Perturbation expansion and optimized death rate in a lattice ecosystem

The investigation of perturbation experiments is important not only to forecast the effect of human management but also to know community interactions. In the present paper, we study the press perturbation, where the death rate d of a target species is altered and held at higher or lower levels. Lattice Lotka–Volterra model (LLVM) is applied to know response of ecosystem. We also apply the theory of perturbation expansion to both mean-field and pair approximations (PA). Both computer simulation for lattice model and perturbation expansion theory reveal that the density of the target species takes the maximum value at a non-zero value of d. Extreme decrease of death rate leads to its density decrease: avoidance of death in the target species indirectly causes not only decrease of its prey but also increase of predators. An evolutionary meaning of the optimized death rate is discussed. Especially, we describe ecological apoptosis: individuals or organisms have a positive meaning of death.