Mendelian Genetics
Before the 1800's, it was common belief that a offspring inherit a "blended" version of their parents' traits. This hypothesis is analogous to mixing white and black paint to make grey. However, this explanation has a few shortcomings. First, wouldn't all the individuals in an entire population become identical after an extended period of time? Of course, that is not the case because genetic variation is evident among the vast majority of multicellular organisms. Second, sometime offspring may exhibit traits that their parents do not have. How can the blending hypothesis explain for this?
In the mid-1800's, an Austrian monk called Gregor Mendel offered an alternative explanation to the blending hypothesis - the "particulate" hypothesis. Mendel suggested that heritable units (or genes) are passed from one generation to the next. This is analogous to a deck of cards, where each parent gives the offspring a copy of half of their deck, thereby the offspring will have a full deck. This way, genes that affect the offspring's traits are passed without any dilution. In addition, it explains why populations do not "blend" into uniformity. Because the genetic basis of heredity does not dilute, neither does the physical expression of these genes.
In the mid-1800's, an Austrian monk called Gregor Mendel offered an alternative explanation to the blending hypothesis - the "particulate" hypothesis. Mendel suggested that heritable units (or genes) are passed from one generation to the next. This is analogous to a deck of cards, where each parent gives the offspring a copy of half of their deck, thereby the offspring will have a full deck. This way, genes that affect the offspring's traits are passed without any dilution. In addition, it explains why populations do not "blend" into uniformity. Because the genetic basis of heredity does not dilute, neither does the physical expression of these genes.
Mendel's Pea Experiments
In Mendel's famous pea experiment, he found that peas from pure-bred parents always express one of the parents' traits. In other words, the first generation all look like one of the parents; it seems like the other trait has disappeared completely. However, when the first-generation offspring are cross-bred with each other, the "disappeared" trait reappears again in a simple-number ratio of 1:4 (one out of four offspring express the disappeared trait). Mendel repeated this experiment multiple times, and with different traits. Nevertheless. he always came up with the same result. This is strong evidence to refute the blending model of genetic inheritance.
But how can traits disappear in one generation and reappear in the next? Mendel proposed that because each pure-bred parent (homozygous) donates one set of genes to the offspring, all of the offspring receives one copy of each gene (heterozygous). However, the two genes are not expressed equally by the organism. One trait was "dominant" over the other. In other words, the "recessive" trait was suppressed by the "dominant" trait. This makes sense because as the first generation reproduces with each other, a quarter of the offspring will receive two sets of the recessive gene and the rest will receive at least one copy of the dominant gene. Therefore, one quarter of the second generation will express the recessive gene while three quarters will express the dominant gene.
To familiarize ourselves with some vocabulary, genotype means the combination of certain genes that is present in an organism (e.g. AaBb), whereas phenotype simply refers to the appearance of an organism (e.g. white flowers).
But how can traits disappear in one generation and reappear in the next? Mendel proposed that because each pure-bred parent (homozygous) donates one set of genes to the offspring, all of the offspring receives one copy of each gene (heterozygous). However, the two genes are not expressed equally by the organism. One trait was "dominant" over the other. In other words, the "recessive" trait was suppressed by the "dominant" trait. This makes sense because as the first generation reproduces with each other, a quarter of the offspring will receive two sets of the recessive gene and the rest will receive at least one copy of the dominant gene. Therefore, one quarter of the second generation will express the recessive gene while three quarters will express the dominant gene.
To familiarize ourselves with some vocabulary, genotype means the combination of certain genes that is present in an organism (e.g. AaBb), whereas phenotype simply refers to the appearance of an organism (e.g. white flowers).
A monohybrid cross
What happens when two parents with different genotypes mate? If we're only focusing on one particular characteristic, then we perform a monohybrid cross.
Let's look at an example: A pure-bred white flower (WW) is crossed (mated) with a red flower (RR); the R gene is dominant over the W gene.
Number 1 stands for the parents, number 2 stands for the first generation, and number 3 stands for the second generation.
*Note: Do not confuse the parent generation with the first generation. Think of the parent generation as "generation 0".
Let's look at an example: A pure-bred white flower (WW) is crossed (mated) with a red flower (RR); the R gene is dominant over the W gene.
Number 1 stands for the parents, number 2 stands for the first generation, and number 3 stands for the second generation.
*Note: Do not confuse the parent generation with the first generation. Think of the parent generation as "generation 0".
Look at the first generation, all four offspring have red flowers, which follows the condition that the R gene is dominant. Since all four carry both the dominant and recessive alleles, they are considered heterozygous for the flower colour trait. Their genotypes are WR, but their phenotypes are red because the red gene trumps the white gene.
To determine the genotypes and phenotypes of the second generation, we need to construct a punnett square. To do so, take one parent's alleles and put them on top; do the same with the other parent's alleles and put them on the left. Combine the alleles for each quadrant to get the genotypes for the offspring (see above diagram).
What do you see? Out of the four offsprings in the punnett square, one inherits the R gene from both parents (genotype RR, phenotype red), two inherits the R gene from one parent and the W gene from the other (genotype RW, phenotype red), and the last inherits the W allele from both parents (genotype WW, phenotype white). Note that three of the flowers are red and only one is white. The number of squares with a certain genotype or phenotype is proportional to the chance of its occurrence. In the above diagram, the chance of RW occurring is twice the chance of WW or RR because there are two squares for RW and only one square each for WW and RR. Using the same principle, we can determine that red flowers occur three times as often as white flowers since three squares contain red flowers and only one contains white flowers. This classic 3:1 ratio is observed for many of Mendel's pea experiments; this ratio implies a cross between two heterozygous parents for a dominant allele. In a perfect world, the ratio of offspring would be exactly the same as the ratio predicted by a punnett square. However, in practice this is not always true. For small populations, deviations due to pure chance may significantly skew the results.
To determine the genotypes and phenotypes of the second generation, we need to construct a punnett square. To do so, take one parent's alleles and put them on top; do the same with the other parent's alleles and put them on the left. Combine the alleles for each quadrant to get the genotypes for the offspring (see above diagram).
What do you see? Out of the four offsprings in the punnett square, one inherits the R gene from both parents (genotype RR, phenotype red), two inherits the R gene from one parent and the W gene from the other (genotype RW, phenotype red), and the last inherits the W allele from both parents (genotype WW, phenotype white). Note that three of the flowers are red and only one is white. The number of squares with a certain genotype or phenotype is proportional to the chance of its occurrence. In the above diagram, the chance of RW occurring is twice the chance of WW or RR because there are two squares for RW and only one square each for WW and RR. Using the same principle, we can determine that red flowers occur three times as often as white flowers since three squares contain red flowers and only one contains white flowers. This classic 3:1 ratio is observed for many of Mendel's pea experiments; this ratio implies a cross between two heterozygous parents for a dominant allele. In a perfect world, the ratio of offspring would be exactly the same as the ratio predicted by a punnett square. However, in practice this is not always true. For small populations, deviations due to pure chance may significantly skew the results.
A dihybrid cross
If we're interested in two different characteristics, then we perform a dihybrid cross. This is similar in principle to a monohybrid cross. For parents who are both heterozygous for two characteristics, we take the four possible combinations of gametes from each parent (AB, Ab, aB, and ab), arrange them as we would for a monohybrid cross, combine the gametes, and count the number of offsprings with each trait.
Let's try another example. The gene S (short tails) is dominant over s (long tails), and the gene B (coloured fur) is dominant over the gene b (white fur).
Let's try another example. The gene S (short tails) is dominant over s (long tails), and the gene B (coloured fur) is dominant over the gene b (white fur).
As we can see, 9 out of 16 offspring have short tails and coloured fur, 3 have short tails and white fur, 3 have long tails and coloured fur, and 1 has long tails and white fur. This 9:3:3:1 ratio is typical for dihybrid crosses.
Mendel's Laws of segregation and independent assortment
Through his pea experiments, Mendel managed to come up with two generalizations:
The Law of Segregation: During anaphase I of meiosis, alleles are separated into different gametes. Therefore, a parent with genotype Aa will make gametes with either A or a, but not both (unless a mistake has occurred during meiosis).
The Law of Independent Assortment: Two characters will separate independently of each other during metaphase I of meiosis. As we saw in the second example, the alleles for tail length and fur colour are distributed to the alleles randomly; the allele that is present in a gamete does not affect the chances of the other allele being in the same gamete. However, there are exceptions to this rule, as we will later discuss.
The Law of Segregation: During anaphase I of meiosis, alleles are separated into different gametes. Therefore, a parent with genotype Aa will make gametes with either A or a, but not both (unless a mistake has occurred during meiosis).
The Law of Independent Assortment: Two characters will separate independently of each other during metaphase I of meiosis. As we saw in the second example, the alleles for tail length and fur colour are distributed to the alleles randomly; the allele that is present in a gamete does not affect the chances of the other allele being in the same gamete. However, there are exceptions to this rule, as we will later discuss.