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Recent studies have suggested that conventional population dynamic models based on demographic processes and environmental heterogeneity cannot simulate spatial data that conform realistically to Taylor's power law for values of b̂ (the estimated slope) greater than 2, and that b̂ values from replicate simulations may vary widely even when identical parameters are used. Two such models are presented which demonstrate that this is not necessarily so; these produce simulated spatial variance-mean plots which are linear over a wide range of population densities. These models incorporate behaviourally-induced emigration, and are consistent with species-specific responses. A new stepping-stone model is presented involving local movement between contiguous hexagons, which also simulates data conforming realistically to the power law. These results underpin Southwood's suggestion that a variety of mechanisms probably contribute to observed patterns.
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