Journal of Ecology, 2014. doi: 10.1111/1365-2745.12260
We tried to answer the simple question of what fraction of the world's plant species are woody: surprising the answer to this is not known. We surveyed researchers and found a huge range of estimates. We used a trait database that spanned 12% of plant diversity, and found that due to taxonomic patterns of woodiness, the estimates of woodiness were extremely biased. We used Monte Carlo (sampling) methods to correct this bias and found that just under half the world's vascular plant species are woody. Surprisingly this was much higher than estimates from researchers, even with significant botanical training.
See the full analysis, with figures and justifications.