Presentation on theme: "Hardy Weinberg: Population Genetics"— Presentation transcript:
1 Hardy Weinberg: Population Genetics Using mathematical approaches to calculate changes in allele frequencies…this is evidence of evolution.
2 Hardy-Weinberg equilibrium Hypothetical, non-evolving populationpreserves allele frequenciesnatural populations rarely in H-W equilibriumuseful model to measure if forces are acting on a populationmeasuring evolutionary changeG.H. Hardy (the English mathematician) and W. Weinberg (the German physician) independently worked out the mathematical basis of population genetics in 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. HardymathematicianW. Weinbergphysician
3 Evolution of populations Evolution = change in allele frequencies in a populationhypothetical: what conditions would cause allele frequencies to not change?very large population size (no genetic drift)no migration (no gene flow in or out)no mutation (no genetic change)random mating (no sexual selection)no natural selection (everyone is equally fit)H-W occurs ONLY in non-evolving populations!
4 Populations & gene pools Conceptsa population is a localized group of interbreeding individualsgene pool is collection of alleles in the populationremember difference between alleles & genes!allele frequency is how common is that allele in the populationhow many A vs. a in whole population
5 H-W formulas Alleles: p + q = 1 Individuals: p2 + 2pq + q2 = 1 B b BB
6 Hardy-Weinberg theorem Frequencies are usually written as decimals!Counting Allelesassume 2 alleles = B, bfrequency of dominant allele (B) = pfrequency of recessive allele (b) = qfrequencies must add to 1 (100%), so:p + q = 1BBBbbb
7 Hardy-Weinberg theorem Counting Individualsfrequency of homozygous dominant: p x p = p2frequency of homozygous recessive: q x q = q2frequency of heterozygotes: (p x q) + (q x p) = 2pqfrequencies of all individuals must add to 1 (100%), so:p2 + 2pq + q2 = 1BBBbbb
8 Using Hardy-Weinberg equation population: 100 cats84 black, 16 whiteHow many of each genotype?q2 (bb): 16/100 = .16q (b): √.16 = 0.4p (B): = 0.6p2=.362pq=.48q2=.16BBBbbbMust assume population is in H-W equilibrium!What are the genotype frequencies?
9 Using Hardy-Weinberg equation p2=.362pq=.48q2=.16Assuming H-W equilibrium:Expected dataBBBbbbp2=.20p2=.742pq=.102pq=.64q2=.16q2=.16Sampled data 1:Hybrids are in some way weaker.Immigration in from an external population that is predomiantly homozygous BNon-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.bbBbBBObserved dataHow do you explain the data?How do you explain the data?
10 Origin of the Equation p2 + 2pq + q2 Assuming that a trait is recessive or dominantAllele pairs AA, Aa, aa would exist in a populationp + q = 1The probability that an individual would contribute an A is called pThe probability that an individual would contribute an a is called qBecause only A and a are present in the population the probability that an individual would donate one or the other is 100%p2 + 2pq + q2Male Gametes A(p)Male Gametes a(q)Female gametes A(p)AAp2AapqFemale Gametes a(q)aaq2
11 Example of an evolving population: Peppered mothVariation of colors in the population existed (Black, Peppered, White)As environmental conditions changed the frequency of the recessive allele increased.This was seen as an adaptation to the environment that allowed the species to continue to live.