Emory Dent
George Jackson
Biology I
13 December 2013
Fast Plants and their Usage in the Illustration of Simple
Patterns of Mendelian Inheritance
Abstract:
To replicate and solidify Mendel’s Laws of Segregation
and Independent Assortment and their corresponding outcomes,
monohybrid and dihybrid mustard plants from the Wisconsin
Fast Plants program were cultivated, counted, and compared
with Mendel's ratios. In total, 189 of the 250 monohybrids
resulted, 122 possessing purple anthocyanin in their stems,
while 67 experienced a lack thereof. From the 250 dihybrid
seeds, 199 sprouts were recorded: 129 purple-stemmed with
bright green leaves, forty nine with bright green leaves and
non-purple stems, nineteen with yellow-green leaves and
purple stems, and two bearing yellow-green leaves and non-
purple stems. The probability outcome (p) for both species
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of mustards was less than 0.01 when the Chi-square test was
performed on the resulting plant count. According to the
Chi-Square deviation chart utilized, this accounts for
significant deviation from the expected Mendelian ratios,
and thus the experiment failed to accurately reproduce
Mendel's findings.
Introduction:
Genetics can be defined as the study of units of
heredity, called genes, and how they are inherited. These
genes are located in a certain portion of a chromosome
called a locus, and are the building blocks utilized in
forming and defining an individual. Passed on from parent to
offspring, chromosomes consist of tightly wound strands of
DNA intermingled with various proteins.
Genetic variation can be plainly seen all around. Humans
differ in reference to hair color, body type, eye color, and
many other traits. For plants, such traits as height, flower
color and leaf size can be noted as differing amongst
species. These traits and their fluctuation can be credited
primarily to two different factors: environmental and
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inherited. From parents to offspring, some traits can be
simply credited to the combination of genes obtained from
each parent. Environmentally, aspects like humidity, soil
nutrient content, and temperature can greatly affect the
resulting traits of a plant, like the possession of round or
shriveled peas, for example.
Specifically, Mendelian genetics consists of the study
of the genotypes and resulting phenotypes of an organism, in
reference to Mendel’s laws and patterns of inheritance. A
Monrovian monk considered the father of genetics, Gregor
Johann Mendel (1822-1884) discovered and demonstrated what
we now consider basic genetic principles through the
systematic breeding of pea plants. After countless hours of
analyzing and experimenting with thousands of plants, three
postulates resulted from his work:
1. Traits exist in two forms: dominant and recessive
2. An Individual carries two genes for a given
character, and genes have variant forms, which are called
alleles.
3. The two alleles of a gene separate during gamete
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formation, so that each sperm and egg receives only one
allelei (Biology).
With these principles in mind, Mendel continued his
experimentation, dealing with seven specific characters or
traits of variation that differed amongst his annual pea
plants: flower color, flower position, seed color, seed
shape, pod color, pod shape, and plant heightii (Biology).
Through multiple crosses and examinations in reference to
these traits, Mendel began to notice patterns that the
offspring tended to follow. The ratio 3:1 resulted from a
cross (monohybrid) between two parents that varied in regard
to one specific character trait, like pea color. Also, for
crosses between parents possessing two varying character
traits (height and pea shape for example), a ratio of
9:3:3:1 was derived from the resulting offspring. Taking
these tested ratios, and infusing them with modern
terminology, like homozygous and heterozygous, Mendel’s
findings can be understood to a greater extent. For his 3:1
cross, an average of three out of four daughter plants were
either homozygous or heterozygous dominant for the specific
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character, while one remained homozygous recessive. In
reference to the 9:3:3:1 dihybrid cross, an average of nine
were either homozygous or heterozygous dominant for both
traits, six were dominant for one trait, but recessive for
the other, and one was homozygous recessive for both traits.
Instead of Mendel’s pea plants, Brassica rapa Fast Plants
from the mustard family Brassicaceae were utilized in this
experiment. Located on the campus of the University of
Wisconsin in Madison, Wisconsin, the Fast Plants program,
“committed to developing and sharing scientifically
accurate, tried-and-true educational resources, supporting
educators, students, and scientist around the world in the
use of Fast Plants as a model organism for research and
education purposes”iii (About Fast Plants). These Fast Plants
aid immensely in biological studies because of four main
characteristics: speed, productivity, size, and ease of
growthiv (History Fast Plants). From planting to flowering,
only a two-week period is required to span this gap. Through
years of experimentation, Fast Plant developer Professor
Emeritus Paul H. Williams “reduced a 6-month life cycle to 5
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weeks”v (History Fast Plants). Producing lots of seed-
containing pods, Fast Plants are also easy to work with due
to their manageably small size, reaching between 8-14 inches
in this experiment. Able to withstand less-than-ideal
growing conditions, these mustard relatives are capable of
growing just about anywhere. Thus, in light of these
aspects, biologists greatly appreciate and utilize the Fast
Plant program for timely tests and educational purposes.
Materials and Methods:
The experiment was initiated by planting two different
parental species of Field Mustard Fast Plants, P1 and P2.
Placing a seed into each compartment of a Styrofoam growing
tray, fertilizer pellets and a water, wicking triangular
paper was added as well. After filling the cubicles with
potting soil, the foam tray was placed upon a water-wicking
piece of felt, which rested on the lid of a plastic
container. Filled with tap water, this container hydrated
the tail of the wicking felt providing plenty of drink for
the smaller triangular wicks at the base of each developing
plant to absorb. To inhibit mold and mildew, small mold-
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inhibiting paper squares were placed in each vat of water. A
water apparatus for each tray, the entire setup was placed
under a fluorescent light apparatus, which emitted cool
white light continually. This apparatus, constructed out of
PVC pipe, formed a stand from which a fluorescent light
fixture, containing two 4-foot, 32-watt T12 bulbs, could be
hung using lightweight metal chain. After flower blooming,
the species were separately self-pollinated. However, a few
alterations needed to be made in the experimental procedure.
With the water-wicking technique failing to properly
provide needed moisture during the entire experiment, the
plants were few and unhealthy, producing little to no
seedpods. F2 seeds would have been collected from the pods
these F1 plants produced after they were individually self-
pollinated, in order to properly follow experimental
procedure, but the plant population was sparse. Due to a
lack of time, the experiment could not be restarted from the
beginning. Thus, in light of our time frame and to avoid
inaccuracies, a larger quantity of F2 seeds produced by
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identical Fast Plants was purchased and planted instead, 250
of each type to be exact. These F2 seeds were planted under
almost all of the specified growing conditions, this time in
simple trays of potting soil mixed with fertilizer pellets,
watered by a student when needed. Placed under the same
fluorescent light rig, tiny sprouts began to emerge. Far
more successful, a sizable amount of plants was cultivated,
and thus an adequate amount for testing Mendel’s patterns
was obtained. One by one, the tiny sprouts, about seven days
old, were dislodged from their bed of soil, examined
according to their phenotype, sorted and placed with their
similar counterparts on paper towels, and eventually counted
for experimental record.
For both groups of sprout values, Chi-square tests were
conducted in order to discover the level of deviation that
existed between the obtained and expected ratios. After
obtaining such values, they were applied to the Chi-square
distribution chart, found in Appendix B of the utilized
Investigating Biology Laboratory Manual (Table 3). According
to this chart, a p value of 0.05 serves as the line of
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demarcation between significant and non-significant
deviation; thus anything less than 0.05 is deemed
significantly deviating, while anything above 0.05 is not
considered to be deviating substantially from the expected
outcome (Table 3). To further illustrate these crosses,
Punnett Square 1 and Punnett Square 2 show the genotype
organization, layout, and distribution for each, both
monohybrid and dihybrid:
Punnett Square 1.
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Punnett Square 2.
Results:
The resulting sprouts from each of the two different F2 seed
genotypes were recorded.
Table 1. Chi-Square Calculations for F2 Non-Purple Stem,
Hairless Generation (Monohybrid cross)
Anthocyanin Present (Purple Stem)
Anthocyanin Absent (Green Stem)
Observed Value (o) 122 67
Expected Value (e) 142 47
Deviation (O-E) or D
-20 20
Deviation2 (D2) 400 400
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D2/E 2.82 8.51Chi-SquareX2= D∑ 2/E
11.33 11.33
After the observed values were recorded (o), they were
compared with the expected values with Mendelian ratios
applied to the sample size of 189. The single varying trait
in this cross was that of stem color. If the pigment
anthocyanin was present in a plant’s stem, it appeared
purple. In contrast, if anthocyanin were absent from its
stem, a plant would exhibit a green stem. Expecting a
typical 3:1 Mendelian ratio in the final count, 75% purple
to 25% green, the results portrayed a notable deviation from
the expected numbers: 122 to 67 instead of 142 to 47 purple
to green-stemmed plants. Then, the deviation was calculated
to be ±20. After squaring this deviation values and adding
them together, the Chi-square equation was completed, and a
probability value could be assigned to the experiment.
According to Table 1, the resulting p value from the 189
plants that sprung up from this cross with two degrees of
freedom was between 0.01 and 0.001 (Table 3), thus bearing
significant deviation.
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Table 2. Chi-Square Calculations for F2 Non-Purple Stem,
Yellow-Green Leaf Generation (Dihybrid cross)
Bright GreenPurple
Bright GreenNo Purple
Yellow-GreenPurple
Yellow-GreenNo Purple
Observed Value (o)
129 49 19 2
Expected Value (e)
111.9 37.3 37.3 12.4
Deviation (O-E) or D
17.1 11.7 -18.3 -10.4
Deviation2 (D2) 292.4 136.9 334.9 108.16
D2/E 2.61 3.70 9.00 8.72Chi-SquareX2= D∑ 2/E
24.0 24.0 24.0 24.0
For the second portion of the experiment, the sample size of
199 sprouts was categorized according to their phenotypes
(o). Containing two factors of variance, leaf color and stem
color, Mendel’s hypothesis of a 9:3:3:1 resulting ratio was
upheld in this portion of the experiment. To be exact, 56%
of the plants should have possessed bright green leaves and
a purple stem, 19% ought to have been classified with bright
green leaves and a green stem, 19% were supposed to have
yellow-green leaves and a purple stem, and finally 6% would
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have completed the percentage with yellow-green leaves and
green stems. However, significant deviation was noted once
again. From the 199 plants produced and counted, 111.9,
37.3, 37.3, and 12.4 portrayed the application of Mendel’s
hypothesis to the plant population. Yet, with the observed
values of the dihybrid cross being 129, 49, 19, and 2, the
expected outcome greatly differed from the actual yield.
Compared to the hypothetical, these expected values were
then subtracted from the observed outcomes to calculate a
deviation for each phenotype. Squaring these D values and
summing them up, the Chi-square equation was then completed,
and a probability value corresponding with X2 was given. In
referring to Table 2, with three degrees of freedom the
resulting p value for this cross, bearing 199 plants, was
less than 0.001 (Table 3), thus falling under the category
of significant deviation.
Table 3. Chi-Square Distributionvi
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Source: R. A. Fisher and F. Yates, Statistical Tables for Biological, Agricultural, and Medical Research, 6th Edition, Table IV, Longman Group UK Ltd., 1974
Discussion:
The Fast Plants utilized proved to be immensely useful
in this experiment, as they have been in many tests and
demonstrations in the past. Taking into account the short
life cycle, rapid growth, and sizable yield of these
mustards, countless scientists have tested Fast Plants under
a variety of experimental conditions. For example, as
gleamed from a laboratory write-up entitled Ozone affects gas
exchange, growth and reproductive development in Brassica campestris
(Wisconsin Fast Plants), similar Fast Plant varieties served as
test subjects for significant, purposeful studies. Conducted
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in the United Kingdom by a group of Phytologists, the
experiment was conducted in response to real-life, global
conditions. As the lab’s introduction states, “Recent
analysis of tropospheric O3 [Ozone] concentrations between
1990 and 2030 suggest that these will rise in all major
agricultural areas in the northern hemisphere”vii (V. Black,
Roberts, Stewart, and C. Black, 150). With this hazard in
mind, the experiment proceeded by cultivating numerous Fast
Plants, exposing a testing group to an inflow of ozone-
concentrated air for two hours, and setting aside a control
group to compare with. As a result, a ten-day exposure to
the poisonous gas “…reduced vegetative growth and
reproductive site number on the terminal raceme [stem
segment from which flowers protrude]”viii (V. Black, Roberts,
Stewart, and C. Black, 150). Raising awareness of the
impending rise of ozone concentrations, and providing
scientific evidence of the effects of this poisonous gas,
this experiment utilized mere mustard Fast Plants to
accomplish such a task in a short amount of time.
Reflecting on the resulting probability values in this
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experiment, one begs to question the cause of such extreme
fluctuation from the hypothetical outcome, and maybe even
questions the validity of Mendel's laws. The substantial
deviation from Mendel's ratios observed in this experiment
was caused by a few prominent factors.
Primarily, the resulting sample size of less than two
hundred was too much of a window for error, and minuscule in
comparison to Mendel's experiments. As seen in Figure 1, two
experimental outcomes are portrayed from Mendel’s countless
crosses, derived from one of his manuscripts entitled
Experiments on Plant Hybridization.
Figure 1. Portion of Mendel’s Experimental Manuscriptsix
Source: Gregor Mendel, Experiments on Plant Hybridization (Brno, Czech Republic: Proceedings of the Natural History Society of Brünn, 1866), 12.
Despite the differing dialect, the numbers 7342 in
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Experiment 1, and 8023 in Experiment 2 indicate the sample
sizes for two of Mendel’s tests. Due to these enormous
numbers, Mendel achieved ratios far closer to 3:1, which can
also be seen in this excerpt. In calculating out the
probability for each of these experiments, a p value between
0.70 and 0.80 is obtained for Experiment 1, and between 0.95
and 0.90 for Experiment 2. Thus, these very insignificant
levels of deviation show how crucial it is to perform
genetic experiments with a substantial sample size, in order
to inhibit drastic experimental error.
Yet, in the experimental procedure, the planted 250
seeds should have yielded far more sample sprouts than
merely 189 and 199. This lack can possibly be contributed to
a small lull in the plants’ ideal growing conditions. One
weekend, shortly after the seeds were planted, the tray
experienced inadequate water supply. Thus, some of the seeds
could have dried out and became ineffective in producing
their plant species. Also, another factor in this lack of
plant outcome can be considered. As these F2 seeds were
being planted in the soil tray, the seeds were not counted
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to ensure that all 250 (the quantity specified on the seed
packet) of the seeds were present. Thus, the Wisconsin Fast
Plants Organization could have failed to include all 250
seeds in the seed packets we obtained.
Another factor that possibly contributed to the
deviation from Mendel’s ratios was found in categorizing the
sprouts according to their phenotypes. In observation of
each plant, it was very difficult, at times, to decipher
obvious differences between each variation. For example, for
both monohybrid and dihybrid plants, the anthocyanin levels
causing the possession of either a purple stem or a green
stem weren’t as distinctly differing as expected. Thus,
there were many sprouts that resulted with stems that
weren’t overtly purple, yet they couldn’t be considered
green either. This inability to accurately categorize the
plant generation proved to be quite a difficulty in the
experimental procedure, as well as, most likely, an area for
experimental error to emerge.
A prominent aspect of this experiment was that of
applying the Chi-Square test to our outcome of various
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phenotypes, by means of calculating deviation. This test,
applicable to any situation involving experimental and
theoretical frequenciesx (Tallarida and Murray, 140-142), is
widely used and highly favored in the scientific realm. In a
lecture at Cleveland State University entitled Modeling &
Performance Evaluation of Computer Systems, the Chi-Square test was
compared to another distribution test, called the
Kolmogorov-Smirnov (K-S) Test. For large sample sizes, in
any distribution, and in finding differences between
observed and hypothetical probabilities, the Chi-Square test
stands as the best tool for use. Although the outcome is
still an approximation compared to the K-S test, the usage
of the Chi-Square test is ideal in testing the statistical
reliability of experiments such as the one performed herexi
(Chi-Square).
In summation, although Mendel’s ratios seemed
questionable in light of such experimental deviation, his
laws stand as valid after discovering in this experiment
facets of significant error. Yet, despite the significant
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variance, much can be gleamed from the methodologies and
principles portrayed in this laboratory experiment.
References:
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i Eric Widmaier, Linda Grahm, Peter Stiling, and Rob Brooker, Biology
2nd Edition (New York: McGraw-Hill, 2011), 330.
ii Eric Widmaier, Linda Grahm, Peter Stiling, and Rob Brooker, Biology
2nd Edition (New York: McGraw-Hill, 2011), 330.
iii “About the Fast Plants Program” Wisconsin Fast Plants Program: University of
Wisconsin Madison http://www.fastplants.org/about/about_the_program.php
iv “History of the Wisconsin Fast Plants Program” Wisconsin Fast Plants
Program: University of Wisconsin Madison
http://www.fastplants.org/about/history.php
v “History of the Wisconsin Fast Plants Program” Wisconsin Fast Plants
Program: University of Wisconsin Madison
http://www.fastplants.org/about/history.php
vi R. A. Fisher and F. Yates, Statistical Tables for Biological, Agricultural, and
Medical Research, 6th Edition, Table IV, Longman Group UK Ltd., 1974
vii V. J. Black, C. A. Stewart, J. A. Roberts, and C. R. Black, “Ozone
affects gas exchange, growth and reproductive development in Brassica
campestris” (Wisconsin Fast Plants) (New Phytologist: New Phytologist Trust,
2007) 150.
viii V. J. Black, C. A. Stewart, J. A. Roberts, and C. R. Black,
“Ozone affects gas exchange, growth and reproductive development in
Brassica campestris” (Wisconsin Fast Plants) (New Phytologist: New Phytologist
Trust, 2007) 150.
ix Gregor Mendel, Experiments on Plant Hybridization (Brno, Czech Republic:
Proceedings of the Natural History Society of Brünn, 1866), 12.
x Ronald J. Tallarida and Rodney B. Murray “Chi-Square Test”
(Springer Link: Manual of Pharmacologic Calculations, 1987) 140-142.
xi Test, Chit-Square, and Hirundo Rustica. "Chi-Square Test." EEC 686:
785.
