Superstatistics, Biodiversity and All That
Rominger et al. (doi: 10.1126/sciadv.aat0122 https://advances.sciencemag.org/content/5/6/eaat0122 , open access ) have come up with an astonishingly simple explanation for the distributions of fluctuation in biodiversity.
First some definitions. The Phanerozoic is the last half billion years (actually 540 MYr to present.) This work deals with marine invertebrate species during the Phanerozoic eon. Species are classified into increasingly inclusive sets, species, then genus, family, order, class, phylum, kingdom and domain.
[Credit: By Annina Breen – Own work, CC BY-SA 4.0, https://commons.wikimedia.org/w/index.php?curid=40559754 ]
The idea is that throughout the Phanerozoic, the origination and extinction rates within families (and orders) are in equilibrium. But they are not in equilibrium as one broadens the classification to classes and phyla.
This allows application of superstatistics, a statistics of combined distributions. Begin by considering a family composed of many genera. They begin with a set of Gaussians, one for each family, each characterized by a width. These Gaussians describe the distribution of change in number of genera in the family (“richness.”) The Gaussian nature denotes equilibrium statistics. Then they distribute these widths according to a gamma distribution. Unsurprisingly, they wind up with a fat tailed distribution of volatility in richness.
Surprisingly, this fits the data for families and orders.
The conclusion is that within families and orders, the distributions of volatility in richness are in equilibrium, but that breaks down as one goes to larger sets like classes and phyla. The deduce that there is a separation of timescales, that the finer grained taxa achieve equilibrium within observation timespan (half a billion years !) but the coarser grained ones do not.
I have a feeling this is telling us something very deep about evolution. Alas, I am a humble physicist and not an evolutionary biologist, so for more enlightenment, read the paper. Open access is a wonderful thing.