UNIT ____:  More Complex Genetics                  Name:  _____________________

Essential Idea(s):  Genes may be linked or unlinked and are inherited accordingly.

IB Assessment Statements and Class Objectives

10.2.A1:  Completion and analysis of Punnett squares for dihybrid traits.

PROBLEM:  In flowering plants, flower color is coded for by one gene and plant height is coded for by another gene on a different chromosome.  White flowers (F) are dominant over red (f) and short plants (E) are dominant over tall (e).  Two double heterozygote plants were crossed.

• Determine possible allele combinations in gametes for crosses involving two genes.
• Use correct notation to depict a dihybrid cross between two unlinked genes.
• Construct a Punnett square to show the possible genotype and phenotype outcomes in a dihybrid cross.

10.2.S1:  Calculation of the predicted genotypic and phenotypic ratio of offspring of dihybrid crosses involving unlinked autosomal genes.

PROBLEM: In flowering plants, flower color is coded for by one gene and plant height is coded for by another gene on a different chromosome.  White flowers (F) are dominant over red (f) and short plants (E) are dominant over tall (e).  A true breeding short white plant is crossed with a true breeding tall red plant. These plants represent the parental generation.

• Determine the predicted genotype and phenotype ratios of F1 and F2 offspring of dihybrid crosses.

10.2.S3:  Use of chi-squared test on data from dihybrid crosses.

PROBLEM:  In flowering plants, flower color is coded for by one gene and plant height is coded for by another gene on a different chromosome.  White flowers (F) are dominant over red (f) and short plants (E) are dominant over tall (e).  Two double heterozygote plants were crossed (as in 10.2.A1) and the following resulting phenotypes were observed:

        White, short:  206

        Red, short:  83

        White, tall:  65

        Red, tall:  30

• Calculate a chi-square value to compare observed and expected results of a dihybrid genetic cross.
• Using the df and critical chi-square value, determine if there is a significant difference between observed and expected results of a dihybrid cross.

3.4.S2:  Comparison of predicted and actual outcomes of genetic crosses using real data.

PROBLEM:  In cats, fur color is determined by the codominant, sex linked alleles black (XB) and orange (XO).  A calico female (mix of black and orange) is bred (many times) with a black male.  They produce the following offspring:

        Black female:  78

        Calico female:  65

        Black male: 81

        Orange male:  45

• Explain the reason why the outcomes of genetic crosses do not usually correspond exactly with the predicted outcomes.
• Describe the role of statistical tests in deciding whether an actual result is a close fit to a predicted result.   

10.2.U5:  Chi-squared tests are used to determine whether the difference between an observed and expected frequency distribution is statistically significant.

PROBLEM:  Color blindness is a sex-linked trait in Bombats.  A female who is a carrier of the color blind allele mates with a male who is color blind.  The phenotypes of the offspring are:        

Normal female:  132

        Color blind female:  124

        Normal male: 126

        Color blind male:  136

• State the two possible hypotheses of a statistical test.
• Calculate the chi square value to determine the significance of differences between the observed and expected results of a genetic cross.
• Determine the degrees of freedom and critical value for the chi-square test.
• Draw a conclusion of significance by comparing the calculated and critical chi-square values.

10.1.NOS:  Making careful observations- careful observations and record keeping turned up anomalous data that Mendel’s law of independent assortment could not account for. Thomas Hunt Morgan developed the notion of linked genes to account for the anomalies.

• Describe the experiment of Bateson and Punnett that led to results that did not support Mendel’s law of independent assortment.
• Describe the trends and discrepancies that led Morgan to propose the idea of linked genes.

10.2.NOS:  Looking for patterns, trends and discrepancies- Mendel used observations of the natural world to find and explain patterns and trends.  Since then, scientists have looked for discrepancies and asked questions based on further observations to show exceptions to the rules.  For example, Morgan discovered non-Mendelian ratios in his experiments with Drosophila.

AND

10.2.A2:  Morgan's discovery of non-Mendelian ratios in Drosophila.

• Describe the trends and discrepancies that led Morgan to propose the idea of linked genes.

10.2.U2:  Gene loci are said to be linked if on the same chromosome (Oxford Biology Course Companion page 448).

• Define autosome and sex chromosome.
• Describe what makes genes “linked.”

10.2.S2:  Identification of recombinants in crosses involving two linked genes.

PROBLEM:  The genes for pollen shape and flower color are located on the same chromosome as each other, thus are inherited together.   Purple (P) and long pollen (L) are dominant to red (p) and round pollen (l).  What are the possible genotypes and phenotypes of the F1 offspring if the parents are PPLL × ppll?  If two F1 plants are crossed, calculate the genotypes and phenotypes in the F2 generation (without crossing over).  Calculate the relative genotypes and phenotypes in the F2 generation with crossing over in the F1.

• Use correct notation to show alleles of linked genes.
• Construct a Punnett square to show the possible genotype and phenotype outcomes in a dihybrid cross involving linked genes.
• Explain how crossing over between linked genes can lead to genetic recombinants.

10.2.U4:  The phenotypes of polygenic characteristics tend to show continuous variation.

• Explain polygenic inheritance using an example of a two gene cross with codominant alleles.
• State that a normal distribution of variation is often the result of polygenic inheritance.
• State two example human characteristics that are associated with polygenic inheritance.

10.2.A3:  Polygenic traits such as human height may be influenced by environmental factors.

• Outline two example environmental factors that can influence phenotypes.
• Compare continuous to discrete variation.

Linked vs Unlinked Genes

In this unit, we will examine the simultaneous inheritance of two (or more) genes.  The genes we examine can be “unlinked” or “linked.”

Unlinked Genes follow Mendel’s Law of Independent Assortment: 

The amazing                                   did these experiments too (yes, he used peas).  We’ll examine one of his experiments closely.

Let’s look at two genes:  one for seed                                 and one for seed                                    .

Each of the genes has                                                                  (versions of the gene):

• R and r controlling for ____________________________.                                                         

• Y and y controlling for  ______________________________                                                     

The genotype for pure breeding round yellow is written as RRYY while pure breeding wrinkled green is written as rryy.  

Only ________________________________________________________________________ (because of the  ____________________________________________), so the gametes for the pure breeding round yellow must be                         and for the pure breeding wrinkled green                        .  

When the pure breeding smooth yellow RRYY are crossed with the pure breeding wrinkled green rryy, all the _______________________________________________ and have the genotype ________________.

Then the _______________  plants were crossed (_______________  x  _______________ )

 There are four possible gametes created from a RrYy plant

The potential combinations of gametes of a RrYy x RrYy cross can be shown in a 16 square Punnett square:

The results in the F2 generation show a ______________________ ratio of phenotypes

• 9
• 3
• 3
• 1

New combinations of traits different from those shown in the parent line are called ___________________.

In the RrYy x RrYy the parents were round and yellow.  So, the recombinant offspring would be the ones that are:  

Chi Square Goodness of Fit        (X2)                        

Pronounced “kai square”

1. Scientists use a statistical test called Chi Square (X2) Goodness of Fit to determine if there is significant difference between observed results and expected results.  The test is often used in genetics to determine if the actual offspring in a mating match the expected offspring as determined by a Punnett Square.

2. Remember, SIGNIFICANT in statistics means:

3. X2 tests the NULL HYPOTHESIS.  

The null hypothesis predicts that there will be no real significant difference between our observed results and the expected results.  In other words, any observed variation between what we expect and what we actually observe is due to chance alone.

4. When there is a true significant difference, we would call this our ALTERNATIVE HYPOTHESIS:  Something more than chance is causing a difference between the observed results and the expected results.  

5. The first step in the calculation of an X2 value is to determine the expected numbers and actual, observed numbers for each category.

Chi Square Calculation Table

6. Then, use the following formula for each category, where O is observed and E is expected:

(O – E)2

E

7. The results are added together to get a final calculated X2 value.  

8. The calculated X2 value is then compared to the “critical value X2” found in an X2 distribution table.  The X2 distribution table represents a theoretical curve of expected results.  The expected results are based on DEGREES OF FREEDOM.  

Degrees of Freedom =

9. The X2 distribution table is organized by the Level of Significance.  The level of significance is the maximum tolerable probability of accepting a false null hypothesis.  We use 0.05.  This means that we would accept the null hypothesis if the observed results were within 5% of the expected results.  

Critical X2 value =

10. Using our calculated and critical X2 values, we can draw a conclusion of significance:

• If the calculated value is lower than the 5% level of significance, accept the null hypothesis.

• If the calculated value is higher than the 5% level of significance, reject the null hypothesis.  

“The X2 obtained was __________. The critical value X2 (found in the distribution table) was ________.  The calculated value is ____________ (lower or higher) than the 5% level of significance, so we can _____________ (accept or reject) the null hypothesis.  This means that …………………”

Variation

Polygenic Inheritance

Definition:

Example:

Linked Genes DO NOT follow Mendel’s Law of Independent Assortment 

William Bateson and Reginald Punnett conducted a cross in sweet pea involving two different traits; flower color and pollen shape.  

Conclusion:  Crosses produced deviations from the predicted Mendelian Independent Assortment ratios. They suggested that the transmission of the two traits from the parents was somehow coupled.

Thomas Hunt Morgan’s Discovery of Linked Genes

Thomas Hunt Morgan designed a series of experiments using fruit flies (Drosophila melanogaster) that:

• Reinforced Mendel’s principle of Independent Assortment for some traits (observed ratios in offspring as expected by Punnett Square crosses)

• Identified exceptions to Mendel’s principle of Independent Assortment for other traits (observed ratios in offspring that did not match what was expected by Punnett Square crosses).

• Through a series of experiments, Morgan was able to show that some traits are inherited together (for example fruit fly eye color and sex).  He discovered LINKED GENES

• Because they are linked, linked genes ___________________________________________________________

BIG IDEA…

Thomas Hunt Morgan’s Crosses

Linkage is the tendency for a group of genes, on the same chromosome, to be inherited together

Example:

When the genes are linked, the possible games from a heterozygous individual are _______ and _______.  Therefore, if you cross two parents, both heterozygous for two genes AND THE GENES ARE LINKED, the Punnett Square looks like:

What if crossing over occurs between LINKED GENES during meiosis?

Example Problem:

Cross F1 X F1

Identify recombinants in the F2 generation