The Wagner Theory of 2-Dimensional Constant Sprays and its Applications in Evolutionary Biology

Abstract

The present work draws on classical projective geometry of general path spaces to further study biologically motivated models in the theory of Volterra-Hamilton systems with constant coefficients. In particular, it is shown here that 2-species systems of competitive, parasitic or mutualistic type are all projectively flat (time-sequencing equivalent) and unstable. Yet, they possess first integrals of the motion. Proofs are from Wagner theory, which is in essence, just the 2-dimensional Finsler geometry of semi-symmetric connections.