Both species are invasive in Norway. S. altissima (or S. canadiensis) has a wide distribution in wasteland, road verges and also in abandoned, semi-natural grasslands, in particular in the south-eastern part of the country. It is regarded as highly invasive (severe impact, SE) in the Norwegian black list. S. gigantea is presently less widely distributed, and is regarded as having high impact (HI). The species are also invasive in Sweden (and probably in other Nordic countries). The database Artskart (Species mapping) is hihgly useful for checking the status of any species in Norway: https://artskart.artsdatabanken.no/default.aspx
in my country, Italy, Solidago canadensis is present only in the northern part (0-800m) in wetted habitats, while Solidago gigantea is established also in the central-western part of Italy (same altitudinal belt).
in Germany there are both of them and they do hybridize and are invasive - to see the exact locations - please go to the floraweb-page http://www.floraweb.de/ sorry its a page only in german, but you can search for names (on the left side) and by clicking on the map you find the exact distributions. Best,
Both S. canadensis and S. gigantea are widespread in Britain - throughout England, scattered in Wales and in southern Scotland. The best data source is the Online Atlas of the British Flora, which is quality assured, so the records are very reliable:
http://www.brc.ac.uk/plantatlas/index.php?q=plant/solidago-canadensis - select the Maps tab, and then the New Atlas tab.
http://www.brc.ac.uk/plantatlas/index.php?q=plant/solidago-gigantea - this one also has a hectad map showing change over time from pre-1930 to the present.
The most up to date information (constantly updated as new records are submitted) is on the National Biodiversity Network:
https://data.nbn.org.uk/imt/#4-17.368,48.873,10.757,60.192!094K9 - S. canadensis
https://data.nbn.org.uk/imt/#4-17.368,48.873,10.757,60.192!094KD - S. gigantea.
The resolution of the information shown will depend on your level of access though, so I don't know if you will see what I see.
Solidago canadensis was common in the Jura of Switzerland when I was working there, but I'm not sure if it is really canadensis or altissima. I have some colleagues there if you would like specimens or samples.
All of the Solidago canadensis s.l. material from Europe that I have seen including material at BM and K belongs in var. hargeri, which is the more hairy-stemmed race of the species. It is dominant in the southern and western portions of the species range. Typical var. canadensis tends to be more northern in distribution in the NE portion of the Eastern Deciduous Forest. The hairy lower stem of var. hargeri is probably the reason for identifications as S. altissima (synonym: S. canadensis var. scabra). Var. hargeri is diploid. Soliago gigantea in Europe and eastern Asia is tetraploid. Solidago altissima is hexaploid in eastern Asia.
Thanks to all for the useful information and web site links. JCS
In Poland we have three invasive goldenrods: Solidago canadensis (introduced in 19th century, first observation in wildlife - 1872), S. gigantea (1853) and S. graminifolia (1888). The taxonomical status of S. altissima is doubtful, however, some researchers believe that is present in Poland. The first two former species are very common the latter (S. graminifolia) is rare.
Please look at the paper: Szymura, M., & Szymura, T. H. (2013). Soil preferences and morphological diversity of goldenrods (Solidago L.) from south-western Poland. Acta Societatis Botanicorum Poloniae, 82(2), 107-115.
Euthamia graminifolia does not belong in Solidago based on morphology and DNA sequence data. It is not even in the same group of North American genera as Solidago. This is why it is found to be rather different from other "species" of Solidago in ecological studies.
In Switzerland we have two invasive species, Solidago canadensis, introduced in the 19th century and Solidago gigantea, both widespread. Solidago graminifolia, also introduced in the 19th century is rare and limited to the north-east of the country.
It might be interesting to note that from eastern Germany occurrence of a hitherto undescribed Solidago closely allied to S. canadensis was reported, which the author supposed to be of anthropogenic origin (Scholz, H., 1993: Eine unbeschriebene anthropogene Goldrute (Solidago) aus Mitteleuropa. In: Floristische Rundbriefe 27: 7-12.). He invalidly published the name Solidago anthropogena for these plants. Even in Germany this taxon hasn't been accepted by later authors, and it is treated as a synonym of S. canadensis in the German check list (http://www.kp-buttler.de/florenliste/).
В последние 2-3 года Solidago canadensis распространяется по Южному Приморью (Россия) с большой скоростью. Несколько лет назад S. canadensis встречалось редко, обычно, как декоративное растение на приусадебных участках.
In our region (Republic of Mordovia, Central Russia), Solidago gigantea (in contrast to Solidago canadensis) does not show high invasiveness. It is often cultivated species. Sometimes, species is found at disturbed habitats (but always within large settlements).
Solidago altissima is not known in the Republic of Mordovia, yet.
In Ukraine we have two invasive species, Solidago canadensis L. and Solidago gigantea Aiton, and three non-native but not invasive species, Solidago altissima L., Solidago lepida DC., Solidago leavenworthii Torrey & A. Grey (Their status is to be confirmed).
In Slovakia and in the Czech Republic (Central Europe), Solidago gigantea and Solidago canadensis are widesperad invasive plant species, mainly in ruderal habitats, and also in the riparian habitats, e.g. in the floodplain forests.
I personally focused several of my studies to the changes of the alien species proportion in some Slovak cities, and I can state that the proprotion of Solidago gigantea and S. canadensis in the ruderal habitats increases significanly over the time. This species form monodominant stands with low diversity of native species in many ruderal areas.
Thanks for the information on Solidago in the Bratislava area. Solidago canadensis and S. gigantea can be aggressive weedy species even here in North America. Regarding Aster novi-belgii, I suggest you adopt the name Symphyotrichum novi-belgii (L.) Nesom. With one acception (A. alpinus) all species of asters native to North America have been proven to belong in genera other than the Old World genus Aster. Symphyotrichum is the largest of these genera that are recognized in Brouillet et. al. (2006) in Fl. North America and shown to be quite distant from true Aster in the DNA based phylogeny of the Tribe Astereae (Brouillet et al. 2009):
BROUILLET, L., T. LOWREY, L. URBATSCH, V. KARAMAN-CASTRO, G. SANCHO, S. WAGSTAFF, J.C. SEMPLE. 2009. Chapter 37. Astereae. Pp. 449-490. In Systematics, Evolution and Biogeography of the Compositae, Funk, V.A., A. Susanna, T. Stuessy, and R. Bayer (eds.). IAPT, Vienna, Austria.
In Belarus, apparently, there are no Solidago canadensis s.str and S. altissima., but hybrids with their participation are very widespread. Now I am preparing an article describing these hybrids as an independent taxon.