Modelling  Spatially-Structured
Dynamics  for  Benthic  Predation


Figure 1
Figure 1. Intertidal zone as open system

Figure 2
Figure 2. Comparison of four models


We are studying the dynamics of populations of the intertidal mussel Mytilus californianus, a dominant species of the intertidal zones of the North American continent. This species is found in narrow bands in shore sites of moderate to high wave exposure. The predators of M. californianus are the sea star, Pisaster ochraceus, in the low intertidal Pacific Northwest, and the spiny lobster, Panulirus interruptus, in Southern California. We are interested in how zonation occurs in the intertidal zone and what controls the levels of zonation.

We model a region of the intertidal zone as an open system (Figure 1). We assume a constant input of mussel larvae which settle onto the substrate. Mussels grow asymptotically towards a terminal size. Mussels die due to non-predatory mortality or they are consumed by predators. Predators immigrate into the system at a constant rate and emigrate from the system at a rate that decreases with the amount of prey being consumed. As mussels increase in size they become more resistant to predation. In the spatially-explicit models, the recruitment of mussel larvae is enhanced by the presense of surrounding mussels and the vulnerability of a mussel to predation decreases with the size of its neighbors.

We have developed a multiple model approach to the study of predation in benthic communities. Four classes of models have been developed and analyzed: (1) an analytical “mean field” approximation consisting of ordinary differential equations (ODE), (2) a stochastic birth-death (SBD) version of the mean field ODE model, (3) a spatially-explicit cellular automata (CA) model, and (4) a spatially-explicit agent-based model (ABM). A set of model parameters values are common to all four model types. Comparison and cross-validation can be made among models (Figure 2) in order to take advantage of the strengths and that each has to offer.

National Science Foundation This work was supported in part by grants OCE-0089842, OCE-0072836, and HRD-9805529 from the U.S. National Science Foundation. All opinions expressed are those of the authors and not necessarily those of the NSF.

Copyright © 2002, Robert A Desharnais
Department of Biological Sciences
California State University, Los Angeles, CA, 90032-8201