Evolutionary Change in
Populations
Chapter 18
Frequencies
• Gene pool – all the alleles in a population
• Genotype frequency – total = 1.0 (100%)
– homozygous dominant
– heterozygous
– homozygous recessive
• Phenotype frequency – total – 1.0 (100%)
– dominant
– Recessive
• Allele frequency
– A or a
– Each individual has 2: AA, Aa, or aa
Hardy-Weinberg Principle
A way of measuring if a population is evolving
Non-evolving populations ‘fit’ the principle – they
are in genetic equilibrium
Five conditions must be met:
1.
2.
3.
4.
5.
random mating
no net mutations
large population size
no migration
no natural selection
In other words: no evolutionary change
Hardy-Weinberg Principle…
• Shows that the process of inheritance by itself
does not cause changes in allele frequencies
• Explains why dominant alleles are not necessarily
more common than recessive ones
• Seldom occurs in the natural world but instead
provides us with a model for understanding
evolution in sexually reproducing populations
Hardy-Weinberg Principle…
p = frequency of dominant allele
q = frequency of recessive allele
Therefore:
p+q=1
From this we know that:
p = 1 – q (frequency of dominant allele)
q = 1 – p (frequency of recessive allele)
Hardy-Weinberg Principle…
Each individual has 2 alleles, therefore:
p 2 + 2 pq + q 2 = 1
{AA + 2Aa + aa = 1}
remember, there are 2 different ways an individual can inherit Aa
What the heck does this mean??
Problem #1
•
You have sampled a population in which you
know that the percentage of the homozygous
recessive genotype (aa) is 36%. Using that,
calculate the following:
A.
B.
C.
D.
E.
The frequency of the aa genotype
The frequency of the a allele
The frequency of the A allele
The frequencies of the genotypes of AA and Aa
The frequencies of the two possible phenotypes if A
is completely dominant over a
Problem #2
• Sickle-cell anemia is an interesting genetic
disease. Normal homozygous individuals (SS) are
more susceptible to malarial infection. Those with
the sickle-cell trait (ss) often die due to the
condition. Heterozygous individuals (Ss) tend to
survive better than either of the homozygous
conditions. If 9% of an African population is born
with a severe form of sickle-cell anemia (ss), what
percentage of the population will be more resistant
to malaria because they are heterozygous (Ss) for
the sickle-cell gene?
Problem #3
•
There are 100 students in a class. Ninety-six did
well in the course whereas four blew it totally
and received a grade of F. In the highly unlikely
event that these traits are genetic rather than
environmental, if these traits involve dominant
and recessive alleles, and if the 4% represent the
frequency of the homozygous recessive
condition, calculate the following:
A. The frequency of the recessive allele
B. The frequency of the dominant allele
C. The frequency of heterozygous individuals
Problem #4
•
Within a population of butterflies, the
color brown (B) is dominant over the
color white. And 40% of the butterflies are
white. Given this simple information,
calculate the following:
A. The percentage of butterflies in the population
that are heterozygous
B. The frequency of homozygous dominant
individuals
Problem #5
•
A rather large population of Biology instructors have
396 red-sided individuals and 557 tan-sided individuals.
Assume that red is totally recessive. Calculate the
following:
A.
B.
C.
D.
E.
The allele frequencies of each allele
The expected genotype frequencies
The number of heterozygous individuals that you would predict
in this population
The expected phenotype frequencies
Conditions happen to be really good this year for breeding and
next year there are 1,245 young Biology instructors. Assuming
all of the H-W conditions are met, how many of these would you
expect to be red-sided and how many tan-sided?