Probability & Genetics

When introducing Mendelian genetics, I showed that the Mendel found a cross of a purebred dominant and a purebred recessive pea plant resulted in all dominant offspring.

By crossing two of those offspring, he received 3 dominant for every 1 recessive plant.  Random chance indicates that if you run that test a thousand times you’ll get a ratio of 3:1.  The more times you run the cross, the closer to 3:1 you’ll get.  Genetics is partially a lesson in simple probability.

In order to perform crosses by hand, we set up a Punnett square, which will allow us to work out the cross on paper.  Because showing your work is actually advantageous outside of homework and tests, we’ll do some samples.

In the below image, which I’ve beautifully created just for you, you’ll find the Punnett square, with one parent’s genotype on the top and the other on the side.  Which parent goes where, doesn’t matter; just make sure there’s always one allele for each of the 4 boxes (2 on top, 2 on the side).

The first square crosses a purebred dominant tall pea plant with a purebred recessive short pea plant.  Just as Mendel showed, when you cross, you get all tall plants.  The genotype for all 4 is hybrid (heterozygous) tall.

The second square cross two of the offspring from the first square.  2 hybrid tall pea plants result in 4 offspring: 1 purebred (homozygous) tall, 2 hybrid (heterozygous) tall, and 1 purebred (homozygous) short.  So the ratio for phenotype can be described as 3:1 (3 tall : 1 short) and the genotypic ratio can be described as 1:3:1 (1 homozygous dominant : 2 heterozygous : 1 homozygous recessive).

Punnett Squares
Full size for download

Any questions? Let me know!

Think you got it down? Try a few more:

Cross and determine the 1. phenotypic ratio and 2. genotypic ratio of:

1) Ss x Ss
2) Ww x WW
3) PP x Pp
4) A hybrid rough and a homozygous recessive for smooth seeds.


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