1. Math in Genetics
Making Suby Proud

2. Probability
Ex: What is the probability parents will have a boy?

3. Probability
Ex: What is the probability parents will have three children & all will be boys?
Rule of multiplication: 1/2 x 1/2 x 1/2 = 1/8

4. Ex: rule of multiplication
Parent 1 genotype: AABbCc
Parent 2 genotype: AaBbCc
What is the probability the offspring will be: AaBbcc A a B b C c

5. Ex: rule of multiplication
Parent 1 genotype: AABbCc
Parent 2 genotype: AaBbCc
What is the probability the offspring will be: AaBbcc A AA a Aa B b BB Bb bb C c CC Cc cc

6. Ex: rule of multiplication
Parent 1 genotype: AABbCc
Parent 2 genotype: AaBbCc
What is the probability the offspring will be: AaBbcc
½ X ½ X ¼ = 1/16 A AA a Aa B b BB Bb bb C c CC Cc cc

7. Probability
Ex: If there are 4 aces and 4 kings in a deck of 52 cards, what is the probability of getting dealt an ace or a king?
Rule of addition
4/52 + 4/52 = 8/52

8. Probability of height
T = Tall t= Short Parents Tt X Tt T t T t

9. Expected results TT Tt tt
T = Tall ¾ = Tall t= Short ¼ = short Parents Tt X Tt T t T t TT Tt tt

10. Probability of height and shape
T = tall R = round t = short r = square Parents: TtRr X TtRr TR Tr tR tr TR Tr tR tr

11. Expected results TTRR TTRr TtRR TtRr TTrr Ttrr ttRR ttRr ttrr
T = tall R = round t = short r = square Parents: TtRr X TtRr TR Tr tR tr TR Tr tR tr
TTRR
TTRr
TtRR
TtRr
TTrr
Ttrr
ttRR
ttRr
ttrr

12. Expected Results 9/16 = Tall and round 3/16 = Tall and square
3/16 = Short and Round
1/16 = Short and square

13. Mendel rarely saw perfect ratios
Mendel Results:
910 = Tall and round
310 = Tall and square
290 = Short and Round are these results reliable?
90 = Short and square
Do these numbers follow mendel’s rule?

14. What about these results?
850 = Tall and round
349 = Tall and square
252 = Short and Round
149 = Short and square
peas are awesome

15. Chi-square Test
How can we decide if data fits any of the Mendelian ratios?
Chi-Square or Goodness of Fit test

16. chi-square Formula Χ = chi ∑ = sum Obs = the number observed results
Exp = the number of expected results

17. Example An exp. produces 290 purple &110 white flowers
What might be the key for this problem?
PP – purple
Pp – purple
pp – white
What might be the parents genotypes?
Pp X Pp
Based upon this info what results would you expect?
300 purple & 100 white

18. Example Therefore: Plug & chug: What does this number mean?
Purple: obs = 290 & exp = 300
White: obs = 110 & exp = 100
Plug & chug:
2 = ( )2 / ( )2 / 100
2 = 1.333
What does this number mean?

19. qualifications Reasonable: Degrees of Freedom: Critical Value:
A result does not differ significantly from expectations if it could happen at least 1 time in 20.
P = 1/20 = 0.05
Degrees of Freedom:
the number of independent variables (total groups -1)
df = 2 (purp. & white) – 1 = 1
Critical Value:
The number given by 2

20. Critical Chi-Square “reject the null hypothesis” “fail to reject”
If chi-square value is greater than the critical value
Not reliable data
“fail to reject”
If chi-square value is less than the critical value
Reliable data
1.333 < 3.841

21. Another Example: from Mendel
phenotype
observed
expected ratio
expected number
round yellow
315
9/16
312.75
round green
101
3/16
104.25
wrinkled yellow
108
wrinkled green 32
1/16
34.75
total
556 1

22. Chi-Square Use the formula X2 = (315 - 312.75)2 / 312.75
+ ( )2 /
+ ( )2 /
+ ( )2 / 34.75 =
= 0.470

23. D.F. and Critical Value df: 4 - 1 = 3 p = 0.05 critical value: 7.815
0.470 < 7.815
Fail to reject the null hypothesis