1. Basic Mendelian Principles
Mendel’s big ideas:
--Particulate inheritance: the determinants of inherited traits are discrete units that are passed between generations unaltered, not blended together.
--Count large numbers of offspring. The offspring ratios observed are imperfect reflections of underlying simple ratios like 3/4 : 1/4 , etc.

2. Experimental Organism
Mendel worked with peas.
Plants have sexual processes very similar to animals.
--The male gamete, equivalent to the sperm, is the pollen grain.
--The female gamete, equivalent to the egg, is the ovule.
Pea plants have both sexes on the same plant, and they can be self-pollinated: pollen from one plant is used to fertilize ovules from the same plant. This is a closer cross than is possible with animals.
He found 7 lines of peas that differed from each other for 7 distinct traits.

3. Mendel's Traits

4. Monohybrid Cross
We are first going to look at what happens when plants with different traits are crossed, then go through Mendel's explanation.
Purple flowers vs. white flowers. The original parental lines are true-breeding, or pure-breeding. All offspring within the lines gave the same flower color for an arbitrary number of generations.

5. First Cross
True-breeding purple x true-breeding white. All offspring are purple. The parent lines are the P generation; the offspring are the F1 (first filial) generation.
All the F1's are purple regardless of which parent (father or mother) was purple and which was white.
Note: no blending occurs. The purple F1 plants look exactly like the purple parentals.
We say that purple is dominant because it appears in the F1 hybrid. White is recessive because it does not appear in the F1 hybrid.

6. Selfing the F1
Self-pollinate the F1 plants to get the F2 (second filial) generation.
In animals with only 1 sex per individual, the equivalent would be a brother-sister mating.
The F2 appear in a ratio of 3/4 purple to 1/4 white.
Note: white has re-appeared in the F2, unchanged despite having been in a purple F1 plant. The genes are not affected by the organism that carries them.

7. Selfing the F2
Each F2 plant is selfed to produce a group of F3 offspring.
The F3 offspring of the white F2's are all white. The F2 white plants were all true-breeding.
Some of the F2 purples have all purple F3 offspring. These F2 purple plants are true breeding.
Other F2 purples give purple and white F3's in a ratio of 3/4 purple to 1/4 white. This is the same behavior as the F1's had.

8. F2 Behavior
The purple F2 plants come in 2 types: some are true breeding and only give purple offspring. Others are hybrids and give 3/4 purple : 1/4 white offspring. They can be distinguished by the offspring they produce, but not by their physical appearance.

9. Explanation
Pea plants, like humans and most other higher organisms, are diploid: there are 2 copies of each gene. One copy came from the father and the other copy came from the mother.
A gene can have many different versions, called alleles. In this case, the flower color gene has a purple allele (symbolized P) and a white allele (symbolized p).

10. More Explanation
The true breeding lines are homozygous for the gene being examined: both copies of the gene are the same allele. Thus in the initial cross, one parent was PP and the other was pp.
Hybrid lines are heterozygous: the two copies of the gene being examined are different. A Pp plant is a heterozygote.
When diploid organisms reproduce, they make gametes (sperm and eggs) that are haploid: they have only 1 copy of each gene. Which copy goes into the gamete is a random process.
The male and female gametes combine at random to form zygotes, the first diploid cells of the next generation.

11. Still More
In the case we are discussing, the PP plant produces P gametes and the pp plant produces p gametes. These gametes combine to form Pp F1 individuals.
Since P (purple) is dominant to p (white), the Pp plants are purple.
Thus there are 2 forms of purple plant: the PP homozygotes and the Pp heterozygotes. These plants have the same phenotype (physical appearance) but different genotypes (genetic constitution). Much of genetics is an attempt to determine the relationship between phenotypes and genotypes.

12. F1 -> F2 Explanation
When the F1 (Pp) plant makes gametes, each gamete gets either a P allele or a p allele. This happens randomly, so 1/2 of the gametes are P and 1/2 are p.
The gametes combine at random. So:
1/2 x 1/2 = 1/4 of the zygotes come from a P egg meeting a P sperm, giving a PP F2 plant.
1/2 x 1/2 = 1/4 of the zygotes come from a p egg meeting a p sperm = pp F2 plant.
1/2 x 1/2 = 1/4 are P egg meeting a p sperm, and 1/2 x 1/2 = 1/4 are p egg meeting a P sperm. Both of these give a Pp F2 plant, so 1/2 of the F2 are Pp.

13. F2
In summary, 1/4 of the F2 genotypes are PP, 1/2 are Pp, and 1/4 are pp.
Since P (purple) is dominant, both PP and Pp plants are purple. Thus, 3/4 of the phenotypes are purple, and 1/4 are white.
Mendel found that this rule worked for all 7 of his traits, to within what he considered reasonable accuracy.

14. Mendel Monohybrid Results

15. Law of Segregation Mendel's first law of genetics
The two members of a gene pair segregate randomly and equally into the gametes, which then combine at random to form the next generation.

16. Backcross and Test cross
A backcross involves mating the F1 hybrid to one of the parental types. There are 2 possible backcrosses in the system we are examining.
Pp x PP. Back crossing to the dominant parent. The Pp plant will produce 1/2 P gametes and 1/2 p gametes. The PP plant will produce only P gametes. The offspring will thus be 1/2 PP and 1/2 Pp. Both of these types are purple, so the result of a backcross to the dominant parent is all offspring with the dominant type.
Pp x pp. back crossing to the recessive parent. Again, the Pp parent produces 1/2 P gametes and 1/2 p gametes, and the pp parent produces only p gametes. The offspring will be 1/2 Pp (purple) and 1/2 pp (white). Note this is a different ratio from the F1 x F1 (Pp x Pp) intercross we looked at earlier.
A test cross is a mating between a heterozygote (or unknown) to the recessive homozygote (the tester). For monohybrid crosses, the test cross is the same as a backcross to the recessive parental type. The offspring of a test cross are in the same ratio as the gametes from the organism being tested: 1/2 P (purple) and 1/2 p (white).

17. Dihybrid Cross
A dihybrid cross examines 2 different genes. We will use yellow vs. green pods, and round vs. wrinkled seeds.
Yellow (Y) is dominant to green (y).
Round (R) is dominant to wrinkled (r).
Initial cross: YY rr x yy RR (yellow wrinkled x green round). The YY rr plant makes Yr gametes ( one copy of each gene) and the yy RR plant makes yR gametes.
These combine to make F1 plants that are Yy Rr, yellow round. Note that neither parent has this phenotype.

18. F1 -> F2 Dihybrid
When the Yy Rr plant is mated, it makes 4 kinds of gamete. Each gamete gets 1 copy of each gene, so 1/2 are Y and 1/2 are y. Independently, 1/2 are R and 1/2 are r. Thus, 1/4 of the gametes are YR, 1/4 are Yr, 1/4 are yR, and 1/4 are yr. This happens for both male and female gametes.
The gametes combine randomly. The combinations are shown in a 16 cell Punnett square.

19. F2 Dihybrid Results
Examining the Punnett square, we find 1 cell (1/16 of the offspring) that are yy rr, homozygous recessive for both traits: green wrinkled.
Three of the cells are either yy RR or yy Rr. Both of these have the green round phenotype, so 3/16 of the offspring are green and round. We can symbolize this as yy R_, where the _ stands for either R or r. As long as one copy of the gene is the dominant R allele, it doesn’t matter what the other copy is.
Similarly, 3 of the cells are YY rr or Yy rr, yellow wrinkled. 3/16 are Y_ rr
All of the other 9 cells are Y_ R_: yellow round, in various combinations of homozygotes and heterozygotes.
This is the fundamental ratio for the F2 from a dihybrid cross: 9/16 show both dominant traits, 3/16 show one dominant and the other recessive, 3/16 show one recessive and the other dominant, and 1/16 show both recessive traits.

20. F2 dihybrid results are the combination of 2 monohybrid crosses
If you just look at the individual genes separately, you find the same 3/4 : 1/4 ratio seen in the monohybrid cross.
Thus, 9/16 are yellow round and 3/16 are yellow wrinkled. This adds up to 12/16 = 3/4 yellow. And, 3/16 are green round and 1/16 are green wrinkled, which adds up to 4/16 = 1/4 green.
Same is true for round vs. wrinkled.

21. Law of Independent Assortment
Mendel's second law.
For unlinked genes, the alleles from each gene segregate into the gametes independently of one another.
Some genes are linked, which means that they don't segregate independently of each other and thus don't give the 9:3:3:1 ratio of F2 offspring. Linked genes are close together on the same chromosome; we will deal with this phenomenon later.

22. Multiple Genes
For more than 2 genes, Punnett squares get unwieldy. To calculate the ratio of offspring, we use a different method, the forked-line approach.
To do these problems, 3 steps are involved:
1. determine the ratio of phenotypes for each gene separately.
2. Draw a forked line diagram of the offspring, splitting each line for each separate gene, showing the ratio of phenotypes.
3. Combine the phenotypes and multiply the phenotype ratios along each branch to get the final proportions of each type of offspring.