Transcript Quantitative Biology

The Mathematics of Genetics and Evolution
BY: MATT DEAN
Evolution: Requirements for
• Evolution—A change in
the allele frequency of a
population over time.
• Requirements:
• 1. Genetic Variability—
may come from mutations
and immigration.
• 2. More offspring are
produced than can survive
(due to limited resources,
predation, etc…)
• 3. Some organisms must
be better adapted than
others.
• 4. There must be
differential
reproduction rates due
to the adaptive
characteristics of some
members.
• Fitness
• Fecundity
Hardy Weinberg Video Part 1
Hardy Weinberg Video Part 2
Hardy-Weinberg Equilibrium
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Genetic Equilibrium
Hardy-Weinberg Law
Defined evolution by describing
when it would not happen.
There are 5 requirements that must
be met for genetic equilibrium to
occur.
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Requirements
1. No mutations. Germ cell mutations
bring about evolution. Somatic cell
mutations are not passed on to
offspring.
2. No immigration or emigration. (No
gene flow)
3. There must be a very large
population in order to avoid genetic
drift.
Genetic Drift—unpredicted changes in
allele frequencies due to chance.
Usually occurs in small, isolated
populations.
4. There must be no natural selection.
5. There must be no sexual selection.
Mating must be random.
If you can take a square root, you
can solve a Hardy Weinberg
problem!!
Hardy Weinberg Problems
• 1. In humans, brown eyes are dominant over blue
eyes. In a population of 1000 individuals, 750
have brown eyes. What are the frequencies of the
dominant and recessive alleles?
• 2. How many individuals would you expect to be
heterozygous (from #1)?
• 3. What is the expected frequency (percentage) of
each possible genotype?
• 4. What is the frequency of the dominant allele?
• 5. What is the frequency of the recessive allele?
More Hardy Weinberg Problems
• 4. The ability to roll the tongue is dominant over
the allele for the lack of the ability. If 64% of a
population can roll their tongues, what are the
frequencies of the dominant and recessive alleles?
• 5. Give the percentage of the population that
would represent each possible genotype (from #4)
• 6. If the population consisted of 3000 individuals,
how many individuals should be homozygous
dominant for the trait?
More on Hardy Weinberg
• Suppose a teacher does a statistical analysis of the eye
color in her school of mostly black students. She finds that
of the 1000 students, 910 have brown eyes, while only 90
have blue eyes (the recessive trait).
• Five years later, she does her analysis again, since as an
attempt at desegregation, some students are sent to other
schools and new students from neighboring towns are
brought in . She now finds that of the 1000 students, 840
have brown eyes and 160 have blue eyes.
More on Hardy Weinberg
• 1. In the original sample (1981) the frequency of the allele
for brown eyes (B) was:
• 2. The number of students in the original sample that were
expected to be heterozygous for brown eyes was:
• 3. Is the population in Hardy Weinberg equilibrium? Is
evolution occurring? How do you know? What brought
about the change, if there was change?
• 4. In the second sample, what was the frequency of the
recessive allele?
• 5. Give the expected frequency of each possible genotype
for samples 1 & 2.
More Hardy Weinberg
• 1. A recessive trait appears in 81% of the
individuals in a population that is in HardyWeinberg equilibrium. What percent of the
population in the next generation is expected to be
homozygous dominant?
• 2. Nine percent of a population is homozygous
recessive at a certain locus. Assuming the
population is in Hardy Weinberg equilibrium,
what the frequency of the recessive allele?
Trihybrid Crosses
• 1. What is the probability that parents with
the genotypes TtWwMM and TTWwMm
will produce an offspring with the genotype
TTWWMM?
• 2. What is the probability that an offspring
with the genotype NnRrDd will be
produced from parents with the genotypes
nnrrDd and NnRrDd?
Gene Mapping Video
Gene Mapping Questions
• Four genes, A, B, C, and D, occur on the same chromosome. Use the
following crossover frequencies to determine the order of the genes on
the chromosome.
• A—D—5%
• B—C—15%
• A—C—30%
• C—D—35%
• B—D—50%
• A. BCAD
• B. CBDA
• C. BACD
• D. CDAB
• E. CBAD
Genetics Problems
• Questions 1&2 refer to a female Drosophila heterozygous
for ebony body color (recessive) and curly wings
(recessive) that was mated to and ebony-bodied, curlywinged male resulting in the following offspring:
• 200 ebony body, normal wing
• 10 normal body, normal wing
• 5 ebony body, curly wing
• 150 normal body, curly wing
Genetics Problems
• 1.
I.
Choose the correct statement(s).
The genes are linked. In the female, the alleles for normal body and normal
wing are on the same chromosome.
II.
The genes are linked. In the female, the alleles for normal body and curly wing
are on the same chromosome.
III.
The genes are unlinked.
IV.
The genes are linked. In the female, alleles for ebony body and curly wing are
on the same chromosome.
V.
The genes are linked. In the female, the alleles for ebony body and normal
wing are on the same chromosome.
A. I, II
B. II, IV
C. III
D. II, V
E. I, V
Genetics Problem
• 2. Which process must occur in order to obtain the ebony
body, curly wing phenotype in the offspring?
– A. Nondisjunction during meiosis in the female.
– B. Crossing over during gamete formation in the
female.
– C. Crossing over during gamete formation in the male.
– D. A mutation in the female.
– E. A mutation in the male.
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