The minimum habitat-size problem

The constants An are fixed by the initial conditions. It is clear that if L Lc = 7x jD/g no growth occurs and the patch dies, so that Lc can be identified with the minimum patch-size able to support growth. Aside from unimportant geometric factors, the same behavior is found in higher dimensions. 

There are a number of criticisms to this approach. First, the model is incomplete, since once growth begins it continues without limit. Nonlinear saturation and interactions with predators would be needed to stop this. The diffusion coefficient D certainly does not originate from the Brownian motion of the organisms, since this would be irrelevant to these processes above, say, on the millimeter scale. It is rather a turbulent eddy-diffusion coefficient aimed to 

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