Category: My Classroom Material

 

Genetic Terminology:

• Trait – any characteristic that can be passed from parent to offspring
• Heredity – passing of traits from parent to offspring
• Genetics – study of heredity
• Alleles – two forms of a gene (dominant & recessive)
• Dominant – stronger of two genes expressed in the hybrid; represented by a capital letter (R)
• Recessive – gene that shows up less often in a cross; represented by a lower case letter (r)
• Genotype – gene combination for a trait (e.g. RR, Rr, rr)
• Phenotype – the physical feature resulting from a genotype (e.g. tall, short)
• Homozygous genotype – gene combination involving 2 dominant or 2 recessive genes (e.g. RR or Rr); also called pure 
• Heterozygous genotype – gene combination of one dominant & one recessive allele    (e.g. Rr); also called hybrid
• Monohybrid cross – cross involving a single trait
• Dihybrid cross – cross involving two traits
• Punnett Square – used to solve genetics problems

Blending Concept of Inheritance:

• Accepted before Mendel’s experiments
• Theory stated that offspring would have traits intermediate between those of its parents such as red & white flowers producing pink
• The appearance of red or white flowers again was consider instability in genetic material
• Blending theory was of no help to Charles Darwin’s theory of evolution 
• Blending theory did not account for variation and could not explain species diversity
• Particulate theory of Inheritance, proposed by Mendel, accounted for variation in a population generation after generation
• Mendel’s work was unrecognized until 1900

Gregor Mendel:

• Austrian monk
• Studied science & math at the University of Vienna
• Formulated the laws of heredity in the early 1860’s
• Did a statistical study of  traits in garden peas over an eight year period

Why peas, Pisum sativum?

• Can be grown in a small area
• Produce lots of offspring
• Produce pure plants when allowed to self-pollinate several generations
• Can be artificially cross-pollinate

GARDEN PEA

Mendel’s Experiments:

• Mendel studied simple traits from 22 varieties of  pea plants (seed color & shape, pod color & shape, etc.)
• Mendel traced the inheritance of individual traits & kept careful records of numbers of offspring
• He used his math principles of probability to interpret results
• Mendel studied pea traits, each of which had a dominant & a recessive form (alleles)
• The dominant (shows up most often) gene or allele is represented with a capital letter, & the recessive gene with a lower case of that same letter (e.g. B, b)
• Mendel’s traits included:

         a. Seed shape —  Round (R) or Wrinkled (r)
            b. Seed Color —- Yellow (Y) or  Green (y)
            c. Pod Shape — Smooth (S) or wrinkled (s)
            d. Pod Color —  Green (G) or Yellow (g)
            e. Seed Coat Color —  Gray (G) or White (g)
            f. Flower position — Axial (A) or Terminal (a)
            g. Plant Height — Tall (T) or Short (t)
            h. Flower color — Purple (P) or white (p)

•  Mendel produced pure strains by allowing the plants to self-pollinate for several generations
• These strains were called the Parental generation or P1 strain
• Mendel cross-pollinated two strains and tracked each trait through two
  generations (e.g. TT  x  tt )

   

  Trait – plant height
  Alleles – T tall, t short
  P1 cross    TT  x  tt				genotype      —    Tt
  	t	t		phenotype    —    Tall
  T	Tt	Tt		genotypic ratio –all alike
  T	Tt	Tt		phenotypic ratio- all alike

   

 

• The offspring of this cross were all hybrids showing only the dominant trait & were called the First Filial or F1 generation
• Mendel then crossed two of his F1 plants and tracked their traits; known as an F1 cross

 

• When 2 hybrids were crossed, 75% (3/4) of the offspring showed the dominant trait & 25% (1/4) showed the recessive trait; always a 3:1 ratio
• The offspring of this cross were called the F2 generation
• Mendel then crossed a pure & a hybrid from his F2 generation; known as an F2 or test cross

• 50% (1/2) of the offspring in a test cross showed the same genotype of one parent & the other 50% showed the genotype of the other parent; always a 1:1 ratio

Problems: Work the P1, F1, and both F2 crosses for all of the other pea plant traits & be sure to include genotypes, phenotypes, genotypic & phenotypic ratios.

• Mendel also crossed plants that differed in two characteristics (Dihybrid Crosses)
  such as seed shape & seed color
• In the P1 cross, RRYY  x  rryy, all of the F1 offspring showed only the dominant form for both traits; all hybrids, RrYy

• When Mendel crossed 2 hybrid plants (F1 cross), he got the following results

 

 

Problems: Choose two other pea plant traits and work the P1 and F1 dihybrid crosses. Be sure to show the trait, alleles, genotypes, phenotypes, and all ratios. 

Results of Mendel’s Experiments:

• Inheritable factors or genes are responsible for all heritable characteristics
• Phenotype is based on Genotype
• Each trait is based on two genes, one from the mother and the other from the father
• True-breeding individuals are homozygous ( both alleles) are the same
• Law of Dominance states that when different alleles for a characteristic are inherited (heterozygous), the trait of only one (the dominant one) will be expressed. The recessive trait’s phenotype only appears in true-breeding (homozygous) individuals

• Law of Segregation states that each genetic trait is produced by a pair of alleles which separate (segregate) during reproduction

• Law of Independent Assortment states that each factor (gene) is distributed (assorted) randomly and independently of one another in the formation of gametes

 

Other Patterns of Inheritance:

• Incomplete dominance occurs in the heterozygous or hybrid genotype where the 2 alleles blend to give a different phenotype
• Flower color in snapdragons shows incomplete dominance whenever a red flower is crossed with a white flower to produce pink flowers

• In some populations, multiple alleles (3 or more) may determine a trait such as in ABO Blood type
• Alleles A & B are dominant, while O is recessive

• Polygenic inheritance occurs whenever many variations in the resulting phenotypes such as in hair, skin, & eye color
• The expression of a gene is also influenced by environmental factors (example: seasonal change in fur color)

 

 

POPULATION GENETICS AND THE HARDY-WEINBERG LAW

 

The Hardy-Weinberg formulas allow scientists to determine whether evolution has occurred. Any changes in the gene frequencies in the population over time can be detected. The law essentially states that if no evolution is occurring, then an equilibrium of allele frequencies will remain in effect in each succeeding generation of sexually reproducing individuals. In order for equilibrium to remain in effect (i.e. that no evolution is occurring) then the following five conditions must be met:

1. No mutations must occur so that new alleles do not enter the population.
2. No gene flow can occur (i.e. no migration of individuals into, or out of, the population).
3. Random mating must occur (i.e. individuals must pair by chance)
4. The population must be large so that no genetic drift (random chance) can cause the allele frequencies to change.
5. No selection can occur so that certain alleles are not selected for, or against.

Obviously, the Hardy-Weinberg equilibrium cannot exist in real life. Some or all of these types of forces all act on living populations at various times and evolution at some level occurs in all living organisms. The Hardy-Weinberg formulas allow us to detect some allele frequencies that change from generation to generation, thus allowing a simplified method of determining that evolution is occurring. There are two formulas that must be memorized:

 

p2 + 2pq + q2 = 1 and p + q = 1

 

p = frequency of the dominant allele in the population
q = frequency of the recessive allele in the population
p2 = percentage of homozygous dominant individuals
q2 = percentage of homozygous recessive individuals
2pq = percentage of heterozygous individuals

Individuals that have aptitude for math find that working with the above formulas is ridiculously easy. However, for individuals who are unfamiliar with algebra, it takes some practice working problems before you get the hang of it. Below I have provided a series of practice problems that you may wish to try out. Note that I have rounded off some of the numbers in some problems to the second decimal place.

PROBLEM #1    You have sampled a population in which you know that the percentage of the homozygous recessive genotype (aa) is 36%. Using that 36%, calculate the following:

1. The frequency of the “aa” genotype.
2. The frequency of the “a” allele.
3. The frequency of the “A” allele.
4. The frequencies of the genotypes “AA” and “Aa.”
5. The frequencies of the two possible phenotypes if “A” is completely dominant over “a.”

PROBLEM #2.    Sickle-cell anemia is an interesting genetic disease. Normal homozygous individuals (SS) have normal blood cells that are easily infected with the malarial parasite. Thus, many of these individuals become very ill from the parasite and many die. Individuals homozygous for the sickle-cell trait (ss) have red blood cells that readily collapse when deoxygenated. Although malaria cannot grow in these red blood cells, individuals often die because of the genetic defect. However, individuals with the heterozygous condition (Ss) have some sickling of red blood cells, but generally not enough to cause mortality. In addition, malaria cannot survive well within these “partially defective” red blood cells. Thus, heterozygotes tend to survive better than either of the homozygous conditions. If 9% of an African population is born with a severe form of sickle-cell anemia (ss), what percentage of the population will be more resistant to malaria because they are heterozygous (Ss) for the sickle-cell gene?

PROBLEM #3.    There are 100 students in a class. Ninety-six did well in the course whereas four blew it totally and received a grade of F. Sorry. In the highly unlikely event that these traits are genetic rather than environmental, if these traits involve dominant and recessive alleles, and if the four (4%) represent the frequency of the homozygous recessive condition, please calculate the following:

1. The frequency of the recessive allele.
2. The frequency of the dominant allele.
3. The frequency of heterozygous individuals.

PROBLEM #4.    Within a population of butterflies, the color brown (B) is dominant over the color white (b). And, 40% of all butterflies are white. Given this simple information, which is something that is very likely to be on an exam, calculate the following:

1. The percentage of butterflies in the population that are heterozygous.
2. The frequency of homozygous dominant individuals.

PROBLEM #5.     A rather large population of Biology instructors have 396 red-sided individuals and 557 tan-sided individuals. Assume that red is totally recessive. Please calculate the following:

1. The allele frequencies of each allele.
2. The expected genotype frequencies.
3. The number of heterozygous individuals that you would predict to be in this population.
4. The expected phenotype frequencies.
5. Conditions happen to be really good this year for breeding and next year there are 1,245 young “potential” Biology instructors. Assuming that all of the Hardy-Weinberg conditions are met, how many of these would you expect to be red-sided and how many tan-sided?

PROBLEM #6.    A very large population of randomly-mating laboratory mice contains 35% white mice. White coloring is caused by the double recessive genotype, “aa”. Calculate allelic and genotypic frequencies for this population.

PROBLEM #7.    After graduation, you and 19 of your closest friends (lets say 10 males and 10 females) charter a plane to go on a round-the-world tour. Unfortunately, you all crash land (safely) on a deserted island. No one finds you and you start a new population totally isolated from the rest of the world. Two of your friends carry (i.e. are heterozygous for) the recessive cystic fibrosis allele (c). Assuming that the frequency of this allele does not change as the population grows, what will be the incidence of cystic fibrosis on your island?

PROBLEM #8.    You sample 1,000 individuals from a large population for the MN blood group, which can easily be measured since co-dominance is involved (i.e., you can detect the heterozygotes). They are typed accordingly:

 

BLOOD TYPE	GENOTYPE	NUMBER OF INDIVIDUALS	RESULTING FREQUENCY
M	MM	490	0.49
MN	MN	420	0.42
N	NN	90	0.09

 

Using the data provide above, calculate the following:

1. The frequency of each allele in the population.
2. Supposing the matings are random, the frequencies of the matings.
3. The probability of each genotype resulting from each potential cross.

PROBLEM #9.    Cystic fibrosis is a recessive condition that affects about 1 in 2,500 babies in the Caucasian population of the United States. Please calculate the following:

1. The frequency of the recessive allele in the population.
2. The frequency of the dominant allele in the population.
3. The percentage of heterozygous individuals (carriers) in the population.

PROBLEM #10.    In a given population, only the “A” and “B” alleles are present in the ABO system; there are no individuals with type “O” blood or with O alleles in this particular population. If 200 people have type A blood, 75 have type AB blood, and 25 have type B blood, what are the allelic frequencies of this population (i.e., what are p and q)?

PROBLEM #11.    The ability to taste PTC is due to a single dominate allele “T”. You sampled 215 individuals in biology, and determined that 150 could detect the bitter taste of PTC and 65 could not. Calculate all of the potential frequencies.

ANSWERS