Spatial forecasting: Detecting determinism from single snapshots

Abstract

In ecological systems, long, high-quality time series of population abundances is seldom available. However, in some cases populations are scattered over spatial domains where physical conditions appear to be homogeneous, and spatial snapshots of population abundance can be obtained. Since these spatial patterns are generated from underlying dynamical rules, an important problem is to detect the presence of determinism in these structures. In this paper, a simple model of determinism detection from spatial snapshots is presented, using a coupled map lattice formalism. It involves a simple forecasting approach where subparts of the lattice are used in order to make predictions based on the distance between neighbors. It is shown that the method is able to properly detect the presence of low-dimensional dynamics from single snapshots.