Quantifying population dynamics via a geometric mean predator-prey model

An integrable Hamiltonian variant of the two species Lotka-Volterra (LV) predator-prey model, shortly referred to as geometric mean (GM) predator-prey model, has been recently introduced. Here, we perform a systematic comparison of the dynamics underlying the GM and LV models. Though the two models share several common features, the geometric mean dynamics exhibits a few peculiarities of interest. The structure of the scaled-population variables reduces to the simple harmonic oscillator with dimensionless natural time T G M varying as ω G M t with ω G M = c 12 c 21 . We found that the natural timescales of the evolution dynamics are amplified in the GM model compared to the LV one. Since the GM dynamics is ruled by the inter-species rather than the intra-species coefficients, the proposed model might be of interest when the interactions among the species, rather than the individual demography, rule the evolution of the ecosystems.