Lesson #3: Mendel's Peas - part 2
So far we have considered a single gene with two clear cut alternative states - yellow vs green cotyledons in peas. Mendel established that these traits were particulate in nature by observing and counting the number of plants that exhibited each trait in various generations and crosses. However, Mendel also observed that each of his strains of peas had various combinations of traits. Some tall strains of peas might have yellow, wrinkled peas while other tall stains might have green, round peas. Mendel not only kept track of the occurrence of each trait in each generation or cross, but he also kept track of all the traits that each plant had. By crossing a tall, yellow, round strain with a short, green, wrinkled strain Mendel was not only able to study the inheritance of yellow vs green, tall vs short and round vs wrinkled but he also kept records for each seedling as to if it were yellow or green, tall or short and round or wrinkled. For example, the first seedling could be yellow, tall and round while the second seedling would be green, tall and wrinkled; and so on.
In a cross of round, yellow peas with wrinkled, green peas all the F1's were all round and yellow. In the F2 population Mendel observed:
315 round, yellow
If we look at these results we see that there are 416 yellow peas and 108 green peas, for a total of 556. In the F2 generation we expect a 3:1 segregation ratio for dominant:recessive. For 556 plants we would expect to see 417 plants with yellow peas and 139 plants with green peas, which is fairly close to the observed 416 yellow and 140 green. We also expect to see 417 plants with round peas and 139 plants with wrinkled peas. We observe 423 round and 133 wrinkled, which is close to what we expect.
If you look at the number of plants in each group - round and yellow; wrinkled and yellow; round and green; and wrinkled and green you will see that it reduces to a 9:3:3:1 ratio with the double dominants (round and yellow) being the most common and the double recessive (wrinkled and green) being the least common. This is called a dihybrid ratio. The results that Mendel observed were best explained by the independent segregation of the genes for each of these traits. That is, yellow vs green cotyledons is inherited separately from round vs wrinkled peas.
To understand this, we need to look at the gametes that are formed. The F1 hybrid is genotype YyRr. When we looked at the gametes formed by the segregation of a single gene we saw that the eggs and pollen each could only produce two different types of gametes - the gametes either carried the dominant allele or the recessive allele. However, we are now considering two genes, each segregating independently of each other. If we first consider only the yellow (Y) vs the green (y) allele we see that a gamete can be either Y or y. If we now consider the round (R) vs the wrinkled (r) trait, each gamete can be either R or r. However, each gamete that is Y can also be either R or r, and each gamete that is R can also be either Y or y. Thus, instead of having to deal with only two different possibilities for the egg and pollen we now have to consider four possible gametes for each of the egg and pollens that can unite.
That is, a egg cell can either be genotype YR, Yr, yR or yr and the same for the pollen. We don't know which egg is going to fuse with which pollen to produce a embryo. Thus, we need to consider all the possibilities. (POLLEN across the top and EGG CELL down the left side of this table).
Each time a egg fuses with a sperm cell from the pollen it has the possibility of being one of these 16 combinations. To simplify this chart we can use some Mendelian shorthand when a trait is either dominant or recessive. A plant that is genotype YY produces yellow peas just as does plants that are Yy, so when we are concerned with the appearance of the plants we really don't need to know if a plant is either YY or Yy, because both are yellow. We represent this by writing Y_, where the underscore can be either Y or y.
We can simplify the above chart as follows (leaving off the gametes):
We are now interested in combining those genotypes that produce the same phenotype. There are 9 possibilities that the resulting embryo will have phenotype Y_R_ (yellow and round); 3 possibilities for Y_rr (yellow and wrinkled); 3 possibilities for yyR_ (green and round) and one possibility for yyrr (green and wrinkled). Of the 556 plants we would expect 313 yellow and round; 104 yellow and wrinkled; 104 green and round and 35 green and wrinkled. The observed results were 315:101:108:32, which is very close to the expected results.
The example of two traits segregating independently can easily be expanded to three or more traits, but the results become much more complex. If we have three traits segregating then each pollen or egg can have 8 possible combinations. The hypothetical F1 AaBbEe will produce gametes ABE, Abe, AbE, Abe, aBE, aBe, abE and abe. I leave it up to the reader to work out the 64 possible combinations. If there are 4 traits then there are 16 possible gametes and 256 possible resulting embryos. As we can see, it doesn't take too many traits to make the results unmanageable. The number of possible gametes is 2 to the n-th power where n is the number of traits segregating. The number of possible embryos is 2^n times 2^n (2^n is the same as saying 2 to the n-th power).
Although all of this makes it appear difficult to figure out just what the possibility for a particular phenotype may be, it is actually easier than it looks. When we are dealing with traits that are inherited independently, all we have to do is multiply the frequency for each phenotype we are interested in.
Lets take the case of crossing a true breeding strain of yellow, round tall peas with green, wrinkled short peas where the the F1's are yellow, round and tall. If we looked only at yellow vs green we see in the F2 generation 3/4 of the plants will be yellow peas. If we look at only round vs wrinkled we see in the F2 generation 3/4 of the plants will have round peas. If we look at only tall vs short plants in the F2 3/4 will be tall. Now, how many of the F2 plants from this example will be yellow, round and tall? The answer is 3/4 X 3/4 X 3/4 or 27/64. How many will be yellow, wrinkled and short? The answer is 3/4 X 1/4 X 1/4 or 3/64. How many will be green, round and tall? The answer is 1/4 X 3/4 X 3/4 or 9/64.
So far we have consider that genes are inherited independently of each other. Mendel came to this conclusion because, as it turns out, each of the 7 traits he worked with were on separate chromosomes. However, each chromosome has many genes and as it turns out genes that are close to each other on the chromosomes are not inherited independently. We will cover this in more detail later.
We have also only consider genes where there was a clear cut dominant - recessive relationship between the alleles and where the genes acted independently of each other. As we will see later on, genes don't always have a clear dominant - recessive relationship and when we look at particular traits we may discover that many genes are involved. Although these conditions can confuse and make things complex, we will also see that many of these complex situations can be simplified to more understandable examples.