Student Author Name: Linette Guzman
Team Members Name(s):
Student Author ID #:
Team Members ID #’(s):
Lab Assignment #:
Team Name: The Unknowns
Lab Assignment Title: Gene Frequency
Date: 2016/01/26
Background
·
The Hardy-Weinberg Principle states that the allele and genotype of a species will remain constant
if no other evolutionary factors exist in the environment.
·
In order for the Hardy-Weinberg Principle to be proven correct there must be:
·
no mutations
·
no gene flow
·
random mating
·
a large population size
·
no natural selection (Ex10_Evolution)
·
The Hardy Weinberg Principle equation describes how genetic variation remains constant in the
absence of the five factors stated above. Once p and q are discovered, it is possible to determine the
frequency of the three genotypes; homozygous dominant, homozygous recessive, and heterozygous. The
equation is as follows:
p2 + 2pq + q2 = 1
p= frequency of the dominant allele
q= frequency of the recessive allele
p2= frequency of a homozygous dominant genotype
q2=frequency of a homozygous recessive genotype
2pq= frequency of a heterozygous genotype
Purpose / Objective(s):
 Determine the effectiveness of the Hardy Weinberg Principle through multiple test crosses and
compare them with the base case.
 Assess how positive/ negative mutations work as well as how varied survival rates affect the
outcomes of gene frequencies and therefore the genotypes.
Hypothesis (ese):
1. The base case of the experiment is relatively constant throughout six generations due to 100
percent survival of all species. There are no mutations, no natural selection etc., proving that the
Hardy-Weinberg Principle is observed.
2. The second case of the experiment will prove a steady decline of the homozygous recessive (yy)
pair due to a 50 percent survival rate. Because the homozygous dominant genotypes contain no
recessive alleles, the depletion of yellow beads should not have any great effect on homozygous
dominant (BB). There will however be a slow decline in heterozygous genotypes (BY) as the
availability of recessive alleles (y) is constantly decreasing.
3. The third case of the experiment will quickly decrease the population of yellow/yellow pairs due a
zero percent survival rate. This will result in a greater number of homozygous dominant (BB) and
heterozygous (By) pairs in comparison to homozygous recessive (yy) pairs. There will also be a
Page 1 of 27
Document1
slow decline in the heterozygous genotypes (By) as the availability of recessive alleles (y) is
constantly decreasing.
4. The fourth case will show a steady decline in homozygous recessive pairs (yy) due to a zero
percent survival rate. The number of dominant (B) beads and mutation (R) beads will increase
each generation due to the 150 percent survival rate of heterozygous (BR) pairs and 200 percent
survival rate of homozygous mutation (RR) pairs. The addition of these beads will slowly increase
the number of homozygous dominant (BB) and heterozygous (By) pairs.
5. The fifth case will show a steady decline in homozygous recessive pairs (yy) due to a zero
percent survival rate. The number of dominant (B) beads and mutation (R) beads will decrease
each generation due to the 50 percent survival rate of heterozygous (BR) pairs and zero percent
survival rate of homozygous mutation (RR) pairs. The depletion of these beads will slowly affect
each genotype by decreasing the number of reproducing genotypes for the generation.
Subjects / Materials:
 For cases two and three, 50 blue and 50 yellow beads are needed.
 For experiments four and five, 40 blue, 40 yellow, and 20 red beads are needed.
 Additional beads are necessary for cross three in which positive mutation trials occur.
 A total of four plastic cups are needed for experiments two and three, and seven plastic cups
needed for experiments four and five.
 Notebook to record test cross results.
 Optional: Tape for labeling each plastic cup
Methods / Tools / Instrumentation / Procedures:
For crosses 2 & 3
1. Obtain 50 dominant (Blue) beads as well as 50 recessive (yellow) beads. A total of four plastic
cups are also needed.
2. Combine the dominant and recessive beads in one plastic cup. Place another cup on top of the
first and shake to ensure the beads are thoroughly dispersed in the container.
3. Set three plastic cups on the counter and label them homozygous dominant (BB), heterozygous
(BY), and homozygous recessive (yy).
4. At random, pick two beads from the shaken plastic cup and place in one of the three cups stated
in procedure 3. Continue until all beads are in a designated cup.
5. FOR CROSS 2 ONLY: Only 50% homozygous recessive (yy) survive to reproduce in the next
generation. Remove 50% of homozygous recessive pairs from the designated cup before
beginning the next cross in generation 2.
6. FOR CROSS 3 ONLY: There is a 0 percent survival rate for homozygous recessive (yy),
therefore none live to reproduce the next generation. Remove 100% of homozygous recessive
pairs from the designated cup before beginning the next cross in generation 2.
7. Record the number of pairs (genotypes) left in the cup.
For crosses 4 & 5
1. Obtain 40 dominant (Blue) beads, 40 recessive (yellow) beads, and 20 mutation (Red) beads. A
total of seven plastic cups are also needed.
2. Combine the dominant, recessive, and mutation beads in one plastic cup. Place another cup on
top of the first and shake to ensure the beads are thoroughly dispersed in the container.
3. Set six plastic cups on the counter and label them homozygous dominant (BB), heterozygous
(By), homozygous recessive (yy), heterozygous (BR), heterozygous (By), and homozygous
mutation (RR).
4. At random, pick two beads from the shaken plastic cup and place in one of the six cups stated in
procedure 3. Continue until all beads are in a designated cup.
Page 2 of 27
Document1
5. FOR CROSS 4 ONLY: There is a 0 percent survival rate for homozygous recessive (yy),
therefore none live to reproduce the next generation. Remove 100% of homozygous recessive
pairs from the designated cup before beginning the next cross in generation 2. There is a 150
percent survival rate for heterozygous (BR). Before beginning the next cross in generation 2,
divide the total number of pairs in heterozygous (BR) by two and add that many pairs to the total
number of beads. In addition, homozygous mutation (RR) has a 200 percent survival rate. Double
the current number of pairs for homozygous mutation (RR) and add to the total number of beads.
6. FOR CROSS 5 ONLY: There is a 0 percent survival rate for homozygous recessive (yy),
therefore none live to reproduce the next generation. Remove 100% of homozygous recessive
pairs from the designated cup before beginning the next cross in generation 2. There is a 50
percent survival rate for heterozygous (BR). Before beginning the next cross in generation 2,
remove half of the total number of pairs in heterozygous (BR). In addition, homozygous mutation
(RR) has a 0 percent survival rate. Remove all homozygous mutation (RR) beads so they are
unable to reproduce the next generation.
7. Record the number of pairs (genotypes) left in the cup.
Note: If an uneven number of couples is counted, the number of pairs is rounded down. (i.e. if 9 couples
survive with -50% mortality rate, 4 couples will continue in the next generation.
Results:
 The base case represents the Hardy Weinberg Principle accurately as the genotypes portrayed
on the graphs show little to no fluctuation. Figure 2 predicts that the heterozygous (By) genotype
is to remain at 50 percent while both homozygous dominant and recessive genotypes are to
waver around 25 percent. Figure 1 shows the genotype trend across six generations, and figure 2
carries those trends to twelve generations.
 The second cross between the dominant blue and recessive yellow beads with a 50 percent
survival rate produced results that were just as hypothesized. As apparent in figures 3 and 4, the
homozygous recessive (yy) genotype suffered a swift decline. In addition, figure 4, highlights the
growth rate of the homozygous dominant (BB) genotype as well as the slow decline of the
heterozygous genotype due to an increasing lack of yellow beads. The homozygous recessive
genotypes decreased by 12 couples and the heterozygous genotypes decreased by 6 couples.
The homozygous dominant genotypes saw a 3 couple increase.
 The third cross between the dominant blue and recessive yellow beads with a zero percent
survival rate resulted in zero homozygous recessive couples. This number fell quite drastically as
it began the number of genotypes started off at 12. Homozygous dominant genotypes increased
by 7 couples while heterozygous genotypes fell by 15. As was apparent in the previous case,
figures 5 and 6 show how the homozygous dominant genotype has a positive slope, while the
heterozygous genotype begins to decline. Figure 6 makes it apparent that shortly after generation
12, both homozygous recessive and heterozygous genotypes will both reach zero couples.
 Because the third cross incorporated an additional bead, and altered survival rates, the figures
that will be shown are incredibly different from the Hardy Weinberg base case. Like the previous
cases, yellow diminished quickly with a zero percent survival rate. The lack of yellow also led to a
decrease in blue/yellow as well as red/yellow genotypes. Figure 7 exemplifies how the number of
homozygous recessive couples is the lowest and is most likely to reach zero first. Following
pursuit are the blue/yellow and yellow red couples which declined by 14 and 2 couples
respectively. Due to a 150 percent survival rate for blue/red couples and red/red couples, there
was a swift increase in the number of red beads and many blue beads were added as well. The
addition of these beads has an effect in figure 8 where the homozygous mutation (RR) genotype
increases unbounded. The blue/red genotype also continues to increase. The homozygous
mutation genotype rose from 3 to 55 couples in a matter of 6 generations. Heterozygous blue/red
saw an increase from 10 to 27 couples.
Page 3 of 27
Document1


The final cross between the dominant blue, the recessive yellow, and the mutation red beads
once again showed a speedy decline for the homozygous recessive genotype due to a zero
percent survival rate. Figure 9 shows that by generation 3, there are no longer any homozygous
recessive couples in the environment. This leads to a lack of yellow beads and also has an effect
on the other genotypes containing a yellow allele. In addition to the zero percent survival rate for
homozygous recessive genotypes, the homozygous mutation genotypes suffered the same fate.
The zero percent survival rate took the red/red genotypes from 4 couples to 1 and the
yellow/yellow genotypes from 8 to 0. Figure 10 makes it apparent that a decrease in one allele
leads to a decrease of the entire population. Each genotype is expected to have a negative slope
by generation 12.
In each cross except for the base case, the homozygous recessive genotypes decreased very
rapidly due to a varied zero to 50 percent survival rate. Figures 13, 14, and 15 highlight the
depletion of homozygous recessive couples and show their percentage survival rate given the
total number of couples.
Analysis / Discussion:
 Each cross occurred just as hypothesized because there were no external pressures that could
manipulate the data.
 No natural disasters were present to alter the number of total couples. Should they have been a
factor, natural selection would have played a role in determining which individuals were most
capable of surviving such a catastrophe.
 The positive mutation graph continued to grow which is not an adequate simulation of real life
events. The environment has a carrying capacity and thus is only able to sustain so many
organisms. The incredible increase in the positive mutation case would have led to a competition
for resources and drastically altered statistics.
 It is incorrect to keep the survival rate constant over an entire 12 generations. Over time, a
species will evolve and adapt to their environment, increasing their chance for survival.
 The hypotheses were accurate based on what was tested, but cannot be applied in the real world
due to an absence of many factors.
Conclusions / Further Considerations:
 It is likely that an alteration of the initial number of couples would have had an effect on the final
number of couples for each genotype. While this would have slightly changed the results of
generation 6, it is hypothesized that there would have been no unexpected trends to arise.
 The survival rate would have made a huge impact on the number of couples for each genotype
and the overall population as well. This is apparent by the drastically manipulated survival rate of
the homozygous mutation genotypes and the steep incline in couples thereafter.
 While the tests brought accurate results, the data cannot be applied to the real world where there
are many outside factors that prevent unlimited growth.
 The addition of a carrying capacity would make for a more viable and realistic test.
 It would be beneficial to create a Hardy Weinberg NOT case where all the stipulations for a nonevolving species are violated.
Page 4 of 27
Document1
ATTACHMENTS
Figure 1
According to the figure above, the gene frequency for the homozygous recessive genotype
decreased by about 3 percent (27% to 24%) after the first generation and constantly changes by
3 percent through the experiment, however, the gene frequency remains the same by the time
the 6th generation is born. From this, it is concluded that not many factors are present for
evolution. The By genotype has a constant gene frequency of 50% throughout the experiment.
The heterozygous pair is the most common result. Hardy Weinberg is observed.
Figure 2
Page 5 of 27
Document1
The following figure predicts the genotype outcomes of the next 6 generations based on a trend.
The heterozygous pair, By, still accounts for 50% of the total population for the next six
generations. According to the graph, the next most common genotype after 12 generations is
the homozygous dominant genotype, BB, accounting for 26% of the total population. The
homozygous recessive genotype, yy, accounts for 24% percent. There is not much change in
population of genotype pairs even after 12 generations. Natural Selection cannot occur when
the Hardy-Weinberg Principle is met.
Figure 3
Page 6 of 27
Document1
In the figure above, the gene frequency among the population changes more dramatically after
each generation. Especially between the 2nd and 4th generations. A following reason for the
high population of homozygous dominant blue would be the absence of the recessive yellow
allele. Throughout the case, the homozygous recessive genotype slowly faces a continual
decrease in its population and genotypes containing the dominant allele B, are more likely to
occur after successive generations.
Figure 4
Page 7 of 27
Document1
The homozygous recessive genotype becomes extinct after about 9 generations. The dominant
By allele is not affected much by the recessive (y) allele and so, it continues to occur more often
among the population throughout the generations. In this case, the frequency shows the
reduced population of species carrying the yy genotype. There was quite a difference in the
frequency of the yy genotype after 12 generations.
Figure 5
Page 8 of 27
Document1
After 6 generations, there are no more homozygous recessive genotypes in the population due
to a 100% mortality rate. Because there are very few recessive y alleles and an excessive
amount of dominant B alleles in the population, the homozygous dominant genotype becomes
the most common. Despite the absence of homozygous recessive genotypes, the recessive y
allele continues to be carried in the heterozygous genotypes.
Figure 6
Page 9 of 27
Document1
As hypothesized, the homozygous recessive genotype does not grow in population size and
becomes extinct. The homozygous dominant genotype becomes the prominent genotype of the
population, accounting for 86% of the total population and it is projected to continue to rise in
future generations. The heterozygous genotype slowly becomes less common within the
population due to the diminishment of the recessive y allele. Despite the fact that no
homozygous recessive genotypes occur in the 6th generation, the y allele continues to be
carried in the heterozygous genotypes. This means that there is a very slight chance that a
homozygous recessive individual can be produced in future generations.
Figure 7
Page 10 of 27
Document1
In this case, a positive mutation has become present in the population. The RR positive
mutation dramatically becomes more common among the population after each successive
generation. By the 6th generation, the RR positive mutation accounts for 51% of the population.
The homozygous dominant genotype, BB, drops about 5% in population size in 6 generations.
The population of species with a BR positive mutation proportionally increases in size as the RR
mutation until about the 5th generation. Any genotypes with a (y) allele account for the minority
population and continue to decrease after each successive generation.
Figure 8
Page 11 of 27
Document1
The forecast trend shows an increase in the RR and BR Positive Mutation throughout the future
generations. Genotypes with the recessive (y) allele slowly decrease in population size and
become extinct. By the 20th generation, the Ry and BB genotypes become an endangered
species.
Page 12 of 27
Document1
Figure 9
This graph shows the phenotype among the population in the generations to follow. The
majority of the population (about 95%) are red and the odds of being born with a red phenotype
are quite high. Although the red phenotype occurs in 91% of the population, the purple
phenotype also occurs in 72% of the population after about 12 generations. The yellow
phenotype goes extinct by the 6th generation due to its recessive allele.
Page 13 of 27
Document1
Figure 10
The negative mutation results in the extinction of most gene combinations. Each species
genotype is greatly reduced as the RR negative mutation population is slightly reduced. The
population size containing the By genotype dramatically faces extinction through the course of 6
generations. The most common genotypes among the population after 6 generations are BB
and BR.
Page 14 of 27
Document1
Figure 11
After about 7 generations, every allele not containing BB or BR negative mutation goes extinct
in the case of the negative mutation forecast. The By negative mutation faces a sharp decline in
the population. However, the BB and BR mutation will also face extinction in future generations
as it still shows a negative trend.
Figure 12
Page 15 of 27
Document1
In this case, about 20% of the population will have a Blue phenotype. The next most common
phenotype among the population is Purple, which occurs in 9% of the population. There is little
chance for a Red or an Orange phenotype to occur in the population (3-4%). The genotype
containing the (B) allele is dominant over the other genotypes before and after the negative
mutation as the blue phenotype remains to be the majority of the population.
Figure 13
Page 16 of 27
Document1
The graph above displays the trend of the By genotype depending on the abundance of the yy
genotype among the total population. The size of (y) and (B) alleles stay constant in the By base
case, accounting for 50% of the total population. At 50% yy, the occurrence of the By genotype
is dramatically reduced by about 30% in the 2nd generation, but increases even further past the
initial starting population to account for 58% of the population in generation 4. Overall, the By
genotype remains to be about the same after 6 generations regardless of 50% yy. In the case of
100% yy, the By genotype becomes less common among the population after each generation
and it appears to face extinction in the next generations.
Figure 14
Page 17 of 27
Document1
The blue trendline shows a good survival rate for 100% survival of the yy genotype. At 50%
survival yy, the population decreases most rapidly. In the case of 0% survival positive mutation,
the population decreased slowest but still became extinct after about 12 generations.
Page 18 of 27
Document1
Figure 15
Each yy case results in extinction by the 12 generation except the yy base group. In the yy base
case, the yy genotype occurs in around the 25th percentile even after 12 generations proving
the Hardy-Weinberg Principle is being observed. The histogram clearly shows the good survival
rates of the homozygous recessive pair in the yy base case.
Page 19 of 27
Document1
Figure 16
The homozygous dominant genotype, BB, occurs most in the population when there are fewer
homozygous recessive, yy, genotypes in the population. The decreased presence of the recessive y
allele causes a higher proportion of dominant B alleles in the population. This causes a higher number of
homozygous dominant genotypes in the population. In the negative mutation case, the number of
homozygous dominant genotypes in the population does not significantly change. This is because alleles
are being taken out of the gene pool, so the number of homozygous dominant genotypes slightly drops
before stabilizing. The number of BB couples in the 100% survival BB base case is an average of 8. The
same applies for the case containing the negative mutation.
Figure 17 - Genotype
Page 20 of 27
Document1
Figure 18 - Genotype (%)
Page 21 of 27
Document1
Figure 19 - Phenotype
Page 22 of 27
Document1
The info on the chart clearly shows that the most common phenotype of the total
population is blue. In the first two cases, the blue phenotype outnumbers the yellow phenotype
by about 3 times. In the first case, the gene phenotype frequency stays constant but in case 2
and 3, the yellow phenotype faces extinction in future generations. In case 4, a red phenotype
grows in population size after each generation and eventually becomes the most common
phenotype by the sixth generation. ...
Figure 20 - Phenotype (%)
Page 23 of 27
Document1
Just like the previous chart, the numbers stay constant for the first case in which evolution is
unlikely. The blue allele remains dominant over the yellow allele and accounts for the majority of
the population’s phenotype in the first 3 cases. In the positive mutation case, the red phenotype
occurs most of the population. In the negative mutation case, the blue phenotype occurs in the
20% range and is the only phenotype that is not showing a trend toward extinction.
Figure 21 - Hardy-Weinberg Analysis
Page 24 of 27
Document1
Figure 22 - Hardy-Weinberg Analysis (%)
Page 25 of 27
Document1
Page 26 of 27
Document1
Figure 23
In- Progress Pictures
References:
"Charles Darwin Biography." Bio.com. Ed. Biography.com Editors. A&E Networks Television, n.d. Web.
29 Jan. 2016.
"Natural Selection." Virtual Lab. N.p., n.d. Web. 29 Jan. 2016.
<http://www.mhhe.com/biosci/genbio/virtual_labs/BL_12/BL_12.html>.
O'Neil, Dennis. "Modern Theories of Evolution: Hardy-Weinberg Equilibrium Model." Modern Theories of
Evolution: Hardy-Weinberg Equilibrium Model. N.p., 2012. Web. 29 Jan. 2016.
"The What, Why and How of Change in Populations." Bio116 Assignment Hardy Weinberg. Murray State,
n.d. Web. 29 Jan. 2016.
WIdger, David. "On the Origin of Species By Means of Natural Selection By Charles Darwin." Gutenberg.
Ed. Sue Asscher. N.p., 22 Jan. 2013. Web. 28 Jan. 2016.
Page 27 of 27
Document1