1. Completion and analysis of Punnett squares for dihybrid traits
10.2 Inheritance
Understanding:
Unlinked genes segregate independently as a result of meiosis
Gene loci are said to be linked if on the same chromosome
Variation can be discrete or continuous
The phenotypes of polygenic characteristics tend to show continuous variation
Chi-squared tests are used to determine whether the difference between an observed and expected frequency distribution is statistically significant
Applications:
Completion and analysis of Punnett squares for dihybrid traits
Morgan’s discovery of non-Mendelian ratios in Drosophila
Polygenic traits such as human height may also be influenced by environmental factors
Nature of science:
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-Mendelain ratios in his experiments with Drosophila
Skills:
Calculation of the predicted genotypic and phenotypic ratio of offspring of dihybrid crosses involving unlinked autosomal genes
Identification of recombinants in crosses involving two linked genes
Use of a chi-squared test on data from dihybrid crosses

2. Key words Locus: Location of a gene on a chromosome
Homologous chromosome: Two chromosomes with same sequence of genes
Alleles: Different forms of same gene on different chromosomes
Segregation: Separation of two alleles of every gene (in meiosis – chromosomes separate)
Independent Assortment: Alleles for one trait segregate independently from alleles for another trait

3. Linked or Unlinked? Unlinked genes Found on different chromosomes
Segregate independently
Linked genes
On the same chromosome
Do not segregate independently (unless crossed over)
Autosomal linked = on a non-sex chromosome
Sex linked = on an X or Y chromosome
Understanding:
Unlinked genes segregate independently as a result of meiosis
Gene loci are said to be linked if on the same chromosome

6. Variation: Discrete or continuous
Categories = discrete/discontinuous
E.g blood types
AB B A O
Nothing in between
Monogenic inheritance (single gene)
Understanding:
Variation can be discrete or continuous

7. Polygenic inheritance (two or more genes involved)
Variation
Continuous = Complete range in variation
Usually creates a ‘normal’ distribution
Polygenic inheritance (two or more genes involved)
Understanding:
Variation can be discrete or continuous

8. We have looked at Mendel’s tests on peas previously
Morgan’s Tests
We have looked at Mendel’s tests on peas previously
Dihybrid cross
Yellow/Green
Wrinkled/Smooth
Skills:
Calculation of the predicted genotypic and phenotypic ratio of offspring of dihybrid crosses involving unlinked autosomal genes
Understanding:
Variation can be discrete or continuous

9. RY Ry rY ry

10. RY Ry rY
RRYY
RRYy
RrYY
RrYy
RRyy
Rryy
rrYY
rrYy
rryy

11. This is the typical ratio expected in a dihybrid cross.F2 : : : 9 3 3 1
Round
Yellow
Round
Green
Wrinkled
Yellow
Wrinkled
Green
This is the typical ratio expected in a dihybrid cross.

12. Using fruit flies (Drosophila) he crossed red eye and white eye flies
Morgan’s Tests
Thomas Hunt Morgan found some examples to contradict Mendel’s results from his Dihybrid crosses.
Using fruit flies (Drosophila) he crossed red eye and white eye flies
What did he find out?
Nature of science:
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-Mendelain ratios in his experiments with Drosophila
Applications:
Completion and analysis of Punnett squares for dihybrid traits
Morgan’s discovery of non-Mendelian ratios in Drosophila

13. Morgan’s Tests Some traits do not independently assort
Sex-linked genes (Morgan called them ‘sex-limited’)
In this case on the X chromosome
Could become uncoupled by crossing over – but low frequency
Nature of science:
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-Mendelain ratios in his experiments with Drosophila
Applications:
Completion and analysis of Punnett squares for dihybrid traits
Morgan’s discovery of non-Mendelian ratios in Drosophila

14. Complete your work sheet as we go through the example
Chi Squared
Determine whether the difference between an observed and expected frequency distribution is statistically significant
Complete your work sheet as we go through the example
Understanding:
Chi-squared tests are used to determine whether the difference between an observed and expected frequency distribution is statistically significant
Skills:
Use of a chi-squared test on data from dihybrid crosses

15. No independent assortment = no variation
Before we begin…
Independent assortment states that when gametes are produced the segregation of one pair of alleles is independent of the segregation of another pair of alleles.
When homologous chromosomes separate during meiosis I, it is random which pole each chromosome travels to, therefore random which pole the alleles go to
(random orientation)
You can have any combination of alleles (RRYY, RrYY, RRYy, rrYY…) therefore you would expect variation.
No independent assortment = no variation
Skills:
Use of a chi-squared test on data from dihybrid crosses

17. Chi Squared White leghorn chickens with large single combs
Crossed with
Indian game fowl with dark feathers and small pea combs
Ho = the traits are assorted independently (no association)
H1 = the traits do not assort independently (is an association)
Skills:
Use of a chi-squared test on data from dihybrid crosses

18. Chi Squared
All of the F1 generation were white chickens with pea combs
F2 generation was different from the 9:3:3:1 ratio normally expected.
Were these differences statistically significant, random or due to sampling error?
Skills:
Use of a chi-squared test on data from dihybrid crosses

19. Start with a contingency table
Fill in your contingency table with the observed frequencies for F2 generation
White pea
White single
Dark pea
Dark single
Total
Observed
111 37 34 8
190
Expected
Skills:
Use of a chi-squared test on data from dihybrid crosses

20. Expected Values
Expected values calculated using expected probability from Punnett grids, multiplied by actual total
Complete the expected values using what you would expect the ratio to be
(remember 9:3:3:1 when doing di-hybrid crosses)
Then use the total number as already stated
Expected = row total x column total
grand total
White pea
White single
Dark pea
Dark single
Total
Observed
111 37 34 8
190
Expected
(9/16) x 190
(3/16) x 190
(1/16) x 190
Skills:
Use of a chi-squared test on data from dihybrid crosses

21. Then use the total number as already stated
Expected Values
Complete the expected values using what you would expect the ratio to be (remember 9:3:3:1 when doing di-hybrid crosses)
Then use the total number as already stated
White pea
White single
Dark pea
Dark single
Total
Observed
111 37 34 8
190
Expected
106.9
35.6
11.9
Skills:
Use of a chi-squared test on data from dihybrid crosses

22. Degrees of Freedom One less than the total number of outcomes
White pea
White single
Dark pea
Dark single
Total
Observed
111 37 34 8
190
Expected
106.9
35.6
11.9
Skills:
Use of a chi-squared test on data from dihybrid crosses

23. Remember to use a significance level of 0.05 (5%)
Critical Region
Use the critical values table to find the critical region for your chi-squared test
Remember to use a significance level of 0.05 (5%)
Critical value: 7.815
Skills:
Use of a chi-squared test on data from dihybrid crosses

24. Remember to use a significance level of 0.05 (5%)
Critical Region
Use the critical values table to find the critical region for your chi-squared test
Remember to use a significance level of 0.05 (5%)
Critical value: 7.815
Skills:
Use of a chi-squared test on data from dihybrid crosses

25. Σ (O – E)2 E (O – E)2 E (O – E)2 E (O – E)2 E (O – E)2 E
Chi Squared Test
χ2 =
(O – E)2 E Σ
(O – E)2 E
(O – E)2 E
(O – E)2 E
(O – E)2 E

26. Chi Squared Test χ2 = (O – E)2 E Σ (111-106.9)2 106.9 (37-35.6)2 35.6
χ2 =
(O – E)2 E Σ
( )2
106.9
( )2
35.6
( )2
35.6
(8-11.9)2
11.9

27. Chi Squared Value
Chi squared = 1.56

28. Which Hypothesis? Chi squared = 1.56 Critical region = 7.815
Compare calculated chi squared value to critical region
Higher than critical region = reject null hypothesis
(the traits do not assort independently)
Equal to or lower than critical region = keep null hypothesis
Ho = the traits are assorted independently
There is no association between the alleles
95% sure.
Results are statistically significant

29. Remember
Independent assortment states that when gametes are produced the segregation of one pair of alleles is independent of the segregation of another pair of alleles.
Due to crossing over and random orientation
When homologous chromosomes separate during meiosis I, it is random which pole each chromosome travels to.
(This is what you just proved in your chi squared test!)
Variation = independent assortment
Results are statistically significant