I tried to summarize all the findings of a very intriguing paper into the extended title.
Nigel Calder's blogThe higher sea level, the more genera of small organisms in the sea one may find.
Evidence of nearby supernovae affecting life on Earth (PDF, Svensmark's actual paper in Mon. Not. R. Astron. Soc.)
Press release of the Royal Astronomical Society in London
A truly convincing chart with a correlation
If one adjusts the number of genera for the sea level, one gets a residual curve that almost perfectly agrees with the number of supernovae that Svensmark extracted by simulating the patterns in our changing galaxy.
Just to be sure, the sign is such that the supernova explosions are good for the biodiversity. The yummiest things possible. Higher sea level is also good for the biodiversity in the ocean.
Very nearby supernova explosions have been linked to some short-term decrease in the biodiversity, a claim that seems to have the opposite sign than the previous ones. As you can see, I still haven't quite absorbed the claims. Also, I am still not sure whether I believe that such a "pure and simple" theory is actually right and predictive. Is the amount of correlation in the charts really enough to settle this question?
Also, I don't understand whether Svensmark claims that the biodiversity is affected by the supernova explosions directly – by the mutations from the radiation etc. – or through the sea level and the climate. I am sure that someone will quickly answer this question of mine...
A possible lesson is that if we want the life on Earth to be richer, we should try to achieve a "global warming" with some rising sea levels and we should nuclear bomb Iran which may resemble the supernovae a bit... ;-)
Note that there is no role played by the Sun (or CO2) in these considerations.
Bonus: Nastya Petrik and "Oh Darling" at a low enough age. ;-)