# Probability and Genetics Topics Probability

 Date 28.06.2018 Size 81.5 Kb.
Biology 115 (Survey of Biology Laboratory) Spring 2006: Lab 7

## Probability

Punnett Square

Human Genetic Traits

Sex Inheritance

ABO and Rh Blood Typing (handout given in lab.)

#### Introduction

The phenotype of an organism (the way it looks or behaves, or its physiology) is in large part determined by the genes it carries (its genotype). Most organisms are diploid, so that most carry two copies of each chromosome (a homologous pair). One chromosome of a homologous pair comes from the mother, and one comes from the father. In humans, there are 23 pairs of homologous chromosomes. We each received chromosome numbers 1 through 23 from our mother, and 1 through 23 from our father. The 2 chromosomes designated number 1 are a homologous pair, the 2 chromosomes designated number 2 are a homologous pair, and so on.

Each member of a homologous pair carries the same genes. For example, suppose the gene for eye color was on chromosome number 12, the gene for tongue-rolling was on chromosome number 8, and the gene for earlobe attachment was on chromosome number 20 (these are just made-up for the purpose of example, these genes may not actually be on these chromosomes). We would each have received a copy of these genes from each of our parents, on the appropriate chromosome. However, we may not have received exactly the same form of the gene, or allele, from each parent. For instance, in the case of eye color, we may have received the allele for blue eyes from our mother, and the allele for brown eyes from our father. Thus, because we are diploid, we each carry two copies of every gene (except those on the sex chromosomes, which we will cover further on in this lab). The two copies may be exactly the same (i.e. the same alleles), or they may be different, as in the example above for eye color.

When the two alleles are the same (eg. both for blue eyes), the genotype is said to be homozygous. When the two alleles are different (eg. one for blue eyes and one for brown), the genotype is said to be heterozygous. When the genotype is heterozygous, often only one allele of the two is expressed in the phenotype. This allele is said to be dominant, while the other is recessive. In the case of eye color, the brown allele is dominant and the blue allele is recessive. Thus, an individual heterozygous for eye color (as in our example above) would show a brown-eyed phenotype. In the case of recessive and dominant alleles, the only time the phenotype associated with the recessive allele is expressed is when the individual has two copies of the recessive allele (homozygous recessive). Dominant alleles are usually symbolized by an uppercase letter (eg. B for brown eyes), and the recessive allele is usually symbolized by the lower case letter (b). For this example, there are three possible genotypes: BB, Bb, and bb. However, because of dominance, there are only two possible phenotypes: Brown eyes (genotypes BB and Bb), and blue eyes (genotype bb).

For most traits, there exist at least two alleles. The paired alleles are separated (along with the chromosomes that they reside on) during meiosis I. Half of the gametes formed will receive a copy of one allele, while the other half will receive the other. If the genotypes of the parents are known, all possible combinations of alleles (the offspring genotypes) can be determined. However, it is important to realize that which sperm will join with a particular egg is purely a matter of chance. Because of this chance component, the rules of probability play heavily in genetics and inheritance. The following exercise should help to illustrate probability in inheritance.

##### Probability Exercise

1. Work with a partner. Designate one of you as male, and one as female. Each take a penny to represent a trait passed on through your gametes. If we designate heads as a dominant allele “H” and tails as a recessive allele “h”, you are both heterozygous for this trait.

2. Each of you should flip the coin independently. The combination of heads and tails (or H and h) will represent the union of a sperm and an egg. Do forty combinations and keep track of the genotypes (use tick marks) of the offspring you and your partner produce in the table below. We will then total the data for the class, and you can include that in the table on the last line.

Table 1. Hypothetical Offspring Genotypes
 Sperm:Egg Sperm:Egg Sperm:Egg Sperm:Egg Offspring Genotype H : H H : h h : H h : h Number Class Total

• What was the probability of getting either an “H” or an “h” on any single coin-flip? _____________

• What was the percentage of each of the four genotype categories above? _____________

• Do you see a relationship between the two percentages above?

The relationship is called the Product Rule of Probability. The probability of two independent events is the product of their separate probabilities.

If we combine the two categories that are heterozygous, we get a common genotypic ratio: ( 1 : 2 : 1 ). That is, one-quarter homozygous dominant (HH), one-half heterozygous (either Hh or hH), and one-quarter homozygous recessive (hh).

• What would be the ratio of phenotypes? ______________________

A useful tool for predicting all the possible combinations and the expected ratios of offspring genotypes (when the genotypes of the parents are known) is the Punnett Square. We can use the Punnett Square to arrive at the same ratios that you determined empirically, without actually doing the coin-flipping (or the mating in a real biological system).

##### Punnett Square

To construct a Punnett Square, one makes a 2 by 2 table as below. The female gametes are listed across the top of the square, and the male gametes are listed along the left side as shown below.

 Female Gametes H h Male H HH Hh Gametes h hH hh

• What is the ratio between homozygous dominant, heterozygous, and homozygous recessive genotypes? _________________________

Once we have this Punnett Square, we can assign phenotypes to the genotypes, and calculate the phenotypic ratio as well. For example:

 Female Gametes H h Male H HH (dominant) Hh (dominant) Gametes h hH (dominant) hh (recessive)

• What is the ratio between dominant and recessive phenotypes in the offspring? ___________________

Punnett Squares can also be used in reverse, to infer the genotypes of parents when the genotypes of offspring are known. However, because of the chance component, it is not always possible to completely determine the genotypes of the parents.

• If the allele for brown eyes (B) is dominant to the allele for blue eyes (b), and two parents each had brown eyes, what might their genotypes be? Mother______________ Father _______________

• If they had only brown-eyed offspring, what might their genotypes be? Mother___________ Father_____________

• If, however, they had one blue-eyed offspring, what MUST their genotypes be? Mother__________ Father ____________

• If the mother had blue eyes, and the father had brown eyes, and they had a blue-eyed offspring, what MUST their genotypes be? Mother___________ Father________

• If the mother had blue eyes, and the father had brown eyes, and they had only two children, both with brown eyes, what might their genotypes be? Mother_________ Father _________

#### Human Genetic Traits

Several human phenotypic traits are inherited in a simple Mendelian manner. For the following traits, determine your own phenotype, then determine your possible genotype. Record your own data in the table. We will then tabulate all the data for the class.

PTC Tasting

The ability to taste the chemical PTC is due to a dominant allele (T). Obtain a strip of paper that has been treated with PTC and a control paper. Place the control paper (use the end that has not been handled) on your tongue. This allows you to recognize the taste of plain paper so you don’t confuse it with the test substance. Throw the control paper into the waste basket, and then place the PTC paper on your tongue. If you have a dominant allele, you will probably experience a strong, bitter taste (you may need to go get a drink of water). The paper will taste like the control to homozygous recessive individuals (tt). Throw the test paper away when finished.

Tongue Rolling

The ability to roll the tongue up into a tube is a dominant trait and indicates that the individual carries at least one copy of the dominant allele (R). Individuals without this ability are homozygous recessive (rr).

Widow’s Peak

Widow’s Peak, a distinct downward point of the frontal hairline (a V-shaped hairline), indicates that a dominant allele (W) is present. Homozygous individuals (ww) possess a straight hairline.

Earlobe Attachment

Free-hanging or unattached earlobes is dominant (F) to earlobes that are attached directly to the head at the base (ff).

Bent Little Finger

If the tip of the little finger angles toward the other digits, the individual shows the dominant phenotype, and carries at least one dominant allele (B). Homozygous recessive individuals have straight little fingers.

Hitchhiker’s Thumb

If the tip of the thumb can be bent backward so that it is at or near a right angle to the rest of the thumb, the individual is homozygous recessive (hh). Considerable variation exists in the expression of this gene. For classroom purposes, those individuals who can’t bend at least one thumb backward about 45 degrees are probably carrying a dominant allele (H).

Middigital Hair

The presence of hair on the middle segment of the digits is a dominant condition, and persons with this phenotype carry at least one dominant allele (M). Even the slightest amount of fine hair qualifies as a dominant phenotype.

Interlocking Fingers

Clasp your hands together. If your left thumb is crossed over your right, you have a dominant allele (C). If your right thumb is on top of your left you are homozygous recessive for the trait.

Eye Color

Blue/gray eye color indicates that an individual is homozygous recessive (bb) for that trait. If you have any other eye color it is dominant to blue/gray, but we can’t know the genotype for sure so you must record both possible dominant genotypes (BB or Bb).

## TRAIT

OWN PHENOTYPE

OWN GENOTYPE

# IN CLASS - DOMINANT

# IN CLASS - RECESSIVE

PTC Tasting

Tongue Rolling

Widow’s Peak

Earlobe Attachment

Bent Little Finger

Hitchhiker’s Thumb

Mid-digital Hair

Interlocking Fingers

Eye Color

Once you have completed the table we will demonstrate genetic individuality. All PTC tasters will stand on one side of the room and non-tasters at the other side. Then, each group will further divide, according to tongue rolling. Continue dividing for each trait until each person stands alone. How many traits did we have to consider before you stood alone?

##### Sex Inheritance

In humans, the 23rd pair of chromosomes are the sex chromosomes, X and Y. Females are homozygous X (XX), while males are heterozygous (XY). The X chromosome is large and the Y chromosome is small. The male inherits only one X chromosome from his mother, while the female inherits an X chromosome from each parent.

• What percentage of human offspring would you expect to be daughters? _______________

• What percentage of sons receive a Y chromosome from the father? _______________

• What percentage of daughters receive an X chromosome from the father? _______________

• Which parent determines the sex of the offspring? _______________

In addition to determining the sex of the individual, some genes for other traits are carried on the sex chromosomes, primarily on the X chromosome. Because males only have one copy of the X chromosome, if they inherit a recessive allele for one of these traits from their mother, they will show the recessive phenotype. For this reason, sex-linked recessive phenotypes occur more often in males than in females.

For example, in humans the genes for red-green color blindness is carried on the X chromosome and the phenotype for color blindness is recessive to the normal phenotype.

The genotypes are as follows:

Normal female = XCXC Normal male = XCY

Carrier female (not color blind) = XCXc Color blind male = XcY

What is the expected phenotypic ratio of each of the following matings?

• Normal-visioned female X color blind male? _______________

• Carrier female X normal male? _______________

• Why are there more color blind males than females? _______________

• What is the probability that a color blind man and a carrier woman will have a daughter with normal vision? _______________

###### ABO and Rh Blood Typing

See handout in lab.