wild-type Swan Goose x Greylag Goose hybrid, Bonn (Germany) - copyright Joern Lehmhus
(photo ID: 0856)
Swan
Geese and Greylag Geese are the ancestors of all domestic geese and outside of the Far East the only Swan Geese you're likely to encounter are domestic variants. Occasionally undomesticated wild-type Swan Geese can be found, at least in collections, although even if a bird looks like a wild Swan Goose it may be unsafe to assume it has no domestic heritage. The first set of photos here show birds with long sloping bill/head profiles like wild Swan Geese and appear to be wild-type Swan Goose x Greylag Goose hybrids.
wild-type Swan Goose x Greylag Goose hybrids, Bonn (Germany) - copyright Joern Lehmhus
(photo IDs: 0854, 0855, 0857)
Hybrids
between domestic Swan Geese and Greylag Geese are much more frequent. Indeed some domestic breeds of geese have both species in their ancestry and so even some "pure" breed domestic geese are technically hybrids between the two species (e.g. Steinbacher). Given the highly variable appearance of domestic geese it is often impossible to determine whether an individual bird is pure Greylag Goose, pure Swan Goose or a mix of both.
So far as I know, no pure Greylag Goose will have the distinctive contrasting dark 'mane' of a Swan Goose and they lack the raised knob above the bill that's a feature of many domestic Swan Geese. Most pure Swan Geese, even in their domestic forms, will retain the dark mane (unless they are white birds). Elsewhere I have previously suggested that orange on the bill may indicate Greylag ancestry, however British Waterfowl Standards (The British Waterfowl Association, 2008) seems to imply that the orange-billed domestic breed White Chinese Goose is a pure Swan Goose, so perhaps the orange bill colour can be achieved through selective breeding without any genetic input from Greylag Goose? Indeed Joern Lehmhus has confirmed that pure-looking domestic Swan Geese can sometimes show a little orange on the knob or on base of the bill. He thinks that an orange bill colour is a trait of Swan Goose but that the orange is normally hidden beneath black pigment. He likens it to Bean Geese that show a mainly black bill with a patch without black where the orange shows through. That theory makes sense to me and explains a captive but apparently pure (not domestic) Swan Goose that I have seen which showed a little orange on the side of the bill (
here).
The following birds are too Greylag-like to be pure Swan Geese but the black on the bill, and in some the raised knob at the bill base, suggest some domestic Swan Goose ancestry. Note that Swan Goose x Greylag Goose hybrids are fully fertile, so birds in a flock of Greylag Geese that closely resemble Greylag Goose except for a small amount of black on the cutting edge or nail may be the result of domestic Swan Goose influence two or more generations back.
domestic Swan Goose x Greylag Goose hybrid, Thetford (Norfolk, UK) 9th February 2013 - copyright Dave Appleton
(photo IDs: 0918-0919)
domestic Swan Goose x Greylag Goose hybrid, Thetford (Norfolk, UK) 19th November 2016 - copyright Dave Appleton
(photo ID: 2819)
domestic Swan Goose x Greylag Goose hybrids, Graffham Water (Camrbidgeshire, UK), 24th September 2011 - copyright Dave Appleton
(photo IDs: 0915-0917)
domestic Swan Goose x Greylag Goose hybrid, Whitlingham (Norfolk, UK) 1st January 2010 - copyright Dave Appleton
(photo ID: 0920)
domestic Swan Goose x Greylag Goose hybrid, Shcrevenpark, Kiel (Germany) 18th November 2012 - copyright Joern Lehmhus
(photo ID: 0569)
presumed domestic Swan Goose x Greylag Goose hybrids, Abberton Reservoir (Essex, UK), 21st August 2004 - copyright Dave Appleton
(photo IDs: 0921-0922)
presumed
domestic Swan Goose x Greylag Goose hybrid (presumably second or
subsequent generation backcross with Greylag Goose), Malmoe (Sweden), 10th June
2009 - copyright Carl Gunnar Gustavsson
(photo IDs: 0996-0997)
presumed
domestic Swan Goose x Greylag Goose hybrids (presumably second or
subsequent generation backcrosses with Greylag Goose), Malmoe (Sweden), 10th June
2009 (all five are different birds, and different from the photo IDs 0996-0997 above) - copyright Carl Gunnar Gustavsson
(photo IDs: 0998-1002)
presumed domestic Swan Goose x Greylag Goose hybrid (presumably second or subsequent generation backcross with Greylag Goose), Malmoe (Sweden), 13th May 2009 - copyright Carl Gunnar Gustavsson
(photo ID: 1003)
presumed domestic Swan Goose x Greylag Goose hybrid (male, presumably second or subsequent generation backcross with Greylag Goose), Malmoe (Sweden), 12th July 2008 - copyright Carl Gunnar Gustavsson
(photo ID: 1016)
presumed domestic Swan Goose x Greylag Goose hybrid (presumably second or subsequent generation backcross with Greylag Goose), Malmoe (Sweden), 26th April 2008 - copyright Carl Gunnar Gustavsson
(photo ID: 1017)
presumed domestic Swan Goose x Greylag Goose hybrid (presumably second or subsequent generation backcross with Greylag Goose), Malmoe (Sweden), 8th April 2009 - copyright Carl Gunnar Gustavsson
(photo IDs: 1019-1020)
domestic Swan Goose x Greylag Goose hybrids, Celle (Lower Saxony, Germany), 9th August 2014 - copyright Joern Lehmhus
(photo IDs: 1659-1661)
And here is the aforementioned Steinbacher, a breed of fighting goose that was developed and classified in the 1920s-30s and which has both Swan Goose and Greylag Goose in its ancestry. Note that domestic Swan Geese and domestic Greylag Geese left to their own devices can produce birds that are identical to the Steinbacher breed, so as with other domestic waterfowl breeds the breed name shouldn't really be applied unless the pedigree is known or demostrated by further on-breeding.
domestic Swan Goose x Greylag Goose hybrids: 'Steinbacher' Geese, Hannover (Lower Saxony, Germany), 26th October 2014 - copyright Joern Lehmhus
(photo IDs: 1678-1679)
More typical domestic Swan Goose x Greylag hybrids:
domestic Swan Goose x Greylag Goose hybrid, location not given (probably Midlands/NW England, UK), on or around 9th April 2010 - copyright Steve Graby
(photo IDs: 1937-1941)
domestic Swan Goose x Greylag Goose hybrids (with domestic Greylag Geese and Canada Geese), Etherow Country Park (Greater Manchester, UK), 6th October 2010 - copyright Steve Graby
(photo IDs: 1967-1968)
Swan Goose Anser cygnoides
Greylag Goose Anser anser