Hardy-Weinberg equilibrium Hypothetical, non-evolving population preserves allele frequencies Serves as a model (null hypothesis) natural populations rarely in H-W equilibrium useful model to measure if forces are acting on a population measuring evolutionary change G.H. Hardy (the English mathematician) and W. Weinberg (the German physician) independently worked out the mathematical basis of population genetics in 1908. Their formula predicts the expected genotype frequencies using the allele frequencies in a diploid Mendelian population. They were concerned with questions like "what happens to the frequencies of alleles in a population over time?" and "would you expect to see alleles disappear or become more frequent over time?" G.H. Hardy mathematician W. Weinberg physician

Hardy-Weinberg theorem Counting Alleles assume 2 alleles = B, b frequency of dominant allele (B) = p frequency of recessive allele (b) = q frequencies must add to 1 (100%), so: p + q = 1 BB Bb bb

Hardy-Weinberg theorem Counting Individuals frequency of homozygous dominant: p x p = p2 frequency of homozygous recessive: q x q = q2 frequency of heterozygotes: (p x q) + (q x p) = 2pq frequencies of all individuals must add to 1 (100%), so: p2 + 2pq + q2 = 1 BB Bb bb

H-W formulas B b B BB Bb b Bb bb Alleles: p + q = 1 Individuals: p2 + 2pq + q2 = 1 B b BB Bb bb BB Bb bb

Using Hardy-Weinberg equation population: 100 cats 84 black, 16 white How many of each genotype? q2 (bb): 16/100 = .16 q (b): √.16 = 0.4 p (B): 1 - 0.4 = 0.6 p2=.36 2pq=.48 q2=.16 BB Bb bb Must assume population is in H-W equilibrium! What are the genotype frequencies?

Using Hardy-Weinberg equation p2=.36 2pq=.48 q2=.16 Assuming H-W equilibrium BB Bb bb Null hypothesis p2=.20 p2=.74 2pq=.10 2pq=.64 q2=.16 q2=.16 Sampled data 1: Hybrids are in some way weaker. Immigration in from an external population that is predomiantly homozygous B Non-random mating... white cats tend to mate with white cats and black cats tend to mate with black cats. Sampled data 2: Heterozygote advantage. What’s preventing this population from being in equilibrium. bb Bb BB Sampled data How do you explain the data? How do you explain the data?

HARDY-WEINBERG PRACTICE PROBLEMS p + q = 1 p2 + 2 pq + q2 = 1

Black (b) is recessive to white (B) Bb and BB pigs “look alike” so can’t tell their alleles by observing their phenotype. ALWAYS START WITH RECESSIVE alleles. p= dominant allele q = recessive allele 4/16 are black. So bb or q2 = 4/16 or 0.25 q = 0.25 = 0.5

Once you know q you can figure out p . . . p + q = 1 p + q = 1 http://www.phschool.com/science/biology_place/labbench/lab8/samprob1.html Once you know q you can figure out p . . . p + q = 1 p + q = 1 p + 0.5 = 1 p = 0.5 Now you know the allele frequencies. The frequency of the recessive (b) allele q = 0.5 The frequency of the dominant (B) allele p = 0.5

WHAT ARE THE GENOTYPIC FREQUENCIES? You know pp from problem bb or q2 = 4/16 = 0.25 BB or p2 = (0.5)2 = 0.25 Bb = 2pq = 2 (0.5) (0.5) = 0.5 25% of population are bb 25% of population are BB 50% of population are Bb http://www.phschool.com/science/biology_place/labbench/lab8/samprob1.html

Within a population of butterflies, the color brown (B) is dominant over the color white (b). And, 40% of all butterflies are white. q2 = 0.4 q = 0.4 = 0.6324 p = 1 - 0.6324 = 0.3676 aa = 0.4 = 40% Aa = 2 (0.632) (0.368) = 0.465 =46.5% AA = (0.3676) (0.3676) = .135 = 13.5% Image from: BIOLOGY by Miller and Levine; Prentice Hall Publishing ©2006

PRACTICE HARDY WEINBERG 1 in 1700 US Caucasian newborns have cystic fibrosis. C for normal is dominant over c for cystic fibrosis. Calculate the allele frequencies for C and c in the population Image from: BIOLOGY by Miller and Levine; Prentice Hall Publishing ©2006

1/1700 have cystic fibrosis q2 = 1/1700 q = 0.00059 q = 0.024 p = 1 – 0.024 = 0.976 Frequency of C = 97.6% Frequency of c = 2.4% NOW FIND THE GENOTYPIC FREQUENCIES

CC or p2 = (0.976)2 = .953 Cc or 2pq = 2 (0.976) (0.024) = 0.0468 cc = 1/1700 = 0.00059 CC = 95.3% of population Cc = 4.68% of population cc = .06% of population

Now you can answer questions about the population: How many people in this population are heterozygous? It has been found that a carrier is better able to survive diseases with severe diarrhea. What would happen to the frequency of the "c" if there was a epidemic of cholera or other type of diarrhea producing disease? 0.0468 (1700) = 79.5 ~ 80 people are Cc Cc more likely to survive than CC. c will increase in population

The gene for albinism is known to be a recessive allele. In Michigan, 9 people in a sample of 10,000 were found to have albino phenotypes. The other 9,991 had skin pigmentation normal for their ethnic group. Assuming hardy-Weinberg equilibrium, what is the allele frequency for the dominant pigmentation allele in this population? q2 = 9/10000 q = 0.0009 q = 0.03 p = 1 – 0.03= 0.97 Frequency of C = 97% Frequency of c = 3%

CC or q2 = (0.976)2 = .953 Cc or 2pq = 2 (0.976) (0.024) = 0.0468 cc = 1/1700 = 0.00059 CC = 95.3% of population Cc = 4.68% of population cc = .06% of population