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HARDY-WEINBERG EQUILIBRIUM MODEL ASSIGNMENT #1
Use the following information to answer the three questions below:
PTC non-tasting is a recessive condition.
tt = non-taster
Population = 1000 individuals
tasters = 640
non-tasters = 360
1. What are the relative frequencies of the alleles T and t?
tt = (360/1000) = .36 = q2 (genotype frequency)
To find the frequency of allele t, take square root of .36: t = .60 = q
To find the frequency of allele T, subtract frequency of t from 1: T = (1 - .60) = .40 = p
2. What proportion of the population are heterozygous tasters (carriers)?
Use the Hardy-Weinberg formula to figure out the frequency of heterozygotes (genotype): 2pq = [2(.40)(.60)] = .48 = Tt
3. How many tasters carry the recessive allele t?
This question asks you to determine the number of individuals who are carriers: (1000 * .48) = 480
HARDY-WEINBERG EQUILIBRIUM MODEL ASSIGNMENT #2
Sickle-cell anemia is a malformation of the red blood cells that, as a heterozygous trait (AS), protects individuals against endemic malaria, but that as a homozygous recessive disease (SS), can result in death.
There are 1000 individuals in a Kenyan population (generation #1). By counting phenotypes, the following observations have been made:
640 individuals have normal RBCs (AA)
320 individuals have the sickle-cell trait (AS)
40 individuals have sickle-cell disease (SS)
1. What are the actual frequencies of alleles A and S?
Total number of alleles in population = 1000 (individuals) * 2 (alleles per person) = 2000
Total number of A alleles in population = (640*2) + 320 = (total number of A alleles of AA individuals) + number of A alleles from AS individuals = 1600 Total number of S alleles in population = 320 + (40*2) = number of alleles from AS individuals + (total number of S alleles of SS individuals) = 400 To find the frequency of allele A, divide total number of A alleles by total number of alleles in the population: A = 1600/2000 = .80 To find the frequency of allele S, divide total number of S alleles by total number of alleles in the population: S = 400/2000 = .20 OR subtract the frequency of A from 1: 1 - .80 = .20
2. Using the Hardy-Weinberg formula, find the expected genotype frequencies for this population.
p2 + 2pq + q2 = 1
p2 = AA = (.80)2[squared] = .64
2pq = AS = 2(.80)(.20) = .32
q2 = SS = (.20)2[squared] = .04
3. Using the Hardy-Weinberg formula, answer the following question: Is this population undergoing evolution?
Generation #2:
1920 AA individuals
960 AS individuals
120 SS individuals
The total number of alleles in the gen 2 population is 6000. Of that number, 4800 or 80% (.80) are A alleles and 1200 or 20% (.20) are S alleles.
Using the Hardy-Weinberg formula we find the actual genotype frequencies are:
p2 = (.80)2 = .64
2pq = 2(.80)(.20) = .32
q2 = (.20)2 = .04
Compare these actual numbers to the expected genotype frequencies in question #2 above:
The actual/observed numbers are identical to the expected frequencies. No evolution has occurred. [Go to question #4.]
Generation #3:
6080 AA individuals
1000 AS individuals
920 SS individuals
The total number of alleles in the gen 2 population is 16000. Of that number, 13160 or 82% (.82) are A alleles and 2840 or 18% (.18) are S alleles.
Using the Hardy-Weinberg formula we find the actual genotype frequencies are:
p2 = (.82)2 = .67
2pq = 2(.82)(.18) = .30
q2 = (.18)2 = .03
Compare these actual numbers to the expected genotype frequencies in question #2 above:
The actual/observed numbers are very close to the expected frequencies (this may be a borderline case). But it does appear that some evolution has occurred. [Go to question #4.]
Generation #4:
3000 AA individuals
21560 AS individuals
440 SS individuals
The total number of alleles in the gen 2 population is 50000. Of that number, 27560 or 55% (.55) are A alleles and 22440 or 45% (.45) are S alleles.
Using the Hardy-Weinberg formula we find the actual genotype frequencies are:
p2 = (.55)2 = .30
2pq = 2(.55)(.45) = .50
q2 = (.45)2 = .20
Compare these actual numbers to the expected genotype frequencies in question #2 above:
The actual/observed numbers are very different from the expected frequencies. Clearly, evolution has occurred in this population. [Go to question #4.]
4. What forces of evolution may be acting on this population?
In generation #2, there was no change and so no forces of evolution may be acting on this population. Remember -- no forces of evolution = no evolution/change!
In generation #3, there may be some forces of evolution acting slightly on the population but we have no way of knowing what those forces might be without further research.
In generation #4, there are clearly some forces of evolution working on this population. Again, we do not know what those forces are. Remember -- the Hardy-Weinberg model allows us to determine whether or not evolution is occurring. Not what forces of evolution are acting!
Note, however, that generation #4 is modelled after a more realistic situation of sickle-cell in a malarial environment. In such a situation, stabilizing natural selection is driving the higher frequencies of the heterozygous (AS) condition.
Concept of Race:
1. More of a social term than a scientific one, but the two are often confused.
2. The term race more often refers to ethnic or religious identity. If anthropologists use the term, it refers to biological differences between populations.
3. Most anthropologists prefer to use the term ancestry or ethnicity instead of race. The term population has recently come into wide use.
4. The idea of race fails to work with any consistency on a scientific level.
Race v. Cline:
1. Race: places humans into slots based on discrete differences (group of genetic traits that a group of individuals shares amongst themselves)
2. Cline: no races, but overlapping gradients (continuous traits) among human populations
3. Most anthropologists today do not accept the idea of (biological) race -- prefer instead to look at range of variation and try to understand diversity as result of adaptation.
Problems of Racial Classification:
1. Racial taxonomies (classifications) are typological in nature. That is, the categories they create are discrete in nature and based upon a subjective ideal that is comprised of a specific set of traits.
2. "Races" blend into one another because of continuous traits.
3. Using one set of discrete traits creates one classification, using another set of discrete traits creates a different classification. This process is arbitrary.
4. Human genetic variation is 94% at the individual level, and only 6% at a geographical or "racial" level.
Anthropology in the News
David Shapiro's Zoonosis Web Page
Mendel's Hypothesis
Punnet Square Tutorial
Punnet Square Examples
Population Genetics & Hardy-Weinberg Equilibrium
Genetic Drift Model Calculator
Tutorial: Primate Traits and Classification
Tutorial: Primate Behavior
Article: Bonobo Sex & Society
The Columbus Zoo & Aquarium
Taxonomy & Classification
Theories of Primate Evolution
Tutorial: Primate Evolution
Radio Carbon Dating
Tutorial: Fossils in 3D
Hominid Timeline
Tutorial: Early Hominids
Tutorial: Early Homo
Tutorial: Modern Humans
Virtual Tour: Lascaux Cave
Article: First Americans
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