ALTERNATIVE PERMANENT STATES OF ECOLOGICAL COMMUNITIES

The states to which multispecies communities can tend has been an important issue in ecology, but one in which rather little progress has been made at a theoretical level through lack of a tractable global theory of the dynamics. This paper explores the use of a global theory called ''permanence'' that indicates whether the boundary of a phase space is a repellor to orbits in the phase space. The theory is used to try to identify, at a qualitative level, the states to which solutions tend in the phase space of an arbitrary pool of species. We define a ''permanent state'' of the pool as a subset of the species that is permanent in its own right and uninvadable by any other species from the pool. A simple assembly rule for communities that stems from this is that no permanent state can be a subset of another. Data on coexistence of drosophilid species and also on that of cuckoo-doves, although incomplete, are consistent with this rule. A method is given for finding the permanent states of pools of species with Lotka-Volterra dynamics. Some properties of permanent states are illustrated by means of numerical examples from regional pools of species generated with Lotka-Volterra dynamics. These examples show three kinds of dynamics: a single permanent state, two or more alternative permanent states in which none are subsets of others, and an absence of any permanent states. The statistical distribution of these outcomes in pools of four and five species indicates that a single permanent state is the most likely one to occur, but that alternative states become more probable as the number of interactions among species increases. The implications of these results for understanding and modelling the process of succession driven by population dynamics are discussed.