What is Probability?
To understand Medel’s work, we must learn how DNA is inherited and the probability of what phenotypes the offspring may have. Mendel knew that traits are not guaranteed to show up in offspring, but he could calculate the likelihood of certain traits appearing in offspring. Medel breed tens of thousands of pea plants because the larger the sample size, the more likely he would get the traits’ predicted ratio. For example, when crossing (breeding) two heterozygous pea plants for height (Tt), the probability of getting a tall plant is 75% and 25% for a short plant. It is possible, though less likely that all offspring will be short or half tall and half short. However, if you breed thousands of plants, you will most likely end up with a 3:1 ratio.
Genetics is somewhat of a guessing game, but we can use probability to find the likelihood that a trait will appear in the offspring. For example, if you flip a coin, there is a 50% chance of heads and a 50% chance of tails (1:1 ratio). However, if you flip the coin a second time, you have a 25% chance of getting the same result as you did with the previous flip.
What?
Well, each independent coin flip will result in a 1:1 ratio. However, when you combine a series of coin flips, getting the same results decreases with each flip. Let’s look at the math:
1/2 x 1/2 = 1/4 or 25%
1/2 x 1/2 x 1/2 = 1/8 or 12.5%
As you can see, each independent flip has a 50% chance of heads; however, getting heads twice is 25%, and the chance of getting heads three times is 12.5%. You could flip a coin 10 times and end up with 10 heads, but the odds of this happening are 0.1% or 1 out of 1,024
Gene Shuffling
Gene shuffling is essentially meiosis and fertilization. Meiosis brings genetic variety to gametes by the chromosomes’ random assortment(think of shuffling a deck of cards) and crossing-over. Fertilization is random because the female randomly releases an egg each month from her ovary, and the sperm released by the male during sexual reproduction is random. In the end, gene shuffling leads to a genetically unique organism with probable traits from its biological mother and father.
Punnett Squares
Punnett squares are charts used to predict the possible offspring results when two parents mate. These give a probability that certain traits will show up in the offspring.
To solve a Punnett square you need to know the possible alleles for a trait in each gamete.
- The gene TT makes only T gametes.
- The gene Tt makes 50% T gametes and 50% t gametes
- The gene tt makes only t games
Solving a Punnett Square for Complete Dominant Traits
Complete dominance means that only the trait that the dominant allele codes for will show up in the heterozygous state (Tt). Therefore, if tall is dominant to short, the genotypes TT and Tt will produce a tall child. The only way to get a short child is if their genotype comprises two recessive alleles (tt).
Problem:
In pea plants, tall plants are dominant over short plants. A heterozygous tall plant (Tt) is crossed with a homozygous recessive short plant (tt).
Step 1: Make a Key
TT and Tt = Tall plant; tt = short plant
Step 2: Write out the genotype of each parent
Parent 1 = Tt; Parent 2 = tt
Step 3: Write out the possible gametes of each parent
Parent 1 gametes = T and t; Parent gametes 2 = t and t
Step 4: Place the gamete to one parent on the top of a Punnett square and the gametes to the other parent on the left side of a Punnett square
Step 5: Possible genotypes for the offspring are written in the squares
Step 6: Determine the probability of each genotype and phenotype
Genotypes:
What is the probability of having offspring with TT? 0%
What is the probability of having offspring with Tt? 50%
What is the probability of having offspring with tt? 50%
Genotype ratio = 1:1 or 50%, Tt 50% tt
Phenotypes:
What is the probability of having tall offspring? 50%
What is the probability of having short offspring? 50%
Phenotype ratio = 1:1 or 50% Tall, 50% short