R. A. Fisher and Sewall Wright introduced diffusion approximation methods into genetics; Fisher (1937) was the first to consider spatial disperal using a reaction-diffusion model. I found this quote a useful expression of his acknowledgment of the limits of the model:
The use of the analogy of physical diffusion will only be satisfactory when the distances of dispersion in a single generation are small compared with the length of the wave. In reality diffusion is a complex process, compounded often of the diffusion of gametes, and that of larvae, in addition to adult forms; a more exact treatment than that supplied by a simple coefficient would involve the interaction of these components, and the stages at which the selective advantage was enjoyed. So far as it is applicable, the analogy of physical diffusion, therefore, greatly simplifies the problem (355-356).
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