1. Mendelian Genetics –cont’d
Active Lecture PowerPoint® Presentation for Essentials of Genetics Seventh Edition Klug, Cummings, Spencer, Palladino
Chapter 3b
Mendelian Genetics –cont’d
Copyright © 2010 Pearson Education, Inc.

2. Outline Mendel’s Work Rediscovered Laws of Probability Chi-square Test
Pedigrees
Insights and Solutions

3. Johann Gregor Mendel 1856-1863 - Breeding experiments
Presented results at meeting
Paper published, largely unnoticed
Mendel’s work recognized! (Hugo De Vries, Karl Correns & Erich Tschermak)

4. Mendel’s Work Rediscovered
Mendel began his work in 1856 and published in 1867
But the significance of his work was not appreciated until ~35 years later when three other scientists, Hugo de Vries, Karl Correns and Erich Tschermak, tried to study inheritance of traits in plants
De Vries discovered Mendel’s publications

5. Why Mendel’s work not immediately recognized?
Mendel suggested heredity resulted in discontinuous variation
This opposed existing continuous variation hypothesis of his time in which offspring thought to be blend of parental phenotypes
Mendel’s mathematical analysis of probability events was unusual

6. Mendel’s Postulates and Behavior of Chromosomes
In 1902, two cytologists, Walter Sutton and Theodor Boveri independently studied chromosome behavior and linked their work to Mendel’s results
Separation of chromosomes during meiosis could be basis for Mendel's principles of segregation and independent assortment
This gave rise to chromosomal theory of inheritance
They actually thought chromosomes were the Mendel’s units of inheritance, rather than genes on chromosomes.

7. Figure 3-10 Copyright © 2006 Pearson Prentice Hall, Inc.
Three of Mendel's postulates and their basis in chromosomal segregation during meiosis
Independent segregation
(homologous chromosomes)
Figure 3-11 The correlation between the Mendelian postulates of (a) unit factors in pairs, (b) segregation, and (c) independent assortment, and the presence of genes located on homologous chromosomes and their behavior during meiosis.
Independent assortment
(non -homologous chromosomes)
Figure Copyright © 2006 Pearson Prentice Hall, Inc.

8. Independent Assortment and Genetic Variation
A major consequence of independent assortment is production of genetically dissimilar gametes
Genetic variation is very important to the process of evolution
Number of possible gametes: 2n
N= haploid number of chromosomes
For humans 223 = 8 million or 8x 106
For each gamete it is 8x 106. For both male and female gametes, you can multiply the two= 64x1012 (64 Trillion)

9. Laws of Probability and Genetics
Genetic ratios are expressed as probabilities
Eg: 3/4 tall:1/4 dwarf pea plants
Probability that each zygote having the genetic potential to become tall is 3/4th
Probability that each zygote having the genetic potential to become short is 1/4th
Probabilities vary from
Probability of 1.0 means that the outcome is certain.

10. Laws of Probability and Genetics
Consider a second trait: yellow vs. green seeds
Probability that each zygote having the genetic potential to become yellow seed is 3/4th.
Probability that each zygote having the genetic potential to become green seed is 1/4th.
What is the probability that a zygote will have the potential to become tall plants and yellow seeds?
The probability of two or more independent events occurring simultaneously is equal to the products of their individual probabilities.

11. Laws of Probability and Genetics
Product Law:
Used to calculate probability of two independent events occurring at the same time
The probability of both events occurring is product of the probability of each individual event

12. Laws of Probability and Genetics
Sum law:
Used to calculate probability of a generalized outcome that can be accomplished in more than one way
States probability of obtaining any single outcome, where that outcome can be achieved in ≥ 2 events, is equal to sum of individual probabilities of all such events
Do the penny and nickel exercise

13. Chi-Square Analysis (2)
Used to test how well the data fit an expected ratio
Also called “Goodness-of-fit” test
Chance deviation: Probability predictions of possible outcomes are subjected to chance deviation
Chance deviation from an expected outcome is diminished by larger sample size
As the sample size increases, average deviation from the expected results decreases

14. Chi-Square Analysis Null hypothesis (H0)
When we test whether the data will fit a given ratio, we establish what is called the null hypothesis
Null hypothesis so named because it assumes there is no real difference between observed or measured values (or ratio) and expected or predicted values (or ratio). The apparent difference can be attributed purely to chance

15. Chi-Square Analysis Null hypothesis (H0)
The null hypothesis is tested using statistical analysis
Based on the results of statistical analysis, null hypothesis may either be
a. rejected (deviations not due to chance alone)
b. fail to be rejected (deviation from expected ratio is due to chance alone)

16. Formula for Chi-Square Analysis
X2 = ∑ (o-e)2 e
o - observed value for the category
e - expected value for the category
∑ - sum of calculated values for each category
o-e =d (deviation)
X2 = ∑ d2

17. Table 3-3 Copyright © 2006 Pearson Prentice Hall, Inc.
Table 3-3 Chi-Square Analysis
Table Copyright © 2006 Pearson Prentice Hall, Inc.

18. Chi-Square Analysis
Chi-square (2) analysis requires degree of freedom (df) be taken into account, since more deviation is expected with a higher degree of freedom
degree of freedom = n – 1
where n is # of different categories into which each data point may fall

19. Chi-Square Analysis
Once # of degrees of freedom is determined, 2 value can be interpreted in terms of a corresponding probability value (p)
We usually take a p value from standard table or a graph
P value >0.05 justify failure to reject H0
P value ≤ justify rejecting H0
A hypothesis is never proved or disproved; instead a p value is used to either reject or fail to reject the null hypothesis.

20. FIGURE 3-11a
(a) Graph for converting χ2 values to p values. (b) Table of χ2 values for selected values of df and p. χ2 values that lead to a p value of 0.05 or greater (darker blue areas) justify failure to reject the null hypothesis. Values leading to a p value of less than 0.05 (lighter blue areas) justify rejecting the null hypothesis. For example, using the table in part (b), where χ2 = 0.53 for 1 degree of freedom, the corresponding p value is between 0.20 and The graph in (a) gives a more precise p value of 0.48 by interpolation. Thus, we fail to reject the null hypothesis.

21. FIGURE 3-11
(a) Graph for converting χ2 values to p values. (b) Table of χ2 values for selected values of df and p. χ2 values that lead to a p value of 0.05 or greater (darker blue areas) justify failure to reject the null hypothesis. Values leading to a p value of less than 0.05 (lighter blue areas) justify rejecting the null hypothesis. For example, using the table in part (b), where χ2 = 0.53 for 1 degree of freedom, the corresponding p value is between 0.20 and The graph in (a) gives a more precise p value of 0.48 by interpolation. Thus, we fail to reject the null hypothesis.

22. Chi-Square Analysis Table 3.1 Monohybrid cross
H0: The observed 740:260 ratio is not different from the expected 3:1 (750:250) ratio
X2 =0.53 df=1 0.5>P>0.2
Reject or fail to reject the H0?

23. Chi-Square Analysis Table 3.1 Dihybrid cross
H0: The observed 587:197:168:56 ratio is not different from expected 9:3:3:1 (567:189:189:63) ratio
X2=4.16 df=3 p=0.26
Reject or fail to reject the H0?

24. Chi-Square Analysis
Suppose we rejected the H0 based on our X2 calculation
What does it mean to reject H0?
Read page 51
Observed deviation from the expected ratio is not due to chance alone.
The two gene pairs do not assort independently,
or fertilization is not random
and the viability of all gametes are not equal.
Other factors may be involved.

25. Pedigrees A pedigree shows a family tree with respect to a given trait
Pedigree analysis reveals patterns of inheritance

26. Pedigree conventions FIGURE 3-12
Conventions commonly encountered in human pedigrees.

27. In Autosomal recessive trait pedigree (a)
In Autosomal recessive trait pedigree (a). Both I-3 and I-4 have to be heterozygous, not either
FIGURE 3-13
Representative pedigrees for two characteristics, each followed through three generations.

28. FIGURE 3-13b
Representative pedigrees for two characteristics, each followed through three generations.

29. Pedigree Analysis
Pedigree analysis of human traits has been an extremely valuable tool in human genetic studies
TABLE 3.2
Representative Recessive and Dominant Human Traits

30. Dr. Michael C. Ain, a specialist in the repair of bone defects caused by achondroplasia and related disorders.
Figure 9.9B Dr. Michael C. Ain, a specialist in the repair of bone defects caused by achondroplasia and related disorders.
This physician is afflicted with a dominant inherited disease, achondroplasia.

31. Phenotype = albinism
Genotype = a/a

32. Tay-Sachs Disease
Read box in p48

33. OMIM Online Mendelian Inheritance in man
Is a catalog of human genetic disorders inherited in Mendelian manner.

34. Case study Huntingtons Disease
Is a catalog of human genetic disorders inherited in Mendelian manner.

35. Insights and Solutions (pg 55)
Work on your own s.