Here's a study looking at barcodes (COI) of
canus (s.str.) and
brachyrhynchus. Surprising!
https://link.springer.com/article/10.1007/s10336-009-0490-3
Note however that the descriptive comment in the paper ("North American Mew Gulls
Larus canus grouped together within the shallow multispecies cluster of white-headed Larus gulls, while Scandinavian
L. canus clustered outside the entire group with relatively good bootstrap support (Fig. 5).") is somewhat misleading. The Scandinavian birds indeed "clustered [...] with relatively good support" (BS = 93). But the support for them being "outside the entire group" which supposedly also included the American Mew Gulls (this is measured by the support given to this latter group, with American birds in, and Scandinavian birds out) was in fact desperately low (BS = 52). This tree certainly shows that the sequenced
brachyrhynchus 'differed' significantly from the sequenced
canus; but it can certainly
not be read as demonstrating that the broad
Larus canus is polyphyletic.
A quite similar tree, based on the same marker but with more included birds (7 haplotypes included in the tree, representing all the haplotypes that had been found in 4 Scandinavian + 1 Dutch + 5 Russian [4 of which from the Far East] + 7 American birds), was also published by Kwon et al 2012 (
https://doi.org/10.3109/19401736.2012.660921, free access at
https://www.researchgate.net/publication/221695624). Curiously, though, they did not note that the "two polyphyletic clades", "separated by deep genetic divergence", which they had identified, were linked to geography. One of these clades included exclusively haplotypes from American birds (
brachyrhynchus), the other exclusively haplotypes from Eurasian birds (presumably 5
canus, 1
heinei and 4
kamtschatschensis).
For the position of a few additional specimens based on barcodes (sequences not public yet), you can also go to
http://boldsystems.org/index.php/Public_BarcodeCluster?clusteruri=BOLD:ACE9128, and download the "tree reconstruction of BIN and nearest neighbor" pdf.
Viviane Sternkopf, in 2010, included a chapter on the
canus complex in her thesis (
https://epub.ub.uni-greifswald.de/f...le/Dissertation_Viviane_Sternkopf_Uni_Bib.pdf, pp. 104-110), based on cytb, nd2 and partial control region sequences from 36
canus, 12
heinei, 5
kamtschatschensis and 4
brachyrhynchus. These data also showed that
brachyrhynchus is the most distinct form in the complex, while
kamtschatschensis groups much more closely with
canus/heinei. (She was of the opinion that
brachyrhynchus was worthy of species status.) I don't think this has been published formally, though.
Sonsthagen et al 2012
https://doi.org/10.1002/ece3.240 also found a clear differentiation between
brachyrhynchus (n = 41) on one hand and [
canus (n = 9) +
kamtschatschensis] (n = 11) on the other, based both on mtDNA (partial control region), and microsatellites, suggesting the difference is not 'just' mitochondrial.
(This data set leaves me somewhat uncomfortable, however. In particular, the data show some mtDNA haplotype sharing between
canus/brachyrhynchus and some typical LWHG, which would presumably have to be due to introgression. This is still more obvious in Sonsthagen et al 2016
https://doi.org/10.1016/j.ympev.2016.06.008, free access at
http://gull-research.org/papers/pap...eadedgullcomplexhybridizationrecentorigin.pdf (based in part on the same data), and would also appear to affect
delawarensis (not sampled in the 2012 work). Hybridisation between medium and large white-headed gull taxa is virtually unknown, which makes this haplotype sharing unexpected, and no comparable pattern can be seen in other data sets: I think this would require an explanation. (E.g.: Out of 55
occidentalis/wymani in the 2016 data set, it appears that one had a
heermanni-like haplotype, one had a
canus-like haplotype, 3 had
brachyrhynchus-like haplotypes, 10 had
delawarensis-like haplotypes; out of 19
occidentalis/wymani in Sternkopf's 2010 data set,
zero had such apparent introgressed basal haplotype. The figures seem too far apart to be explained by chance alone.))
Of course, for morphological differentiation in the
canus complex, one should also read Adriaens & Gibbins 2016
http://gull-research.org/papers/papers9/gulls_CommonGulls_identification_Adriaens&Gibbins2016.pdf.