Local Explanations of Landscape Patterns: Can Analytical Approaches Approximate Simulation Models of Spatial Processes?

ABSTRACT Research over the last 100 years has demonstrated the importance of space for ecological processes. Given this importance, it may seem natural to start investigations into broad-scale ecological processes with a comprehensive, broad-scale spatial map. Here we argue that it may sometimes be possible to answer important questions about spatial processes using crude spatial information obtained when a comprehensive map is not available. To present our argument, we first develop a simple simulation model for a perennial plant reproducing and dying on a landscape with different arrangements of suitable and unsuitable sites. We then develop a simple, analytical approximation to predict the fraction of suitable sites that are occupied by the simulated plants. The analytical approximation summarizes the spatial map by using a single parameter that gives the probability that a site adjacent to a suitable site is suitable. Comparing the predictions of both approaches highlights three points: (a) The role of the spatial environment in ecological processes may play out at the local scale. Therefore, studying the local-scale processes may provide insights into landscape patterns. (b) The predictions from the analytical approximation fail noticeably when suitable sites are rare and are distributed randomly (rather than clumped) on the map. In these situations, patches of interconnected suitable sites are very small, and populations within small patches may go extinct via demographic stochasticity. This illustrates how analytical approximations can be used to identify cases when local-scale spatial processes are not sufficient to understand the ecological consequences of space. (c) For many natural systems, constructing the appropriate environmental map needed to study ecological processes is difficult or impossible. However, summary characteristics such as those employed by the analytical approximation may be estimated directly in nature. Therefore, even in the absence of an explicitly spatial broad-scale map, it may be possible to study spatial processes by understanding which local-scale characteristics of space are important.

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