Summary of Theory and Open Problems
This chapter includes a summary of the main theoretical and empirical results that support the hyperbolic theory. It includes, as well, a list of open problems and lines of research that, in the author’s opinion, show promise for future developments. The “big picture” that emerges from this view of natural populations has a satisfying quality of closure in view of the role played by a conic section at the center of things: while planets follow elliptical orbits, species appear to follow hyperbolic ones. The planetary orbit is deterministic, while the species orbit is stochastic; a population may advance and retreat in unpredictable fashion, sometimes less, sometimes more. But according to the stochastic species hypothesis, it will trace out a hyperbolic shape all on its own, given enough time, as a result of all the biotic and physical interactions with the world of which it forms a part. Owing to its simplicity, variants of the hypothesis are inevitable, as in Section 10.4.