Geographical Processes and the Analysis of Point Patterns: Testing Models of Diffusion by Quadrat Sampling

OVER THE past decade or so geographers have become increasingly aware of the potential explanatory and predictive power of theories of location and of spatial evolution. These theories imply the existence of some rational and discernible pattern in spatial distributions of human activity and, in many cases, enable us to generate an 'ideal' landscape. The verification and modification of such theories requires some adequate means of testing these 'ideal' patterns against the real world. Such testing has proved difficult for a number of reasons. In human geography it is clear that the real world pattern is usually the result of highly complex interacting processes, not all of which can be interpreted very easily in terms of some simple system or theory. Most location theories incorporate normative notions-profit maximization, for example-which allow little concession to the inadequacies of the decision-making process in the real world, and even if they did there is plenty of evidence to show that profit maximization on the part of the individual does not necessarily lead to the optimal use of space from the point of view of society as a whole. H. Hotelling's (1957) example of two ice-cream sellers on a beach is a simple example. A. Losch's (1954) system may be similarly criticized, for, although it indicates an optimal solution for society as a whole, it does not follow that this solution will emerge from competition among individual entrepreneurs whose sole aim is profit maximization. If we imagine 'economic man' setting off on some optimizing path with respect to location, we may treat this path, at its simplest, as a movement in which the cost of searching out and moving to a 'better' location are substituted against the benefits to be obtained from moving. If the process is continuous we may expect movement to cease at that point where the marginal cost of moving equals the marginal revenue from moving to the better location. Even assuming perfect knowledge on the part of the individual, this point will be short of the optimum. As R. Radner (1964) has pointed out: Most practical applications of optimising procedures would appear to involve stopping short of the optimum and accepting a less than optimal decision because of cost or feasibility considerations that have not been expressed in the formal representation of the decision problem.