In the "emigration" lists from Ulrika parish I find this:
As far as I can understand this, the "Peter August Andersson" listed fifth in 1870 is my ancestor. This unfortunately doesn't give an age, but indicates he came from "Sten[kullen]," which is the farm where he lived. Also unfortunately, the "clerical survey" (like a census) for this period doesn't seem to exist, so I can't cross check with the page number of the clerical survey listed here. Then my assumption is that the last name here is his grandfather, Peter Magnus Andersson. Why he would be listed separately from the young grandson is a mystery to me. But this indicates he left with a party of two men and two women. The men would be himself and probably his son Franz Otto, who also came to America in 1870; the women presumably his wife Sara Catharina, and then I don't know who the other would be.
But then I found the following ship's passenger list record:
They appear to be bound for Jamestown; far as I can tell, there are three Jamestowns in the US, in Virginia, New York and North Dakota, and none of these states are associated with this family as far as I know. The family, my great-aunt said, came first to Pennsylvania, but then fairly soon to Nebraska.
One can see why this is mysterious . . .