The path of discovery is often complex (e.g., see the convoluted path followed by the Alvarez team in coming up with the bolide hypothesis for the extinction of the dinosaurs, http://undsci.berkeley.edu/article/alvarez_01), and can sometimes be largely uncoupled from the literature (for a wonderful example, see Polanyi’s [1958; Chapter 1.3] account of Einstein’s development of general relativity).

In our case the immediate roots of the Hawaii paper were laid down in an analysis of the dynamics of diversity loss of Cenozoic mammal groups with exquisite fossil records (Quental [Tiago] and Marshall, 2013), a study motivated by an earlier and disturbing discovery that in computer simulations of groups that have lost many species, their molecular phylogenies look like those undergoing exponential growth (Quental and Marshall, 2011).

As Tiago and I were writing up the mammal work, I thought it would be fun to see if I could describe the process mathematically (while at heart I have always been fascinated by evolutionary change over deep time, I have also done a lot of mathematics). So I started modifying the standard differential equation for logistic growth, and after quite a bit of experimentation with Mathematica, found a variant that could be interpreted biologically and that could be solved analytically – a variant where the carrying capacity and intrinsic diversification rate decreased linearly with time.

What I discovered playing with this equation (eq. S17, Quental and Marshall [2013]) really surprised me. The only way to recreate the fossil mammal diversity, and origination and extinction rate, trajectories was to enforce a really rapid rate of decay of the carrying capacity and intrinsic diversification rate, which in turn led to our conclusion that the mammal clades were always (effectively) out of equilibrium.

So, what has this got to do with Hawaii? With the mammal work, Tiago and I had not expected to be discussing carrying capacities at all, but with my numerical experimentation we began wondering what might be controlling the inferred rapid decay in carrying capacity, and how we might quantify it.For mammals at the global scale this was too hard, and so we put it aside. But as often happens for me, hard problems don’t get filed away – instead they continue to prey on me (as the One Ring preys upon those that possess it).

And so, months later, I realized I knew a place where it might be possible to quantify a changing carrying capacity – Hawaii (and I have no idea how the mind makes this sort of association)!I have been teaching the geological evolution of the Hawaiian archipelago to non-majors for some 25 years now, and so the ontogeny of the Hawaiian archipelago is part of my ‘personal knowledge’ (Polanyi 1958). And my quantitative intuition, honed over many years, told me that with four differently aged islands, with each treated as an independent replicate of the same evolutionary processes, it might be possible to estimate the fundamental diversification parameters needed for my (now two) modified logistic equations, enabling us to infer the true diversity dynamics.

After a long and complex process of refining the approach, with painstaking data compilation, and making sure we had mastery of the biological and geological data, a very talented graduate student, Jun Lim, who had begun his Ph.D. work on the biogeography, community ecology and evolutionary dynamics on Hawaii, and I were able to pull it off.

The mammal work (Quental and Marshall, 2013) showed me that I could go from (fossil) diversity trajectories to a quantitative measure of changing carrying capacity. With a quantitative measure of changing carrying capacity from the geologic record, Jun and I have been able to invert the process and infer the diversity trajectories for Hawaii, discovering on the way that the none of the Hawaiian groups are at dynamic equilibrium. Very satisfying!

Written by Charles Marshall.

The Nature paper is here: http://go.nature.com/2mSi0iy

Darwin, C., 1837, On certain areas of elevation and subsidence in the Pacific and Indian oceans, as deduced from the study of coral formations. Proceedings of the Geological Society of London v. 2, p. 552-554.

Polányi, M., 1958, Personal knowledge: towards a post-critical philosophy. Routledge & Kegan Paul, Ltd., London.Pp.428.

Quental, T. B., and Marshall, C. R., 2011, The molecular phylogenetic signature of clades in decline. PLoS One v. 6, e25780.

Quental, T. B., and Marshall, C. R., 2013, How the Red Queen drives terrestrial mammals to extinction. Science v. 341, p. 290-292.