A FRAGMENTED POPULATION IN A VARYING ENVIRONMENT

When speaking about spatially distributed populations, a conceptual di stinction is made between two spatial scales and, hence, between two c lasses of populations which are termed as ''pure'' metapopulation stru ctures and ''pure'' within-population structures. We study a model whi ch belongs to an intermediate type named a ''patchy population''. It i s characterized by independent density fluctuations in patches and by a ''fast'' migration flow. The model includes the Allee effect for den sity dependence in order to allow (deterministically) for population e xtinction when reaching very low levels of abundance. We study equilib rium points and their stability in the case of a constant external inf luence which is modelled by a density-independent death rate. In a var iable environment, we obtain explicit expressions for population fluct uations and calculate their lags behind environmental changes. Regardi ng the influence of the migration rate, we obtain that, under the assu mptions made in this model, particularly the Allee effect in local pop ulation dynamics, an increase of the migration rate is not always prof itable for the persistence of the population. (C) 1997 Academic Press Limited.