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Changing Base Pairs to Centimorgans « Louis Kessler’s Behold Weblog Get hold of US

DNA Testing firms give you your matches and quantify how intently you match every individual by supplying you with a complete worth in centimorgans (cM).

As well as, firms apart from Ancestry DNA additionally give you all of your particular person section matches and let you know the centimorgans of each section. For every section additionally they let you know the section’s beginning and ending base pair location.

For instance, at Household Tree DNA, I share 2009 cM with my uncle. These are what Household Tree DNA gives for the matches I’ve with my uncle on chromosome 1:

The Begin Location and Finish Location are the place in base pairs (bp) alongside the chromosome the place every match begins and ends as decided by Household Tree DNA.


The Centimorgans worth is a measure of the how seemingly it’s that the section will recombine in a single era. A section of 1 centimorgan has a 1% likelihood of recombining. The final equation is:

Likelihood of recombination in a single era = 1 – (e ** (cM of section / 100))

the place e is the fixed generally known as Euler’s quantity = 2.718281828…


  • a 1 cM section has a 1 – (e ** –0.01) = 1.0% likelihood of recombining
  • a ten cM section has a 1 – (e ** –0.1) = 9.5% likelihood of recombining
  • a 30 cM section has a 1 – (e ** =0.3) = 25.9% likelihood of recombining
  • a 75 cM section has a 1 – (e ** –0.75) = 52.8% likelihood of recombining
  • a 200 cM section has a 1 – (e ** –2.0) = 86.5% likelihood of recombining

On the ISOGG Wiki’s Centimorgan page, there’s a good graph of the chance of crossover by section size.

Additionally on the ISOGG web page you may see from their cM values per chromosome desk that the centimorgans for chromosome 1 as of 2015 have been:

  • 267.21 at Household Tree DNA
  • 281.5 at GEDmatch
  • 284 at 23andMe

So every firm gives barely completely different estimates of centimorgans. For all of the autosomes (chromosomes 1 to 22 and X), the totals vary between 3580 and 3783 cM.

Recombinations are essential as a result of they characterize a crossover of the 2 parental chromosomes, and that leads to an endpoint for matches.

Women and men considerably differ in centimorgan values. Most firms don’t take care of female and male values, however use a mixed common. That’s as a result of when you’re speaking about cousins and extra distant family members, the values are likely to common out.

Base Pairs

A base pair is one particular person place on a chromosome. It’s made up as a pair of alleles which can be bonded collectively, one from the chromosome’s ahead strand and one from its reverse strand. Every allele has the worth A, C, G or T, so the worth of the bottom pair usually is proven as a pair of the values, e.g. AA or CT.

Surprisingly, ISOGG doesn’t have a desk of the variety of base pairs per chromosome, so you must go to the Chromosome page on Wikipedia for it.

The autosomes (chromosomes 1 to 22 and X) whole 3,022,102,095 base pairs, and chromosome 1 alone has 247,199,719 base pairs.

The variety of base pairs given are very precise. They’re all outlined exactly in order that references can me made to the precise base pairs of curiosity and everybody can “speak the identical language” and be referring to the identical section on the chromosome.

Sadly, science remains to be working to completely outline the human genome, so these base pair definitions are persevering with to be up to date. The Nationwide Library of Medication maintains the Genome definitions. Right here for instance is GRCh37 from 2009, often known as Construct 37 and as hg19. It was preceded by Construct 36 (hg18) and by many different definitions earlier than that. Construct 37 itself has undergone 29 revisions and in 2013 was changed by GRCh38 which itself is now at revision 14.

Clearly, DNA firms can’t be always altering their base pair a number of occasions annually. Luckily, all the businesses all determined to stay with a standard model of Construct 37 to outline their allele areas. That is good as a result of it permits DNA testers to switch our uncooked information between platforms.

For the aim of relative matching, solely about 700,000 out of the three billion areas are examined, as a result of these are those which can be almost definitely to have variations between folks or be of medical curiosity. These SNPs (Single nucleotide polymorphisms) typically are well-defined and will stay sooner or later builds of the human genome, though their place will proceed to vary as different positions between them are added and eliminated.

Why Do We Have to Map Mbp to cM?

For ancestry analysis, the cM worth is essential to have. Due to the best way section matching works, you may have segments that match just by likelihood, the place both allele of 1 individual is matching both allele of the opposite individual at every place of the section. The cM worth is an efficient measure of how seemingly that is to occur.

For those who have been evaluating segments which can be phased (separated accurately into their two dad and mom) for each folks, then this by likelihood matching wouldn’t occur. The ISOGG wiki has a nice graph of the probability a match survives phasing which signifies that segments below 15 cM are topic to being a by likelihood match, also known as a false match.

When utilizing triangulated segments, you might be evaluating 3 folks’s segments with one another they usually should all match. The probability of false matches on this case is decreased and folks like Jim Bartlett have indicated that by likelihood triangulated matches might begin occurring below 7 cM.

Due to this fact centimorgans inform us what segments are “too small” for our evaluation.

If centimorgans have been all the time out there, then we’d be glad. However they don’t seem to be all the time out there.

Allow us to say you match two folks, one on a 20 cM section and the opposite on a 25 cM section and the 2 segments overlap.


The issue is in figuring out what number of centimorgans is the overlapping area between 30 Mbp and 50 Mbp? You don’t know that. You solely know that the overlapping area is 20 Mbp. You would want to calculate the centimorgans it if you would like it.

The Relationship Between Base Pairs and Centimorgans

Base pairs are giant numbers expressing the place on the chromosome in tens of millions to a whole bunch of tens of millions. To simplify and approximate them, we are able to divide the values by 1 million and seek advice from Megabase pairs (Mbp).

So there are about 3,022 Mbp within the autosomes and 247 Mbp in chromosome 1 alone. Evaluate this to about 3,600 cM within the autosomes and 270 cM in chromosome 1. The Mbp and cM are comparable. A easy rule of thumb is that the variety of cM is roughly the identical because the size of the section in Mbp.

However there’s fairly a little bit of variation. For instance, the desk above of my matches with my uncle might be re-expressed as:


As you may see, the ratio between cM of a section and Mbp for the section for this small pattern of segments ranges from 0.83 to 2.37. It’s because recombination charges fluctuate significantly relying on which a part of what chromosome you’re looking at.

Family Tree DNA wrote this about how they decide the cM worth for a DNA section:

The Household Tree DNA bioinformatics workforce works with centiMorgan (cM) information from the International HapMap project.

Present data of centiMorgan values throughout the human genome comes from the Worldwide HapMap undertaking testing. The undertaking examined father-mother-child trios from international inhabitants teams. Utilizing this info, they mapped recombination charges throughout the human genome.

The tables they might be utilizing may very well be the ones the NBCI made available in 2008. Right here’s the start of Chromosome 1:


That is saying the cM/Mbp ratio could be very low originally of Chromosome 1, however when you attain place 711,153, the ratio has risen to 2 cM per Mbp. 

To calculate the cM for a section, subtract the cM worth on the finish place from the cM worth in the beginning place. e.g. from 554,461 to 730,720, the cM can be calulated as 0.042 – 0.001 = 0.041 cM.

If in case you have a place between these listed, then you definitely would interpolate to find out the cM for the place desired.

Checking the Calculations

Jonny Perl, the developer of DNA Painter, lately talked about to me the work of Amy Williams, a pc scientist and geneticist at Cornell. Jonny supplied me with Amy’s Minimal viable genetic map which reduces the HapMap from almost 3.4 million entries to only over 32,000 entries. Jonny instructed me that this file works fairly properly for 23andMe and MyHeritage matches.

I took this map information and checked it towards all of the chromosome 1 segments from a Household Tree DNA check that I’ll name “Terry”. I used to be shocked to see poor outcomes.

So I re-did this however used my very own check’s matches at Household Tree DNA, 23andMe, MyHeritage and GEDmatch. I discovered that Jonny was right and each 23andMe and MyHeritage gave good outcomes, however Household Tree DNA and GEDmatch gave poor outcomes.


Household Tree DNA and GEDmatch had an ordinary deviation between 1.2 and 1.7 cM which meant they have been solely correct 95% of the time to inside 3 cM. In case you are attempting to see if a section is above or under a 7 cM or perhaps a 15 cM threshold, an accuracy of +/- 3 cM is actually not superb. 

Not solely that, the GEDmatch cM values on common have been 1.1 cM completely different from the map calculations, so there have to be a bias within the GEDmatch values.

I then took a take a look at the acute values, those the place the map’s calculations have been furthest from the corporate’s calculations, by cM distinction, and by proportion distinction::


Out of 5221 segments, each one among MyHeritage’s calculations have been inside 0.1 cM of the Map calculation. They weren’t precise nonetheless, so MyHeritage will need to have been utilizing a mapping very near what Amy produced.

23andMe weren’t fairly as shut, however have been nonetheless shut sufficient that Amy’s mapping may very well be used for them. 

Whereas Household Tree DNA and GEDmatch have to be utilizing a distinct mapping.

Strategies to Calculate cM from Mbp.

There are just a few completely different Mbp to cM calculators out there on the market. First there’s Amy’s personal calculator utilizing her minimal map, referred to as Lookup segment cM. I can take my excessive valued segments from above. Of the ten, 8 are completely different. If I plug these 8 segments into Amy’s calculator, I get:


These are all the identical as I received when utilizing and interpolating Amy’s desk myself, aside from one worth which got here out as 3.4 cM as a substitute of three.7 cM.  I’m undecided why the distinction in that one, however 7 out of 8 ain’t unhealthy.

Amy allowed Jonny Perl to port her program so that you’ll additionally discover it as the cM Estimator tool on his DNA Painter site.

There may be a web-based service for estimating recombination charges alongside the genome referred to as MareyMap Online. Genealogists will usually wish to choose Homo sapiens, and will select imply, male or feminine. They’ve 3 completely different estimation strategies you may select from:  Sliding window, Loess, and Cubic Splines. When you try this, you may then calculate the Genetic cM place from a bodily place (bp):


I used the default settings (Loess methodology) and located the genetic positions for every of the 16 begin and finish factors, I did this for the each the imply values and the male values. Subtracting the genetic finish level from the beginning level provides the centimorgan worth for the section.

Hendrick Wendland created a MapS Converter program that you just have been at one time in a position to obtain. Appears the obtain isn’t working at present. However I nonetheless had it on my laptop and tried it out.


It has a pleasant characteristic of with the ability to convert between Construct 36 and Construct 37 base pair areas, and you may choose between imply, feminine and male

I in contrast the outcomes of the three instruments to the acute values I had. I marked these closest to the corporate worth in inexperienced and people not closest however nonetheless inside 1 cM of the corporate worth in yellow:


Nicely the outcomes are everywhere in the board. The information I used to be utilizing are the acute outliers for Amy’s mappings so it was a tricky check.

It’s potential that MapS is giving comparable outcomes as GEDmatch, so possibly GEDmatch is utilizing an analogous mapping. And MareyMap On-line’s male values give the closest match to the acute FTDNA values. Extra testing with an even bigger dataset can be wanted to substantiate these statements.

What this all says is that there are a lot of completely different mapping tables that can be utilized and it appears like every firm has chosen their very own mapping methodology.

Why I Investigated This

My program Double Match Triangulator (DMT) screens small segments out by utilizing a cM threshold for single segments and one other one for triangulations. For triangulations, 3 segments are concerned, they usually should all be not less than the default 7 cM (which the person can set to one thing else). The section match information provides cM values. However they don’t all the time give the dimensions of the triangulation itself. You continue to might have three 15 cM segments that each one overlap, and that overlap which is the triangulating area may be solely 2 cM. It might be good to filter these out.

Additionally there are some inferred segments the place the cM can’t be calculated as a result of it the section adjoining to a triangulation the place Individual A now not matches. If that extension cM may very well be calculated, then these which can be too small may very well be filtered out.

When Jonny supplied me with Amy’s information, I began to implement it into DMT however didn’t just like the outcomes for Household Tree DNA information. I seemingly wouldn’t have observed it if I had first tried it for MyHeritage or 23andMe information.

Going ahead, if I do resolve to attempt to decide the centimorgans of the unknown triangulating sections and inferred match extensions, I’ll take the cM values that the corporate supplied with the matches and construct an inner map of Mbp to cM. Then I’ll use that map to interpolate the cMs of the wanted segments. At the least that method, the estimate that’s used might be reflective of the corporate’s mapping.

This isn’t a serious factor for DMT. Including it will gradual DMT down and I don’t really feel the advantages of figuring out the centimorgans of triangulations and inferred section extensions is well worth the slowdown.

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