Math in Genetics Making Suby Proud

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

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

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

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

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

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

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

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

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

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

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

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?

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

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

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

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

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

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

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

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

Chi-Square Use the formula X2 = (315 - 312.75)2 / 312.75 + (101 - 104.25)2 / 104.25 + (108 - 104.25)2 / 104.25 + (32 - 34.75)2 / 34.75 = 0.016 + 0.101 + 0.135 + 0.218 = 0.470

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