A correct formulation for a spatially implicit predator-prey metacommunity model

In order to mitigate the problem of increasing model complexity with increasing number of occupation states in spatially implicit metacommunity models, the assumption of independency among species distributions is often required. In the present paper, we show that this approach only works correctly if set relations among patch occupancy states are considered adequately. This is illustrated by means of a well-known, although incorrectly formulated, predator-prey metacommunity model devised by Bascompte and Solé[1]. We demonstrate that this model shows anomalous dynamical behavior caused by inconsistence between the model formulation and its assumptions. In order to formalize our finding we develop a corrected model formulation that accounts for the principles of set theory so that the sum of the system compartments change rate is nulled. Applying this method successfully rules out the occurrence of anomalous dynamical behavior found in the original model. Finally we discuss the implications of our findings for the accuracy of model predictions.