Sex determination

Probability: Probability is a branch of mathematics that applies to events entirely dependent on chance.

Mathematically,

Probability = Number of times an event occurs / Total number of trials

For example, a common event that depends on chance is the tossing of an unbiased coin. When a coin is tossed, there are two possible outcomes: the coin may land with the head up or with the tail up.

The probability that the coin will land with the head up is 1 out of 2, or 50%, which can be expressed as 1/2. Probability is typically expressed in values ranging from 0 to 1.

Mendel’s works are based on probability. Two principles are essential to understanding the role of probability in genetics:

• The result of one trial of a chance event does not affect the result of later trials of the same event.
• The probability that two independent events will occur simultaneously is the product of their individual probabilities of occurring separately.

The Rule of Addition

The rule of addition states that the probability of an event that can occur in two or more independent ways is the sum of the separate probabilities of each individual way.

Example

In a Mendelian cross between pea plants heterozygous for flower colour (Pp), what is the probability that the offspring will be heterozygous (Pp)?

There are two possible ways a heterozygote may be produced:

• The dominant allele (P) may be in the egg and the recessive allele (p) in the sperm, or
• The dominant allele may be in the sperm and the recessive allele in the egg.

Thus, the probability that the offspring will be heterozygous is the sum of the probabilities of these two possibilities:

• The probability that the dominant allele is in the egg and the recessive allele is in the sperm is 1/2 X 1/2 = 1/4
• The probability that the dominant allele is in the sperm and the recessive allele is in the egg is 1/2 X 1/2 = 1/4

Therefore, the overall probability that a heterozygous offspring will be produced is:

1/4 + 1/4 = 1/2

The Rule of Multiplication

Mendel demonstrated that the characteristics of pea plants were passed as discrete units from parents to offspring. He also discovered that different traits were transmitted independently of one another, allowing each to be analyzed separately in terms of probability.

For example, a cross between a plant with green, wrinkled seeds and a plant with yellow, round seeds resulted in offspring with a 3:1 ratio for green vs. yellow seeds and a 3:1 ratio for round vs. wrinkled seeds. The traits for colour and texture were independent of each other.

The rule of multiplication, or the product rule of probability, applies to the independent transmission of traits. It states that the probability of two independent events occurring simultaneously is the product of their individual probabilities.

Example

In a Mendelian cross between pea plants heterozygous for flower colour (Pp), what is the probability that the offspring will be homozygous recessive (pp)?

• The probability that an egg from the F1 generation (Pp) will receive a p allele = 1/2
• The probability that sperm from the F1 generation will receive a p allele = 1/2

The overall probability that two recessive alleles will combine (one from the egg and one from the sperm) at fertilization is:

1/2 X 1/2 = 1/4

Linkage

Linkage is a phenomenon where two or more linked genes are consistently inherited together in the same combination for more than two generations. It refers to the inheritance of two DNA segments that reside on the same chromosome for multiple generations.

Thomas Hunt Morgan conducted experiments on Drosophila melanogaster (fruit flies) to explain how sexual reproduction generates variations. He chose to work with fruit flies for his research. In one of his experiments, he crossed a purebred white-eyed male with a purebred red-eyed female.

As expected, following Mendel’s laws, the F1 progeny all had red eyes. However, when the F1 generation was crossed, the resulting F2 progeny exhibited a 3:1 ratio of red-eyed to white-eyed flies. Notably, there were no white-eyed females in the F2 generation.

To investigate further, Morgan crossed a heterozygous red-eyed female with a white-eyed male. This produced progeny in a 1:1:1:1 ratio: 1 white-eyed female, 1 red-eyed female, 1 white-eyed male, and 1 red-eyed male.

This observation led Morgan to hypothesize a linkage between the traits and sex chromosomes. Through further experiments, he determined that the gene responsible for eye colour was located on the X chromosome.

Types of Linkages

There are two types of linkages:

1) Complete Linkage

This occurs when the combination of two or more traits are inherited together and are visible in subsequent generations. These traits are found in the same chromosome type. An example is the genes for long wings and grey body in male Drosophila.

2) Incomplete Linkage

This type of linkage produces some non-parental combinations. The genes are located at a distance on the chromosomes, allowing occasional recombination due to crossing over. In incomplete linkage, new gene combinations are formed in the progeny as a result of chiasma formation or crossing over between the linked genes.

Recombination

Recombination is the process through which new allele combinations are created by rearranging DNA molecules.

This process generates offspring with a mix of traits, resulting from the exchange of genetic material during crossing over, which happens in meiosis.

Recombination occurs in both eukaryotic and prokaryotic organisms, enhancing genetic diversity in species that reproduce sexually. In prokaryotic cells, recombination can happen through conjugation, transduction, or transformation.

Types of Recombination

1. Homologous recombination: This type occurs between chromosomes with similar sequences, such as homologous chromosomes in diploid organisms, and happens during meiosis.
2. Non-homologous recombination: Occurs between chromosomes that are dissimilar. This form of recombination repairs chromosomal double-strand breaks in the DNA of somatic cells.
3. Site-specific recombination: Takes place between very short sequences that usually contain similarities.
4. Mitotic recombination: Generally harmful, as it can lead to tumour formation. Mitotic recombination occurs during interphase and increases with radiation exposure.

Sex Linkage in Humans

Sex-linked traits are characteristics determined by genes found on the X chromosome, rather than on autosomes.

Genes located on the same chromosome are considered "linked" because they tend to be inherited together. A sex-linked gene is one situated on the X chromosome, meaning these genes are passed along with the X chromosome itself. These traits are usually controlled by recessive genes.

Examples of sex-linked traits include hemophilia, color blindness, albinism, sickle cell anemia, and baldness.

Examples of Sex-linked Traits

Haemophilia

Haemophilia is a condition where bleeding takes an unusually long time to stop, or may not stop at all, due to the lack of blood clotting. Even minor injuries like punctures or tooth extractions can result in severe bleeding, potentially leading to death if left unmanaged.

Colour Blindness

Individuals with colour blindness struggle to distinguish certain colours. This is due to a gene abnormality that affects the production of cone cells—light receptors in the retina—responsible for colour perception.

Albinism

Albinism is a condition marked by a lack of pigmentation in the skin due to an absence of melanin. This results in a noticeably lighter skin tone in affected individuals.

Sickle Cell Anaemia

Sickle cell anaemia is caused by a recessive gene that leads to some red blood cells becoming sickle-shaped. The haemoglobin in these cells is inefficient in transporting oxygen and, in low oxygen conditions, breaks down, causing cells to form a sickle shape.

The sickle-shaped cells can block small blood vessels, obstructing blood flow, which deprives affected body parts of oxygen and nutrients. This often results in a crisis, marked by joint and bone pain, low haemoglobin levels, decreased blood oxygen concentration, and fluid loss. Individuals with this condition are commonly referred to as “sicklers.”

Baldness

Baldness results in the inability of hair to grow on the top of the head or the premature loss of hair. This condition is more commonly observed in males.