The Linear Spatial‐Temporal Interaction Process and its Relation to 1/ω‐Noise

If we are to gain an understanding of the evolutionary processes which generate pattern then time cannot be ignored, since a purely spatial viewpoint disregards the fundamental generating mechanism of the underlying process. We therefore develop a spectral approach based on a general growth-interaction model; individuals grow at intrinsic rate λ, while two individuals a distance r apart interact at rate a, times their size difference. Special cases considered involve nearest neighbour, geometric, logarithmic and Cauchy-type dependence. A separate study is made of «long-term persistence»; an autoregressive binomial weight structure is used to generate processes with power law spectra ω d

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