1.1 Mendel’s principles
Gregor Johann Mendel (1822–1884), known as the Father of Genetics, was an Austrian monk. In 1856, he published
the results of hybridization experiments titled Experiments on Plant Hybrids in a journal “The proceeding of the
Brunn society of natural history” and postulated the principles of inheritance which are popularly known as Mendel’s
laws. But his work was largely ignored by scientists at that time. In 1900, the work was independently rediscovered
by three biologists - Hugo de Vries of Holland, Carl Correns of Germany and Erich Tschermak of Austria. Mendel did
a statistical study (he had a mathematical background). He discovered that individual traits are inherited as discrete
factors which retain their physical identity in a hybrid. Later, these factors came to be known as genes. The term
was coined by Danish botanist Wilhelm Johannsen in 1909. A gene is defined as a unit of heredity that may
influence the outcome of an organism’s traits.
Mendel’s experiment
Mendel chose the garden pea, Pisum sativum, for his experiments since it had the following advantages.
1. Well-defined discrete characters
2. Bisexual flowers
3. Predominant self fertilization
4. Easy hybridization
5. Easy to cultivate and relatively short life cycle
Genetics
Characters studied by Mendel
The characteristics of an organism are described as characters or traits. Traits studied by Mendel were clear cut and
discrete. Such clear-cut, discrete characteristics are known as Mendelian characters. Mendel studied seven characters/
traits (all having two variants) and these are:
Dominant Recessive
1. Stem length Tall Dwarf
2. Flower position Axial Terminal
3. Flower colour Violet White
Seed coat colour Grey White
4. Pod shape Inflated Constricted
5 pod colour greeen Yellow
6. Cotyledon colour Yellow Green
7. Seed form Round Wrinkled
Flower colour is positively correlated with seed coat colours. Seeds with white seed coats were produced by plants
that had white flowers and those with gray seed coats came from plants that had violet flower.
Allele
Each gene may exist in alternative forms known as alleles, which code for different versions of a particular inherited
character. We may also define alleles as genes occupying corresponding positions on homologous chromosomes
and controlling the same characteristic (e.g. height of plant) but producing different effects (tall or short).
The term homologous refers to chromosomes that carry the same set of genes in the same sequence, although
they may not necessarily carry identical alleles of each gene.
Wild-type versus Mutant alleles
Prevalent alleles in a population are called wild-type alleles. These alleles typically encode proteins that are made
in the right amount and function normally. Alleles that are present at less than 1% in the population and have been
altered by mutation are called mutant alleles. Such alleles usually result in a reduction in the amount or function of
the wild-type protein and are most often inherited in a recessive fashion.
Dominant and Recessive alleles
A dominant allele masks or hides expression of a recessive allele and it is represented by an uppercase letter. A
recessive allele is an allele that exerts its effect only in the homozygous state and in heterozygous condition its
expression is masked by a dominant allele. It is represented by a lowercase letter.
Homozygous and Heterozygous
Each parent (diploid) has two alleles for a trait — they may be:
1. Homozygous, indicating they possess two identical alleles for a trait.
a. Homozygous dominant genotypes possess two dominant alleles for a trait (TT).
b. Homozygous recessive genotypes possess two recessive alleles for a trait (tt).
2. Heterozygous genotypes possess one of each allele for a particular trait (Tt ]
Lethal alleles
Certain genes are absolutely essential for survival. The alleles created by mutations in these genes are called lethal
alleles. The phenotypic manifestation of these alleles is the death of the organism. Lethal alleles may be recessive
or dominant. Recessive lethal alleles are lethal when present in homozygous conditions whereas dominant lethal
alleles show lethal effects even in heterozygous conditions. Dominant lethal alleles are very rare. Lethal alleles fall
into four categories:
• Early onset : Lethal alleles which result in early death of an organism, during embryogenesis.
• Late onset : Lethal genes which have delayed effect so that the organism can live for some time but eventually
succumb to the disease.
• Conditional : Lethal alleles which kill organism under certain environmental conditions only. For example, a
temperature sensitive lethal allele may kill organism at high temperature, but not at low temperature.
• Semilethal : Lethal alleles which kill only some individuals in the population but not all.
Penetra ance and expressivity
The percentage of individuals that shows a particular phenotype among those capable of showing it, is known as
penetrance. Let us take an example of polydactyly in human, which is produced by a dominant gene. Homozygous
recessive genotype does not cause polydactyly. However, some heterozygous individuals are not polydactylous. If
suppose 20% of heterozygous individuals do not show polydactyly, this means that the gene has a penetrance of
80%. Degree of expression of a trait is controlled by a gene. A particular gene may produce different degrees of
expression in different individuals. This is known as expressivity. Different degrees of expression in different
individuals may be due to variation in the allelic constitution of the rest of the genome or to environmental factors.
Thus, the terms penetrance and expressivity quantify the modification of gene expression by varying environment
and genetic background; they measure respectively the percentage of cases in which the gene is expressed and the
level of expression.
Phenocopy
A phenotype that is not genetically controlled but looks like a genetically controlled one is called phenocopy. It is an
environmentally induced phenotype that resembles the phenotype determined by the genotype. An example of a
phenocopy is Vitamin-D-resistant rickets. A dietary deficiency of vitamin D, for example, produces rickets that is
virtually indistinguishable from genetically caused rickets.
Probability
The chance that an event will occur in the future is called the event’s probability. For example, if you flip a coin, the
probability is 0.50, or 50%, that the head side will be showing when it lands. The probability depends on the number
of possible outcomes. In this case, there are two possible outcomes (head and tail), which are equally likely. This
allows us to predict that there is a 50% chance that a coin flip will produce head. The general formula for the
probability is:
Probability =
Number of times an event occurs
Total number of events
Phead = 1 head/(1 head + 1 tail) = 1/2 = 50%
A probability calculation allows us to predict the likelihood that an event will occur in the future. The accuracy of this
prediction, however, depends to a great extent on the size of the sample.\
In genetic problems, we are often interested in the probability that a particular type of offspring will be produced.
For example, when two heterozygous tall pea plants (Tt) are crossed, the phenotypic ratio of the offspring is
3 tall : 1 dwarf. This information can be used to calculate the probability for either type of offspring:
Probability =
Number of individuals with a given phenotype
Total number of individuals
Ptall = 3 tall/(3 tall + 1 dwarf) = 3/4 = 0.75 = 75% and Pdwarf = 1 dwarf/(3 tall + 1 dwarf) = 1/4 = 0.25 = 25%
The probability of obtaining a tall plant is 75% and a dwarf plant 25%. When we add together the probabilities of all
the possible outcomes (tall and dwarf), we should get a sum of 100% (here, 75% + 25% = 100%).
There are two basic laws of probability that are used for genetic analysis. The first law, the multiplicative law
(product rule) of probability, states that the chance of two or more independent events occurring together is the
product of the probability of the events occurring separately. Independent events are events whose outcomes do
not influence one another. This is also known as the and rule. The product rule can be used to predict the
probability of independent events that occur in a particular order.
Example 1,
A Mendelian cross has been made between pea plants that are heterozygous for plant height (Tt). What is the
probability that the offspring will be homozygous recessive (tt)?
We can find the answer by applying the product rule. First, the probability that an egg will receive a ‘t’ allele = 1/2
and a sperm will receive a ‘t’ allele = 1/2. The overall probability that two recessive alleles will unite, one from the
egg and one from the sperm, simultaneously, at fertilization is: 1/2 × 1/2 = 1/4.
Example 2,
A cross has been made between two plants of genotypes AabbCcDd and AaBbCcdd. What is the probability that the
offspring will be of genotype aabbccdd?
If we assume that all the gene pairs assort independently, then we can do this calculation easily by using the
product rule. The four different gene pairs are considered individually, as if four separate crosses, and then the
appropriate probabilities are multiplied together to arrive at the answer. From Aa × Aa, one-fourth of the progeny
will be aa; from bb × Bb, one-half of the progeny will be bb; from Cc × Cc, one-fourth of the progeny will be cc; and
from Dd × dd, one-half of the progeny will be dd. Therefore, the overall probability of progeny of genotype
aabbccdd will be 1/4 × 1/2 × 1/4 × 1/2 = 1/64.
The second law is the additive law (sum rule) of probability. It states that the probability that one of two or more
mutually exclusive events will occur is equal to the sum of the individual probabilities of the events. This is also
known as the either or rule. The sum rule can be used to predict the occurrence of mutually exclusive events.
Mutually exclusive events are events in which the occurrence of one possibility excludes the occurrence of the other
possibilities.
Example 1,
In a Mendelian cross between pea plants that are heterozygous for flower colour (Rr), what is the probability of the
offspring being a heterozygote?
There are two ways in which a heterozygote may be produced: the dominant allele (R) may be in the egg and the
recessive allele (r) in the sperm or the dominant allele may be in the sperm and the recessive in the egg. Consequently,
the probability that the offspring will be heterozygous is the sum of the probabilities of those two possible ways:
Probability that the dominant allele will be in the egg with the recessive in the sperm is 1/2 × 1/2 = 1/4.
Probability that the dominant allele will be in the sperm and the recessive in the egg is 1/2 × 1/2 = 1/4.
Therefore, the probability that a heterozygous offspring will be produced is 1/4 + 1/4 = 1/2.
Example 2,
A heterozygous pea plant that is tall with yellow seeds, TtYy, is allowed to self-fertilize. What is the probability that
an offspring will be either tall with yellow seeds, tall with green seeds, or dwarf with yellow seeds?
The problem involves three mutually exclusive events, we can use the sum rule to solve it.
