Biology 30
Unit D: Population and Community Dynamics
Outcome #1 – Topic 1: Hardy-Weinberg Equilibrium – Population Equilibrium
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Population: A group of individuals of the same species living in a specific area at a specific time
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Allele frequency: The proportion of gene copies in a population of a given allele
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Scientists use frequencies to study changes in populations.
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Note that a fixed frequency refers to the frequency of an allele within a population when only a single allele is
present for a particular gene (the frequency is 100%)
Hardy-Weinberg Equilibrium
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If all factors remain constant, the gene pool of a population will have the same composition generation after
generation. (This is referred to as “genetic equilibrium”)
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If a population is in genetic equilibrium, gene frequencies will remain unchanged and the population is not evolving.
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Hardy / Weinberg equilibrium can be used to:
1. Determine genotype frequencies in a population.
2. Determine if evolution is occurring.
Conditions of Hardy-Weinberg Equilibrium
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Allele (gene) frequencies within a population will not change if the following conditions are met:
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Populations are large
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To ensure that gene frequencies don’t change as a result of chance
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Mating between individuals is random
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No mutations
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No migrations
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No new genes enter or leave population
No natural selection occurs
Hardy / Weinberg Mathematics:
- The following applies to any gene with only possible alleles
p+q=1
p = frequency of the dominant allele in a population (ex. A)
q = frequency of the recessive allele in a population (ex. a)
Hardy / Weinberg Mathematics:
Hardy-Weinberg equation
p2 + 2pq + q2 = 1
p2 = homozygous dominant genotype (ex. AA)
2pq = heterozygous genotype (ex. Aa)
q2 = homozygous recessive genotype (ex. aa)
Examples
Problem #1: Suppose that 9 % of a population have a recessive genetic disorder. What percentage of this population
would be expected to be carriers (heterozygous) for the disorder?
Problem #2: A dominant trait is found in 38 % of the population. What percentage of the population would be expected
to be heterozygous for this trait?
Problem #3: 60% of the moths in a population are white (WW, Ww) 40% of the moths in the population are black (ww).
After a 3 year period, 65% of the moths are white and 35% are black. How do the allele frequencies compare before
and after?
Problem #4: The allele for black coat is recessive. The illustration below represents the pig population
a.
Calculate q.(Hint: Count the individuals that are
homozygous recessive in the illustration)
b. Calculate p.
c. Calculate the percentage of the population that is heterozygous.
a. What is the frequency of the HbA allele in central Africa?
b. What percentage of people in central Africa would have higher resistance to malaria?
c. In which part of Africa is the HbS allele most frequent?
Topic 1 – Hardy-Weinberg Equilibrium
Review Sheet
A population of 200 includes 32 individuals that are homozygous recessive (bb) for a given trait. Assuming the
population meets the conditions for Hardy–Weinberg equilibrium, how many of the 200 individuals would you expect to
be homozygous dominant (BB)?
Cystic fibrosis is a recessive condition that affects about 1 in 2500 people in the Caucasian population of Canada.
Calculate the following:
(a) the population frequencies for the dominant (C) and recessive (c) alleles
(b) the percentage of the population that is a carrier of the recessive allele
(c) the number of students in your school that are likely to be carriers of the cystic fibrosis allele
A recessive allele (h) codes for complete hair loss in chimpanzees. Homozygous recessive individuals lose all their hair by
about six months of age. Chimpanzees with one or two dominant alleles (H) show no signs of this disorder. In a
population of captive chimpanzees, 16 % of the chimpanzees lose all their hair.
(a) Calculate the allele frequencies of H and h.
(b) What percentage of the chimpanzees could not be the parents of chimpanzees with this condition.
(c) Hairless chimpanzees have reduced survival rates and lower reproductive success. Predict how the allele frequencies
will change over time. Explain your reasoning as it relates to the Hardy–Weinberg equilibrium assumptions.
A large population consists of 400 individuals, of which 289 are homozygous dominant (MM), 102 are heterozygous
(Mm), and 9 are homozygous recessive (mm). Determine the allele frequencies of M and m.
The gene pool of a certain large population of fruit flies contains only two eye-colour alleles: the dominant red allele, R,
and the recessive white allele, r. Only 1 % of the population has red eyes. Determine the allele and genotype frequencies
of this population
Manx cats have no tails (or have very short tails) and have large hind legs. The no-tail trait results from a heterozygous
genotype, Tt. Interestingly, TT genotypes are normal cats, while the tt genotype is lethal and cat embryos that possess it
do not survive. In a population of 1000 cats, only 1 % are Manx and 99 % are normal.
(a) What are the allele frequencies in this population?
(b) Determine the expected frequency of each genotype in the next generation.
(c) Determine the allele frequencies of the population of cats from (b).
(d) Predict the long-term result of a lethal homozygous recessive trait in a wild population.