# Why Ti/Tv ratio?

I'm interested in the transition/transversion (Ti/Tv) ratio:

In substitution mutations, transitions are defined as the interchange of the purine-based A↔G or pryimidine-based C↔T. Transversions are defined as the interchange between two-ring purine nucleobases and one-ring pyrimidine bases.

• How exactly does this ratio imply false positives? Too high ==> high false positive rates? Or too low?
• Why is the expected value for random substitutions for the Ti/Tiv ratio 0.5?
• If the ratio is expected to be 2.10 for WGS, but I get 3.00 what does that mean? What if I get 1.00?
• I know nothing about this ratio (I had to search to know that it is about transitions to the number of transversions), but this link might help others. – llrs May 25 '18 at 13:06

I more like to use "ts/tv" for transition-to-transversion ratio. This abbreviation had been used in phylogenetics. When NGS came along, some important developers started to use "ti/tv", but I am still used to the old convention.

Why is the expected value for random substitutions for the Ti/Tv ratio 0.5?

There are six types of base changes. Two of them are transitions: A<->G and C<->T and the other four types are transversions. If everything were random, you would expect to see twice as many transversions – ts:tv=2:4=0.5.

If the ratio is expected to be 2.10 for WGS

The expected ratio is not "2.10 for WGS". It is 2–2.10 for human across the whole genome. You see this number when you align the human genome to chimpanzee or when you focus on an accurate subset of human variant calls. However, in other species, the expected ts/tv may be very different. Also, this number is correlated with GC content. You get a higher ts/tv in high-GC regions, or in coding regions which tend to have higher GC, too. Partly as a result, it is hard to say what is expected ts/tv in exact.

but I get 3.00 what does that mean? What if I get 1.00?

If you get 3.00, your callset is highly biased. If you get 1.00, your callset has a high error rate. Suppose the exact ts/tv is $\beta$ and you observe ts/tv $\beta'\le\beta$, you can work out the fraction of wrong calls to be (assuming random errors have ts/tv=0.5) $$\frac{3(\beta-\beta')}{(1+\beta')(2\beta-1)}$$ This is of course an approximate because $\beta$ is not accurate in the first place and because errors are often not random, so their ts/tv is not really 0.5.

How exactly does this ratio imply false positives? Too high ==> high false positive rates? Or too low?

Too low ==> high false positive rate; too high ==> bias. In practice, you rarely see "too high" ts/tv.

I haven't done variant calling myself, but 5 seconds of googling lead me to this:

This metric is the ratio of transition (Ti) to transversion (Tv) SNPs. If the distribution of transition and transversion mutations were random (i.e. without any biological influence) we would expect a ratio of 0.5. This is simply due to the fact that there are twice as many possible transversion mutations than there are transitions. However, in the biological context, it is very common to see a methylated cytosine undergo deamination to become thymine. As this is a transition mutation, it has been shown to increase the expected random ratio from 0.5 to ~2.01. Furthermore, CpG islands, usually found in primer regions, have higher concentrations of methylcytosines. By including these regions, whole exome sequencing shows an even stronger lean towards transition mutations, with an expected ratio of 3.0-3.3. A significant deviation from the expected values could indicate artifactual variants causing bias. If your TiTv Ratio is too low, your callset likely has more false positives.

Since methylated cytosine deamination is a fairly universal phenomenon, if you're seeing a ratio that deviates substantially from this expectation, you've either discovered some exciting new biology, or there are issues with your variant calling pipeline.