Dear researchers,

The problem above is of research interest if no any suitable algorithm have existed. Since the percentage identify and similarly is generally same results for any pairwise comparison of S0 S1-S21.

This shows that the four (4) algorithms considered (as mentioned above) have neglected the existing variations due to position-specific and nucleotide-specific changes.

I think we need to have a shared opinion and suggestions.

Hi Kabir,

Your example dataset just shows satellite haplotypes differing by a single mutation from the reference. It's nothing you would tackle with simple pairwise similarity approaches. Biologically, interpreting these data is trivial: S0 is the ancestral genetic variant, S1–S21 are direct derivates of S0, they differ by one mutation from S0 and zero or two mutations from each other (a free-to-use haplotype network software is e.g. NETWORK: https://www.fluxus-engineering.com/sharenet.htm).

Since we usually have no information about how probable a mutation is at a given SNP site, we have no reason to make an a priori difference whether a mutation happened at the first, second, third etc. site when calculating pairwise distances to get "better" similarity measures. What we do when inferring trees is to use the Gamma distribution to model changing rates from site to site.

(Note that NETWORK allows you to reweight each site, in case you have such prior information. Usually reweighting is used to downweigh sites that appear to have high levels of homoplasy, random convergence.)

Regarding the higher mutation probabilty for transitions vs. transversions. All models used for phylogenetic tree inference under Maximum likelihood and Bayesian inference (see e.g. this list: http://www.iqtree.org/doc/Substitution-Models) can also be applied to calculating pairwise distances (implemented in a huge range of tree-inference softwares and R), with the consequence that the pairwise model-based distance between e.g. S0 and S1 (AG transition) would be smaller than between S0 and S2 (AT transversion), the latter equal to S0 and S4 (AT transversion at a different site). Note that RAxML, for instance, the main software to infer maximum likelihood trees these days and analyse extremely large SNP data sets (classic version: https://cme.h-its.org/exelixis/web/software/raxml/index.html; new version: https://github.com/amkozlov/raxml-ng/releases), can export model-based pairwise distances optimised during inferences that take into account not only differences between the substitution categories (AC, AG, etc.) but, in addition, model per site rate variation using the Gamma function.

So, I'm afraid, there nothing really to research here.

Cheers, Guido.

Dear Guido,

Thank you very much for the clarification, further explanation and recommendations.

I doubt how this type of problem and comparison is trivial looking at its mathematical or statistical implication. I guess that a good model/algorithm/methods in this context should be able to consider any existing variations based on any variables or parameters recognized computationally important. As such, i wonder if such a problem (problem of nucleotide base position in the sequence order and it magnitude relative to the other sequence in comparison) is not significant to be addressed. Even the need for such a pairwise comparison is unimportant, but it is good to be computationally considered in the design of the such related algorithms.

Beside that, let us look at other computational complications with higher probabilities rather than just one-point base mutation.

Suppose we have the following sequences:

Reference DNA sequence

Seq.-0 = A G C T T C A C T G A T

Variant DNA sequences

Seq.-1,1 = T T C T T C G G T G A T → Mismatches

Seq.-1,2 = - - C T T C - - T G A T → Gabs

Seq.-1,3 = - - C T T C G G T G A T → Mismatches and Gabs

Seq.-2,1 = A G C T A A C G T G A T → Mismatches

Seq.-2,2 = A G C T - - - - T G A T → Gabs

Seq.-2,3 = A G C T - - C G T G A T → Mismatches and Gabs

Seq.-3,1 = T A T A T C A C T G A T → Mismatches

Seq.-3,2 = - - - - T C A C T G A T → Gabs

Seq.-3,3 = T A - - T C A C T G A T → Mismatches and Gabs

Seq.-4,1 = A G G G G G A C T G A T → Mismatches

Seq.-4,2 = A G A A A A A C T G A T → Mismatches

RESULTS OF PAIRWISE COMPARISONS

Mismatches

% similarity (% gabs)

Seq.-0 and Seq.-1,1 = 66.7%

Seq.-0 and Seq.-2,1 = 66.7%

Seq.-0 and Seq.-3,1 = 66.7%

Seq.-0 and Seq.-4,1 = 66.7%

Seq.-0 and Seq.-4,2 = 66.7%

Gabs/Indels

% similarity (% gabs)

Seq.-0 and Seq.-1,2 = 66.7% (33.3%)

Seq.-0 and Seq.-2,2 = 66.7% (33.3%)

Seq.-0 and Seq.-3,2 = 66.7% (33.3%)

Mismatches and Gabs

% similarity (% gabs)

Seq.-0 and Seq.-1,3 = 83.3% (16.7%)

Seq.-0 and Seq.-2,3 = 83.3% (16.7%)

Seq.-0 and Seq.-3,3 = 83.3% (16.7%)

Questions:

1. Please, what further explanations can we obtain from you regarding this sort of dataset?

2. Can we conclude that these set of sequences with same results are mathematically and biologically the same?

2. Can we still have to accept that these alignment-base algorithms for pairwise sequence comparison are not position-specific and base-specific computationally .

With Kind regards,

Kabir Abdullahi Bindawa.

Dear Researchers,

The pairwise sequence comparisons above presented was by Needle algorithm using the online software at https://www.ebi.ac.uk/Tools/psa/emboss_needle/

You can access it for confirmation and validation.

Thank you once again.