Objectives

1. To understand the Principles of Segregation and Independent Assortment.

2. To understand how Mendel’s principles can explain transmission of characters from one generation to the next.

3. To understand and use the χ2 goodness-of-fit statistical test to evaluate hypotheses about mechanisms of inheritance.

I. Background

Much of our understanding of genetics today is taken for granted, as the use of DNA has become common in forensics and medicine. However, compared to many fields in biology, genetics is relatively young. Mendel’s “Laws” of inheritance were rediscovered in the early 1900s, and Watson and Crick described the structure of DNA only about fifty years ago (if you are interested in exploring the history of genetics, you can find a list of good web sites at http://dmoz.org/Science/Biology/Genetics/History/)

People have always been interested in explaining how traits were passed from one generation to the next. In the 19th century, the leading hypothesis of heritability was that offspring resembled their parents because parental traits blended. A prediction of this hypothesis is that offspring of a cross of purple-flowered and white-flowered peas will have pale purple flowers. We can sum up their position and the outcome of Mendel’s experiments in the following table:

OBSERVATION / The characters of the offspring appear to be a blend of the parental traits.
QUESTION / How are traits inherited?
HYPOTHESIS / PREDICTION / Blending of heritable information from both parents produces offspring with intermediate traits.
EXPERIMENT(S) / Mendel’s pea experiments.
Data: The offspring from certain crosses, such as purple x white-flowered peas, resemble only one parent, not a blend.
EVALUATION/ DRAW INFERENCES / The data do not support the hypothesis. Mendel proposed alternative models.

Mendel conducted these breeding experiments over and over again, with different traits; all of them with two phenotypes, and from his results developed his “laws” of segregation and independent assortment. We place Mendel’s experiments into our structure for the scientific method in the following table:

OBSERVATION / Pea flower colour is either white or purple, but never a blend.
QUESTION / If blending does not explain how traits are inherited, then how are traits inherited?
HYPOTHESIS / PREDICTION / Some “particle” determining flower color is passed intact from parent to offspring (Mendel did not coin the term “gene”). Prediction: the “particle” determining white color is still present in the offspring, but its expression is masked.
EXPERIMENT / Cross the offspring resulting from purple x white crosses (F1), and see if some “grand-offspring” (F2) are white .
Data: about 25% of the F2 are white, the remainder are purple
EVALUATE/DRAW INFERENCES / The data support the hypothesis. Mendel predicted (and then experimentally confirmed) that about 2/3 of the purple F2 would carry the “white” particle (i.e. had both a purple and a white particle), and that other characteristics such as pea color and plant height would show similar patterns of inheritance.

We can put this experiment into the context of modern genetics by using modern terminology. In the parental generation (P), plants are true-breeding: for the trait of interest such as flower color, crosses within the true-breeding group always produce offspring that resemble the parents. This is because the parents are homozygous (identical alleles) for either the purple or white color. When Mendel crossed the true-breeding purple and white flowers, he always obtained plants, the F1 generation, with purple flowers, but the allele for “white” is not lost: we refer to these individuals as heterozygous. When he then crossed two F1 heterozygotes and determined the flower color of the F2, he found 705 individuals with purple flowers and 224 individuals with white flowers. He referred to this as “Segregation” because he stated that the particle for white color segregated (separated) from the particle for purple color. He further proposed that these two “particles” are alternative states (alleles) for the same character (“gene”). In modern terms; these two states are two different alleles for the same gene, where we define a gene (or genetic locus) as a specific section of a chromosome coding for a particular protein. Different alleles of one genetic locus, code for different versions of the same protein.

II. The monohybrid cross

The experiment described above is a monohybrid cross: the true-breeding parents are homozygous for different flower colors, and the F1 are hybrids for that one trait. Our understanding of meiosis provides a mechanistic explanation for the pattern of segregation in monohybrid crosses. In meiosis, when the gametes are being formed, each gamete only gets one copy of each chromosome (one member of each chromosome “pair”). In the F1 plants, each gamete will either get the allele for purple or the allele for white flower color: no gametes can have both alleles because these alleles are on each of the homologous (paired) chromosomes.

One gamete from one parent combines with one gamete from the other parent, but which gamete combines with which (i.e., purple with purple or with white) is random. For each gamete type (purple or white) from one parent, there is a 50:50 chance it will combine with either white or purple from the other parent. This will produce, in the F2 generation, purple/purple: purple/white (or white/purple): white/white genotypes in a 1:2:1 ratio. Since the purple allele “masks” or is dominant to the white allele, the phenotypes of the F2 generation will be 3 purple: 1 white.

Female (genotype Ww) / This is represented here in a Punnett Square. P represents the allele for the dominant purple flower trait and p represents the allele for the recessive white flower trait.
Male
(genotype Ww) / gamete genotypes / P p
P / PP / Pp
p / Pp / pp

III. Dihybrid cross.

Mendel also conducted experiments where he crossed true-breed plants that differed in two different traits, producing F1 offspring that were hybrids at two genetic loci, or dihybrids. Now it can be imagined that two traits affecting the same structure, pea color and shape for instance, might move jointly to the next generation: if the original homozygous parents have smooth, yellow peas then all descendents with smooth peas will have yellow peas. The alternative hypothesis is that the traits are separate, and that the inheritance of pea color will be independent of the inheritance of pea shape. These two alternative hypotheses can be put into our table of the scientific method, and a single experiment can test both of them:

Observation / Peas display four different phenotypes with respect to their seed characteristics: for color yellow or green, for shape smooth or wrinkled
Question / Does the inheritance of one trait (shape) influence the inheritance of another trait (color)?
Hypothesis 1,
Prediction 1 / Yes: if the original pea parents have either smooth and yellow peas or green and wrinkled peas, all the F2 offspring will have one of these combinations.
Hypothesis 2,
Prediction 2 / No: no matter what combination of traits the original parents have, all possible combinations will be found in the F2 generation.
Experiment / Cross true-breeding plants then cross the F1 offspring. Rear the resultant F2 plants and determine the frequencies of the different combinations of traits.
Data: in the F2, all possible combinations of traits are found.
Evaluation,
Inferences / Hypothesis 1 is rejected; there is no “linkage” of the two different traits as they are passed from generation to generation.

In modern terminology, the inference drawn from this result is that the two genetic loci, pea color and pea shape, are not “linked”. The predicted genotype and phenotype distribution in offspring of a dihybrid cross using unlinked genetic loci can be calculated in two fashions. First, you can do a 4 x 4 Punnett square (you should finish filling in all possible genotypes):

Female: WwYy
Male:
WwYy / gametes: / WY / Wy / wY / wy
WY / WWYY / WWYy / WwYY / WwYy
Wy / WWYy
wY / WwYY
wy / WwYy

Since W- is always round and Y- is always green, we can determine the phenotypes of these offspring, and find a 9:3:3:1 ratio for W-Y- : wwY- : W-yy : wwyy.

A second, and much quicker, way to predict phenotype frequencies is to recall that in a monohybrid cross, 3/4 of the offspring will have the dominant phenotype and 1/4 will have the recessive phenotype. To estimate how many offspring from a dihybrid cross will have, for instance, the phenotype “round green” (W-Y-) you simply multiply the proportion of W- by the proportion of Y-, or 3/4 x 3/4 = 9/16. Similarly, 1/4 x 3/4 = 3/16 will have the phenotype “wrinkled green” (wwY-). This approach has the benefit that it is easily expanded to many more genetic loci, when Punnett’s squares become awkward or impossible to draw (one needs an additional dimension for every additional genetic locus!)

It is important to note that not all genetic loci assort independently. If two genetic loci are relatively close together on the same chromosome, they will not move independently into the gametes and hence will appear “linked” in experimental crosses.

Again, we can look to our understanding of meiosis for a mechanistic explanation of independent assortment. Remember that, during meiosis, homologous chromosomes pair along the center of the cell during metaphase I. When they are lined up, however, the orientation of each pair of chromosomes is independent of the orientation of every other pair. In other words, there is equal chance that the w-carrying chromosome will be aligned with the y-carrying chromosome or with the Y-carrying chromosome.
Assigning letters to each allele (W:round, w:wrinkled, Y: green, y: yellow), we can diagram these possibilities in a drawing of metaphase I.

IV. Today’s Lab with Corn.

Corn Genetics: Kernel color and sugar content

Ears of corn are good study systems for learning about genetics, because each kernel represents an independent union of gametes, and thus a cob has a population of genetically unique kernels. The cobs you will be studying are variable for two traits of interest, color and sugar content. You can detect sugar content differences because high-sugar kernels are wrinkled and low-sugar kernels are smooth. Each of these characteristics is determined by a single gene, with two alleles.

There are four kernel phenotypes in the above ear of corn: Purple & Smooth (A), Purple & Wrinkled (B), Yellow & Smooth (C) and Yellow & Wrinkled (D).

For your experiments today, you will use what you have learned about the principles of segregation and independent assortment to infer the mechanisms of inheritance for color and sugar content in corn. You will collect data to test four hypotheses concerning these traits by sampling kernels on the cob. Finally, you will evaluate your hypotheses by comparing your data with your predicted results using the c2 statistical test (Chi Square).

Evaluating Hypotheses by Predicting results:

Part of testing hypotheses is to describe what results you would expect to find if your hypothesis is correct. The more exact your predictions are, the easier it is to use your data to test the hypothesis.

Today’s Observation: Individual kernels of corn on a cob vary in color and shape.

Hypotheses and predictions: Below are four hypotheses regarding the inheritance of corn kernel color and shape. Working with your partner and the teaching fellow, develop predictions of what you would observe in the population of corn kernels if the hypothesis is correct. These will be the “working hypotheses” guiding your experiments.

Hyp. 1. The genes for color and shape assort independently.

Prediction 1

Hyp.2. Purple is dominant to yellow. (or use the reverse)

Prediction 2

Hyp. 3. Sugar is dominant to starch (wrinkled dominant to smooth) (or the reverse)

Prediction 3

Hyp. 4. The corncob you are examining represents the result of a dihybrid cross.

Prediction 4

Analysis of Experimental Results: You will use the χ2 goodness-of-fit test to determine if your observed results are consistent with the predictions made based on Mendel’s principles.

The c2 test allows you to determine whether your results could have happened by chance alone. Typically, the null hypothesis being tested is that the observed results (O) and the expected results (E) are not different (Ho: O = E). The alternative hypothesis is that the observed counts and the expected counts are different (Ha: O ≠ E).

The general equation for the chi-square value for a particular experiment is:

Chi-Square = the sum over all categories for (observed cell counts – expected cell counts)2 /expected cell counts or c2 =

The last ingredient needed for the test is the “degrees of freedom” (df), which is calculated as the number of classes, less one. Here, the “degrees of freedom” are related to the number of categories contained in the characteristic under study. For example if the characteristic under study is the sex ratio of a trait there are two possible classes (male or female) and one degree of freedom. This is the case since one class (e.g. female) is “free” to vary in % of the total, but once its value is known the % of the other class (male) is determined by default (no longer “free”). Likewise if there are three values that make up 100% of the characteristics (such as red, pink and white) there are two degrees of freedom, two could vary but the last will be determined by default, and so on for increasing numbers of classes.