what conditions would have to exist for the gene frequencies to stay the same

Biology 198
PRINCIPLES OF Biology
Hardy-Weinberg practice questions

Updated: 21 August 2000

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POPULATION GENETICS AND THE HARDY-WEINBERG Law

The Hardy-Weinberg formulas allow scientists to determine whether evolution has occurred. Any changes in the gene frequencies in the population over time can be detected. The police force essentially states that if no development is occurring, then an equilibrium of allele frequencies will remain in effect in each succeeding generation of sexually reproducing individuals. In order for equilibrium to remain in consequence (i.eastward. that no development is occurring) then the following five conditions must be met:

1. No mutations must occur so that new alleles do not enter the population.
2. No cistron flow can occur (i.e. no migration of individuals into, or out of, the population).
3. Random mating must occur (i.e. individuals must pair by chance)
4. The population must be large so that no genetic drift (random chance) can crusade the allele frequencies to change.
5. No selection can occur so that certain alleles are non selected for, or against.

Patently, the Hardy-Weinberg equilibrium cannot exist in existent life. Some or all of these types of forces all human action on living populations at various times and evolution at some level occurs in all living organisms. The Hardy-Weinberg formulas allow us to detect some allele frequencies that change from generation to generation, thus allowing a simplified method of determining that evolution is occurring. In that location are two formulas that must be memorized:

p^two + 2pq + q² = one and p + q = 1

p = frequency of the ascendant allele in the population
q = frequency of the recessive allele in the population

p² = percentage of homozygous dominant individuals
qⁱⁱ = percent of homozygous recessive individuals
2pq = percentage of heterozygous individuals

Individuals that have aptitude for math find that working with the above formulas is ridiculously easy. However, for individuals who are unfamiliar with algebra, it takes some practice working bug before you go the hang of it. Below I have provided a serial of practice problems that y'all may wish to try out. Note that I have rounded off some of the numbers in some problems to the second decimal place:

1. PROBLEM #one.

   You have sampled a population in which you know that the percentage of the homozygous recessive genotype (aa) is 36%. Using that 36%, calculate the following:

   1. The frequency of the "aa" genotype.
   2. The frequency of the "a" allele.
   3. The frequency of the "A" allele.
   4. The frequencies of the genotypes "AA" and "Aa."
   5. The frequencies of the two possible phenotypes if "A" is completely dominant over "a."
2. Problem #2.

   Sickle-jail cell anemia is an interesting genetic disease. Normal homozygous individials (SS) accept normal blood cells that are easily infected with the malarial parasite. Thus, many of these individuals get very sick from the parasite and many die. Individuals homozygous for the sickle-cell trait (ss) take red claret cells that readily collapse when deoxygenated. Although malaria cannot grow in these cherry-red blood cells, individuals ofttimes die because of the genetic defect. However, individuals with the heterozygous status (Ss) have some sickling of red blood cells, but generally non enough to crusade mortality. In addition, malaria cannot survive well inside these "partially defective" red blood cells. Thus, heterozygotes tend to survive better than either of the homozygous weather condition. If ix% of an African population is born with a severe class of sickle-prison cell anemia (ss), what percentage of the population will exist more resistant to malaria considering they are heterozygous (Ss) for the sickle-prison cell gene?

3. PROBLEM #3.

   There are 100 students in a class. Ninety-vi did well in the course whereas four blew it totally and received a class of F. Sorry. In the highly unlikely outcome that these traits are genetic rather than ecology, if these traits involve ascendant and recessive alleles, and if the 4 (iv%) correspond the frequency of the homozygous recessive status, please summate the post-obit:

   1. The frequency of the recessive allele.
   2. The frequency of the dominant allele.
   3. The frequency of heterozygous individuals.
4. PROBLEM #iv.

   Inside a population of butterflies, the color brown (B) is dominant over the colour white (b). And, forty% of all butterflies are white. Given this simple information, which is something that is very likely to be on an test, calculate the post-obit:

   1. The percent of collywobbles in the population that are heterozygous.
   2. The frequency of homozygous ascendant individuals.
5. Trouble #5.

   A rather large population of Biology instructors accept 396 red-sided individuals and 557 tan-sided individuals. Assume that red is totally recessive. Please summate the following:

   1. The allele frequencies of each allele.
   2. The expected genotype frequencies.
   3. The number of heterozygous individuals that you lot would predict to exist in this population.
   4. The expected phenotype frequencies.
   5. Conditions happen to exist actually good this twelvemonth for convenance and next year there are 1,245 young "potential" Biology instructors. Assuming that all of the Hardy-Weinberg conditions are met, how many of these would you expect to exist red-sided and how many tan-sided?
6. Problem #6.

   A very big population of randomly-mating laboratory mice contains 35% white mice. White coloring is acquired past the double recessive genotype, "aa". Calculate allelic and genotypic frequencies for this population.

7. Trouble #7.

   After graduation, yous and 19 of your closest friends (lets say 10 males and 10 females) charter a aeroplane to go on a round-the-world tour. Unfortunately, you all crash land (safely) on a deserted isle. No ane finds you lot and you lot start a new population totally isolated from the residue of the earth. Two of your friends bear (i.east. are heterozygous for) the recessive cystic fibrosis allele (c). Assuming that the frequency of this allele does not change as the population grows, what will be the incidence of cystic fibrosis on your island?

8. Problem #8.

   You lot sample 1,000 individuals from a large population for the MN blood group, which can easily be measured since co-dominance is involved (i.e., you can observe the heterozygotes). They are typed appropriately:

   BLOOD Type	GENOTYPE	NUMBER OF INDIVIDUALS	RESULTING FREQUENCY
   G	MM	490	0.49
   MN	MN	420	0.42
   N	NN	90	0.09

   Using the data provide to a higher place, calculate the following:

   1. The frequency of each allele in the population.
   2. Supposing the matings are random, the frequencies of the matings.
   3. The probability of each genotype resulting from each potential cross.
9. PROBLEM #nine.

   Cystic fibrosis is a recessive condition that affects almost 1 in 2,500 babies in the Caucasian population of the United States. Please summate the following.

   1. The frequency of the recessive allele in the population.
   2. The frequency of the dominant allele in the population.
   3. The percent of heterozygous individuals (carriers) in the population.
10. PROBLEM #10.

    In a given population, only the "A" and "B" alleles are present in the ABO system; there are no individuals with type "O" blood or with O alleles in this detail population. If 200 people take type A blood, 75 accept type AB blood, and 25 have blazon B blood, what are the alleleic frequencies of this population (i.e., what are p and q)?

11. Problem #xi.

    The ability to taste PTC is due to a single boss allele "T". You lot sampled 215 individuals in biology, and adamant that 150 could detect the bitter taste of PTC and 65 could not. Calculate all of the potential frequencies.

12. Problem #12. (You will not have this type of problem on the examination)

    What allelic frequency volition generate twice as many recessive homozygotes as heterozygotes?

ANSWERS TO THE QUESTIONS

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