MathBench > Probability

Mice with Fangs: Intro to Punnett Squares

Review Chez Punnett

A Punnett Square shows all the possible combinations all two sets of alleles, where the first set of alleles shows all possible zygote types contributed by the mother, and the second set shows possible types contributed by the father. We put the mother accross the top and the father accross the left hand side, but you could do it the other way around.

The Punnett Square for a mother that was Tt and a father that was Tt would yield approximately a 3:1 ratio of dominant to recessive phenotypes (and approximately a 1:2:1 ratio of AA, Aa, aa genotypes). Any other combination of parental genotypes can be figured out similarly, and will yield different ratios of genotypes and phenotypes (so don't assume that 3:1 is the answer to every problem!!!)

If you are trying to find the results of a cross involving 2 genes (i.e., fur AND teeth), then you need a bigger Punnett Square. With 2 genes, each parent can contribute 4 different zygote types, and you need to list each of the 4 on the top (mother) or side (father) of the Punnett Square. For example, in a double hybrid cross (AaBb x AaBb):

This gives the famous 9:3:3:1 ratios for phenotypes. Again, note that this ratio ONLY holds if you specifically have a dihybrid cross. If you cross, say, AABb x Aabb, you will get a completely different ratio (8:8:0:0, in case you're curious). If you are asked to find the phenotypic ratios, check first whether the problem involves a dihybrid cross -- if not, always work out the Punnett Square.

All of these phenotypic ratios are approximate, because they're being produced by random processes -- just like you get approximately 50% heads when you flip a coin.

The probability of a given phenotype can also be found by using the laws of probability. First, you need to identify all possible genotypes that would produce the desired phenotype. Then you use the Law of AND (multiply probabilities) to determine how likely each genotype is (i.e., multiply the probability of getting each of the four alleles in the genotype). Finally, you use the Law of OR (add the probabilities) to determine how likely it is that one of the possible genotypes was created.




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