Pattern Analysis and Rates of Change in Mean Order Distance

Abstract

Pattern Analysis and Rates of Change in Mean Order Distance PHILLIPM. FOWLER, DOUGLAS D. EIER, and DOUGLAS WHITLOCK* The role of spatial structure in geographic research was outlined by the Swedish geographer Sten DeGeer, who argued that geography was a "general science, like statistics, mathematics" . . . and as such we . . . "are restricted to the study of a certain abstract quality in the objects or to purely abstract problems."1 Since the time of Sten DeGeer numerous geographers have suggested that spatial structure should play a fundamental role in geographic models. Spatial structure is employed herein as a general geographic term encompassing such distributive properties as pattern, density, and dispersion. Nonetheless, the nature and extent of the role which spatial structure should playin geographictheory is largelyunknown. Christaller's central place theory was one of the earlier and better known geographic models which incorporated spatial structure .2 Losch, Brush, Dickinson and others also have worked within a framework of urban marketing and competitive interaction as major mechanisms generating economic patterns.3 Considerable re- * This manuscript was read at the annual meeting of the Association at Bellingham in 1968. At that time Dr. Fowler was Assistant Professor of Geography , Douglas Eier was a graduate student in geography, and Douglas Whitlock was an undergraduate in geography at the University of Idaho, Moscow 83843. 1 Sten DeGeer, "On the Definition, Method and Classification of Geography ," Geografiska Annaler, Vol. 5, 1923, pp. 1-37. 2 Walter Christaller, Central Pkces in Southern Germany, translated by Carlisle W. Baskin, (Englewood Cliffs, New Jersey: Prentice-Hall, Inc., 1966). 3 August Losch, Economics of Location, translated by W. H. Wogloan. (New Haven, Connecticut: Yale University Press, 1954); J. E. Brush, "The 139 140association of pacific coast geographers search has developed about intra-city structural relationships. Harris and Ullman's multiple nuclei concept, Hoyt's sector hypothesis, and Burgess' concentric zone theory all attempt to rationalize verbally a functional linkage between the economic character of commercial activity and its location in space.* Other models incorporating spatial structure as an integral component include those of Greenhut, von Thiinen, and McCarty.5 Greenhut hypothesized that market structure, a nonspatial property of the firm, is inextricably linked to spatial structure. He contended that market structures such as pure competition, oligopoly, and monopoly resulted from the influence exercised by the distribution of buyers and sellers in space. This is one of the few works to relate an economic model to spatial structure. Both McCarty and von Thiinen developed models relating to agricultural location theory. McCarty predicated his model upon variables from the physical environment, whereas von Thiinen utilized economic factors. The resulting spatial structures, though based on differing sets of variables , yield similar arrangements of agricultural production, i.e., concentric zonation. In fields such as ecology, physics, and chemistry considerable work has also been carried out on spatial structure. Ecologists in particular have been in the forefront in research on spatial structure in plant and animal communities. They have done much to develop Hierarchy of Central Places in South Western Wisconsin," Geographical Review , Vol. 43, 1953, pp. 380-402; Robert E. Dickinson, City Region and Regionalism (London: Routledge and Kegan Paul Ltd., 1956). 4 C. D. Harris and E. L. Ullman, "The Nature of Cities," The Annals of the American Academy of Political and Social Science, Vol. 242, November 1945, pp. 7-17; Homer Hoyt, "Recent Distortions of the Classical Models of Urban Structure," Land Economics, Vol. 40, 1964, pp. 199-212; Ernest W. Burgess, "Growth of the City," in Robert E. Park, Ernest W. Burgess, and Roderick D. McKenzie (eds.), The City (Chicago, Illinois: University of Chicago Press, 1925). 5 Melvin L. Greenhut, "Space and Economic Theory," Papers and Proceedings of the Regional Science Association, Vol. 5, 1959, pp. 267-280; Edgar S. Dunn, The Location of Agricultural Production (Gainesville, Florida: University of Florida Press, 1954). Contains a restatement and extension in modern economic terms of the von Thiinen Schema; Harold H. McCarty and James B. Lindberg, A Preface to Economic Geography (Englewood Cliffs, New Jersey: Prentice Hall, Inc., 1966), pp. 56-65. yearbook · volume 32 · 1970141 the role of spatial structure in écologie models and in operationalizing the concept of pattern. The models in...