Demographic Theory for an Open Marine Population with Space‐Limited Recruitment

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Abstract
We introduce a demographic model for a local population of sessile marine invertebrates that have a pelagic larval phase. The processes in the model are the settling of larvae onto empty space, and the growth and mortality of the settled organisms. The rate of settlement per unit of unoccupied space is assumed to be determined by factors outside of the local system. The model predicts the number of animals of each age in the local system through time. The model is offered in both discrete and continuous—time versions. The principal result is that the growth of the settled organisms is destabilizing. In the model, there is always a state where recruitment balances mortality. However, growth can interfere with recruitment and can destabilize this steady state, provided also that the settlement rate is sufficiently high. The model suggests that two qualitatively distinct pictures of population structure result, depending on the settlement rate. In the high settlement limit, the intertidal landscape is a mosaic of cohorts, punctuated with occasional gaps of vacant substrate. In the low settlement limit, the intertidal landscape has vacant space and organisms of all ages mixed together and spatial variation in abundance is caused by microgeographic variation in settlement and mortality rates.