This paper is by a group of palaeontologists from the University of Bristol and the Natural History Museum, London. The abstract is not easy for the non-specialist, so I posted a lay interpretation of it on twitter, as follows:
There are several major types of plants, with different body plans. Some are single celled, others are much more complex. We don’t know how this diversity evolved. Here we use a big dataset to provide new evidence that the different types are very different (even when fossils are included). This is especially true of the structures that they use to reproduce. Assuming that the types evolved from each other, we build a model that shows that intermediates forms once existed; these must have disappeared without trace and we can't be specific about what they were. The major plant types have evolved in unique ways. Types with simple body plans can have lots of diversity in them, so it is not necessary to be complex to be diverse. More complex types tend to have larger gene families within them, so genome duplications are important for plant evolution. The different types of plants don’t appear all at once: each one appears suddenly and in diversity at a different time point (we also completely disprove the idea that the major types all appeared at once). The pattern we find in plants is a similar pattern to that shown by the major types of animals and fungi.
Judging by the level of engagement this tweet has had, readers seem to have found this interpretation helpful, so I also share it here.
The paper states "The morphological distances ... between angiosperms and gymnosperms... are maintained even with the inclusion of fossils". This upholds "Darwin's abominable mystery": the sudden appearance of angiosperm fossils in the Cretaceous with no clear intermediates between them and gymnosperms. I made this point in another tweet and Phil Donoghue FRS, the lead author of the paper responded that this is "surely the greatest conundrum in the whole of palaeontology".
Charles Darwin hoped that future fossil finds would fill the gap between gymnosperms and angiosperms. This was a clear prediction of his theory, a prediction that is corroborated by the model in the present paper. But 150 years after Darwin, we are still looking. The abominable mystery persists.