Metaphase Il of meiosis.
The orientation of each bivalent is random and is unaffected by how other bivalents are oriented.
The probability of each combination of alleles is therefore equal.
This is an independent assortment.
Genes that assort independently, because they are on different chromosomes, are unlinked.
Segregation and independent assortment were discovered by Gregor Mendel, who performed careful dihybrid crosses and recorded the results meticulously.
D3.2.17—Punnett grids for predicting genotypic and phenotypic ratios in dihybrid crosses involving pairs of unlinked autosomal genes
NOS: 9:3:3:1 and 1:1:1:1 ratios for dihybrid crosses are based on what has been called Mendel’s second law. This law only applies if genes are on different chromosomes or are far apart enough on one chromosome for recombination rates to reach 50%. Students should recognize that there are exceptions to all biological “laws” under certain conditions.
Unlinked genes segregate independently as a result of meiosis.
Mendel discovered the law of independent assortment by doing crosses in which the parents differed in two characteristics that are controlled by two different genes. These are called dihybrid crosses.
When double heterozygotes are crossed with double homozygous recessives ( test cross) then the expected ratio for unlinked genes is 1:1:1:1.;
When double heterozygotes are crossed together then the expected ratio for unlinked genes is 9:3:3:1;
If fewer than expected recombinants are seen then the genes are considered linked as linked genes are expressed together more often than expected.
D3.2.18—Loci of human genes and their polypeptide products
Application of skills: Students should explore genes and their polypeptide products in databases. They should find pairs of genes with loci on different chromosomes and also in close proximity on the same chromosome.
There are about 20,000 genes in the human genome that code for the amino acid sequence of a polypeptide.
Each gene has a characteristic base sequence, varying somewhat between alleles.
Each gene has a locus, which is its specific position on one of 22 types of autosomes (numbered 1-22) or one of the two types of sex chromosomes (X and Y).
The databases Ensembl and NCBI can be used to find the locus of any human gene
how many genes are located on each chromosome
whether pairs of genes are linked or unlinked depending on whether they are on the same or different chromosomes
how close the loci of linked genes are and therefore how high the recombination frequency between them will be
the protein products of protein-coding genes.
D3.2.19—Autosomal gene linkage
Some pairs of genes do not follow Mendel's second law (independent assortment) and the expected 9:3:3:1 or 1:1:1:1 ratio is not found in dihybrid crosses.
Instead, the parental combinations of alleles tend to be inherited together.
This is called gene linkage.
It is due to a pair of genes being located on the same chromosome.
In most cases, this is an autosome (non-sex chromosome) so the inheritance pattern is autosomal gene linkage.
Linkage is rarely 100% because crossing over during meiosis between the linked genes can generate new combinations of alleles.
Crossing over results in an exchange of DNA between chromatids.
The generation of new combinations of alleles is recombination.
Individuals that have a different combination of alleles or phenotypic traits from parents, due to crossing over, are recombinants.
If the genes are always linked and no crossing over occurs, then the predicted ratio in the F2 generation is 1:1 in dihybrid crosses.
Thus fewer than expected recombinants are produced if genes are linked.
when recombinants in the cross are 50% and above then it indicates that there is no linkage between the two traits and the traits assort independently;
Example of autosomal gene linkage
The first case of autosomal gene linkage to be discovered was in the plant Lathyrus odoratus.
A variety with purple flowers and long pollen grains was crossed with a variety with red flowers and round pollen grains.
All the Fl hybrids had purple flowers and long pollen grains.
When these Fl plants were self-pollinated, four phenotypes were observed as expected in the F2 generation, but not in the familiar 9:3:3:1 ratio.
The results of the cross are shown below.
Linked genes are indicated with a line to represent the chromosome and letters
alongside it for the alleles
There were more of the purple long and red round plants than expected.
Purple round and red long individuals were recombinants because they had a new combination of traits that neither of the original pure-breeding parents had.
The recombinants were the result of crossing over between the loci of the genes for flower colour and pollen shape.
D3.2.20—Recombinants in crosses involving two linked or unlinked genes
A recombinant is an individual with a different combination of alleles (and therefore traits) from either parent.
To find the recombination frequency between two genes, an individual heterozygous for both genes is crossed with an individual homozygous recessive for
both genes.
1. Outcome with unlinked genes
The Punnett grid predicts the outcome of a cross between pea plants with round yellow seeds that were heterozygous and plants with wrinkled green seeds that were homozygous recessive.
When Mendel performed this cross his results were 55 round yellow, 51 round green, 49 wrinkled yellow and 52 wrinkled green.
This is close to a 1:1:1:1 ratio.
The round green and wrinkled yellow offspring are recombinants because they have a new combination of traits.
The expected recombination frequency due to the independent assortment of unlinked genes is 50%.
2. Outcome with linked genes
The following diagram shows a cross between pure-breeding purple and starchy seeds and white and waxy seeds.
The F, hybrid offspring were back-crossed to white and waxy seeds. The observed results in the F, generation are far from a 1:1:1:1 ratio.
There are more offspring with parental combinations of alleles and traits and fewer recombinants with new combinations of alleles and traits. ( recombinants less than 50%)
This shows that the genes are linked.
NOS: Students should recognize that statistical testing often involves using a sample to represent a population. In this case, the sample is the F2 generation. In many experiments, the sample is the replicated or repeated measurements.
Chi-squared tests in genetics on data from dihybrid cross
Chi-squared tests in genetics are used to determine whether the difference between an observed and expected (predicted) frequency distribution is statistically significant;
There are two possible hypotheses:
a. Ho: there is no difference between predicted and observed results/ Genes assort independently
b. H1: there is a difference between predicted and observed results/ genes do not assort independently
Method for Chi-squared test
1. Draw a contingency table of observed frequencies, which are the numbers of individuals of each phenotype resulting from the cross;
2. Calculate the expected frequencies, based on the Mendelian ratio and the total number of offspring;
3. Determine the number of degrees of freedom, which is one less than the total number of possible phenotypes. In a dihybrid cross, there are four phenotypes so there are 3 degrees of freedom;
4. Find the critical region for chi-squared from a table of chi-squared values, using the degrees of freedom that you have calculated and a significance level (p) of 0.05%(5%). The critical region is any value of chi-squared larger than the value in the table;
5. Calculate chi-squared using this equation
6. Compare the calculated value of chi-squared with the critical region.
If the calculated value is in the critical region ( same or more than the critical value), the differences between the observed and the expected results are statistically significant and we reject the null hypothesis. There is significant evidence that the ratio is not 1:1:1:1.
If the calculated value is outside the critical region ( less than the critical value), the differences between the observed and the expected results are not statistically significant and there is no evidence to reject the Mendelian ratio.
Example 1.
At the 0.05 level of significance, the critical value is 7.815.
The calculated value for chi-squared is in the critical region ( more than the critical value) the probability is less than 5% so the null hypothesis is rejected.
The results do not fit the 1:1:1:1 ratio, so we conclude that the genes for coat colour and spotting do not assort independently and are linked.