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Nucmer and delta-filter not symmetric for reference and query

Dear all, I was surprised by the fact that running the following two sets of commands I obtained different results

Command 1:

nucmer --prefix=Ref_1_vs_Ref_2 Ref_1.fasta Ref_2.fasta
delta-filter -1 Ref_1_vs_Ref_2.delta > Ref_1_vs_Ref_2_filtered.delta
show-coords -rcl Ref_1_vs_Ref_2_filtered.delta > Ref_1_vs_Ref_2_filtered.coords

Command 2:

nucmer --prefix=Ref_2_vs_Ref_1 Ref_2.fasta Ref_1.fasta
delta-filter -1 Ref_2_vs_Ref_1.delta > Ref_2_vs_Ref_1_filtered.delta
show-coords -rcl Ref_2_vs_Ref_1_filtered.delta > Ref_2_vs_Ref_1_filtered.coords

The difference is already present in the first output file, with one file showing approximately 10% more hits than the second. At present, I am not too worried about this (I am going to use both sense of analysis), but I was really surprised because, theoretically nucmer should perform an all-vs-all alignment, and thus I was expecting it to be symmetrical with respect to query and reference choice.

However, I am afraid I am missing some important information about nucmer. Would you expect it to give different results when switching query and reference?

Note:

Also the delta-filter -1, being the intersection of -q and -r (respectively align each reference against the best hit, and align the query against the best hit), should be symmetrical (but as I already told, the problem already arose before the filter).

nucmer alignment multifasta

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