Classical Genetics

In module 2 we studied molecular genetics. Here we are concerned with classical genetics, which is the study of inheritance of characteristics at the whole organism level. It is also known as transmission genetics or Mendelian genetics, since it was pioneered by Gregor Mendel.

Gregor Mendel  [back to top]

Mendel (1822-1884) was an Austrian monk at Brno monastery. He was a keen gardener and scientist, and studied at Vienna University, where he learnt statistics. He investigated inheritance in pea plants and published his results in 1866. They were ignored at the time, but were rediscovered in 1900, and Mendel is now recognised as the “Father of Genetics”. His experiments succeeded where other had failed because:

• Mendel investigated simple well-defined characteristics (or traits), such as flower colour or seed shape, and he varied one trait at a time. Previous investigators had tried to study many complex traits, such as human height or intelligence.
• Mendel use an organism whose sexual reproduction he could easily control by carefully pollinating stigmas with pollen using a brush. Peas can also be self-pollinated, allowing self crosses to be performed. This is not possible with animals.
• Mendel repeated his crosses hundreds of times and applied statistical tests to his results.
• Mendel studied two generations of peas at a time.

A typical experiment looked like this: 

Mendel made several conclusions from these experiments:

1.       There are no mixed colours (e.g. pink), so this disproved the widely-held blending theories of inheritance that characteristics gradually mixed over time.

2.       A characteristic can disappear for a generation, but then reappear the following generation, looking exactly the same. So a characteristic can be present but hidden.

3.       The outward appearance (the phenotype) is not necessarily the same as the inherited factors (the genotype) For example the P1 red plants are not the same as the F1 red plants.

4.       One form of a characteristic can mask the other. The two forms are called dominant and recessive respectively.

5.       The F2 ratio is always close to 3:1. Mendel was able to explain this by supposing that each individual has two versions of each inherited factor, one received from each parent. We’ll look at his logic in a minute.

6.       Mendel’s factors are now called genes and the two alternative forms are called alleles. So in the example above we would say that there is a gene for flower colour and its two alleles are “red” and “white”. One allele comes from each parent, and the two alleles are found on the same position (or locus) on the homologous chromosomes. With two alleles there are three possible combinations of alleles (or genotypes) and two possible appearances (or phenotypes):

The Monohybrid Cross  [back to top]

A simple breeding experiment involving just a single characteristic, like Mendel’s experiment, is called a monohybrid cross. We can now explain Mendel’s monohybrid cross in detail.

 At fertilisation any male gamete can fertilise any female gamete at random. The possible results of a fertilisation can most easily be worked out using a Punnett Square as shown in the diagram. Each of the possible outcomes has an equal chance of happening, so this explains the 3:1 ratio (phenotypes) observed by Mendel.

This is summarised in Mendel’s First Law, which states that individuals carry two discrete hereditary factors (alleles) controlling each characteristic. The two alleles segregate (or separate) during meiosis, so each gamete carries only one of the two alleles.

The Test Cross

You can see an individual’s phenotype, but you can’t see its genotype. If an individual shows the recessive trait (white flowers in the above example) then they must be homozygous recessive as it’s the only genotype that will give that phenotype. If they show the dominant trait then they could be homozygous dominant or heterozygous. You can find out which by performing a test cross with a pure-breeding homozygous recessive. This gives two possible results:

• If the offspring all show the dominant trait then the parent must be homozygous dominant.

• If the offspring are a mixture of phenotypes in a 1:1 ratio, then the parent must be heterozygous.

How does Genotype control Phenotype?

Mendel never knew this, but we can explain in detail the relation between an individual’s genes and its appearance. A gene was originally defined as an inherited factor that controls a characteristic, but we now know that a gene is also a length of DNA that codes for a protein. It is the proteins that actually control phenotype in their many roles as enzymes, pumps, transporters, motors, hormones, or structural elements. For example the flower colour gene actually codes for an enzyme that converts a white pigment into a red pigment:

• The dominant allele is the normal (or “wild-type”) form of the gene that codes for functioning enzyme, which therefore makes red-coloured flowers.
• The recessive allele is a mutation of the gene. This mutated gene codes for non-functional enzyme, so the red pigment can’t be made, and the flower remains white. Almost any mutation in a gene will result in an inactive gene product (usually an enzyme), since there are far more ways of making an inactive protein than a working one.

Sometimes the gene actually codes for a protein apparently unrelated to the phenotype. For example the gene for seed shape in peas (round or wrinkled) actually codes for an enzyme that synthesises starch! The functional enzyme makes lots of starch and the seeds are full and rounded, while the non-functional enzyme makes less starch so the seeds wrinkle up.

This table shows why the allele that codes for a functional protein is usually dominant over an allele that codes for a non-function protein. In a heterozygous cell, some functional protein will be made, and this is usually enough to have the desired effect. In particular, enzyme reactions are not usually limited by the amount of enzyme, so a smaller amount will have little effect.

Sex Determination [back to top]

In module 2 we saw that sex is determined by the sex chromosomes (X and Y). Since these are non-homologous they are called heterosomes, while the other 22 pairs are called autosomes. In humans the sex chromosomes are homologous in females (XX) and non-homologous in males (XY), though in other species it is the other way round. The inheritance of the X and Y chromosomes can be demonstrated using a monohybrid cross:

This shows that there will always be a 1:1 ratio of males to females. Note that female gametes (eggs) always contain a single X chromosome, while the male gametes (sperm) can contain a single X or a single Y chromosome. Sex is therefore determined solely by the sperm. There are techniques for separating X and Y sperm, and this is used for planned sex determination in farm animals using IVF.

Sex Linkage

The X and Y chromosomes don’t just determine sex, but also contain many other genes that have nothing to do with sex determination. The Y chromosome is very small and seems to contain very few genes, but the X chromosome is large and contains thousands of genes for important products such as rhodopsin (a protein in the membrane of a photoreceptor cell in the retina of the eye, basically a light absorbing pigment), blood clotting proteins and muscle proteins. Females have two copies of each gene on the X chromosome (i.e. they’re diploid), but males only have one copy of each gene on the X chromosome (i.e. they’re haploid). This means that the inheritance of these genes is different for males and females, so they are called sex linked characteristics.

The first example of sex linked genes discovered was eye colour in Drosophila fruit flies. Red eyes (R) are dominant to white eyes (r) and when a red-eyed female is crossed with a white-eyed male, the offspring all have red eyes, as expected for a dominant characteristic (left cross below). However, when the opposite cross was done (a white-eye male with a red-eyed female) all the male offspring had white eyes (right cross below). This surprising result was not expected for a simple dominant characteristic, but it could be explained if the gene for eye colour was located on the X chromosome. Note that in these crosses the alleles are written in the form X^R (red eyes) and X^r (white eyes) to show that they are on the X chromosome.

Males always inherit their X chromosome from their mothers, and always pass on their X chromosome to their daughters.

Another well-known example of a sex-linked characteristic is colour blindness in humans. 8% of males are colour blind, but only 0.7% of females. The genes for green-sensitive and red-sensitive rhodopsin are on the X chromosome, and mutations in either of these lead to colour blindness. The diagram below shows two crosses involving colour blindness, using the symbols X^R for the dominant allele (normal rhodopsin, normal vision) and X^r for the recessive allele (non-functional rhodopsin, colour blind vision).

Other examples of sex linkage include haemophilia, premature balding and muscular dystrophy.

Codominance  [back to top]

In most situations (and all of Mendel’s experiments) one allele is completely dominant over the other, so there are just two phenotypes. But in some cases there are three phenotypes, because neither allele is dominant over the other, so the heterozygous genotype has its own phenotype. This situation is called codominance or incomplete dominance. Since there is no dominance we can no longer use capital and small letters to indicate the alleles, so a more formal system is used. The gene is represented by a letter, and the different alleles by superscripts to the gene letter.

A good example of codominance is flower colour in snapdragon (Antirrhinum) plants. The flower colour gene C has two alleles: C^R (red) and C^W (white). The three genotypes and their phenotypes are:

In this case the enzyme is probably less active, so a smaller amount of enzyme will make significantly less product, and this leads to the third phenotype. The monohybrid cross looks like this:

Note that codominance is not an example of “blending inheritance” since the original phenotypes reappear in the second generation. The genotypes are not blended and they still obey Mendel’s law of segregation. It is only the phenotype that appears to blend in the heterozygotes.

Another example of codominance is sickle cell haemoglobin in humans. The gene for haemoglobin Hb has two codominant alleles: Hb^A (the normal gene) and Hb^S (the mutated gene). There are three phenotypes:

Other examples of codominance include coat colour in cattle (red/white/roan), and coat colour in cats (black/orange/tortoiseshell).

Lethal Alleles  [back to top]

An unusual effect of codominance is found in Manx cats, which have no tails. If two Manx cats are crossed the litter has ratio of 2 Manx kittens to 1 normal (long-tailed) kitten. The explanation for this unexpected ratio is explained in this genetic diagram:

 The gene S actually controls the development of the embryo cat’s spine. It has two codominant alleles: S^N (normal spine) and S^A (abnormal, short spine). The three phenotypes are:

Many human genes also have lethal alleles, because many genes are so essential for life that a mutation in these genes is fatal. If the lethal allele is expressed early in embryo development then the fertilised egg may not develop enough to start a pregnancy, or the embryo may miscarry. If the lethal allele is expressed later in life, then we call it a genetic disease, such as muscular dystrophy or cystic fibrosis.

Multiple Alleles  [back to top]

An individual has two copies of each gene, so can only have two alleles of any gene, but there can be more than two alleles of a gene in a population. An example of this is blood group in humans. The red blood cell antigen is coded for by the gene I (for isohaemaglutinogen), which has three alleles I^A, I^B and I^O. (They are written this way to show that they are alleles of the same gene.) I^A and I^B are codominant, while I^O is recessive. The possible genotypes and phenotypes are:

 The cross below shows how all four blood groups can arise from a cross between a group A and a group B parent.

Other examples of multiple alleles are: eye colour in fruit flies, with over 100 alleles; human leukocyte antigen (HLA) genes, with 47 known alleles.

Multiple Genes

So far we have looked at the inheritance of a single gene controlling a single characteristic. This simplification allows us to understand the basic rules of heredity, but inheritance is normally much more complicated than that. We’ll now turn to the inheritance of characteristics involving two genes. This gets more complicated, partly because there are now two genes to consider, but also because the two genes can interact with each other. We’ll look at three situations:

• 2 independent genes, controlling 2 characteristics (the dihybrid cross).

• 2 independent genes controlling 1 characteristic (polygenes)

• 2 interacting genes controlling 1 characteristic (epistasis)

The Dihybrid Cross

Mendel also studied the inheritance of two different characteristics at a time in pea plants, so we’ll look at one of his dihybrid crosses. The two traits are seed shape and seed colour. Round seeds (R) are dominant to wrinkled seeds (r), and yellow seeds (Y) are dominant to green seeds (y). With these two genes there are 4 possible phenotypes:

Mendel’s dihybrid cross looked like this:

All 4 possible phenotypes are produced, but always in the ratio 9:3:3:1. Mendel was able to explain this ratio if the factors (genes) that control the two characteristics are inherited independently; in other words one gene does not affect the other. This is summarised in Mendel’s second law (or the law of independent assortment), what states that alleles of different genes are inherited independently.

We can now explain the dihybrid cross in detail.

The gametes have one allele of each gene, and that allele can end up with either allele of the other gene. This gives 4 different gametes for the second generation, and 16 possible genotype outcomes.

Dihybrid Test Cross  [back to top]

There are 4 genotypes that all give the same round yellow phenotype. Just like we saw with the monohybrid cross, these four genotypes can be distinguished by crossing with a double recessive phenotype. This gives 4 different results:

Polygenes   [back to top]

Sometimes two genes at different loci (i.e. separate genes) can combine to affect one single characteristic. An example of this is coat colour in Siamese cats. One gene controls the colour of the pigment, and black hair (B) is dominant to brown hair (b). The other gene controls the dilution of the pigment in the hairs, with dense pigment (D) being dominant to dilute pigment (d). This gives 4 possible phenotypes:

The alleles are inherited in exactly the same way as in the dihybrid cross above, so the same 9:3:3:1 ratio in the F2 generation is produced. The only difference is that here, we are looking at a single characteristic, but with a more complicated phenotype ratio than that found in a monohybrid cross.

A more complex example of a polygenic character is skin colour in humans. There are 5 main categories of skin colour (phenotypes) controlled by two genes at different loci. The amount of skin pigment (melanin) is proportional to the number of dominant alleles of either gene:

 Some other examples of polygenic characteristics are: eye colour, hair colour, and height. The important point about a polygenic character is that it can have a number of different phenotypes, and almost any phenotypic ratio

Epistasis   [back to top]

In epistasis, two genes control a single character, but one of the genes can mask the effect of the other gene. A gene that can mask the effect of another gene is called an epistatic gene (from the Greek meaning “to stand on”). This is a little bit like dominant and recessive alleles, but epistasis applies to two genes at different loci. Epistasis reduces the number of different phenotypes for the character, so instead of having 4 phenotypes for 2 genes, there will be 3 or 2. We’ll look at three examples of epistasis.

 1. Dependent genes. In mice one gene controls the production of coat pigment, and black pigment (B) is dominant to no pigment (b). Another gene controls the dilution of the pigment in the hairs, with dense pigment (D) being dominant to dilute pigment (d). This is very much like the Siamese cat example above, but with one important difference: the pigment gene (B) is epistatic over the dilution gene (D) because the recessive allele of the pigment gene is a mutation that produces no pigment at all, so there is nothing for the dilution gene to affect.  This gives 3 possible phenotypes: 

  2. Enzymes in a pathway. In a certain variety of sweet pea there are two flower colours (white and purple), but the F2 ratio is 9:7. This is explained if the production of the purple pigment is controlled by two enzymes in a pathway, coded by genes at different loci.        

Gene P is epistatic over gene Q because the recessive allele of gene P is a mutation that produces inactive enzyme, so there is no compound B for enzyme Q to react with. This gives just two possible phenotypes:

3. Duplicate Genes. This occurs when genes at two different loci make enzyme that can catalyse the same reaction (this can happen by gene duplication). In this case the coloured pigment is always made unless both genes are present as homozygous recessive (ppqq), so the F2 ratio is 15:1.

So epistasis leads to a variety of different phenotype ratios.

Expected ratios, observed ratios and the chi-squared test  [back to top]

In the monohybrid cross, the F₂ ratio was 3:1, and with the dihybrid cross the ratio was 9:3:3:1.  These are expected ratios, calculated from genotypes of the parental generation - assuming independent assortment, no sex linkage, or codominance.  In real crosses the offspring produced depends on chance fusion of gametes (fertilisation), leading to observed ratios.  There are differences between expected and observed ratios and the questions is, are these differences due to chance alone, or are they statistically significant?  If they are, then the assumptions used to predict the expected ratio might be wrong, for example, the gene(s) might be sex linked.

Chi-squared (c²) is used to decide if differences between sets of results/data are significant.  This compares observed counts with some expected counts and tells you the probability (P) that there is no difference between them

E.g. Dianthus (campion) has flowers of three different colours, red, pink and white.  Two pink flowered plants were crossed and the collected seeds grown to the flowering stage.

The next stage is to assess the degrees of freedom.  This value is always one less than the number of classes of results.  In this case there are three classes i.e. red, pink and white.

                        Degrees of freedom = (3-1) = 2

Now check the c² value against the table:

• Go to the 2 degrees freedom line

• Find the nearest figures to 1.2, which comes between 75% and 50% columns

• A c²   value of 1.2 shows that it is at least 50% probable that the result is by chance alone.

• For a significant difference the value should fall between 1-5% columns.  The difference of this result against the expected is not significant.  Therefore the null hypothesis is accepted.

Variation
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Variation means the differences in characteristics (phenotype) within a species. There are many causes of variation as this chart shows:

 Variation consists of differences between species as well as differences within the same species.  Each individual is influenced by the environment, so this is another source of variation.  
                                                    genotype + environment = phenotype

The alleles that are expressed in the phenotype can only perform their function efficiently if they have a supply of suitable substances and have appropriate conditions. Any study of variation inevitably involves the collection of large quantities of data.

When collecting the data there is a need for random sampling.  This involves choosing a sample ‘at random’ from a population.  This means that every member of the population has the same chance of being chosen, and that the choices are independent of one another.  In choosing a random sample some things are very important:

• the selection criteria must not correspond to what you are studying i.e. not introduce any systematic bias.
• you must try to maintain independence of the sample points
• you muse be careful in making inference: the population might not be what you wish it were

 Variation in a population can be studied by measuring the characteristic (height, eye colour, seed shape, or whatever) in a large number of different individuals and by then plotting a frequency histogram. This graph has the values of the characteristic on the X axis (grouped into bins if necessary) and the number of individuals showing that characteristic on the Y axis. These histograms show that there are two major types of variation: discontinuous and continuous.

Discontinuous Variation   [back to top]

Sometimes the characteristic has just a few discrete categories (like blood group). The frequency histogram has separate bars (or sometimes peaks).

This is discontinuous variation. The characteristics:

• have distinct categories into which individuals can be placed

• tend to be qualitative, with no overlap between categories

• are controlled by one gene, or a small number of genes

• are largely unaffected by the environment

Discontinuous characteristics are rare in humans and other animals, but are more common in plants. Some examples are human blood group, detached ear lobes, flower colour, seed colour, etc. these characteristics are very useful for geneticists because they give clear-cut results.

Continuous Variation  [back to top]

Sometimes the character has a continuous range of values (like height). The frequency histogram is a smooth curve (usually the bell-shaped normal distribution curve).

This is continuous variation. The characteristics:

• have no distinct categories into which individuals can be placed

• tend to be quantitative, with overlaps between categories

• are controlled by a large number of genes (polygenic)

• are significantly affected by the environment

Continuous characteristics are very common in humans and other animals. Some examples are height, hair colour, heart rate, muscle efficiency, intelligence, growth rate, rate of photosynthesis, etc.

Characteristics that show continuous variation are controlled not by one, but by the combined effect of a number of genes, called polygenes.  Therefore any character, which results from the interaction of many genes, is called a polygenic character.    The random assortment of genes during prophase I of meiosis ensures that individuals possess a range of genes from any polygenic complex. 

Sometimes you can see the effect of both variations. For example the histogram of height of humans can be bimodal (i.e. it’s got two peaks). This is because the two sexes (a discontinuous characteristic) each have their own normal distribution of height (a continuous characteristic).

Standard Deviation and Standard Error  [back to top]

Standard deviation is a measure of the spread of results at either side of the mean (average). 

• These sets of data have the same mean (average).

• The data shows a normal distribution about the mean value – there is a bell-shaped and even distribution of values above and below the mean.

• The diagram on the left shows a smaller standard deviation, indicating there is less variation between individuals for the character mentioned.

• The diagram on the right shows a greater standard deviation, indicating there is greater variation.

The standard error is the standard deviation of the mean.

• If individuals in a number of samples are measured, then each sample will have its own mean.

• These means will usually be slightly different from each other – reflecting chance differences in samples – giving a range of values for sample means.

• Standard error is a measure of how much the value of a sample mean is likely to vary.

• The greater the standard error, the greater the variation of the mean.
  

Variation , Gene Pool and Populations  [back to top]

It is at the population level that evolution occurs. A population is a group of individuals of the same species in a given area whose members can interbreed. Because the individuals of a population can interbreed, they share a common group of genes known as the gene pool. Each gene pool contains all the alleles for all the traits of all the population. For evolution to occur in real populations, some of the gene frequencies must change with time. The gene frequency of an allele is the number of times an allele for a particular trait occurs compared to the total number of alleles for that trait.

Hardy – Weinberg Equation  [back to top]  

G. H. Hardy, an English mathematician, and W.R. Weinberg, a German physician, independently worked out the effects of random mating in successsive generations on the frequencies of alleles in a population. This is important for biologists because it is the basis of hypothetical stability from which real change can be measured

An important way of discovering why real populations change with time is to construct a model of a population that does not change. This is just what Hardy and Weinberg did. Their principle describes a hypothetical situation in which there is no change in the gene pool (frequencies of alleles), hence no evolution.

Consider a population whose gene pool contains the alleles A and a. Hardy and Weinberg assigned the letter p to the frequency of the dominant allele A and the letter q to the frequency of the recessive allele a. Since the sum of all the alleles must equal 100%, then p + q = 1. They then reasoned that all the random possible combinations of the members of a population would equal (p+q)² or p²+ 2pq + q².

The Hardy-Weinberg equation p² + 2pq + q² = 1

The frequencies of A and a will remain unchanged generation after generation if the following conditions are met:

1. Large population. The population must be large to minimize random sampling errors.
2. Random mating. There is no mating preference. For example an AA male does not prefer an aa female.
3.  No mutation. The alleles must not change.
4. No migration. Exchange of genes between the population and another population must not occur.
5. No natural selection. Natural selection must not favour any particular individual.

The results show that Hardy-Weinberg Equilibrium was not maintained. The migration of swimmers (genes) into the pool (population) resulted in a change in the population's gene frequencies. If the migrations were to stop and the other agents of evolution (i.e., mutation, natural selection and non-random mating) did not occur, then the population would maintain the new gene frequencies generation after generation. It is important to note that a fifth factor affecting gene frequencies is population size. The larger a population is the number of changes that occur by chance alone becomes insignificant. In the analogy above, a small population was deliberately used to simplify the explanation.

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Last updated 20/06/2004