Space‐Limited Recruitment in Open Systems: The Importance of Time Delays

We study the dynamic behavior of open systems where older or larger individuals can inhibit the recruitment of juveniles into the population. Our approach is to examine the predictions of simple dynamic models. In these models, settlement rate into open space is decoupled from local population density. Our more elaborate models are special cases of Roughgarden et al.'s (1985) model for an open marine population with space—limited recruitment. We found, as did Roughgarden et al., that two qualitatively different dynamic outcomes were possible: a stable steady state, and cyclic fluctuation in population density and space occupied. The crucial factor needed to produce cyclic fluctuations is a time delay between settlement and recruitment into the adult population. The introduction of density—dependent mortality in adults serves to stabilize the limit cycle. The effect of growth or development rate on stability depends upon the relationship between these rates and individual size or age. This is because increased growth may act to increase the area occupied at equilibrium (a destabilizing factor), but can cause developmental time lags to either increase or decrease in length. As a result, an unstable system can be stabilized by either an increase or a decrease in juvenile growth rate when adults do not grow, or grow more slowly than juveniles.