AP  Biology
Notes:  Mendel

In 1857 Mendel was living in an Augustinian monastery where he bred 
garden peas in the abbey garden.
        *  They were available in many easily distinguishable varieties
        * Strict control over mating was possible 
        Character: Detectable inheritable feature of an organism
        Trait: variant of an inheritable character

Mendel's characters in pea plant 
    1.  Flower color ( purple or white)
    2.  Flower position (axial or terminal)
    3.  Seed color (yellow or green)
    4.  Seed shape (round or wrinkled)
    5.  Pod shape (inflate or constricted)
    6. Pod color (green or yellow)
    7.  Stem length (tall or dwarf)

        True breeding: Always producing offspring with the same traits as the 
                                  parents when the parents are self-fertilized. 

        * The true-breeding parental plants are called the P generation
        * The hybrid offspring of the P generation are the F₁ generation (first filial)
        * Allowing F₁ generation plants to self-pollinate, produces the next 
            generation, the F₂ generation (second filial)

When Mendel crossed true-breeding plants with different character traits, he 
 found that the traits did not blend.
        * a cross between true-breeding varieties, one with purple flowers and 
           one with white flowers, produced F₁ progeny (offspring) with only 
            purple flowers.

    Hypothesis:  Mendel hypothesized that if the inheritable factor for white flowers 
    had been lost, then a cross between F₁ plants should produce only purple-
    flowered plants.

        * Mendel allowed the F₁ plants to self-pollinate
        * There were 705  purple-flowered and 224 white-flowed plants in the 
            F₂ generation--a ration of 3:1.  The inheritable factor for white flowers was 
            not lost, so the hypothesis was rejected.
        * From these types of experiments and observations.  Mendel concluded that 
           since the inheritable factor for white flowers was not lost in the F₁ generation, it
            must have been masked by the presence of the purple-flower factor.  Mendel's
            factors are now called genes.  In Mendel's terms, purple flower is the dominant 
            trait and white flower is the recessive trait.

From these observations he developed a hypothesis
    * Alternative forms of genes
    * For each character, an organism inherits two alleles, one form each parent
    * If the two alleles differ, one is fully expressed (dominate allele); the other is 
        completely masked (recessive allele)
            * Dominate alleles are designated by a capital letter P
            * Recessive alleles are designated by a lower case letter p
    * The two alleles for each character segregate during gamete production
            *Without any knowledge of meiosis, Mendel deduced that a sperm cell or 
               ovum carries only one allele for each inherited characteristic, because 
                allele pairs separate (segregate) from each other during gamete production
            * Gametes of true-breeding plants will all carry the same allele.
            * This sorting of alleles into separate gametes is known as Mendel's law of 
                the parried condition is restored by the random fusion of gametes at fertilization.

Mendel's law of segregation: Allele pairs segregate during gamete formation 
and the paired condition is restored by the random fusion of gametes at fertilization
The combinations resulting form a genetic cross may be predicted by using a 
Punnett square.

    Homozygous:   having two identical alleles for a given grating
    * All gametes carry that allele
    *  Homozygotes are true-breeding
    Heterozygous:  having two different alleles
    * Half of hate gametes carries one allele (P) and the remaining half carries 
        the other (p).
    Phenotype: an organisms expressed traits
    * In Mendel's experiment above, the F₂ generation was a 1:2:1 (1PP:2Pp:1pp)
    Testcross: the breeding of an organism of unknown genotype with a 
    homozygous recessive

Mendel deduced the law of segregation from experiments with monohybrid 
crosses, breeding experiments that sued parental varieties differing in a single trait.
 
He then performed crosses between parental varieties that differed in two 
characters of dihybird crosses.

Mendel's law of independent assortment: each allele pair segregates independently 
of other gene pairs during gamete formation

Mendelian inheritance reflects rules of probability
    * The probability scale ranges from 0 to 1; an event that is certain to occur has a 
        probability of 1, and an event that is certain not to occur has a probability of 0.
    * The probabilities of all possible outcomes for an event must add up to 1.  
    * For example, when tossing a coin of rolling a six-sided die:

Random events are independent of one another
    * The outcome of a random event is unaffected by the outcome of previous 
        such events
    * For example, it is possible that five successive tosses of a normal coin will 
        produce five heads; however the probability of heads on the sixth toss is still 1/2.

Rule of Multiplication
rule of multiplication: the probability that independent events will occur 
simultaneously is the product of their individual probabilities. For example

Question: In a Mendelian cross between pea plants that are heterozygous for flower 
                  color (Pp), what is the probability that the offspring will be homozygous 
                  recessive?

Answer: Probability that an egg from the F1 (Pp) will receive a p allele = 1/2.  Probability 
that a sperm will form the F1 will receive a p allele = 1/2 the overall probability that two
 recessive alleles will unite at fertilization : 1/2 x 1/2 = 1/4

The rule also applies to dihybrid crosses. For example:

Question: For a dihybrid cross YyRr x YyRr, what is the probability for an F2 plant
                  having the genotype YYRR

Answer:  Probability that an egg from a YyRr parent will receive 
the Y and R alleles 1/2 x 1/2 = 1/4  Probability that a sperm from a YyRr parent 
will receive the Y and R alleles 1/2 x 1/2 = 1/4  The overall probability of an F3 plant 
having the genotype YYRR 1/4 x 1/4 = 1/16

Rule of addition
Rule of addition:  the probability of an event that can occur in two or more
 independent ways is the sum of the separate probability of the different ways.  
For example:

Question: Inn a Mendelian cross between pea plants that are heterozygous for flower color (Pp),
 what is the probability that the offspring will be heterozygote?

Answer: There are two ways in which a heterozygote may be produced: the dominant allele (P) may be in the egg and the recessive allele (p) in the sperm,, or the dominant allele may be in the sperm and the recessive in the egg.  Consequently, the probability of the offspring will be heterozygous if the sum of the probability of those two possible ways:
Probability that the dominant allele will be in the egg with the recessive in the sperm is 1/2 x 1/2 = 1/4.
Probably that the dominate allele will be in the sperm and the recessive in the egg is 1/2 x 1/2 = 1/4
Therefore, the probability that a heterozygous offspring will be produced is 1/4 + 1/4 = 1/2

Question: What is the probability that a trihybrid cross between two organisms with the genotypes AaBbCc and AaBbCc will produce an offspring with the genotype aabbcc.

Answer:  probability for aa offspring =  1/4
               probability for bb offspring = 1/4
               probability for cc offspring = 1/4
The probability that these independent events will occur simultaneously is the product of their independent probability (rule of multiplication).  So the probability that the offspring will be aabbcc is:
        1/4 aa x 1/4bb x 1/4 cc = 1/64

Question:  recessive phenotypes for at least two of the three traits? PpYyRr x Ppyyrr

Answer:  First list those genotypes that are homozygous recessive for at least two traits, (note that this includes the homozygous recessive for all three traits).  Use the rule of multiplication to calculate the probability that offspring would be one of these genotypes.  Then use the rule of addition to calculate the probability that two of the three traits would be homozygous recessive?

Genotypes with at least two                                               Probability of
homozygous recessives                                                           genotype 
            ppyyRr        1/4 x 1/2 x 1/2    =                                           1/16
            ppYyrr        1/4 x 1/2 x 1/2    =                                           1/16
            Ppyyrr        1/2 x 1/2 x 1/2     =                                           2/16
            PPyyrr        1/4 x 1/2 x 1/2     =                                           1/16
            ppyyrr         1/4 x 1/2 x 1/2     =                                           1/16 
                                                           =                                           6/16 or 3/8 chance of  at least two
                                                                                                         recessive traits.