Download Hardy Weinberg Equilibrium Vocabulary and Calculations Review

Hardy Weinberg Equilibrium Vocabulary and Calculations Review
A. How are traits passed down from parents to offspring?
1. Basic Genetics Information Given in Previous Notes:
-“DNA (or deoxyribonucleic acid) is a molecule found in the cells of all living things. The code found in DNA
determines the inherited traits found in an organism. An inherited trait is one that can be passed from parents
to offspring.”
-“We call the particular alleles a person has for a certain trait his/her genotype for that trait. The genotype
determines the actual physical trait, or phenotype.”
- “Within human cells, DNA is organized into 46 chromosomes […] 23 of the 46 chromosomes in one of your
cells came from your mother, and the other 23 chromosomes came from your father. Each chromosome from
your mother has a complementary chromosome from your father that contains the same types of genes in the
same places on the chromosome. We call these pairs of complementary maternal and paternal
chromosomes “homologous chromosomes.”
2. Because the chromosomes in your cells are arranged in homologous pairs, you have two alleles for each
gene. Therefore, the combination of these two alleles determines your genotype for a particular trait.
Typically, one allele form will “cover up” or “mask” the expression of the other allele. We call this allele the
dominant allele, and we use a capital letter to represent this allele. When present, this allele determines the
physical trait or phenotype that is expressed. We call the allele that is covered up or masked the recessive
allele, and we use a lowercase letter to represent this allele. There must be two copies of this allele for the
recessive phenotype to be expressed.
3. When there are two copies of the same allele, we call a genotype homozygous. There are two types of
homozygous genotype. When there are two dominant alleles, we call this genotype homozygous dominant.
When there are two recessive alleles, we call this genotype homozygous recessive. When there is one copy
of the dominant allele and one copy of the recessive allele, we call this genotype heterozygous. An example
is given below.
4. Let’s say there are two alleles for eye color, brown (B) and blue (b). The possible genotypes and their
corresponding phenotypes are given below:
Genotype Letters
BB
Bb
bb
Genotype Descriptions
Homozygous Dominant
Heterozygous
Homozygous Recessive
Phenotypes
Dominant (Brown Eyes)
Dominant (Brown Eyes)
Recessive (Blue Eyes)
5. Though real populations almost always evolve, scientists have come up with two equations to mathematically
model the frequencies of alleles and genotypes in a population that is NOT evolving (i.e. the frequencies of
alleles are not changing across generations, though the frequencies of genotypes may change). We call this
artificial state of “non-evolution” Hardy Weinberg Equilibrium (named for the scientists who developed the
model). To be in Hardy Weinberg Equilibrium, NONE of the factors discussed in #8 can be in effect. In other
words, to be in Hardy Weinberg Equilibrium, a population of organisms must meet the following conditions:
-No genetic drift
-No gene flow
-No mutation
-No sexual selection (i.e. random mating)
-No natural selection
B. How can we mathematically model Hardy Weinberg Equilibrium?
6. There are two equations that comprise the Hardy Weinberg Model. I will simply list the equations here, and
define them in the space below.
Equation #1: p + q = 1
Equation #2: p2 + 2pq + q2 = 1
7. Explaining Equation #1: This equation is true for any population where there are only two alleles, one
dominant and one recessive for a particular trait. Let’s say our alleles are “A” and “a”. In this equation “p”
represents the frequency of “A” (the dominant allele) expressed as a decimal in the range of 0-1. (For
example: 0.4 means that 40% of the alleles found in the population are “A). “q” represents the frequency of
“a” (the recessive allele) expressed as a decimal in the range of 0-1. If there are only two alleles for this trait
in the population, it would make sense that their frequencies would add to 1 (which represents 100% of the
alleles in the population). We call Equation #1 the Allele Frequency Equation.
8. Explaining Equation #2: We call Equation #2 the Genotype Frequency Equation because it expresses the
frequencies of the three possible genotypes when there are only two alleles for a trait (homozygous dominant,
heterozygous, and homozygous recessive). If there are only two alleles for this trait and only three possible
genotypes, it would make sense that these three genotype frequencies would add to 1 (which represents
100% of the genotypes in the population. The meanings of each “term” in the equation are given below.
-p2 represents the frequency of having two dominant alleles (or, in other words, having the homozygous
dominant genotype) expressed as a decimal in the range of 0-1. The mathematics behind this term are
shown below…
Frequency of having two “A’s” = frequency of having one “A” (p) x frequency of having another “A” (p) = p x p = p2
Why do we multiple the frequencies?
We do this to follow the Multiplication Rule of Probabilities (i.e. frequencies), which states that you must
determine the probability that two or more independent events (like receiving “A” from each parent) will occur
together in some specific combination (like genotype AA) by multiplying the probability of one event by the
probability of the other event.
-q2 represents the frequency of having two recessive alleles (or, in other words, having the homozygous
recessive genotype) expressed as a decimal in the range of 0-1. The mathematics behind this term are
shown below…
Frequency of having two “a’s” = frequency of having one “a” (q) x frequency of having another “a” (q) = q x q = q2
-2pq = the frequency of having one dominant allele and one recessive allele (or, in other words, having the
heterozygous genotype) expressed as a decimal in the range of 0-1. The mathematics behind this term are
shown below…
Frequency of having one “A” and one “a” = frequency of receiving p from mom and q from dad + frequency of receiving p
from dad and q from mom = pq + pq = 2pq
Why do we add the frequencies once we have used the Multiplication Rule to find pq and pq?
We do this to follow the Addition Rule of Probabilities, which states that you must determine the probability of
two mutually exclusive events (meaning they can’t occur at the same time) by adding together their individual
probabilities. Our terms pq and pq are considered mutually exclusive because you can’t receive p from mom
and q from dad at the same time as receiving p from dad and q from mom.
9. Suppose we want to use our genotype frequencies to determine our phenotype frequencies. In other words,
suppose we want to determine the frequencies of the actual physical traits in the population.
-There are two genotypes (AA and Aa) that give us a dominant phenotype, so we determine the frequency of
the dominant phenotype by adding together the frequencies of AA and Aa. In other words…
Frequency of showing the dominant phenotype = frequency of genotype “AA” (p2) + frequency of genotype “Aa” (2pq) = p2
+ 2pq
-There is only one genotype (aa) that gives us a recessive phenotype, so the frequency of the recessive
phenotype is equal to the frequency of the recessive genotype (q2)
C.
How can we use our two equations to predict the allele, genotype, and phenotype frequencies of a
population in Hardy Weinberg Equilibrium?
Use the cheat sheet given below to help you answer the following sample problems. (The answers are given in red for
your reference)
Sample Problem #1
The frequency of two alleles in a gene pool is 0.1 (A) and 0.9 (a). What is the percentage in the population of the
heterozygous individuals?
Given: p = 0.1, q = 0.9
Find: 2pq x 100 (because 2pq is normally a decimal and we need to convert to a percentage value)
Work (answer in blue):
2pq x 100 = 2(0.1)(0.9) x 100 = 18%
Sample Problem #2
Allele (B), for white wool, is dominant over allele (b), for black wool. In a sample of 900 sheep, 891 are white and 9 are
black. How many sheep are homozygous dominant for coat color?
Given: q2 = 9/900 = 0.01 (because q2 represents the decimal frequency of the recessive phenotype… or the frequency of
black sheep in this example)
Find: p2 x 900 (because p2 is normally a decimal and we need a whole number of sheep, so we multiply the decimal
frequency by the total population size)
Work (answer in blue):
q2 = 0.01  q = 0.1
p + q = 1 so p = 1 – q
p = 1 – 0.1 = 0.9
p2 x 900 = (0.9)2 x 900 = 0.81 x 900 = 729 sheep
Sample Problem #3
The allele (T), the ability to taste a particular chemical, is dominant to allele (t), the inability to taste it. At Cornell
University, out of 400 surveyed students, 64 were found to be non-tasters. What is the frequency of the recessive allele?
Given: q2 = 64/400 = 0.16 (because q2 represents the decimal frequency of the recessive phenotype… or the frequency of
non-tasters in this example)
Find: q
Work (answer in blue):
q2 = 0.16  q = 0.4
Sample Problem #4
In humans, Rh positive blood is produced by the dominant gene (R), while Rh negative blood is produced by the allele (r).
If the frequency of “r” is 0.4, what percentage of the population has Rh positive blood (the dominant phenotype)?
Given: q = 0.4
Find: (p2 + 2pq) x 100 (because there are two genotypes RR and Rr that could give you the dominant phenotype, Rh
positive blood. p2 represents the frequency of the homozygous dominant genotype, RR, and 2pq represents the
frequency of the heterozygous genotype, Rr. Therefore, to get the frequency that an individual would have either
genotype RR or genotype Rr, and therefore show the dominant phenotype, we need to add their individual frequencies
together, thus p2 + 2pq. p2 and 2pq are both decimal frequencies, so we will need to multiple the sum by 100 to get a
percent value.)
Work (answer in blue):
q = 0.4
p + q = 1 so p = 1 – q
p = 1 – 0.4 = 0.6
p2 = (0.6)2 = 0.36
2pq = 2(0.4)(0.6) = 0.48
(p2 + 2pq) x 100 = (0.36 +0.48) x 100 = 0.84 x 100 = 84%