Measuring Evolution of Populations

Measuring Evolution of Populations

5 Agents of evolutionary change Mutation Gene Flow Non-random mating Genetic Drift Selection

Populations & gene pools Concepts u a population is a localized group of interbreeding individuals u gene pool is collection of alleles in the population remember difference between alleles & genes! u allele frequency is how common is that allele in the population how many A vs. a in whole population

Evolution of populations Evolution = change in allele frequencies in a population u hypothetical: what conditions would cause allele frequencies to not change? u non-evolving population REMOVE all agents of evolutionary change 1. very large population size (no genetic drift) 2. no migration (no gene flow in or out) 3. no mutation (no genetic change) 4. random mating (no sexual selection) 5. no natural selection (everyone is equally fit)

Hardy-Weinberg equilibrium Hypothetical, non-evolving population u preserves allele frequencies Serves as a model (null hypothesis) u natural populations rarely in H-W equilibrium u useful model to measure if forces are acting on a population measuring evolutionary change G.H. Hardy mathematician W. Weinberg physician

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

Hardy-Weinberg Equilibrium How do we determine if a population is in Hardy-Weinberg equilibrium? u Find out the genotype frequencies in the population. u Calculate the frequencies of the dominant and recessive alleles (p and q). u Calculate what the allele frequencies would be in one generation of random mating.

Hardy-Weinberg Equilibrium If the allele frequencies after one round of random mating change at all from the original frequencies, the population is not in Hardy-Weinberg equilibrium and evolution has occurred within the population.

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

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

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

Using Hardy-Weinberg equation Assuming H-W equilibrium Null hypothesis p 2 =.36 2pq=.48 q 2 =.16 BB Bb bb Sampled data p 2 =.20 =.74 2pq=.64 2pq=.10 q 2 =.16 BB Bb bb How do you explain the data?

Application of H-W principle Sickle cell anemia u inherit a mutation in gene coding for hemoglobin oxygen-carrying blood protein recessive allele = H s H s w normal allele = H b u low oxygen levels causes RBC to sickle breakdown of RBC clogging small blood vessels damage to organs u often lethal

Sickle cell frequency High frequency of heterozygotes u 1 in 5 in Central Africans = H b H s u unusual for allele with severe detrimental effects in homozygotes 1 in 100 = H s H s usually die before reproductive age Why is the H s allele maintained at such high levels in African populations? Suggests some selective advantage of being heterozygous

Malaria Single-celled eukaryote parasite (Plasmodium) spends part of its life cycle in red blood cells 1 2 3

Heterozygote Advantage In tropical Africa, where malaria is common: u homozygous dominant (normal) die of malaria: H b H b u homozygous recessive die of sickle cell anemia: H s H s u heterozygote carriers are relatively free of both: H b H s survive more, more common in population Hypothesis: In malaria-infected cells, the O 2 level is lowered enough to cause sickling which kills the cell & destroys the parasite. Frequency of sickle cell allele & distribution of malaria

HARDY-WEINBERG PRACTICE PROBLEMS p + q = 1 p 2 + 2 pq + q 2 = 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 q 2 = 4/16 or 0.25 q = 0.25 = 0.5

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 q 2 = 4/16 = 0.25 BB or p 2 = (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. q 2 = 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 q 2 = 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 p 2 = (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? 0.0468 (1700) = 79.5 ~ 80 people are Cc 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? 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? q 2 = 9/10000 q = 0.0009 q = 0.03 p = 1 0.03= 0.97 Frequency of C = 97% Frequency of c = 3%

CC or q 2 = (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