Introduction

Every day we observe heritable variations (eyes of brown, green, blue, or gray) among individuals in a population. These traits are transmitted from parents to offspring. One mechanism for this transmission is the "blending" hypothesis. This hypothesis proposes that the genetic material contributed by each parent mixes in a manner analogous to the way blue and yellow paints blend to make green.

Over many generations, a freely mating population should give rise to a uniform population of individuals. However, the "blending" hypothesis appears incorrect as everyday observations and the results of breeding experiments contradict its predictions. An alternative model, "particulate" inheritance, proposes that parents pass on discrete heritable units - genes - that retain their separate identities in offspring. Genes can be sorted and passed on, generation after generation, in undiluted form. Modern genetics began in an abbey garden, where a monk names Gregor Mendel documented the particulate mechanism of inheritance.

1. Mendel brought an experimental and quantitative approach to genetics

Mendel grew up on a small farm in what is today the Czech Republic. In 1843, Mendel entered an Augustinian monastery. He studied at the University of Vienna from 1851 to 1853 where he was influenced by a physicist who encouraged experimentation and the application of mathematics to science and a botanist who aroused Mendel's interest in the causes of variation in plants.

These influences gelled in Mendel's experiments.

• After the university, Mendel taught at the Brunn Modern School and lived in the local monastery.
• The monks at this monastery had a long tradition of interest in the breeding of plants, including peas.
• Around 1857, Mendel began breeding garden peas to study inheritance.
• Pea plants have several advantages for genetics.
• Pea plants are available in many varieties with distinct heritable features (characters) with different variants (traits).

Another advantage of peas is that Mendel had strict control over which plants mated with which.

• Each pea plant has male (stamens) and female (carpal) sexual organs.
• In nature, pea plants typically self-fertilize, fertilizing ova with their own sperm.
• However, Mendel could also move pollen from one plant to another to cross-pollinate plants.

In a typical breeding experiment, Mendel would cross-pollinate (hybridize) two contrasting, true-breeding pea varieties.

• The true-breeding parents are the P generation and their hybrid offspring are the F1 generation.
• Mendel would then allow the F1 hybrids to self-pollinate to produce an F2 generation.
• It was mainly Mendel's quantitative analysis of F2 plants that revealed the two fundamental principles of heredity: the law of segregation and the law of independent assortment.

2. By the law of segregation, the two alleles for a characters are packaged into separate gametes If the blending model were correct, the F1 hybrids from a cross between purple-flowered and white-flowered pea plants would have pale purple flowers. Instead, the F1 hybrids Tall have purple flowers, just as purple as the purple-flowered parents.

When Mendel allowed the F1 plants to self-fertilize, the F2 generation included both purple-flowered and white-flowered plants.

• The white trait, absent in the F1, reappeared in the F2.
• Based on a large sample size, Mendel recorded
• 705 purple-flowered F2 plants and
• 224 white-flowered F2 plants from the original cross.

This cross produced a three purple to one white ratio of traits in the F2 offspring, Mendel reasoned that the heritable factor for white flowers was present in the F1 plants, but it did not affect flower color. Purple flower is a dominant trait and white flower is a recessive trait. The reappearance of white-flowered plants in the F2 generation indicated that the heritable factor for the white trait was not diluted or "blended" by coexisting with the purple-flower factor in F1 hybrids.

Mendel found similar 3 to 1 ratios of two traits among F2 offspring when he conducted crosses for six other characters, each represented by two different varieties.

For example, when Mendel crossed two true-breeding varieties, one of which produced round seeds, the other of which produced wrinkled seeds, all the F1 offspring had round seeds, but among the F2 plants, 75% of the seeds were round and 25% were wrinkled. Mendel developed a hypothesis to explain these results that consisted of four related ideas.

1. Alternative version of genes (different alleles) account for variations in inherited characters.

• Different alleles vary somewhat in the sequence of nucleotides at the specific locus of a gene.
• The purple-flower allele and white-flower allele are two DNA variations at the flower-color locus.

2. For each character, an organism inherits twoalleles, one from each parent.

• A diploid organism inherits one set of chromosomes from each parent.
• Each diploid organism has a pair of homologous chromosomes and therefore two copies of each locus.
• These homologous loci may be identical, as in the true-breeding plants of the P generation.
• Alternatively, the two alleles may differ

In the flower-color example, the F1 plants inherited a purple-flower allele from one parent and a white-flower allele from the other.

3. If two alleles differ, then one, the dominant allele, is fully expressed in the the organism's appearance. The other, the recessive allele, has no noticeable effect on the organism's appearance. Mendel's F1 plants had purple flowers because the purple-flower allele is dominant and the white-flower allele is recessive.

4. The two alleles for each character segregate (separate) during gamete production.

This segregation of alleles corresponds to the distribution of homologous chromosomes to different gametes in meiosis. If an organism has identical allele for a particular character, then that allele exists as a single copy in all gametes. If different alleles are present, then 50% of the gametes will receive one allele and 50% will receive the other. The separation of alleles into separate gametes is summarized as Mendel's law of segregation.

Mendel's law of segregation accounts for the 3:1 ratio that he observed in the F2 generation.

• The F1 hybrids will produce two classes of gametes, half with the purple-flower allele and half with the white-flower allele.
• During self-pollination, the gametes of these two classes unite randomly.
• This can produce four equally likely combinations of sperm and ovum.

A Punnett square predicts the results of a genetic cross between individuals of known genotype.

• A Punnett square analysis of the flower-color example demonstrates Mendel's model.
• One in four F2 offspring will inherit two white-flower alleles and produce white flowers.
• Half of the F2 offspring will inherit one white-flower allele and one purple-flower allele and produce purple flowers.
• One in four F2 offspring will inherit two purple-flower alleles and produce purple flowers too.

Mendel's model accounts for the 3:1 ratio in the F2 generation

Genetics has some unique, useful vocabulary.

• An organism with two identical alleles for a character is homozygous for that character.
• Organisms with two different alleles for a character is heterozygous for that character.
• A description of an organism's traits is its phenotype.
• A description of its genetic makeup is its genotype.
• Two organisms can have the same phenotype but have different genotypes if one is homozygous dominant and the other is heterozygous.

For flower color in peas, both PP and Pp plants have the same phenotype (purple) but different genotypes (homozygous and heterozygous). The only way to produce a white phenotype is to be homozygous recessive (pp) for the flower-color gene.

• It is not possible to predict the genotype of an organism with a dominant phenotype.
• The organism must have one dominant allele, but it could be homozygous dominant or heterozygous.
• A test cross, breeding a homozygous recessive is crossed with dominant phenotype, but unknown geneotype, can determine the identity of the unknown allele.

3. By the law of independent assortment, each pair of alleles segregates into gametes independently

Mendel's experiments that followed the inheritance of flower color or other characters focused on only a single character via monohybrid crosses. He conduced other experiments in which he followed the inheritance of two different characters, a dihybrid cross.

In one dihybrid cross experiment, Mendel studied the inheritance of seed color and seed shape.

• The allele for yellow seeds (Y) is dominant to the allele for green seeds (y).
• The allele for round seeds (R) is dominant to the allele for wrinkled seeds (r).
• Mendel crossed true-breeding plants that had yellow, round seeds (YYRR) with true-breeding plants that has green, wrinkled seeds (yyrr).

One possibility is that the two characters are transmitted from parents to offspring as a package. The Y and R alleles and y and r alleles stay together. If this were the case, the F1 offspring would produce yellow, round seeds. The F2 offspring would produce two phenotypes in a 3:1 ratio, just like a monohybrid cross. This was not consistentwith Mendel's results.

An alternative hypothesis is that the two pairs of alleles segregate independently of each other. The presence of one specific allele for one trait has no impact on the presence of a specific allele for the second trait. In our example, the F1 offspring would still produce yellow, round seeds. However, when the F1's produced gametes, genes would be packaged into gametes with all possible allelic combinations.

• Four classes of gametes (YR, Yr, yR, and yr) would be produced in equal amounts.
• When sperm with four classes of alleles and ova with four classes of alleles combined, there would be 16 equally probable ways in which the alleles can combine in the F2 generation.
• These combinations produce four distinct phenotypes in a 9:3:3:1 ratio.
• This was consistent with Mendel's results.

Mendel repeated the dihybrid cross experiment for other pairs of characters and always observed a 9:3:3:1 phenotypic ration in the F2 generation.

• Each character appeared to be inherited independently.
• The independent assortment of each pair of alleles during gamete formation is now called Mendel's law of independent assortment.
• One other aspect that you can notice in the dihybrid cross experiment is that if you follow just one character, you will observe a 3:1 F2 ratio for each, just as if this were a monohybrid cross.

4. Mendelian inheritance reflects rule of probability

Mendel's laws of segregation and independent assortment reflect the same laws of probability that apply to tossing coins or rolling dice.

The probability scale ranged from zero (an event with no chance of occurring) to one (an event that is certain to occur).

The probability of tossing heads with a normal coin is 1/2.

The probability of rolling a 3 with a six-sided die is 1/6, and the probability of rolling any other number is 1 - 1/6 = 5/6.

When tossing a coin, the outcome of one toss has no impact on the outcome of the next toss.

Each toss is an independent event, just like the distribution of alleles into gametes.

Like a coin toss, each ovum from a heterozygous parent has a 1/2 chance of carrying the dominant allele and a 1/2 chance of carrying the recessive allele.

The same odds apply to the sperm.

We can use the rule of multiplication to determine the chance that two or more independent events will occur together in some specific combination.

Compute the probability of each independent event.

Then, multiply the individual probabilities to obtain the overall probability of these events occurring together.

The probability that two coins tossed at the same time will land heads up is 1/2 x 1/2 = 1/4.

Similarly, the probability that a heterogyzous pea plant (Pp) will produce a white-flowered offspring (pp) depends on an ovum with a white allele mating with a sperm with a white allele.

This probability is 1/2 x 1/2 = 1/4.

The rule of multiplication also applies to dihybrid crosses.

For a heterozygous parent (YyRr) the probability of producing a YR gamete is 1/2 x 1/2 = 1/4. We can use this to predict the probability of a particular F2 genotype without constructing a 16-part Punnett square. The probability that an F2 plant will have a YYRR genotype from a heterozygous parent is 1/16 (1/4 chance for a YR ovum and 1/4 chance for a YR sperm).

The rule of addition also applies to genetic problems.

Under the rule of addition, the probability of an event that can occur two or more different ways is the sum of the separate probabilities of those ways.

For example, there are two ways that F1 gametes can combine to form a heterozygote.

The dominant allele could come from the sperm and the recessive from the ovum (probability = 1/4).

Or, the dominant allele could come from the ovum and the recessive from the sperm (probability = 1/4).

The probability of a heterozygote is 1/4 + 1/4 = 1/2.

We can combine the rules of multiplication and addition to solve complex problems in Mendelian genetics.

Let's determine the probability of finding two recessive phenotypes for at least two of three traits resulting from a trihybrid cross between pea plants that are PpYyRr and Ppyyrr.

There are five possible genotypes that fulfill this condition: ppyyRr, ppYyrr, Ppyyrr, PPyyrr, and ppyyrr.

We would use the rule of multiplication to calculate the probability for each of these genotypes and then use the rule of addition to pool the probabilities for fulfilling the condition of at least two recessive trait.

The probability of producing a ppyyRr offspring:

The probability of producing pp = 1/2 x 1/2 = 1/4.

The probability of producing yy = 1/2 x 1 = 1/2.

The probability of producing Rr = 1/2 x 1 = 1/2.

Therefore, the probability of all three being present (ppyyRr) in one offspring is 1/4 x 1/2 x 1/2 = 1/16.

For ppYyrr: 1/4 x 1/2 x 1/2 = 1/16.

For Ppyyrr: 1/2 x 1/2 x 1/2 = 2/16

for PPyyrr: 1/4 x 1/2 x 1/2 = 1/16

for ppyyrr: 1/4 x 1/2 x 1/2 = 1/16

Therefore, the chance of at least two recessive traits is 6/16.

5. Mendel discovered the particulate behavior of genes: a review

While we cannot predict with certainty the genotype or phenotype of any particular seed from the F2 generation of a dihybrid cross, we can predict the probabilities that it will fit a specific genotype of phenotype.

Mendel's experiments succeeded because he counted so many offspring and was able to discern this statistical feature of inheritance and had a keen sense of the rules of chance.

Mendel's laws of independent assortment and segregation explain heritable variation in terms of alternative forms of genes that are passed along according to simple rule of probability.

These laws apply not just to garden peas, but to all other diploid organisms that reproduce by sexual reproduction.

Mendel's studies of pea inheritance endures not only in genetics, but as a case study of the power of scientific reasoning using the hypothetico-deductive approach.