Table of Contents
- Foundation of Classical Genetics
- Application of Basic Probability for Solving Genetics’ Problems
- Application of Probability to Test Crosses
- Probability for Predicting Monohybrids and Dihybrid Test Cross
- Prediction of Unknown Genotype Through Test Cross
- Limitations to Mendel’s Laws
- Modern Genetics is Beyond Mendelism
Foundation of Classical Genetics
Reproduction is a feature of living beings which allows them to transfer biological traits to future generations through the phenomenon of hereditary. Hereditary information is transferred from parents to offspring’s through genes.
Foundation of classical genetics was laid by an Austrian monk, Gregor Mendel. His work on plant hybridization was published in 1866 which became basis of genetics although his work did not get recognition and was not welcomed at that stage.
The era of classical genetics began with rediscovery of Mendelism in 1900 till the discovery of DNA in 1953 by Watson and Crick. These discoveries led to understanding of genes and their functions at molecular level. Mendel put forth his experimental conclusions which were later established as ‘Mendel’s laws of inheritance’.
Mendel’s first law
Law of segregation: pair of genes, i.e., alleles separate from each other during gamete formation and each gamete carries only one allele.
Mendel’s Second law
Law of independent assortment: Genes for different traits assort independently with respect to each other during gamete formation.
Application of Basic Probability for Solving Genetics’ Problems
Probability is the likely frequency of an event to occur over the series of possibilities or it is quantifying likelihood of an event to occur. If an event doesn’t occur, probability is 0, while if it can occur probability is equal to 1, i.e., there is a 100 % chance of an event to occur. For an uncertain event which may or may not occur, value of probability is between 0 and 1.
According to the hypothesis put forth by Mendel, passing of allele to the gamete is random, i.e., chance of both alleles entering any gamete is equal. Moreover, post-fertilization combination of gametes is also made at random.
The concept of probability plays a major role in Mendelian genetics due to randomness of the hereditary events. Combinations are mostly of the following two types:
- Mutually exclusive
Mutually exclusive combinations: In such combination occurrence of one event nullifies the probability of occurrence of the other events.
Independent combinations: Possibility of an event to occur or not to occur does not impact the possibility of occurrence of any other event that means these events are independent of each other.
Two different rules of probability are applied to predict the outcomes of both mutually exclusive and independent events.
Probability of occurrence of either one or the other ‘mutually exclusive’ events is equal to the sum of probability of occurrence of each individual event. Rule of addition is applied to only mutually exclusive events. Addition rule is applied to ‘either/or’ cases only.
One thing to consider is that addition rule cannot be applied to allele P and allele Q of two different genes, as in this case both alleles would not be mutually exclusive.
Probability of occurrence of an ‘independent’ event is equal to the product of probability of occurrence of each individual event. Segregation of genes produce equal numbers of alleles which will assort independently. Outcomes of such crosses are predicted through multiplication rule of probability. Multiplication rule is applied to ‘both … and’ cases.
Application of Probability to Test Crosses
Phenotype can be explained while observing an individual as opposed to genotype. For a tall plant genotype can be either homozygous (Ee) or heterozygous (Tt).
- Homozygous is the ‘pure breed’ as only one type of gametes are produced.
- Heterozygous are known as hybrids and produces two different types of gametes, i.e., half of gametes will carry gene T and the other half will carry gene t.
In order to identify genotype of dominant phenotypes of plants, Mendel performed tests and used test crosses to confirm validity of his conclusions. He devised a system where an individual of an unknown genotype by a dominant phenotype is crossed with a homozygous recessive individual to reveal the genotype of the unknown.
Punnett square were devised by Reginald C. Punnett who discovered gene linkage 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, it gets hard to apply it to six gene problems and so on as it is just the visual representation of possible combinations.
Test cross is used to determine the homozygosity of heterozygosity of an individual, i.e., the unknown genotype. By application of addition and multiplication rule of probability to test cross dihybrid, trihybrid and other cumbersome test crosses can be solved.
Probability for Predicting Monohybrids and Dihybrid Test Cross
Probability of appearance of homozygous or a heterozygous trait in next generation can be predicted by application of addition rule to a monohybrid test cross. In the following example, dominant combination is (BB) for brown eye color and for recessive trait is (bb) for blue eye color. A heterozygous individual will show brown eye color (Bb). Its frequency can be calculated as follows:
Results: probability of a homozygote and heterozygote in F2 generation
- ¼ Bb + ¼ Bb = ½ Heterozygous individual
- ½ B (male) + ½ B (female) = ¼ homozygous dominant
- ½ b (male) + ½ b (female) = ¼ homozygous recessive
Dihybrid and trihybrid crosses
Dihybrid cross or trihybrid cross where more than one trait are under consideration; probabilities are based on possibilities of monohybrid crosses. Dihybrid cross can be easily understood by making two separate monohybrid crosses.
The two traits are considered to be inherited independently the probability of a seed to be green or yellow is independent of the seed being round or wrinkled. However, yellow and round characteristics of the seed are dominant. Independent assortment of these traits allowed application of product rule of probability to the case of dihybrid cross.
Prediction of Unknown Genotype Through Test Cross
Unknown genotype of an individual can be predicted through the method devise by Mendel, i.e., creating a cross between homozygous recessive individual and the individual with unknown genotype but dominant phenotype. This method will uncover the unknown genotype. This signifies the importance of monohybrid test cross as it helps with detection of recessive alleles which impacts negatively on the population.
In the following example, brown is the dominant eye color while blue is the recessive. An individual with an unknown genotype but brown colored eyes is crossed with homozygous recessive individual.
Results can be predicted as follows:
- If 50 % individuals have brown colored eyes and 50 % has blue colored eyes, it indicates that the unknown genotype is a heterozygote (Bb).
- If all individuals in the next generation have brown colored eyes, it indicates that the unknown genotype is a homozygote (BB).
Limitations to Mendel’s Laws
Limitation to Mendel’s laws is posed by the fact that nearly all genes for the traits that he studied were fortunately localized on different chromosomes or at a significant distance on the same chromosome, hence, outcomes were predictable. In a case where more pairs of genes are tracked, different and unexpected phenotypes appear due to the phenomenon of crossing over.
In natural populations many traits are seen to appear as continuously varying due to polygenic inheritance. Polygenic inheritance arises when multiple genes are responsible for the appearance of a single characteristic or trait. Environmental factors together with the number of genes responsible for a single trait result in huge variation in phenotype of a trait in a natural population.
An example of such traits is eye color, skin color and height etc. The amount of pigment is higher in brown eyes while lesser is found in blue, green or grey eyes. Such continuously varying traits are represented typically by a bell graph.
At times a single gene impacts more than one phenotype or trait of a person which is known as pleiotropy. These traits can be unrelated and these 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 height, eye lens, fingers and heart seem to function abnormally. At times it can be responsible for embryonic lethality as shown in the following example.
The phenomenon of dominance is applied to diploid individuals where at least two alleles for the same gene are present. Mendel believed that one allele is fully dominant over the other gene. However, this is not the case, dominance is not always complete; at times both alleles express themselves to give rise to a different phenotype. Internal and environmental factors influence the expression of genes.
A gene can have more than one copy of alleles, i.e., more than two allelic variants for the same gene, the phenotype in this case is also different than the one predicted via Mendalism. In such a case where multiple alleles are present and different alleles are fully expressed, it is known as co-dominance.
For example, in 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.
When an intermediate phenotype is observed in a heterozygous individual it is known as incomplete dominance. It happens when the dominant allele is unable to completely mask the effect of recessive allele. However, Mendel did not support appearance of such blended phenotype.
When a heterozygote offspring of the two homozygote parents shows phenotype beyond the range of the parents, it is known as over dominance.
Impact of environment over phenotypes
At times changes in expression of genes is observed as a result of changing environmental factors like temperature etc.
Himalayan rabbits have black hair on tail, ears, nose and legs. However, hair on trunk are white in color. The reason for this phenomenon is the temperature sensitive expression of genes for tyrosinase enzyme. Himalayan rabbits are homozygous for a mutant form of tyrosinase enzyme; it is responsible for production of melanin pigment which give darker color to the hair.
This enzyme only works when environmental temperature is below 33° C (91.4.F). The trunk region stores a fair amount of heat, hence, hair on the trunk appears light. Siamese cats appear lighter in summers and darker during winters for the same reason; they have the same temperature sensitive version of tyrosinase enzyme.
Epistasis alters phenotypic ratios
Epistasis is defined as interaction of genes at different loci. Expression of one gene is dependent on the presence of a specific genotype on other loci. It is also responsible for 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 are cross-fertilized to give rise to purple colored flower in F1 generation. Further crossing results in appearance of both white and purple flowers in F2 generation. Hence, epistasis can change the expected phenotypic ratios. Appearance of purple color in F1 generation is due to the interdependence of enzymes as a result of epistatic phenomenon.
Modern Genetics is Beyond Mendelism
Mendelian genetics laid the foundation for modern genetics and it holds good for many traits. It is good for basic principles of genetics but modern genetics is a whole new story and an exception from Mendelian genetics due to 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 is not applicable to closely linked genes which are inherited together due to localization at a close proximity.
- Due to epistasis Mendel’s assumption that one gene cannot influence the other, cannot be applied universally.
- Mendel put forth the concept of two alleles for one a single gene is also no more valid due to concept of multiple alleles.
- Mendel suggested that characters can either be dominant or recessive, but incomplete dominance, co-dominance and overdominance don’t comply with his concept.