Ancestry of South Germans, Austrians, Swiss, Alsace Germans

So, it is known that the Germanic tribes of Germania Magna and German culture in general originates from Scandinavia. The Scandinavian tribes went from their homeland and conquered south into the mainland of Europe killing or culturally converting the Celtic tribes there and founding Germanic and later German culture. There has always been somewhat of a north/south divide in Germany phenotypically and culturally (kind of like the North/South divide in the USA). The northern Germans phenotypically appear more nordic and closer to Scandinavians, they are more liberal, ruder, protestant, secular, and industrious while south Germans appear more alpine phenotypically, and are more hospitable, rural, catholic, religious, and conservative. The south Germans, Austrians, Swiss, Alsace Germans all seem to be in places that were home to Romanized Celts during the Roman era and were only conquered and displaced (either culturally or literally) after the empire fell. 

My question is how Germanic vs Celtic, Slavic, Roman etc are the south Germans, Austrians, Swiss and other groups such as these? Do the south Germans predominately descend from Germanic tribes or are they La Tene Celts speaking German today?