The present work draws on classical projective geometry of general path spaces to further study biological motivated models of heterochrony 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 Jacobi unstable. Yet, they possess first integrals of the motion. Proofs of this are based on 2-dimensional Finsler geometry and the theory of semi-symmetric connections. A concrete model of lichens is briefly discussed.