Showing papers by "Nanako Shigesada published in 1987"

The Speeds of Traveling Frontal Waves in Heterogeneous Environments

Abstract: Since Fisher’s pioneering work (Fisher 1937), many studies on traveling waves in a growing population have been performed. The model proposed by Fisher consists of a diffusion equation with a logistic growth term: $${u_t} = d{u_{xx}} + \left( {\varepsilon - u} \right)u\quad for\quad x \in \left( { - \infty ,\infty } \right)$$ . Here u(x,t) denotes the population density at position x and time t, and d and e are diffusivity and intrinsic growth rate, respectively. It has been shown from this equation that, starting from a localized distribution, the population evolves into a propagating wave of constant speed, \( 2\sqrt {\varepsilon d} \).

Evolutionary and Ecological Stability of Prey-Predator Systems with Predatory Switching

Abstract: Most predators utilize more than one prey species, and it is known that their diets do not directly reflect population densities of available prey species. We consider two prey species which live in two different patches and one predator which allocates its foraging (including searching and handling) activity between the two prey species according to their relative densities. Murdoch(1969) introduced the term “switching” to refer to the case in which the relative amount of prey in the predator’s diet increases more than proportionally to the relative prey density. Predatory switching has been postulated for predators ranging from protozoa to birds (reviewed by Murdoch & Oaten, 1975), and it may be a simple consequence of the predator’s searching behavior (May, 1977).