Press Perturbation in Lattice Ecosystems: Parity Law and Optimum Strategy

Press perturbation, in which the reproduction raterof a target species is altered and held at higher or lower levels, is studied by computer simulation. We apply a lattice Lotka-Volterra model to idealized ecosystems, and obtain the optimum strategyroptdefined as follows: the steady-state density of the target species takes a maximum value atr=ropt. It is found thatropttakes a finite value, and it usually locates at a phase transition point. Moreover, we find that the long-term response to applied perturbation can be significantly predicted byparity law, where the parity is defined by whether the system contains an even or odd number of species. If the parity is even (odd), the density of the target species increases (decreases) with increasingr. An evolutionary meaning ofroptis discussed in connection with the origin of sexual reproduction.