There is some heavy duty mathematical modelling going on here, examining long term diversification and extinction of species. Whether or not we agree with this particular conclusion, it’s impressive work, and I think we will see more studies like this as others adopt and refine the methods.
Do they say anything about what is causing this tendency for some lineages in their model? Do they mean to say that declining speciation rates is the cause of increased probability of extinction?
As I understand it, it’s that species within the clade tend to become more specialized for a particular environment over time, with a occasional exceptions that are able to diversify and survive. It’s the species going extinct that drive the trend, rather than a trend for a lineage going extinct.
I think this is the preprint version but I haven’t looked really hard to verify. For the Nature version I will get the PDF very soon (tonight) and can share it on request.