title: Evolution of host-parasitoid network through homeochaotic dynamics.
abstract: Host-parasitoid systems with evolving mutation rates are studied. By increasing the growth rate of hosts, the diversity of both species is maintained dynamically. For the lower growth rate, diversity is brought about by mere parasitism. The average mutation rate for parasites is elevated to a high value, while that for hosts is suppressed at a low level. For the higher growth rate, the mutation rates for both hosts and parasites are elevated to form a symbiotic cluster connected by on-going mutation. This symbiotic state is sustained through a chaotic oscillation keeping some coherency among species. For a flat landscape for hosts, dynamical clustering of oscillation is observed. Lyapunov spectra of such oscillations show that high dimensional chaos with small positive exponents underlies in the symbiotic state. This weak high dimensional chaos, termed "homeochaos," is essential to the maintenance of symbiosis in ecosystems.
authors.affiliation: The Graduate School of Science and Technology, Kobe University, Rokkodai, Nada-ku, Kobe 657, JapanDepartment of Pure and Applied Sciences, College of Arts and Sciences, University of Tokyo, Komaba 3-8-1, Meguro-ku, Tokyo 153, Japan.
authors.forename: Takashi
authors.initials: T
authors.lastname: Ikegami
authors.forename: Kunihiko
authors.initials: K
authors.lastname: Kaneko