Mendelian Genetics
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[edit] Introduction
Although Mendel was, in some subtle respects, wrong, the classical understanding of genetics is a very good first approximation to the truth, useful for many purposes, and the further development of genetics was a refinement of Mendel's ideas, rather than a flat contradiction of it. Indeed, as tends to be the case in science, the chromosome theory of inheritance which succeeded Mendel's model allows us to understand why Mendelian genetics is nearly accurate nearly all of the time.
[edit] Characters and traits
Geneticists use the word character to refer to a feature of an organism that displays inheritable variation. Each possible variant is known as a trait. So, for example, in the pea plants used by Mendel in his experiments, flower color was a character, which came in two variant traits: purple and white.
The collection of traits exhibited by an organism is called its phenotype.
[edit] Genes and alleles
In the simplest cases, as studied by Mendel, each character is controlled by one gene, which comes in different variants called alleles. So, for example, his peas had a gene for flower color, with two possible alleles, white, and purple. We may say that allele is to gene as trait is to character.
The next paragraph should be read carefully, as it is crucial (it is also one of the parts of Mendel's theory which is not always true, as we shall discuss elsewhere):
All plants and animals have two alleles of each gene, which may be, but need not be, the same. So a pea plant may have two purple alleles of its flower color gene, or two white alleles, or one purple allele and one white allele. The phenotype of the organism is determined by these pairs of alleles, as will be discussed below.
An organism with two identical alleles of a gene is said to be homozygous for that gene; if they are different, it is said to be heterozygous.
An organism's assortment of alleles is known as its genotype.
[edit] Note on notation
Geneticists often use a sort of shorthand for recording the genotype. One gene is represented by a single letter of the alphabet, such as P or Y. If there are two allele for the gene, one (the dominant allele: see our discussion of dominant and recessive alleles below) will be represented by the capitalized version of the letter (e.g. P), while the other, recessive allele is represented by the same letter in lowercase (e.g. p). If we call the purple allele P and the white allele p, then we can write PP for the genotype of a plant with two purple alleles, Pp for a plant with one purple and one white allele, and pp for a plant with two white alleles.
If we want to talk about more than one gene, , we can simply string these shorthand description together. So, for example, if we write Y for the allele for producing yellow peas, and y for the allele for producing green peas, then the meaning of PpYY, for example, is obvious.
[edit] Dominant and recessive alleles
As you will notice, in the simple case where each Character|character is controlled by one gene, we have two alleles for each trait. It is easy enough to see what will happen to a pea plant with two purple alleles (PP) for flower color: it will be purple. Again, if it is homozygous for the white allele (pp) it will be white. But what happens to heterozygous (Pp) plants? Well, in this instance they all turn out to be purple, and not a pale, whitish shade of purple, but a purple indistinguishable from plants with a PP genotype. We say that the purple allele is dominant, and the white allele is recessive.
Mendel had the insight or good fortune to work with characters displaying only two variant traits. This is not always the case. For example, the peppered moth has three possible alleles for wing color, black (M), whitish (m) and mottled gray (M´). M dominates M´ and m, and M´ dominates m, so that moths with genotype MM, MM' or Mm will be black, moths with genotype M´M´ or M'm will be gray, and moths with genotype mm will be white.
Sometimes we see incomplete dominance. For example, snapdragons have two alleles for flower color, red (R) and white (W). Obviously, an RR snapdragon will be red and a WW snapdragon will be white. An RW snapdragon will be pink: neither allele dominates the other.
[edit] Reproduction
When plants or animals reproduce, each of the parents contributes one of each of its pairs of alleles to its offspring. (We overlook here, as Mendel overlooked, the existence of sex chromosomes). Mendel proposed two principles describing how this happens.
The Principle of Segregation: each parent is equally likely to pass on either of its alleles to each of its offspring. A pea plant with genotype Pp is equally likely to pass on the P or the p allele.
The Principle of Independent Assortment: furthermore, the probability of passing on one allele of one gene is independent of the probability of passing on another allele of a different gene. So a pea plant with genotype PpYy has an equal chance of passing on PY, pY, Py or py to the next generation.
[edit] Mendel's experiments
Mendel's experiments provide a nice illustration of the difference between a theory and a law. Each of the laws or principles stated above, on its own, is untestable. But the theory as a whole can be tested by performing breeding experiments.
Suppose we establish two true-breeding populations of pea plants, one with purple flowers, one with white flowers. By true-breeding, we mean that the purple population, crossed amongst themselves, never produce a white "sport", and the white-flowered plants, similarly, never produce any purple offspring. Then if Mendel is right, each population is homozygous, one having genotype PP, the other having genotype pp.
If we then breed the two lines together, breeding each purple plant with a white plant, then we get a generation entirely of purple plants (Geneticists call this the F1 population). If Mendel is right, this is because all the plants in this generation are heterozygous, having genotype Pp, with the trait of having purple flowers dominating the trait of having white flowers.
And this allows us to make a prediction about what will then happen if we breed this heterozygous population with itself, producing what geneticists call the F2 generation. For if Mendel is right, each plant in this generation has genotype Pp, and by the law of segregation it is equally likely to pass on either P or p to its offspring. This means that, statistically, one time in four both parents will pass on a p allele, and so one in four of the F2 generation will have white flowers. And this is what we find.
We can make further predictions. Suppose we take the purple flowered peas from the F2 generation and cross them with the population of true-breeding white-flowered peas.
If Mendel is correct, one quarter of the F2 generation will have received P alleles from both parents, and so be homozygous; as the purple-flowered plants are three-quarters of the F2 population, this means that plants with genotype PP should be one-third of the purple flowered plants in the F2 generation, with the remainder having genotype Pp.
So if we cross the purple flowered plants from the F2 generation with a true-breeding line of white plants, we should find that one-third of these flowers only produce purple offspring, and the other two-thirds should produce a 50:50 mix of white and purple: as is the case. This procedure is called a test-cross, because it allows us to test whether a particular plant is heterozygous or homozygous for a dominant allele.
So far, we have not mentioned predictions that rest on the law of independent assortment. To test this, we need to do experiments involving more than one character. For example, take two true-breeding populations of peas, one of which produces smooth, round peas that are yellow when ripe, and the other of which produces wrinkled peas that remain green. Using Mendelian notation, we shall write Y for yellow, y for green, S for smooth, and s for wrinkled.
If we cross these two together to produce an F1 generation, then they all turn out to have yellow, smooth peas, so if Mendel is right, S dominates s, Y dominates y, and the entire F1 generation has genotype SsYy.
At this point we can make a prediction, based on the law of segregation and the law of independent assortment, of what will happen if we cross the F1 generation with itself. According to these laws, each plant has an equal, one in four chance of passing on either SY, Sy, sY or sy in each gamete. By simple application of probability theory, we find that 9/16 of the F2 generation should produce smooth yellow peas, 3/16 should produce smooth green peas, 3/16 should produce wrinkled yellow peas, and 1/16 should produce wrinkled green peas; as turns out to be the case.
[edit] Lethal mutations
Some mice have yellow fur, but it is impossible to produce a true-breeding line of yellow mice. Instead, for however many generations you go on breeding yellow mice together, while discarding brown mice from the gene pool, you will, keep finding two-thirds yellow mice and one-third brown mice in each generation.
At first, this seems inexplicable in terms of Mendel's rules. However, there is an explanation. Suppose we have a fur color gene with two alleles, Y and y, so that a mouse with a yy genotype has brown fur, a mouse with a Yy genotype has brown fur, and a mouse with a YY genotype never develops, because two copies of the allele are fatal to embyrological development. We can test this by crossing yellow mice with a true-breeding line of brown mice: this explanation predicts that the resulting mice will be 50:50 brown and yellow, as turns out to be the case.
Similar patterns of inheritance are seen in the allele in Manx cats that makes them tailless, and in the allele for achondroplasia, the most common genetic cause of dwarfism in humans.
[edit] One character, one gene?
In Mendel's experiments, each gene controlled a different character. This need not be the case. The color of budgerigars, for example, comes in four colours: green, blue, yellow and white. The table below shows the results of crossing true-breeding lines of green, blue, yellow and white budgies.
| Green | Blue | Yellow | White | |
| Green | green | green | green | green |
| Blue | green | blue | green | blue |
| Yellow | green | green | yellow | yellow |
| White | green | blue | yellow | white |
If this was the result of one gene having four alleles, then breeding blue and yellow budgies wouldn't produce green ones. Or suppose that it was the result of three alleles (blue, yellow, and white) of one gene, such that the blue and yellow alleles exhibited incomplete dominance, producing green budgies. But in that case, there would be no such thing as a true-breeding line of green budgies.
No, the only way to make sense of this data is that there are two genes controlling color: there is a yellow-or-not gene, which comes in two alleles, yellow (Y) and no yellow (y), with Y dominant to y; and a blue-or-not gene with two alleles: blue (B) and no blue (b) with B dominant to b. A bird having both a B allele and a Y allele will therefore be green (since blue and yellow make green). The reader may check that all the data in the table above on crosses of true-breeding lines is consistent with this theory.
This might seem to go against Mendel's original idea of "one gene, one character", but we can restore this notion by regarding the characters in question as being, not feather color; but rather the production (or not) of blue pigment, and the production (or not) of yellow pigment. As we shall see in our article on DNA, the slogan "one gene, one polypeptide" would be an accurate modern formulation of the principle.
[edit] Influence of the environment
A trait, as we have defined it, is a heritable variation in a character. However, not all such variations are heritable. A hydrangea, for example, will grow blue flowers in acidic soil and pink flowers in alkaline soil. This presents no real problem for classical genetics, since it is easy to determine experimentally which traits are or aren't heritable.
[edit] Beyond classical genetics
The classical theory of genetics deals with alleles as abstract bits of information which determine traits as though by magic. For many purposes this is quite sufficient: however, there are also many aspects of heredity that can best be understood by studying the underlying details of inheritance.
For this reason, we direct the reader to the article on the chromosome theory of inheritance.
