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We need a mathematical tool to measure how much the population is evolving.

Numbers will enable us to evaluate, compare, and then predict evolutionary processes. Population GeneticsAndThe Hardy-Weinberg ModelSuppose we could quantify, give numbers, how fast a population is evolving in terms on one single trait.

How would this be useful for medicine, studying the wildlife, other?Lets Define:a Population is a localized group of interbreeding individuals.Gene pool is the entire collection of alleles in the population.(What is the size of our class gene pool?)Allele frequency is how common (in %) an allele (H or h) is in the population. (What are the frequencies in our cards?) 33Evolution = a change in the allele frequencies. How can we tell if the allele frequencies are changing from a single observation?We predict how a gene pool should be like if there is no change. Then we compare to the actual gene pool.

W. WeinbergphysicianG.H. HardyMathema-ticianHardy and Weinberg: At equilibrium (not evolving) the frequencies of the alleles do not change. Mix alleles, try again: What are the frequencies of H, h in our class?5 Agents of evolutionary change

MutationGene FlowGenetic DriftSelectionNon-random mating66Hypothetical conditions under which the allele frequencies do not change:1. very large population size 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)Under the Hardy-Weinberg conditions:We assume 2 alleles = H, hfrequency of dominant allele (H) = p frequency of recessive allele (h) = q 1) Frequencies must add up to 1 (100%), so: p + q = 1

hhHhHH88h (q)H (p)Accordingly what are the chances to select a certain genotype? Phenotype?H (p)h (q)pxqqxpp2q2HHHhHhhh

q2Hardy-Weinberg theoremCounting Individuals:frequency of HH: pxp = p2 frequency of hh: qxq = q2 frequency of Hh: (pxq) + (qxp) = 2pq2) Frequencies of all individuals must add to 1 (100%), so: p2 + 2pq + q2 = 1

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What are the genotype frequencies?Using Hardy-Weinberg equationq2 (bb): 16/100 = .16q (b): .16 = 0.4p (B): 1 - 0.4 = 0.6population: 100 cats84 black, 16 whiteHow many of each genotype?bbBbBBp2=.362pq=.48q2=.16Must assume population is in H-W equilibrium!1111Using Hardy-Weinberg equation

bbBbBBp2=.362pq=.48q2=.16Assuming H-W equilibriumActual data

bbBbBBp2=.742pq=.10q2=.16How do you explain the data? p2=.202pq=.64q2=.16How do you explain the data? Null hypothesis 1212Sampled 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.

Whats preventing this population from being in equilibrium.In this population, we find that the frequency of heterozygotes is greater than expected under the H-W assumption. Therefore: The population is not at equilibrium (Why???)There might be an advantage to being a heterozygote. Why??Lets try it with alleles in our handsh = albinoH = non-albinoEach student gets two alleles at random.

Will the allele frequencies agree with the H-W equation? AP Biology 2008 writing question: Evolution involves change in the frequencies of alleles in a population. For a particular genetic locus in a population, the frequency of the recessive allele (a) is 0.4 and the frequency of the dominant allele (A) is 0.6.a. What is the frequency of each genotype (AA, Aa, aa) in this population? b. What is the frequency of the dominant phenotype?To Conclude:* The H-W equation describes a rare population that is at equilibrium.* By Comparing an actual population to the H-W frequencies, we can detect an instability in allele frequency.We can then ask which of the five H-W assumptions is not met.Hardy-Weinberg formulasAlleles:p + q = 1

Individuals:p2 + 2pq + q2 = 1

hhHhHHHHHhHhhhFor a population at equilibrium:1717In the scarlet tiger moth (Panaxia dominula), coloration had been previously shown to behave as a single-locus, two-allele system with incomplete dominance. Data for 1612 individuals are given below: White-spotted (AA) =1469 Intermediate (Aa) = 138 Little spotting (aa) =5 Calculate: ()A, ()a, ()AA, ()Aa, ()aa

Scarlet tiger moth (Panaxia dominula)Application of H-W principleSickle cell anemiainherit a mutation in gene coding for hemoglobinoxygen-carrying blood proteinrecessive allele = HsHsnormal allele = Hblow oxygen levels causes RBC to sicklebreakdown of RBCclogging small blood vesselsdamage to organsoften lethal

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Sickle cell frequencyHigh frequency of heterozygotes 1 in 5 in Central Africans = HbHsunusual for allele with severe detrimental effects in homozygotes1 in 100 = HsHsusually die before reproductive ageWhy is the Hs allele maintained at such high levels in African populations?Suggests some selective advantage of being heterozygous2121Sickle Cell:In tropical Africa, where malaria is common, the sickle-cell allele is both an advantage & disadvantage. Reduces infection by malaria parasite.

Cystic fibrosis: Cystic fibrosis carriers are thought to be more resistant to cholera: 1:25, or 4% of Caucasians are carriers Cc

Malaria

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

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Heterozygote AdvantageIn tropical Africa, where malaria is common:homozygous dominant (normal)die or reduced reproduction from malaria: HbHbhomozygous recessive die or reduced reproduction from sickle cell anemia: HsHsheterozygote carriers are relatively free of both: HbHssurvive & reproduce more, more common in populationHypothesis:In malaria-infected cells, the O2 level is lowered enough to cause sickling which kills the cell & destroys the parasite.Frequency of sickle cell allele & distribution of malaria2323Hardy-Weinberg equilibriumHypothetical, non-evolving populationpreserves allele frequenciesServes as a model (null hypothesis)natural populations rarely in H-W equilibriumuseful model to measure if forces are acting on a populationmeasuring evolutionary change

W. WeinbergphysicianG.H. Hardymathematician2525G.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?"We can count the phenotypes, and accordingly, calculate the frequency of the genotypes, under equilibrium conditions. Suppose we know which allele is recessive. The chances for an offspring to inherit a b are qxq = q2