Time Evolution of Space-Structure and Strategy for a Population Dynamics in the Lotka-Volterra Lattice

Haruyuki Irie¹ and Takao Bogaki²

¹Information Processing Center, Hiroshima University, Higashi-Hiroshima, Japan
²Faculty of Science, Hiroshima University, Higashi-Hiroshima, Japan

(Received April 25, 1996; Accepted June 28, 1996)

Keywords: Lotka-Volterra Lattice, Population Dynamics, Genetic Strategy, Spiral Pattern Formation

Abstract. Time evolution of prey-predator population dynamics is considered on a two-dimensional lattice. Both of prey and predator have strategy in battle and add to their years. When they leave offspring, they copy the strategy to their child. Predator has its life span. Initially, the random configuration of two species is given. It is found that the population decreases in early stage along time evolution, and then the prey-predator cluster with length and breadth pattern is formed, spreads in the lattice space, and reaches to a quasi-stationary state in population. Another prey-predator cluster with another strategy is born by mutation, spreads with slant pattern expelling the former quasi-stationary state and finally reaches a stationary state in population. In spreading the lattice space and reaching stationary in population, both patterns form spiral patterns with kernels which consist of spatial and strategic combination of empty spaces, preys and predators.