Mendel's Second Law & Its Application

Instructor: Laura Foist

Laura has a Masters of Science in Food Science and Human Nutrition and has taught college Science.

In this lesson, we'll explore how genes can assort independently according to Mendel's second law. We'll also use Punnett squares to see whether or not genes are linked and how this relates to research.

Mendel's Second Law

If you flip a quarter and a penny, the results you get from the quarter are not going to affect the results you get from the penny. Both are going to be randomly distributed between heads and tails. Our genes are the same way. Being right vs. left-handed is not going to affect your having blue vs. brown eyes. This is known as Mendel's second law or the law of independent assortment.

Just as a side note, there are some genes which are dependent on each other. These genes are linked together. For example, red hair and freckles tend to happen at the same time and are a linked gene. Mendel's second law only applies to genes which are not linked together.

Mendel's Discovery

Mendel discovered this law with an experiment on peas. Pea color has two alleles, yellow or green, and pea shape has two alleles, rough or wrinkled. An allele refers to the two (or more) options that a gene can be represented as. Typically, there is a dominant and recessive allele for each gene. Between yellow and green, yellow is the dominant color. Between round or wrinkled, round is the dominant shape.

If these characteristics are linked, for example if dominant alleles for color are linked to dominant alleles for shape (so a yellow pea is typically round, and a green pea is typically wrinkled), then we would not expect the results to follow the results obtained from a Punnett square. For color, let's use Y and y: capital Y is yellow and lower case y is green. For shape, let's use R and r: capital R is round and lower case r is wrinkled.


Mendel Punnett Square


When we count up the results, we see that we got the following:

  • 9 Yellow Round
  • 3 Yellow Wrinkled
  • 3 Green Round
  • 1 Green Wrinkled

Mendel did the experiment and found that he got the same proportions of each type of pea as predicted using the Punnett square. From this, we know the alleles for color and shape are independently assorted.

Think back to flipping a quarter and a penny. The result of one doesn't affect the other's result, and we still have a 50/50 chance for what we'll get on either flip. Similarly, the result the pea gets for color won't affect the result it gets for shape. It also doesn't matter if one allele is dominant; we still have the same chances of getting a dominant or recessive allele for a different gene.

Applying Mendel's Second Law

When we are studying genes we will often look at a large distribution of data. If we start to see a link between something like freckles and red hair which doesn't follow the distribution we would expect from the Punnett square, then we can start to hypothesize that those genes are linked. Once we start exploring the link between two genes, we can better understand what causes certain conditions and possibly how to better treat undesired conditions.

So, in order to apply Mendel's second law, we need to know how to use the Punnett square. Pick two characteristics you are interested in studying, let's say hair color and skin type. Our options for hair color are brown hair (dominant, let's represent it with B) and red hair (recessive, represented with b). Our options for skin type are clear (dominant, represented with C) and freckled (recessive, represented with c). The actual letters used to represent each allele aren't that important, but dominant alleles need to be upper case letters while recessive alleles are the same letters only lower case.

First, let's set up our Punnett square:


Punnett set up


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