Genetics, Probabilty and Chance
April 10, 2002


Readings: Ch 10, p 152 - 159


Terms to know before you begin: (please define before class)

1. Gene:

2. Allele:

3. Genotype:

4. Phenotype:

5. Dominant:

6. Recessive:

7. Homozygous:

8. Heterozygous:

9. Trait:

Note: We will be doing lots of genetics problems today (in groups). You will not need a calculator. Read the notes and define the terms above, but don't worry about doing the problems until we are in class.


I. Overview: How are Traits passed from Generation to Generation?

Genetics is the study of heredity - traits inherited from parent to offspring.

Blending theory In ~1850, scientists thought that some fluid substance in the blood of animals or in the sap of plants was the hereditary material. The combination of the parent's characteristics in the offspring was thought to occur by a "blending" of this fluid.

 

A different theory was put forth by Gregor Mendel in 1850. Mendel was an Austrian monk who was interested in plant breeding. He performed careful experiments with the garden pea, Pisum sativum, collected large amounts of data, and in doing so, was able to uncover the basic principles of genetic inheritance that still hold true today!

Mendel discovered that traits are interited in discrete units (we now know these to be genes). Mendel's discoveries were not understood by other scientists for over 35 years!

 


II. Mendel's experiments with the Garden Pea

Mendel's work started when he bred two types of pea plants - ones with purple flowers and ones with white flowers - that were true-breeding for flower color (meaning that the purple flowers produced only plants with purple flowers and the white plants produced only plants with white flowers).

Mendel cross-pollinated the flowers (pea plants usually are self-fertile).

In the first filial (F1) generation, the white trait was masked (Note that a light purple "blended" color was NOT observed. Mendel took this observation one step forther, by allowing the F1 to "self".

Result: The white trait re-appears in the F2 generation in a ratio of 3 purple plants to 1 white.

Mendel did this experiment with a total of 7 different traits, studying 22 strains of peas and always using large sample sizes, and he always saw a ~3:1 ratio in the F2 generation (not shown = flower position on stem)


III. Mendel thought about how to explain what he saw:

Mendel realized that these results were explainable if three things were true. He hypothesized that:

1. Every trait (like flower color, or seed shape, or seed color) is controlled by two "heritable factors". [We know now that these are genes - we each have two copies of every gene].
 
2. If the two alleles differ, one is dominant (will be observed in the organisms appearance or physiology) and one is recessive (cannot be observed unless the individual has two copies of the recessive allele). Dominant traits mask the appearance of recessive traits.
 
3. Alleles are randomly donated from parents to offspring - the factors (alleles) separate when the gametes are formed by meiosis, allowing all possible combinations of factors to occur in the gametes.
 

Mendel's Law of Segregation - The two factors (alleles) separate when the gametes are formed, and only one factor (allele) is present in each gamete.


IV. Doing a genetic cross (monohybrid = 1 gene):

Geneticists use letters be used to represent alleles.

Examples

= Flower color: P= purple, p= white
= Seed color: Y= yellow, y = green
= Seed shape: W = wrinkled, w = round

In humans...

= Widow's peak: W = widow's peak, w = continuous hairline (which are you?)
= Freckles: F = Freckles, f = no freckles (which are you?)
= Earlobes: E = unattached, e = attached (which are you?)
= Cystic fibrosis C = no CF, c = cystic fibrosis
 

E-Z steps for doing genetics problems:

1. Indicate the genotype of the parents using letters
 
2. Determine what the possible gametes are
 
3. Determine the genotype and phenotype of the children after reproduction. To consider every type of offspring possible, use a Punnett Square in which all possible types of sperm are lined up vertically and all types of eggs are lined up horizontally:
 
4. Fill in the squares by "multiplying" the alleles from mom and dad:

Genetics Problem 1: (a) A man with a widow's peak (WW) marries a woman with a continuous hairline (ww). A widow's peak is dominant over a continuous hairline. What kind of hairline will their children have?

 

1. P1 Widow's peak (WW) x continuous hairline (ww)

2. Gametes: Male: W only, Female: w only

3. Children: (the F1 generation):

 

Genotype: Ww (all children will be heterozygous)

Phenotype: Widow's peak (phenotype of all children)


(b) Suppose one of their children (Ww) marries someone who is also heterozygous (Ww). What type of hairline will their children have?

1. P1 Widow's peak (Ww) x Widow's peak (Ww)

2. Gametes: Male: W and w; Female: W and w

3. Children:

 

Genotype: Their children have a 25% (1/4) chance of being WW, a 50% (2/4) chance of being Ww, and a 25% (1/4) chance of being ww. (Note that this is a 1:2:1 genotypic ratio IF both parents were heterozyhous to begin with)

Phenotype: Their children will have a 3/4 chance of having a widow's peak and a 1/4 chance of having a continuous hairline (3:1 phenotypic ratio)


With small numbers of offspring (like humans vs pea plants) remember that these numbers represent the child's chance of having that trait. Each individual child has the same chance to inherit a trait from their parents.

Genetics problem 2: A man and a woman are heterozygous for freckles. Freckles (F) are dominant over no freckles (f). What are the chances that their children will have freckles?

 

 

 


Genetics problem 3: A woman is homozygous dominant for short fingers (SS). She marries a man who is heterozygous for short fingers (Ss). Will any of their children have long fingers (ss)? yes / no

 

 

Could any of their grandchildren potentially have long fingers? y / n Why or why not?

 


Genetics problem 4: Jane and John are expecting a baby and know that they are both carriers (ie heterozygous) of cystic fibrosis (Cc). What is the probability that their child will have cystic fibrosis (cc)? What is the probability that their child will be a carrier of cystic fibrosis?

 

Chance of child being:

_______ % Disease free Genotype: ___________

_______ % Cystic fibrosis carrier Genotype: ___________

_______ % Cystic fibrosis Genotype: ___________

 

Remember that this is only a probability, and the same probability occurs with each pregnancy!


V. Studying Two Traits at once: (Dihybrid Cross)

Mendel also did a type of cross where two traits were followed at one time - a Dihybrid Cross.

AA or Aa = purple; aa = white
BB or Bb = tall; bb = short

One really important thing that Mendel noticed from this type of cross was that traits (like flower color, height) are inherited independently - not together as a unit. This has become known as

Mendel's Law of Independent Assortment - Genes for various traits assort into gametes independently (due to homologues lining up randomly at the metaphase plate).

Summary:  
Type of cross Phenotypic Ratio
Monohybrid (Pp) x monohybrid (Pp) 3:1 (and 1:2:1 genotypic)
Dihybrid (PpBb) x dihybrid (PpBb) 9:3:3:1

VI. A simpler way to do a Dihybrid Cross or beyond...
(or, how to avoid making anything larger than a simple Punnitt square for any genetics problem.)

Mendelian genetics reflect the laws of probability

Mendel's laws are basically real-life applications of the rules of probability that apply to a coin toss, rolling a dice, or drawing from a deck of cards

Rule of multiplication: Segregation of the alleles into gametes is like a coin toss (heads or tails = equal probability). In the case of two CF carriers (Cc), the probability of the egg having the CF allele (c) is 1/2 and the sperm having the (c) allele is 1/2:

1/2 x 1/2 = 1/4 chance of having child with CF (cc).

(note that you didn't need to do a Punnitt square to figure this out)



For a dihybrid cross - the chance that 2 independent events will occur together is the product of their chances of occuring separately.

The chance of yellow (YY or Yy) seeds = 3/4 (the dominant trait)
The chance of round (RR or Rr) seeds  = 3/4 (the dominant trait)
The chance of green (yy) seeds = 1/4 (the recessive trait)
The chance of wrinkled (rr) seeds = 1/4 (the recessive trait)
 
So...
 
The chance of yellow and round = 3/4 x 3/4 = 9/16
The chance of yellow and wrinkled = 3/4 x 1/4 = 3/16
The chance of green and round = 1/4 x 3/4 = 3/16
The chance of green and wrinkled = 1/4 x 1/4 = 1/16

Sound familiar? And no Punnitt square needed (whew). Therefore, you can avoid doing a Punnett square if you can reduce the problem to a series of probability statements.


With a tri-hybrid cross, you can avoid a huge Punnett square with 64 boxes:

The chance of yellow (YY or Yy) seeds  = 3/4 (the dominant trait)
The chance of round (RR or Rr) seeds = 3/4 (the dominant trait)
The chance of purple (PP or Pp) flowers = 3/4 (the dominant trait)
The chance of green (yy) seeds = 1/4 (the recessive trait)
The chance of wrinkled (rr)seeds = 1/4 (the recessive trait) 
The chance of white (pp) flowers = 1/4 (the recessive trait)

FILL IN THE BLANKS AND EXPECTED PROPORTIONS:

1. Pea plant with purple flowers and round, yellow seeds: = 3/4 x 3/4 x 3/4 = 27/64
 2. Pea plant with purple flowers and wrinkled, yellow seeds: = 3/4 x 3/4 x 1/4 = 9/64
 3. Pea plant with purple flowers and round, green seeds: =
 4. Pea plant with purple flowers and wrinkled, green seeds: =
 5. Pea plant with white flowers and round, yellow seeds:
 6. Pea plant with white flowers and wrinkled, yellow seeds =
 7. Pea plant with white flowers and round, green seeds =
 8. Pea plant with white flowers and wrinkled, green seeds: =

Try this problem:

You have freckles, dimples, and a widow's peak. Your S.O. has freckles and dimples, but a continuous hairline. In other words,

 You

 

 Your S.O.

 FfDdWw

 x

 FfDdWw

Question: What is the chance your darling child would have all three recessive phenotypes: no freckles (ff), no dimples (dd) or a continuous hairline (ww)?

 

Hint: do three quick Punnett squares for each single trait. Take the proportions of the recessives and multiply away...!

But what if:

 You

 

 Your S.O.

 FfDdWw

 x

 Ffddww

Question: What is the chance your darling child would have all three recessive phenotypes: no freckles (ff), no dimples (dd) or a continuous hairline (ww)?


Objectives:

1. Know the definitions of the words at the beginning of today's notes
2. Be able to explain Mendel's original experiments and findings, including the Law of Segregation and the Law of Independent Assortment
3. Know how to set up and analyze a Punnett square for a monohybrid and a dihybrid cross
4. Be able to work problems with monohybrid and dihybrid crosses