Dynamics of a metapopulation with space-limited subpopulations

Abstract

Most population models in ecology refer to a closed population where the recruits to a population are produced from the adults in that population. Many marine organisms have a long-lived pelagic larval phase followed by a sessile adult phase. The adults of such organisms are typically studied on a spatial scale that is very small relative to the dispersal distances of the larvae. A study site might be only a few square centimeters to a few hundred square meters (e.g., Connell, 1961; Dayton, 1971; Crisp, 1974; Paine, 1974; Menge and Lubchenco, 1981; Palmer and Strathman, 1981; Grosberg, 1982; Keough and Downes, 1982; Underwood et al., 1983; Wethey, 1983; Gaines and Roughgarden, 1985). The adults within such a site comprise a “local” population. Yet, the dispersal distance of the larvae is measured on a scale of kilometers (dewolf, 1973; Scheltema, 1975; Geraci and Romairone, 1982; Hawkins and Hartnoll, 1982). As a result, the local population is almost completely open since virtually all the recruits come from distant places. To develop a theory that is more representative of the dynamics of marine populations than that currently available, we have taken two steps. The first was to develop a model for the demography of an open spacelimited population (Roughgarden et al., 1985). In that model, larvae were assumed to settle onto vacant space in the local population. The rate of settlement per unit of vacant space was considered to be a parameter, s, the settlement coefficient. This coefficient reflects properties of the surface that the settlement is occurring on, the accessibility of that surface to water containing the larvae, and the concentration of larvae in the water. This paper presents our second step in developing theory for the dynamics of marine populations. We present a model for a metapopulation