Define the Historical Process of Spatial processes?

In year 1952 Alan Turing developed his theory of the generation of pattern in systems of reaction diffusion equations, now known as Turing instabilities. One underlying assumption is that there is one species that is autocatalytic (so an increase in that species fuels further increases in that species), or as an ecologist would phrase it, exhibits positive density dependence. The 2nd set of assumptions is that the controlling species has a higher movement rate as compared to the species that can potentially increase. Mainly the controlling species diffuses away from outbreaks, thus permitting the development of spatial pattern.

Basically applied to questions of morphogenesis and development, which in more than one dimension relates to classic mathematical problems for eigenvalues, after that this theory was applied to ecological problems in general (Levin, 1974). More currently, mathematical approaches related to this theory have been tied to particular ecological systems such as the western Tussock moth and its parasitoids (Hastings et al., 1997), where the models define apparently anomalous spatial distributions of the host species, so answering basic questions about spatial distributions of abundance.