How to Calculate Centimorgans

In everyday life, we measure distances in terms of meters, feet, miles, millimeters, etc. But how would you express the distance between two genes on a chromosome? All of the standard units of measurement are much too big and don't really apply to our genetics.

That's where the unit centimorgan (often abbreviated to cM) comes in. While centimorgans are used as a unit of distance to represent genes on a chromosome, it's also used as a unit of probability for recombination frequency.

Recombination is a natural phenomenon (that's also used in genetic engineering) where during crossover events genes are "swapped" around on chromosomes. This rearranges the genes, which can add to genetic variability of gametes and can also be used for artificial genetic engineering.

What Is a Centimorgan?

A centimorgan, also known and written as a genetic map unit (gmu), is, at heart, a unit of probability. One cM is equal to the distance of two genes that gives a recombination frequency of one percent. In other words, one cM represents a one percent chance that one gene will be separated from another gene due to a cross over event.

The larger the amount of centimorgans, the farther away the genes are from each other.

This makes sense when you think about what crossing over and recombination is. If two genes are right next to each other, there's a much smaller chance that they're going to be separated from each other simply because they're close together, which is why the percentage of recombination that a single cM represents is so low: It's much less likely to occur when genes are close together.

When two genes are farther apart, aka the cM distance is larger, that means they're much more likely to separate during a cross over event, which corresponds to the higher probability (and distance) represented by the centimorgan unit.

How Are Centimorgans Used?

Because centimorgans represent both recombination frequency and gene distances, they have a few different uses. The first is to simply map the location of genes on chromosomes. Scientists have estimated that one cM is roughly equivalent to one million base pairs in humans.

This allows scientists to perform tests to understand the recombination frequency and then equate that to gene length and distance, which allows them to create chromosome and gene maps.

It can also be used in the reverse way. If you know the distance between two genes in base pairs, for example, you can then calculate that in centimorgans and, thus, calculate the recombination frequency for those genes. This is also used to test whether genes are "linked," meaning very close together on the chromosome.

If recombination frequency is less than 50 cM, it means the genes are linked. This, in other words, means that the two genes are close together and are "linked" by being on the same chromosome. If two genes have a recombination frequency greater than 50 cM, then they are not linked and are thus on different chromosomes or very far apart on the same chromosome.

Centimorgan Formula and Calculation

For a centimorgan calculator, you'll need the values of both the total number of progeny and the number of recombinant progeny. Recombinant progeny are progeny that have a non-parental allele combination. In order to do this, scientists cross a double heterozygote with a double homozygous recessive (for the genes in interest), which is called the "tester."

For example, let's say there's a male fly with a genotype JjRr and a female fly with jjrr. All of the female's eggs are going to have the genotype "jr". The male's sperm without crossover events would only give JR and jr. However, thanks to crossover events and recombination, they could also potentially give Jr or jR.

So, directly inherited parental genotypes would be either JjRr or jjrr. Recombinant progeny would be those with the genotype Jjrr or jjRr. Fly progeny with those genotypes would be recombinant progeny since that combination wouldn't normally be possible unless a crossover event had occurred.

You'll need to look at all of the progeny and count both the total progeny and the recombinant progeny. Once you have the values for both total and recombinant progeny in an experiment you're running, you can calculate recombination frequency using the following centimorgan formula:

Recombination Frequency = (# of recombinant progeny / total # of progeny) * 100m

Since one centimorgan is equal to one percent recombination frequency, you can also write that percentage you get as in centimorgan units. For example, if you got an answer of 67 percent, in centimorgans that would be 67 cM.

Example Calculation

Let's continue with the example used above. Those two flies mate and have the following number of progeny:

JjRr = 789

jjrr = 815

Jjrr = 143

jjRr = 137

Total progeny is equal to all of those progeny added, which is:

Total progeny = 789 + 815 + 143 +137 = 1,884

Recombinant progeny is equal to the progeny number of Jjrr and jjRr, which is:

Recombinant progeny = 143 + 137 = 280

So, recombination frequency in centimorgans is:

Recombination frequency = (280 / 1,884) * 100 = 14.9 percent = 14.9 cM

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