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Principles of Biology
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contents
Mendelian Inheritance
Inheritance follows the rules of probability.
Dice and the law of probability.
Predicting the likelihood of inheriting a particular trait is similar to predicting the possible outcomes of rolling dice. It is
important to understand probability to study genetic inheritance.
Adrienne Hart-Davis/Science Source.
Topics Covered in this Module
Laws of Probability
The Punnett Square
Major Objectives of this Module
Analyze a basic Punnett square problem.
Analyze a test cross problem.
Determine probabilities in monohybrid and dihybrid crosses.
page 198 of 989
4 pages left in this module
Principles of Biology
38 Mendelian Inheritance
Laws of Probability
Probability examines how likely it is that an event will occur. Probabilities
range from 0, where an event has absolutely no chance of occurring, to 1,
where there is no chance that the event will not occur. There are two basic
rules to calculating probabilities depending on the type of events.
Multiplication rule: Predicts the probability of independent events (a
particular event in one experiment does not affect the probability of event in a
second experiment). For example, when rolling a dice twice, the outcome in
the first roll will not affect the probable outcomes when the dice is rolled a
second time. The results of the two dice rolls are independent of each other.
Each individual probability is multiplied to obtain an overall probability.
Addition rule: Predicts the probability of mutually exclusive events. Mutually
exclusive means that if one event occurs (such as a flipped coin comes up
as a heads), the other event cannot simultaneously occur (i.e., it cannot be
tails). The probability of either of the mutually exclusive events, either A or B,
occurring is equal to the probability of event A added to the probability of
event B (in the simple coin tossing case, the additions rule tells us that the
probability that a flipped coin will be either heads or tails is 100%, because it
will turn up heads approximately half of the time and tails the other half).
Gregor Mendel studied the patterns of inheritance by breeding pea plants. In
one set of experiments, he bred lines of plants that each had a different trait
(for example, seed color or shape). He then crossed those lines with different
traits to create a monohybrid cross; the offspring (F1) did not have all of the
traits that he observed in the parent generation. After crossing individuals in
this F1 generation, the traits that had disappeared in the F1 generation
reappeared in the offspring of these crosses (F2). However, the trait did not
reappear in all of the offspring — on average, it appeared in 1 of 4 plants. He
called this trait recessive because it could be masked by the other, dominant
trait. What if Mendel had bred only four plants instead of hundreds? Would
he have seen this pattern?
What does probability have to do with genetics?
The products of a genetic cross can be predicted using laws of probability.
Mendel's principle of segregation states that two alleles in a parent
segregate to form gametes with only one of those alleles through meiosis
(Figure 1). The discovery of chromosomes in the latter part of the nineteenth
century by Walther Flemming, along with the identification of the cell division
process that gives rise to gametes (meiosis), reestablished the importance of
Mendel's work. In meiosis, the parent reproductive cell, which contains a pair
of each chromosome (called homologous chromosomes), undergoes two
steps of division (meiosis I and meiosis II). Each parent cell divides into two
cells during meiosis I, and the homologous chromosomes separate, followed
by a second division in meiosis II where the two sister chromatids separate,
forming four gametes that all contain a single allele (Figure 1). When alleles
are described as dominant or recessive, it is important to keep in mind that
dominance and recessiveness are not intrinsic allelic properties. Instead,
they are effects that may only be measured in relation to the effects of the
alternative alleles of the same gene.
contents
Figure 1: Mendel's principle of segregation.
Homologous chromosomes contain alternative versions of the same
allele. In this case, the blue chromosomes contain the allele "G" or "g," and
the red chromosomes contain either "W" or "w." Note how the homologous
chromosomes and their sister chromatids randomly segregate into the
four different gametes based on their positions during meiosis I, leading to
the two alternative pathways. The properties of the allele (dominant or
recessive) do not influence the location of the alleles in gametes.
© 2013 Nature Education All rights reserved.
Figure Detail
Which allele ends up in which gamete is random. However, one could predict
the likelihood of the offspring possessing specific alleles (the genotype), and
ultimately the phenotype, using the rules of inheritance that are governed by
probability. Probability examines how likely it is that an event will occur.
BIOSKILL
What Is the Probability of a Coin Toss?
Every time one flips a standard (fair) coin, the chance of getting heads is 1 in
2, or 50% (Figure 2). Each toss is one independent probability event —
the outcome of one toss does not impact the outcome of any other tosses.
You likely understand the reasoning behind the concept of independent
probability, but it is not so easy to observe. If one flips a coin twice, there is a
good chance that it may be heads both times. If one flips a coin 10 times,
there is a chance, but a much smaller chance, that it will be heads all 10
times. During World War II, a South African statistician, John Kerrich, passed
some of the time he spent as a prisoner of war flipping a coin 10,000 times.
He ended up with heads 50.67% of the time. The more events there are, the
more the results reflect the predicted probabilities.
Figure 2: Calculating the probability of several independent events.
The total probability of multiple independent events is calculated by first
determining the probability of one of the independent events. In this case,
the probability of a single coin toss resulting in heads is one-half, or 50%.
Therefore, the total probability of four coin tosses resulting in heads is ½ ×
½ × ½ × ½, or one-half to the fourth power.
© 2014 Nature Education All rights reserved.
Figure Detail
Consider a person flipping a coin four times. What is the chance of getting
heads on all four tries? Each of the four tries has a probability of 1/2 that it
will be heads. Since none of the flips will impact the outcome of any of the
other flips, you multiply the probability of heads for each flip together to
determine the probability of four heads in a row.
½ x ½ x ½ x ½ = (½)4 = 1/16 = 0.0625 = 6.25%
There is a bit more than a 6% chance of getting heads on all four coin flips.
This example demonstrates the multiplication rule for independent
probability.
BIOSKILL
How does the multiplication rule apply to genetics?
A recessive trait is expressed only when the allele coding for the recessive
trait is inherited from both parents (that is, the organism is homozygous for
the recessive trait). If the recessive allele is only inherited from one parent
(i.e., the organism is heterozygous), the dominant trait is expressed. In
Mendel's pea plants, white flowers were recessive, and purple flowers were
dominant. Mendel reasoned that if each parent carried the alleles coding for
one dominant and one recessive trait, the offspring had a 50% chance of
inheriting the allele coding for the recessive trait from one parent and a 50%
chance of inheriting the allele coding for the recessive trait from the other
parent.
Test Yourself
Imagine that two heterozygous plants, each with one dominant allele and one recessive allele,
are mated with each other. Since a plant has a 50% chance of inheriting a particular allele from
each parent, what is the probability that the offspring of the two plants will inherit two copies
of the allele coding for the recessive trait?
Submit
There is a 25% chance that such a plant will have white flowers and,
conversely, a 75% chance that it will have purple flowers. The reason that
white flowers, the recessive trait, are less likely is that the recessive trait can
only occur under one scenario: namely, the offspring's inheritance of both
recessive alleles; conversely, there is a greater chance that the offspring will
have purple flowers because purple flowers can result in two different ways:
plants that are homozygous for the dominant trait and those that are
heterozygous both express the purple flower trait. As a result, when counting
plants with different flower colors, we expect that purple flowers should occur
in a 3:1 ratio with white flowers.
Mendel wanted to test this hypothetical ratio, but he knew that patterns in
probability are most reliable when the numbers are large. As a result, he
measured hundreds of offspring from multiple monohybrid crosses over
many generations of pea plants.
IN THIS MODULE
Laws of Probability
The Punnett Square
Summary
Test Your Knowledge
PRIMARY LITERATURE
Using sterile mates and
engineered toxins to beat bugs
Suppressing resistance to Bt cotton with
sterile insect releases.
View | Download
Classic paper: How scientists
cloned the first mammal (1997)
Viable offspring derived from fetal and adult
mammalian cells.
View | Download
Classic paper: Fruit fly research
reveals how complex organisms
form (1980)
Mutations affecting segment number and
polarity in Drosophila.
View | Download
SCIENCE ON THE WEB
Genetics in the Lab
Simulate a laboratory to discover the genetic
inheritance patterns of fruit flies
Let the Computer Do the Work
Use this website to compare observed and
expected frequencies using the chi-square
test
Roll the Dice
Observe the odds of rolling a certain number
Model Organism
Explore this NIH website about model
organisms used in biomedical research
In Mendel's Words
Read Gregor Mendel's original paper
Experiments in Plant Hybridization (1865)
Understanding the Spectrum of Dominance
Alleles are never exclusively "dominant" or
"recessive."
page 199 of 989
3 pages left in this module
Principles of Biology
38 Mendelian Inheritance
The Punnett Square
The Punnett square, invented by geneticist Reginald Punnett, is used to
assess probability in genetics (Figure 3). The father's alleles are listed on
one side of the square and the mother's on the other side. The cells of the
table represent offspring, each of which receives one allele from the father
and one from the mother. Drawing a Punnett square is one way to figure out
the probability of parents with particular genotypes having offspring of a
certain genotype or phenotype. Punnett squares are often easier to visualize
than mathematical calculations of probability.
Illustrating probability and the Punnett square with Mendel's peas.
Not all pea plants with purple flowers have the same set of alleles. A purpleflowered plant may be homozygous, having inherited the dominant allele
from each parent, or heterozygous, having inherited one dominant and one
recessive allele. What is the probability that a plant with heterozygous
parents will also be heterozygous?
A plant is heterozygous when it receives
an allele coding for the dominant trait from the female and an allele
coding for the recessive trait from the male (event A)
or
an allele coding for the dominant trait from the male and an allele
coding for the recessive trait from the female (event B).
These two possibilities are not independent — in fact, they are mutually
exclusive. In such cases, probabilities are calculated using the addition rule.
What is the probability that one of these events will occur?
In this case, the two events have the same likelihood of occurring. A
monohybrid cross between two heterozygotes gives four offspring. The
probability of event A is one-quarter, and the probability of event B is
one-quarter. Applying the addition rule to this situation, we would add
one-quarter to one-quarter to conclude that there is a 50% chance (¼ + ¼ =
½ ) that one of the offspring will be heterozygous. Thus, if two heterozygotes
breed, half of their offspring, on average, will also be heterozygotes.
Because purple flowers are dominant, this phenotype does not reveal the
plant's genotype. What is the probability that a plant is heterozygous if its
parents are heterozygotes with purple flowers? The probability that a plant is
heterozygous, given that it has purple flowers, is two-thirds. Note that this is
higher than the chance of the plant being heterozygous when its phenotype
is unknown, which we calculated to be one-half. An easier way to visualize
these probabilities is by taking the alleles of each parent and combining them
by means of a Punnett square (Figure 3).
contents
Figure 3: Probability predicts genotype and phenotype in Mendel's
monohybrid cross.
Probability is used to assess the genetic outcomes (both genotype and
phenotype of the offspring). This Punnett square is a straightforward way
to visualize the possible combinations of alleles the offspring of two
parents will have. In this example, two individuals that are heterozygous
(Pp) are mated. The alleles in the parental gametes are on the outside of
the square, and each cell of the Punnett square represents the possible
allelic combinations for the offspring. (Each offspring, of course, receives
one allele from the male's gametes (sperm) and one allele from the
female's gametes (egg).) The cells show that on average three of every
four offspring should have purple flowers; on average, two out of those
three will be heterozygous (Pp), and one out of three will be homozygous
for the dominant trait (PP). Only one of four offspring, on average, will have
white flowers as a result of being homozygous recessive (pp).
© 2014 Nature Education All rights reserved.
How do I use a Punnett square?
The body of a fruit fly may be black or brown. Brown is the dominant color (B)
and black is the recessive color (b). You can create a Punnett square to
figure out what the offspring will look like given the parents' genotypes
(Figure 4).
Figure 4: How to draw a Punnett square.
Punnett squares may predict the traits of the offspring that result from a
particular cross.
© 2013 Nature Education All rights reserved.
Figure Detail
The below instructions describe how to create a Punnett square for a cross
between a homozygous brown female fly (BB) and a homozygous black male
fly (bb). These instructions could also be used for monohybrid and dihybrid
crosses. Larger crosses, however, are more complicated.
Step 1. Write down the genotype of the female and male. In this case, the
female's genotype is BB, and the male's is bb. Count each parent's alleles and
multiply the numbers. The result determines how big the Punnett square
needs to be. In this case, because there are only two alleles for each parent,
there are four possible outcomes of allelic combinations (2 * 2 = 4), and a
square with 4 cells is needed.
Step 2. Draw a square with the required number of cells.
Step 3. List the female's alleles along one side of the square and the male's
alleles along the other. In this case, the alleles from the female are written in
the column on the left (B and B) and the alleles from the male are written in
the row on the top (b and b).
Step 4. Copy each combination of alleles that can be received from each
parent in the respective cells. Each B from the female is combined with each
b from the male in each cell, thereby providing the possible genotypes of the
offspring.
Step 5. Determine the phenotypes of the offspring based on their genotypes.
In this case, all of the individuals are heterozygous (Bb), and because the
allele for brown (B) is dominant over the allele for black (b), all the fruit flies of
this pairing would be brown.
BIOSKILL
Crossing Flies: Practicing the Punnett Square
Practice determining phenotypes and phenotypic ratios expected from the
offspring (F1 generation) and the offspring's offspring (F2 generation) of a
monohybrid cross between a brown female with dominant homozygous
alleles (BB) and a black male with recessive homozygous alleles (bb) (Figure
5).
Figure 5: Monohybrid crosses.
Determine the phenotypes and phenotypic ratio expected from the
offspring (F1 generation) and the offspring's offspring (F2 generation) of a
monohybrid cross between a brown female with dominant homozygous
alleles (BB) and a black male with recessive homozygous alleles (bb).
© 2013 Nature Education All rights reserved.
Transcript
Test Yourself
What are the possible genotypes that could produce a brown phenotype? What about a black
phenotype?
Submit
BIOSKILL
Using Punnett squares for dihybrid crosses.
The F2 generation in the interactive in Figure 5 represented a monohybrid
cross, which is a pairing of two parents that are both heterozygous for one
trait (in this case body color). What if the parents differ not just in one trait but
in two or more? Fruit flies may have brown or black bodies and brown or red
eyes. A dihybrid cross is a cross between parents that are heterozygous for
two traits. Although a Punnett square for a dihybrid cross is more complex
than Punnett squares for monohybrid crosses, the purpose of the square is
the same: determining the probable genotypes and phenotypes of the
offspring.
Figure 6: Dihybrid Cross.
When both parents are heterozygous for two traits, the offspring may have
any of four possible phenotypes (brown body and red eyes, brown body
and brown eyes, black body and red eyes, and black body and brown
eyes). Note that allele combinations for a dihybrid cross are made by
determining the possible combinations of alleles from the two different
genes.
© 2013 Nature Education All rights reserved.
Figure Detail
Test Yourself
What is the phenotypic ratio among the offspring of the dihybrid cross shown in Figure 6?
Submit
What is a test cross?
In Mendel's peas, the purple trait is dominant, so a purple flower could either
be homozygous (PP) or heterozygous (Pp) for the purple allele. How could
you experimentally determine the genotype if you had a pea plant and all
that you knew about it was that it had a purple flower? In a test cross, the
purple flower, whose genotype is unknown, is bred with a white flowered pea
plant that expresses the recessive trait (Figures 7 and 8). If the purple plant
is homozygous, all of the offspring will be purple because they will all have
at least one copy of the dominant purple allele. If the parent plant is
heterozygous, having both an allele coding for the dominant trait and an
allele coding for the recessive trait, half of the offspring will be white and the
other half will be purple. Therefore, you could determine whether the plant
with an unknown genotype is heterozygous or homozygous by looking at the
phenotypes of the offspring from a test cross.
Figure 7: Test cross.
Crossing an organism of unknown genotype with one expressing
recessive traits will determine the genotype of the unknown parent (i.e.,
whether it is homozygous or heterozygous).
© 2014 Nature Education All rights reserved.
Figure Detail
Figure 8: Test-cross problem.
What is a brown female parent's
genotype if half of her offspring are
brown (B), the other half are black (b),
the black allele is recessive, and the
male parent is black (bb)?
© 2013 Nature Education All rights
reserved.
Test Yourself
In a cross between a brown female fly and a black male fruit fly, if half of the offspring are
black, what is the female's genotype? What if all of the offspring are brown?
Submit
BIOSKILL
A Chi-Square Test Uses Probability to Detect Differences between
Expected and Observed Values
The predictions made in Mendel's monohybrid and dihybrid cross are based
on some assumptions that certain events are random and will occur with a
certain probability. For example, it assumes that alleles randomly and
independently assort into gametes and that fertilization between gametes is
random. Therefore, the simple predictions from Mendelian genetics are not
always observed. If the observed data differ substantially from what would
have been expected from our Punnett square and probability calculations,
we can infer that the simple assumptions, such as independent assortment,
are not true. When we assume that the observed data of a genetic cross will
fit a given Mendelian ratio, a null hypothesis (H0) is generated, which is that
there will be no real difference between the measured values (or ratio) and
the expected values (or ratio). The null hypothesis can either be rejected or
not rejected for a given set of data measured using statistical analysis.
One of the simplest statistical tests for assessing whether the observed
values differ substantially from those expected is the chi-square test, often
abbreviated χ2. In figure 9, a chi-square test is illustrated using a cross
between genes for body color and wing type in fruit flies. In these genes,
brown bodies (B) and normal wings (W) are dominant traits, and black bodies
(b) and vestigial wings (w) are recessive traits. A female fruit fly heterozygous
for brown body and normal wings (BbWw) was crossed with a male fruit fly
with a black body and vestigial wings (bbww) (Figure 9).
Figure 9: Crossing a heterozygous dominant female with a
homozygous recessive male.
Four equally probable phenotypes are expected in the offspring.
© 2013 Nature Education All rights reserved.
If the assumptions are that these two genes are independent and randomly
assort into gametes, we can predict the proportions of genotypes and
phenotypes using a Punnett square as above. In this cross, we expect a
1:1:1:1 ratio of the following phenotypes: brown body, normal wings; black
body, vestigial wings; black body, normal wings; and brown body, vestigial
wings. That is, on average, one-quarter (25%) of the offspring from this cross
should be in each of the four phenotype categories. If a scientist breeds
2,300 fruit flies, each phenotype should be represented by approximately
575 flies (one-quarter expected in each group x 2,300 flies = 575 flies per
group). Remember that it may take many crosses before a reliable estimate
of proportions can be calculated (if the scientist only bred five or 10
individuals, the proportions would almost certainly differ from the expected
ratios, but this could have easily happened by chance). However, in this
case, the observed results look rather different from the results that would be
expected from random processes (Figure 10). Are these results significantly
different than expected?
Figure 10: Data for χ2 analysis.
A chi-square analysis is used to determine if the observed counts are
significantly different from the expected counts for each of these four fruit
fly phenotypes.
© 2011 Nature Education All rights reserved.
This is where the chi-square test comes in. The formula is
χ2 = the sum of ([observed count - expected count]2/expected count)
If the observed counts were exactly as expected, the χ2 value will be 0. As
the observed results increasingly differ from the expected results, the χ2
value increases. To interpret the χ2 result, the degrees of freedom (df) must
be also determined, which are equal to "n-1," where "n" is the number of
different categories into which the data are divided. In the example above,
there are 4 possible phenotypes, and thus "n" is 4; the df is 3 (4-1).
A χ2 probability table is used to determine the statistical significance of the χ2
value we calculate; that is, the table tells us what the probability is that our
observed values differ from the expected value by chance alone. A high
probability (p), such as p > 0.5, tells us that there is more than a 50% chance
that the differences that we found between the observed and the expected
results could have been simply due to chance. This would not give us much
confidence that the results were in fact significantly different and we would
not reject the null hypothesis that any observed differences were simply due
to chance. To find the significance value, match the df and χ2 values in a χ2
probability distribution table (available in most statistical textbooks or online).
One common statistical standard is p < 0.05, which means that there is less
than a 5% probability that the observed results would have occurred simply
by chance and were due to random sampling; as a corollary, there is a
greater than 95% probability that the observed results are due to
non-random factors, and that the null hypothesis can be rejected.
For these fruit fly crosses, χ2 = 1,002.65, and df = 3. For three degrees of
freedom, the χ2 value that must be found for there to be only a 5% that the
differences are due to chance (p < 0.05) is 7.82. That is, any χ2 value greater
than 7.82 has less than a 5% probability of occurring by chance. Our χ2
value of more than 1,000 is much greater than 7.82! In other words, this
result is highly unlikely to have occurred by chance. What could account for it?
Observed phenotypic ratios often differ from those expected by Mendelian
inheritance. This is because many genes are not inherited according to
Mendel's three principles of inheritance (dominance, segregation and
independent assortment). For example, some genes do not code for clear
dominant or recessive traits, violating the principle of dominance. In addition,
genes that are near each other on the same chromosome are sometimes
linked so that they are not sorted independently into gametes, violating the
principle of independent assortment. Although Mendelian inheritance only
applies to a minority of genes, Mendel's work pioneered the quantitative
genetic methods that allowed the discovery of non-Mendelian traits.
BIOSKILL
BIOSKILL
What Makes a Suitable Model Organism?
A model organism is one that is well suited to scientific research.
Experiments using model organisms help scientists understand the
fundamentals of biological principles, which can then be extended to other
organisms, including humans. Gregor Mendel used pea plants as a model
organism in the mid-1800s, and in the early 1900s Thomas Morgan used the
fruit fly Drosophila melanogaster. Other organisms now commonly used in genetic
research include Caenorhabditis elegans (a nematode worm), Arabidopsis thaliana (a
small plant in the mustard family), mice and yeast. What makes these
organisms useful as models?
Pea plants are inexpensive and easy to grow from seeds. They
mature quickly, produce many seeds, and show a number of visible
variations in flower color, seed color and shape. Gregor Mendel also
cut the flowers' male reproductive appendages, or stamens, to only
allow cross-pollination. This allowed the parents of the offspring to be
known and traced. Today, the most common plant used as a model
organism is Arabidopsis thaliana, which shares some of the same
advantages as pea plants, such as high variability in traits, but is also
much smaller and can grow more rapidly. It also has a small genome
with relatively few chromosomes, making modern genetic analyses
more streamlined.
Drosophila melanogaster and Caenorhabditis elegans offer many of the same
benefits described above. These invertebrates are small and easy to
raise in a lab. Both lay many eggs, and their eggs mature quickly,
allowing many generations of inheritance to be observed over a short
period of time. Drosophila, in particular, have many visible variable
characteristics, such as wing type, body color and eye color (as
mentioned above), which allow their genotypes to be traced. Fruit
flies also have relatively small genomes with only four pairs of
chromosomes.
Mice are mammals and share many characteristics with humans. In
fact, about 75% of rodent genes share largely the same function as
those in humans, making mice genetically closer to humans than any
of the other common model organisms. Mice may be used to
examine questions that researchers are interested in but that would
be unethical to test using human subjects. The mouse genome is
also useful in research because genes may be "knocked out," an
experimental technique in which scientists inactivate a target gene or
replace it with an inactivated mutant version to see how its absence
affects the organism. The other model organisms may also have their
genes knocked out to address important questions in gene function.
The simplicity of baker's yeast (Saccharomyces cerevisiae), a eukaryotic
organism that is unicellular, has made it useful for studying cell
division and gene regulation — how genes are turned "on" and "off."
It is the easiest eukaryotic genome to manipulate because it is so
simple compared to other eukaryotes, but its genes still share many
of the basic functions of more complex eukaryotes. This helps
scientists identify how genes work on a cellular level in yeast, and
apply that understanding to organisms like humans.
Test Yourself
Why have so many genetic experiments been done on fruit flies? Name two characters that
make fruit flies a good model organism.
Submit
BIOSKILL
IN THIS MODULE
Laws of Probability
The Punnett Square
Summary
Test Your Knowledge
page 200 of 989
2 pages left in this module
Principles of Biology
38 Mendelian Inheritance
Summary
Analyze a basic Punnett square problem.
Punnett squares are a way to visualize the probabilities of genotypes and
phenotypes in offspring using parental genotypes. For example, using a
Punnett square to analyze a monohybrid cross, a phenotypic ratio of 3:1
dominant to recessive in offspring may be predicted. In this case, one-third of
the offspring with the dominant phenotype are homozygous, and two-thirds
are heterozygous for the trait.
OBJECTIVE
Analyze a test cross problem.
To identify the unknown genotype of an organism showing the dominant
phenotype, a test cross of an organism expressing the dominant phenotype
is made with an organism displaying recessive traits. The distribution of
phenotypes in the offspring will reveal whether the unknown parent genotype
is heterozygous or homozygous. A chi-square test is used to evaluate
whether the difference between the observed results and the expected
results of a test cross is likely to have occurred by chance or whether it
represents an inheritance pattern different from the one predicted.
OBJECTIVE
Determine probabilities in monohybrid and dihybrid crosses.
The principle of independent assortment states that when gametes form,
each pair of alleles assorts independently. Which offspring inherit which
alleles is random, but we are able to predict the likelihood of phenotypes in
the offspring based on the parents' genotypes and the rules of probability. In
a monohybrid cross, the ratio of the phenotypes in the offspring is 3:1
dominant:recessive, or three-quarters dominant and one-quarter recessive.
In a dihybrid cross, the ratio of phenotypes in the offspring is 9:3:3:1
(dominant, dominant):(dominant, recessive):(recessive, dominant):
(recessive, recessive); stated differently, 9/16 of the offspring have both
dominant phenotypes, 3/16 of the offspring have the dominant phenotype for
gene 1 and the recessive phenotype for gene 2, 3/16 have the recessive
phenotype for gene 1 and the dominant phenotype for gene 2, and 1/16 of
the offspring have both recessive phenotypes.
OBJECTIVE
Key Terms
addition rule
Considering mutually exclusive events, the probability of both occurring is the sum
of the probabilities of each event.
heterozygous
Having two different alleles for a trait.
homozygous
Having identical alleles for a trait.
independent probability
Probability of one event occurring has no effect on the probability of the other.
model organism
An organism that is well suited for scientific research for a variety of reasons.
multiplication rule
If the events are truly independent, the probability of both events happening is
found by multiplying the probabilities of each event.
null hypothesis
A hypothesis assuming that there is no difference between the observed values
contents
and the expected values.
probability
Calculation of the chance of an event occurring.
Punnett square
Table method used to assess probabilities of genotypic and phenotypic outcomes
among genetic crosses.
test cross
A cross between an organism with a dominant phenotype but an unknown
genotype and an individual that is homozygous recessive.
IN THIS MODULE
Laws of Probability
The Punnett Square
Summary
Test Your Knowledge
PRIMARY LITERATURE
Using sterile mates and
engineered toxins to beat bugs
Suppressing resistance to Bt cotton with
sterile insect releases.
View | Download
Classic paper: How scientists
cloned the first mammal (1997)
Viable offspring derived from fetal and adult
mammalian cells.
View | Download
Classic paper: Fruit fly research
reveals how complex organisms
form (1980)
Mutations affecting segment number and
polarity in Drosophila.
View | Download
SCIENCE ON THE WEB
Genetics in the Lab
Simulate a laboratory to discover the genetic
inheritance patterns of fruit flies
Let the Computer Do the Work
Use this website to compare observed and
expected frequencies using the chi-square
test
Roll the Dice
Observe the odds of rolling a certain number
Model Organism
Explore this NIH website about model
organisms used in biomedical research
In Mendel's Words
Read Gregor Mendel's original paper
Experiments in Plant Hybridization (1865)
Understanding the Spectrum of Dominance
Alleles are never exclusively "dominant" or
"recessive."
page 201 of 989
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Principles of Biology
38 Mendelian Inheritance
Test Your Knowledge
1. Huntington's disease, a progressive nervous system disorder, is inherited as a
dominant trait. The songwriter Woody Guthrie died of Huntington's disease. If he
was heterozygous for the trait and his wife did not carry it, what was the probability
that their son would develop Huntington's disease?
40%
25%
66%
10%
50%
2. If both parents are heterozygous for a trait, what is the probability that a given
offspring of theirs will display the recessive trait? Assume the gene for the trait is
not sex-linked.
2/3
3/4
1/2
1/4
1/3
3. In fruit flies, brown body color (B) is dominant to black body color (b). A brown fruit
fly is crossed with a black fruit fly. Both flies are purebred. What will the offspring's
genotypes be?
1/2 BB, 1/2 bb
1/4 bb, 3/4 Bb
all Bb
1/4 bb, 1/2 Bb, 1/4 BB
1/3 BB, 2/3 Bb
4. In humans, dry earwax is recessive to wet earwax. Consider a woman with dry
earwax and her male partner who has wet earwax. If he is heterozygous for the
trait of wet earwax, what is the probability that their child will have wet earwax?
This cannot be predicted based on the information provided.
50%
75%
25%
100%
5. In peas, yellow color and round shape are dominant to green color and wrinkled
shape, which are recessive. If you have a round, yellow pea and want to know its
genotype, what kind of pea should you breed it with?
yellow-round
yellow-wrinkled
green-wrinkled
green-round
any type
contents
Submit
IN THIS MODULE
Laws of Probability
The Punnett Square
Summary
Test Your Knowledge
PRIMARY LITERATURE
Using sterile mates and
engineered toxins to beat bugs
Suppressing resistance to Bt cotton with
sterile insect releases.
View | Download
Classic paper: How scientists
cloned the first mammal (1997)
Viable offspring derived from fetal and adult
mammalian cells.
View | Download
Classic paper: Fruit fly research
reveals how complex organisms
form (1980)
Mutations affecting segment number and
polarity in Drosophila.
View | Download
SCIENCE ON THE WEB
Genetics in the Lab
Simulate a laboratory to discover the genetic
inheritance patterns of fruit flies
Let the Computer Do the Work
Use this website to compare observed and
expected frequencies using the chi-square
test
Roll the Dice
Observe the odds of rolling a certain number
Model Organism
Explore this NIH website about model
organisms used in biomedical research
In Mendel's Words
Read Gregor Mendel's original paper
Experiments in Plant Hybridization (1865)
Understanding the Spectrum of Dominance
Alleles are never exclusively "dominant" or
"recessive."
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