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The law of independent assortment

Learn about the law of independent assortment, dihybrid crosses, and how to solve 4 x 4 Punnett squares.

Introduction

The law of segregation lets us predict how a single feature associated with a single gene is inherited. In some cases, though, we might want to predict the inheritance of two characteristics associated with two different genes. How can we do this?
To make an accurate prediction, we need to know whether the two genes are inherited independently or not. That is, we need to know whether they "ignore" one another when they're sorted into gametes, or whether they "stick together" and get inherited as a unit.
When Gregor Mendel asked this question, he found that different genes were inherited independently of one another, following what's called the law of independent assortment. In this article, we'll take a closer look at the law of independent assortment and how it is used to make predictions. We'll also see when and why the law of independent assortment does (or doesn't!) hold true.
Note: If you are not yet familiar with how individual genes are inherited, you may want to check out the article on the law of segregation or the introduction to heredity video before you dive into this article.

What is the law of independent assortment?

Mendel's law of independent assortment states that the alleles of two (or more) different genes get sorted into gametes independently of one another. In other words, the allele a gamete receives for one gene does not influence the allele received for another gene.

Example: Pea color and pea shape genes

Let's look at a concrete example of the law of independent assortment. Imagine that we cross two pure-breeding pea plants: one with yellow, round seeds (YYRR) and one with green, wrinkled seeds (yyrr). Because each parent is homozygous, the law of segregation tells us that the gametes made by the wrinkled, green plant all are ry, and the gametes made by the round, yellow plant are all RY. That gives us F1 offspring that are all RrYy.
The allele specifying yellow seed color is dominant to the allele specifying green seed color, and the allele specifying round shape is dominant to the allele specifying wrinkled shape, as shown by the capital and lower-case letters. This means that the F1 plants are all yellow and round. Because they are heterozygous for two genes, the F1 plants are called dihybrids (di- = two, -hybrid = heterozygous).
A cross between two dihybrids (or, equivalently, self-fertilization of a dihybrid) is known as a dihybrid cross. When Mendel did this cross and looked at the offspring, he found that there were four different categories of pea seeds: yellow and round, yellow and wrinkled, green and round, and green and wrinkled. These phenotypic categories (categories defined by observable traits) appeared in a ratio of approximately 9:3:3:1.
Image credit: "Laws of inheritance: Figure 2," by OpenStax College, Biology, CC BY 4.0.
This ratio was the key clue that led Mendel to the law of independent assortment. That's because a 9:3:3:1 ratio is exactly what we'd expect to see if the F1 plant made four types of gametes (sperm and eggs) with equal frequency: YR, Yr, yR, and yr. In other words, this is the result we'd predict if each gamete randomly got a Y or y allele, and, in a separate process, also randomly got an R or r allele (making four equally probable combinations).
We can confirm the link between the four types of gametes and the 9:3:3:1 ratio using the Punnett square above. To make the square, we first put the four equally probable gamete types along each axis. Then, we join gametes on the axes in the boxes of the chart, representing fertilization events. The 16 equal-probability fertilization events that can occur among the gametes are shown in the 16 boxes. The offspring genotypes in the boxes correspond to a 9:3:3:1 ratio of phenotypes, just as Mendel observed.

Independent assortment vs. linkage

The section above gives us Mendel's law of independent assortment in a nutshell, and lets us see how the law of independent assortment leads to a 9:3:3:1 ratio. But what was the alternative possibility? That is, what would happen if two genes didn't follow independent assortment?
In the extreme case, the genes for seed color and seed shape might have always been inherited as a pair. That is, the yellow and round alleles might always have stayed together, and so might the green and wrinkled alleles.
To see how this could work, imagine that the color and shape genes are physically stuck together and cannot be separated, as represented by the boxes around the alleles in the diagram below. For instance, this could happen if the two genes were located very, very close together on a chromosome (an idea we'll explore further at the end of the article).
Rather than giving a color allele and, separately, giving a shape allele to each gamete, the F1 dihybrid plant would simply give one “combo unit” to each gamete: a YR allele pair or a yr allele pair.
We can use a Punnett square to predict the results of self-fertilization in this case, as shown above. If the seed color and seed shape genes were in fact always inherited as a unit, or completely linked, a dihybrid cross should produce just two types of offspring, yellow/round and green/wrinkled, in a 3:1 ratio. Mendel's actual results were quite different from this (the 9:3:3:1 ratio we saw earlier), telling him that the genes assorted independently.

The reason for independent assortment

To see why independent assortment happens, we need to fast-forward half a century and discover that genes are physically located on chromosomes. To be exact, the two copies of a gene carried by an organism (such as a Y and a y allele) are located at the same spot on the two chromosomes of a homologous pair. Homologous chromosomes are similar but non-identical, and an organism gets one member of the pair from each of its two parents.
The physical basis for the law of independent assortment lies in meiosis I of gamete formation, when homologous pairs line up in random orientations at the middle of the cell as they prepare to separate. We can get gametes with different combos of "mom" and "dad" homologues (and thus, the alleles on those homologues) because the orientation of each pair is random.
To see what this means, compare chromosome arrangement 1 (top) and chromosome arrangement 2 (bottom) at the stage of metaphase I in the diagram below. In one case, the red "mom" chromosomes go together, while in the other, they split up and mix with the blue "dad" chromosomes. If meiosis happens many times, as it does in a pea plant, we will get both arrangements—and thus RY, Ry, rY, and ry classes of gametes—with equal frequency.
Image modified from "The laws of inheritance: Figure 5," by OpenStax College, Concepts of Biology, CC BY 4.0
Genes that are on different chromosomes (like the Y and R genes) assort independently. The seed color and seed shape genes are on chromosomes 1 and 7 of the pea genome, respectively, in real life1. Genes that are far apart on the same chromosome also assort independently thanks to the crossing over, or exchange of homologous chromosome bits, that occurs early in meiosis I.
There are, however, gene pairs that do not assort independently. When genes are close together on a chromosome, the alleles on the same chromosome tend to be inherited as a unit more frequently than not. Such genes do not display independent assortment and are said to be linked. We'll take a closer look at genetic linkage in other articles and videos.

Check your understanding

  1. Suppose you cross a pure-breeding, black-coated dog with curly fur to a pure-breeding, yellow-coated dog with straight fur. In the F1 generation, all the puppies have straight, black coats. Next, you interbreed the F1 dogs with one another to get an F2 generation.
    If coat color and coat texture are controlled by two genes that assort independently, what fraction of the F2 puppies are expected to have yellow, straight fur?
    Choose 1 answer:

Want to join the conversation?

  • leaf green style avatar for user tk12
    I understand this, but I still get confused on the Mendelian laws.
    Here is what I think I know:
    The law of segregation states that the two alleles of a single trait will separate randomly, meaning that there is a 50% either allele will end up in either gamete. This has to do with 1 gene.
    The law of independent assortment states that the allele of one gene separates independently of an allele of another gene. This has has to do with 2 genes.
    Is my understanding of these laws correct?
    (51 votes)
    Default Khan Academy avatar avatar for user
    • leaf grey style avatar for user Anshari Hasanbasri
      That is correct. But as an addition, there is also the concept of linkage, where the allele of one gene is very close to an allele of another gene in the same DNA strand, that it is very unlikely for the two allele to separate independently (in other words, they are inherited as one unit). This has to do with 2 genes. This concept is essentially independent assortment, but deals with unit of multiple alleles, rather than just an allele.
      (42 votes)
  • duskpin ultimate style avatar for user cook.katelyn
    What is the difference between segregation and independent assortment? :)
    (11 votes)
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    • leafers tree style avatar for user Aditya Dubey
      Segregation means that the chromosomes or any gene present on chromosome did not lose its identity or get mixed up with other genes. During gametogenesis it keeps its identity.
      While independent assortment means that the chromosomes whether dominant or recessive after gametogenesis goes into any of the gametes i.e in simple language the movement of chromosomes is not affected by movement of other chromosomes
      (19 votes)
  • blobby green style avatar for user harshulsurana5000
    For the experiment of F1 generation how did Mendel know for sure that the tall parent's genotype is (TT) ?
    (4 votes)
    Default Khan Academy avatar avatar for user
    • leaf green style avatar for user tk12
      The pea plants he used self-fertilized, meaning that each parent ends up having the same set of genes as the offspring. (This is before he crossed them.) This means that there were pure lines of descent from the original pea plants without variation. The genotypic variation of the offspring (heterozygotes) was introduced by Mendel, who crossed 2 plants of different traits.
      (7 votes)
  • orange juice squid orange style avatar for user AbdullhMohamed64
    The phenotypes are a 9:3:3:1 ratio, but what are the possible genotypes?
    (3 votes)
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    • blobby green style avatar for user Jmsmarlowe
      there are 9 different genotypes in a F1 dihybrid cross and the ratio is
      1:2:1 :2:4:2: 1:2:1

      in a monohybrid cross the phenotype ratio is 3:1 which gets compounded when doing a dihybrid cross into 9:3:3:1

      the genotype ratio in a monohybrid is 1:2:1
      and gets compounded to my answer in a dihybrid cross. I show the work below.

      F1 generation is heterozygote for both traits: AaBb or Aa and Bb
      A a
      A AA Aa
      a Aa aa
      and
      B b
      B BB Bb
      b Bb bb

      here are the possible genotypes and ratios made from the squares above:
      AABB(1) AABb(2) AAbb(1) AaBB(2) AaBb(4)Aabb(2)aaBB(1) aaBb(2) aabb(1)

      this is nothing more than a 1:2:1 compounded to two characters.
      (2 votes)
  • duskpin sapling style avatar for user 25399
    Does this mean that any living organism (Pea plant, dogs etc.)
    will show phenotypic ratio of 9:3:3:1 ? Where 9 plants have all dominant alleles and 1 plant has all recessive alleles ?
    (3 votes)
    Default Khan Academy avatar avatar for user
  • female robot amelia style avatar for user Sancha.Natalie
    I understand this, but I still get confused on the Mendelian laws.
    Here is what I think I know:
    The law of segregation states that the two alleles of a single trait will separate randomly, meaning that there is a 50% either allele will end up in either gamete. This has to do with 1 gene.
    The law of independent assortment states that the allele of one gene separates independently of an allele of another gene. This has has to do with 2 genes.
    Is my understanding of these laws correct?
    (4 votes)
    Default Khan Academy avatar avatar for user
    • primosaur sapling style avatar for user Esa Eah
      That is correct. But as an addition, there is also the concept of linkage, where the allele of one gene is very close to an allele of another gene in the same DNA strand, that it is very unlikely for the two allele to separate independently (in other words, they are inherited as one unit). This has to do with 2 genes. This concept is essentially independent assortment, but deals with unit of multiple alleles, rather than just an allele.
      (1 vote)
  • blobby green style avatar for user rawan019.student
    Can you explain to me what is the difference between linked and not linked. Also, how to identify if an allele is not linked.
    (3 votes)
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    • female robot grace style avatar for user Jennifer Johnson
      Linkage or whether 2 genes are linked or not depends upon the distance between them. If the distance between 2 genes are small or if they are next to each other in a chromosome, most probably when meiosis occur these genes remain together. So genes that remain together and almost never segregate are called linked genes.
      Hope this helps.
      (3 votes)
  • piceratops tree style avatar for user Priya K
    Does the law of independent assortment apply to two genes on different chromosomes or two alleles on different chromosomes?
    (3 votes)
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  • duskpin ultimate style avatar for user dyhmondwallace
    If the genes are the same, then why is it that many people look different form their parents?
    That's just if they were the same though.
    (2 votes)
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    • spunky sam blue style avatar for user Jay
      In each of your parents, there are genes coding for their appearence, i.e bone structure, hair color, eye collar, that are shown. However, there are also genes that aren't expressed by your parent that they have, such as something different. Considering there are billions of genes that code for even one thing, there is an extremely high liklihood of you expressing a gene that wasn't expressed in your parents, (but was still there)
      (3 votes)
  • blobby green style avatar for user aalnahas
    If 4 gametes are produced after meiosis, then why does the punnett square show 2 possibilities for each gamete, such as TT or Tt?
    (2 votes)
    Default Khan Academy avatar avatar for user