Finally, a plant that the taxonomists haven’t messed with … too much. At this point, cross your fingers, there is but one species in the Phryma genus … the American Lopseed.
If so, you ask, why then have “American” in front of it? That would suggest some foreign species of Lopseed. Well, it turns out that this same species, which is found in eastern North America, is also found in eastern Asia. At one time they were thought to be a different species, but are now all considered one species. Woohoo! No need to look at the gynoecium to see if its pseudomonomerous or not. Just look at the seedheads. They are folded over in nice neat little pairs up and down the stem.
This brings us to the obvious question that you are asking. How did one species of plant establish itself on two different continents? Well, here’s an interesting study that explains, among other things, that these two populations diverged from each other about 3-5 million years ago, and that there are a number of species from eastern Asia and eastern North America that had divergent populations in approximately the same time frame. The suggestion is that the land bridge across the Bering Sea was open and at the time the environments of eastern North America and eastern Asia were similar enough that a lot of species spanned the whole area. You’ll need to look at a globe to get the picture.