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Image: “Frozen samples for eDNA analysis stored in freezer at Midwest Fisheries Center.” by
USFWSmidwest. License: CC BY 2.0

## Foundation of Classical Genetics

Reproduction allows living beings to transfer biological traits to future generations through the phenomenon of heredity. Hereditary information is transferred from parents to offspring through genes.

The foundation of classical genetics was laid by an Austrian monk, Gregor Mendel. His work on plant hybridization, published in 1866, became the basis of genetics. His experimental conclusions were later referred to as “Mendel’s laws of inheritance.” The era of classical genetics began with the rediscovery of Mendel’s work in 1900 and lasted until Watson and Crick discovered DNA in 1953. These discoveries led to our current understanding of genes and their functions at a molecular level.

### Mendel’s first law

Law of segregation: a pair of genes, i.e., alleles, separate from each other during gamete formation. Each gamete carries only one allele.

### Mendel’s second law

Law of independent assortment: Genes for different traits assort independently during gamete formation.

## Application of Basic Probability for Solving Genetics’ Problems

Probability is the likely frequency that an event will occur over the series of possibilities or quantifying the likelihood that an event will occur. If an event doesn’t occur, the probability is 0; if it does, the probability is 1, so there is a 100% chance the event will occur. For an uncertain event that may or may not occur, the probability is between 0 and 1.

According to Mendel’s hypothesis, the passing of an allele to the gamete is random, i.e., both alleles have an equal chance of entering any gamete. Moreover, the post-fertilization combination of gametes is also random.

The concept of probability plays a major role in Mendelian genetics due to the randomness of hereditary events. Combinations are mostly one of the following two types:

1. Mutually exclusive
2. Independent

Mutually exclusive combinations: The occurrence of one event means the other events will not occur, so their probability is zero.

Independent combinations: The probability that an event will occur or not has no effect on the probability that any other event will occur, so the events are independent of each other.

Two different probability rules predict the outcomes of both mutually exclusive and independent events.

This rule means the probability that either one or the other ‘mutually exclusive’ events will occur equals the sum of probability that the individual event will occur. The rule of addition applies only to mutually exclusive events. The addition rule is applied to ‘either/or’ cases only.

For example, the probability of either allele P (probability y) or allele p (probability z) is y+z, i.e., ½ + ½ = 1. The addition rule cannot be applied to allele P and allele Q of two different genes because both alleles would not be mutually exclusive.

### Multiplication Rule

The probability of occurrence of an ‘independent’ event is equal to the product of the probability of occurrence of each individual event. The segregation of genes produces equal numbers of alleles, which will assort independently. The outcomes of such crosses are predictable through the multiplication rule of probability. The multiplication rule is applied to ‘both … and’ cases.

For example, suppose genes Pp (probability y) and Qq (probability z) are assorting independently. The probability of gamete PQ is y*z, i.e., ½ * ½ = ¼ = 0.25

## Applying Probability to Test Crosses

A phenotype can be explained by observing an individual rather than a genotype. A tall plant genotype can be either homozygous (TT) or heterozygous (Tt).

• Homozygous is the “pure breed” because only one type of gamete is produced.
• Heterozygous is the hybrid. It produces two different types of gametes, i.e., half of the gametes will carry gene T, and the other half will carry gene t.

Mendel set out to identify the genotype of dominant phenotypes of plants, using test crosses to confirm the validity of his conclusions. He devised a system to test an individual’s genotype by crossing it with an individual of a known genotype. Thus, an individual with an unknown genotype by a dominant phenotype is crossed with a homozygous recessive individual, which will reveal the unknown genotype.

### Punnett square

The Punnett square is named for Reginald C. Punnett, who discovered the gene-linkage phenomenon to learn about genetics and problem-solving. By making a Punnett square, all possible random fertilization events and probable genotypes and phenotypes can be viewed. However, applying it to six gene problems and so on can become challenging since it is just a visual representation of possible combinations.

A test cross is used to determine the homozygosity or heterozygosity of an individual, i.e., the unknown genotype. Dihybrid, trihybrid, and other cumbersome test crosses can be solved using the addition and multiplication rules of probability to test cross experiments.

## Probability for Predicting Monohybrids and Dihybrid Test Cross

### Monohybrid cross

The probability that a homozygous or a heterozygous trait will appear in the next generation can be predicted by applying the addition rule to a monohybrid test cross. In the following example, the dominant combination is (BB) for brown eye color and (bb) for the recessive trait blue eye color. A heterozygous individual will have brown eyes (Bb). The frequency can be calculated as follows:

Image: “A Punnett Square showing a BB x Bb cross for eye color. Here, a homozygous dominant brown-eyed parent and a w: heterozygous brown-eyed parent produce 50% homozygous dominant brown-eyed offspring and 50% heterozygous brown-eyed offspring. The example discussed in the text is concerned with the cross-test between a Bb and a Bb ” by Purpy Pupple. License: CC BY-SA 3.0

Results: the probability of a homozygote and a heterozygote in the F2 generation if both parents are heterozygous.

• 25% of the offspring will have a homozygous dominant genotype (BB).
• 25% of the offspring will have a homozygous recessive genotype (bb).
• 50% of the offspring will have a heterozygous genotype (Bb).

### Dihybrid and trihybrid crosses

A dihybrid cross or trihybrid cross has more than one trait under consideration.  The probabilities are based on the possible monohybrid crosses. The dihybrid cross can be easily understood by making two separate monohybrid crosses.

The two traits are considered to be inherited independently. The probability that a seed will be green or yellow is independent of the probability that the seed will be round or wrinkled. However, yellow and round characteristics of the seed are dominant. Because of the independent assortment of these traits, we can apply the product rule of probability to the case of the dihybrid cross.

Image: “RrYy x RrYy Dihybrid Cross Tree Method” by Tim DeJulio. License: Public Domain

## Prediction of an Unknown Genotype Through Test Cross

The unknown genotype of an individual can be predicted using Mendel’s method, i.e., creating a cross between the homozygous recessive individual and the individual with unknown genotype but a dominant phenotype. This method will reveal the unknown genotype. This signifies the importance of the monohybrid test cross; it helps detect recessive alleles that harm the population.

In the following example, brown is the dominant eye color, while blue is recessive. An individual with an unknown genotype who has brown colored eyes can be crossed with the homozygous recessive individual.

Results can be predicted as follows:

• If 50% of individuals have brown eyes and 50% have blue eyes, then the unknown genotype is a heterozygote (Bb).
• If all individuals in the next generation have brown eyes, then the unknown genotype is a homozygote (BB).

## Limitations to Mendel’s Laws

### Unexpected phenotypes

One limitation of Mendel’s laws is that nearly all genes for the traits he studied were localized on different chromosomes or at a significant distance on the same chromosome; hence, the outcomes were predictable. If more pairs of genes are tracked, different and unexpected phenotypes will appear due to the crossover phenomenon.

### Continuous variations

In natural populations, many traits seem to vary continuously due to polygenic inheritance, which occurs when multiple genes are responsible for a single characteristic or trait. Environmental factors, along with the number of genes responsible for a single trait, cause a huge variation in the phenotype of a trait in a natural population.

Examples of such traits include eye color, skin color, or height. The amount of pigment is higher in brown eyes and lower in blue, green, or grey eyes. Such continuously varying traits are represented typically by a bell graph.

### Pleiotropy

At times, a single gene affects more than one phenotype or trait of a person, which is known as pleiotropy. These traits can be unrelated, and the alleles are transmitted in the same way as other non-pleiotropic alleles.

This phenomenon is also responsible for multiple disorders in humans, like phenyl keto urea and Marfan disease. In Marfan disease, the eye lens, fingers, and heart seem to function abnormally. At times it can be responsible for embryonic lethality, as shown in the following example.

Image: “Punnett square illustrating the lethal yellow coat allele in mice.” by Jcfidy. License: CC BY-SA 4.0

### Dominance

The phenomenon of dominance is applied to diploid individuals, where at least two alleles for the same gene are present. However, dominance is not always complete; at times, both alleles express themselves to give rise to a different phenotype. Internal and environmental factors influence gene expression.

### Co-dominance

A gene can have more than one copy of an allele, i.e., more than two allelic variants for the same gene. In this case, the phenotype is also different from the one predicted via Mendelism. If multiple alleles are present and different alleles are fully expressed, it is known as co-dominance.

For example, in the case of blood group types, alleles iA and iB for antigen A and B are dominant over recessive allele i0; they are fully expressed in heterozygous individuals with blood group AB.

The following is an example of co-dominance from Roan cattle for the coat color.

Image: “This diagram shows co-dominance. In this example, a white bull (WW) mates with a red cow (RR), and their offspring exhibit co-dominance expressing both white and red hairs.” by Hhughes15. License: CC BY-SA 4.0

### Incomplete dominance

An intermediate phenotype in a heterozygous individual is known as incomplete dominance. It happens when the dominant allele is unable to mask the effect of the recessive allele completely.

Example: Two snapdragon plants are crossed. One plant had red flowers, and the other had white flowers. The offspring generation had pink flowers, i.e., an intermediate phenotype. This is an example of incomplete dominance.

### Overdominance

Overdominance occurs when a heterozygote offspring from two homozygote parents has a phenotype beyond the parents’ range.

For example, two homozygous plants with fruit length 10 cm (SS) and 20 cm (ss) are crossed. The next generation is a heterozygote (Ss) with a 30 cm fruit length.

### Impact of the environment over phenotypes

At times gene expression changes are a result of changing environmental factors like temperature etc.

Himalayan rabbits

Himalayan rabbits have black hair on the tail, ears, nose, and legs. However, the trunk hair is white. The reason for this phenomenon is the temperature-sensitive expression of genes for the tyrosinase enzyme. Himalayan rabbits are homozygous for a mutant form of tyrosinase enzyme; it is responsible for the production of melanin pigment, which gives a darker color to the hair.

This enzyme only works when the environmental temperature is below 33° C (91.4.F). The trunk region stores a fair amount of heat, so the hair on the trunk appears light. Siamese cats appear lighter in summers and darker in winters for the same reason; they have the same temperature-sensitive version of the tyrosinase enzyme.

### Epistasis alters phenotypic ratios

Epistasis is defined as the interaction of genes at different loci. The expression of one gene depends on the presence of a specific genotype on other loci. It is also responsible for the complete suppression of a mutant phenotype in some cases.

For example, the homozygous parent generation of white flowers, where two alleles are responsible for flower color, is cross-fertilized to produce purple flowers in the F1 generation. Further crossing produces both white and purple flowers in the F2 generation. Hence, epistasis can change the expected phenotypic ratios. The appearance of the purple color in the F1 generation is due to the interdependence of enzymes as a result of the epistatic phenomenon.

## Modern Genetics is Beyond Mendelism

Mendelian genetics laid the foundation for modern genetics and remains valid for many traits. It is a good introduction to the basic principles of genetics, but modern genetics departs from Mendelian genetics due to the following aspects:

• Mendel’s one-gene-one character hypothesis is not universal due to multigene inheritance, where many genes control a single character.
• Independent assortment of genes does not apply to closely linked genes that are inherited together due to localization at close proximity.
• Due to epistasis, Mendel’s assumption that one gene cannot influence the other is not applicable universally.
• Mendel’s concept of two alleles for one single gene is no longer valid due to the emergence of the concept of multiple alleles.
• Mendel suggested that characters can either be dominant or recessive, but we now know about the concepts of incomplete dominance, codominance, and overdominance.
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