Mendelian Genetics

Chapter 14

Werewolf Genetics

Gene:

Werewolfism

Allele 1: werewolf

dominant allele

W

Allele 2: human

recessive allele

w

Monohybrid Cross

 

Crossing two individuals and looking at ONE trait

 

 

 

Genotype:
Phenotype:

 

 

What happens when you cross two heterozygous parents?

 

 

Mendelís First Law: Law of Segregation

Allele pairs segregate (separate) during gametic formation

(paired condition (2n) restored by random fusion of gametes at fertilization)

When crossing two heterozygous individuals in a monohybred cross, one will always get a 3:1 phenotypic ratio

Genotype:   


Phenotype:  

 

Test Cross

 

Dihybrid cross

 

Crossing two individuals and looking at TWO traits

 

Werewolf Genetics

Gene 1: Werewolfism

Allele 1: werewolf; dominant allele W

Allele 2: human; recessive allele w

Gene 2: Personality

Allele 1: nerd; dominant allele N

Allele 2: cool; recessive allele n

WWNN X wwnn

 

 

Genotype:
Phenotype:

 

Cross a heterozygous male with a heterozygous female.

 

Cross a heterozygous male with a heterozygous female.

Cross a heterozygous male with a heterozygous female.

 

 

 

Dihybrid results

Phenotypic ratio:

 

 

Genotypic ratio:

1WWNN: 2WwNN: 2WWNn: 4WwNn: 1WWnn: 2Wwnn: 1wwNN: 2wwNn: 1wwnn

Mendelís Second Law: Law of Independent Assortment

Each allele pair segregates independently of other gene pairs during gamete formation.

When crossing two heterozygous individuals in a dihybred cross, one will always get a 9:3:3:1 phenotypic ratio

 

Genotype:

Phenotype:

 

 

Genotype:

Phenotype:

 

Mendelian inheritance reflects rule of probability

Mendelís laws of segregation and independent assortment reflect the same laws of probability that apply to tossing coins or rolling dice.

 

The probability scale ranged from zero (an event with no chance of occurring) to one (an event that is certain to occur).

The probability of tossing heads with a normal coin is Ĺ.

The probability of rolling a 3 with a six-sided die is 1/6, and the probability of rolling any other number is 1 - 1/6 = 5/6.

 

When tossing a coin, the outcome of one toss has no impact on the outcome of the next toss.

Each toss is an independent event, just like the distribution of alleles into gametes.

 

We can use the rule of multiplication to determine the chance that two or more independent events will occur together in some specific combination.

Compute the probability of each independent event.

Then, multiply the individual probabilities to obtain the overall probability of these events occurring together.

The probability that two coins tossed at the same time will land heads up is 1/2 x 1/2 = 1/4.

Similarly, the probability that a heterogyzous werewolf (Ww) will produce a human offspring (pp) depends on an ovum with a human allele mating with a sperm with a human allele.

This probability is 1/2 x 1/2 = 1/4.

 

The rule of multiplication also applies to dihybrid crosses.

For a heterozygous parent (WwNn) the probability of producing a WN gamete is 1/2 x 1/2 = 1/4.

We can use this to predict the probability of a particular F2 genotype without constructing a 16-part Punnett square.

The probability that an F2 werewolf will have a WWNN genotype from a heterozygous parent is 1/16 (1/4 chance for a WN ovum and 1/4 chance for a WN sperm).

 

The rule of addition also applies to genetic problems.

Under the rule of addition, the probability of an event that can occur two or more different ways is the sum of the separate probabilities of those ways.

For example, there are two ways that F1 gametes can combine to form a heterozygote.

The dominant allele could come from the sperm and the recessive from the ovum (probability = 1/4).

Or, the dominant allele could come from the ovum and the recessive from the sperm (probability = 1/4).

The probability of a heterozygote is 1/4 + 1/4 = 1/2.

 

We can combine the rules of multiplication and addition to solve complex problems in Mendelian genetics.

Letís determine the probability of finding two recessive phenotypes for at least two of three traits resulting from a trihybrid cross between werewolves that are WwNnRr and Wwnnrr.

There are five possible genotypes that fulfill this condition: wwnnRr, wwNnrr, Wwnnrr, WWnnrr, and wwnnrr.

We would use the rule of multiplication to calculate the probability for each of these genotypes and then use the rule of addition to pool the probabilities for fulfilling the condition of at least two recessive trait.

 

The probability of producing a wwnnRr offspring:

The probability of producing ww =

The probability of producing nn =

The probability of producing Rr =

Therefore, the probability of all three being present (wwnnRr) in one offspring is

For wwNnrr:

For Wwnnrr:

for WWnnrr:

for wwnnrr:

Therefore, the chance of at least two recessive traits is

 

The probability of producing a wwnnRr offspring:

The probability of producing ww = 1/2 x 1/2 = 1/4.

The probability of producing nn = 1/2 x 1 = 1/2.

The probability of producing Rr = 1/2 x 1 = 1/2.

Therefore, the probability of all three being present (wwnnRr) in one offspring is 1/4 x 1/2 x 1/2 = 1/16.

For wwNnrr: 1/4 x 1/2 x 1/2 = 1/16.

For Wwnnrr: 1/2 x 1/2 x 1/2 = 2/16

for WWnnrr: 1/4 x 1/2 x 1/2 = 1/16

for wwnnrr: 1/4 x 1/2 x 1/2 = 1/16

Therefore, the chance of at least two recessive traits is 6/16 (3/8).

Mendel discovered the particulate behavior of genes: a review

While we cannot predict with certainty the genotype or phenotype of any particular seed from the F2 generation of a dihybrid cross, we can predict the probabilities that it will fit a specific genotype of phenotype.

Mendelís experiments succeeded because he counted so many offspring and was able to discern this statistical feature of inheritance and had a keen sense of the rules of chance.

 

Mendelís laws of independent assortment and segregation explain heritable variation in terms of alternative forms of genes that are passed along according to simple rule of probability.

These laws apply not just to garden peas, or werewolves but to all other diploid organisms that reproduce by sexual reproduction.

Mendelís studies of pea inheritance endures not only in genetics, but as a case study of the power of scientific reasoning using the hypothetico-deductive approach.

 

Male

Homozygous recessive

wwnn

Nerdy human

Female

Homozygous dominant

WWNN

Cool werewolf