The concept of the population-density function, which is usually applied within the context of an urban area, is extended to the scale of a metropolitan-area-based region or city region. A form for such a regional density function is proposed, and this is examined for selected regions of the UK and North America. It is demonstrated how such a region-wide density function may be related to other density functions which have been used to characterise the structures of the metropolitan and non-metropolitan parts of the region. Consideration is also given to problems associated with constructing and interpreting the regional density function and to its underlying theoretical basis. Finally, the application of the density-function approach in the analysis of regional structure is briefly discussed.
References
1.
Ajo, R. ( 1965). On the structure of population in London's field . Acta Geographica, Vol. 18: 1-17.
2.
Alonso, W. (1964). Location and Land Use. Cambridge, Mass: Harvard University Press.
3.
Berry, B.J.L. (1967). Geography of Market Centers and Retail Distribution . Englewood Cliffs N.J: Prentice-Hall .
4.
Berry, B.J.L., Gobeen, P.G. and Goldstein, H. (1968). Metropolitan Area Definition: a Re-evaluation of Concept and Statistical Practice (Bureau of the Census, Working Paper No. 28). Washington, D.C.: Bureau of the Census.
5.
Berry, B.J.L. and Horton, F.E. (1970). Geographic Perspectives on Urban Systems. Englewood Cliffs, N.J.: Prentice-Hall.
6.
Blumenfeld, H. (1950). The dominance of the metropolis. Land Economics, Vol. 26: 194-96.
7.
Bogue, D.J. (1950). The Structure of the Metropolitan Community. Ann Arbor, Mich.: Horace H. Rackham School of Graduate Studies.
8.
Boisvert, M. (1978). The Correspondence Between the Urban System and the Economic Base of Canada's Regions. Ottawa: Economic Council of Canada.
9.
Boudeville, J.R. (1966). Problems of Regional Economic Planning. Edinburgh: Edinburgh University Press.
10.
Bussière, R. and Snickars, F. (1970). Derivation of the negative exponential model by an entropy-maximising method. Environment and Planning, Vol. 2: 295-301.
11.
Casetti, E. (1969). Alternate urban population density models: an analytical comparison of their validity. In A. J. Scott (ed.), Studies in Regional Science. London: Pion. 105-16.
12.
Champion, A. and Coombes, M.G. (1983). Functional regions: definitions, applications, advantages. Factsheet No. 1, Centre for Urban and Regional Development Studies, University of Newcastle-upon-Tyne.
13.
Christaller, W. (1933). Die zentralen Orte in Süddeutschland. Jena: Gustav Fischer. Translated by C. Baskin as Central Places in Southern Germany. Englewood Cliffs, N.J.: Prentice-Hall ( 1966 ).
14.
Clark, C. (1951). Urban population densities. Journal of the Royal Statistical Society, Series A, Vol. 114: 490-96.
15.
Clark, C. (1968). Population Growth and Land Use. New York: Macmillan.
16.
Cliff, A.D., HAGGETT, P., ORD, J. K., BASsETr, K. and DAVIES, R. B. (1975). Elements of Spatial Structure: a Quantitative Approach. Cambridge: Cambridge University Press.
17.
Dickinson, R.E. (1947). City, Region and Regionalism. London: Routledge and Kegan Paul.
18.
Evans, A.W. (1973). The Economics of Residential Location. London: Macmillan.
19.
Friedmann, J.R.P. (1956). Locational aspects of economic development. Land Economics, Vol. 32: 213-27.
20.
Gras, N.S.B. (1922). An Introduction to Economic History. New York: Harper.
21.
Haggett, P. (1965). Locational Analysis in Human Geography. London: Edward Arnold.
22.
Hoover, E.M. and Vernon, R. (1962). Anatomy of a Metropolis. Garden City, NY: Anchor Books.
23.
Isard, W. (1960). Methods of Regional Analysis. Cambridge, Mass: The MIT Press.
24.
Kansky, K.J. (1963). Structure of transport networks: relationships between network geometry and regional characteristics. Research Paper No. 84, Department of Geography, University of Chicago.
25.
King, L., Casetti, E. and Jeffrey, D. (1969). Economic impulses in a regional system of cities . Regional Studies, Vol. 3: 213-18.
26.
Lösch, A. (1941). Die räumliche Ordnung der Wirtschaft. Jena: Gustav Fischer. Translated by Woglom, W. H. and Stolper, W. F. as The Economics of Location. New Haven, Conn.: Yale University Press (1954).
27.
McKenzie, R.D. (1933). The Metropolitan Community. New York: McGraw-Hill.
28.
Mills, E.S. (1972). Studies in the Structure of the Metropolitan Economy . Baltimore: Johns Hopkins Press .
29.
Muth, R. (1969). Cities and Housing. Chicago : University of Chicago Press.
30.
Newling, B.E. (1969). The spatial variation of urban population densities . Geographical Review, Vol. 59: 242-52.
31.
Nystuen, J.D. and Dacey, M.F. (1961). A graph theory interpretation of nodal regions . Papers and Proceedings of the Regional Science association , Vol. 7: 29-42.
32.
Parr, J.B. (1979). Spatial structure as a factor in economic adjustment and regional policy. In D. Maclennan and J. B. Parr (eds.), Regional Policy: Past Experience and New Directions. Oxford: Martin Robertson. 191-210.
33.
Parr, J.B. (1985a). The form of the regional density function. Regional Studies, Vol. 19: forthcoming.
34.
Parr, J.B. (1985b). The regional density function: applications of the concept. Unpublished manuscript, Department ofSocial and Economic Research, University of Glasgow.
35.
Parr, J.B. and Jones, C. (1983). City size distributions and urban density functions: some interrelationships. Journal of Regional Science, Vol. 23: 293-307.
36.
Philbrick, A.K. (1957). Principles of areal, functional organization in regional human geography. Economic Geography, Vol. 33: 299-336.
37.
Rees, P. (1968). The functional ecology of metropolitan Chicago. Master's thesis, University of Chicago.
38.
Reilly, W.J. (1953). The Law of Retail Gravitation, 3rd ed. New York: Pilsbury Publishers .
39.
Rhind, D.W., Stanness, K. and Evans, I.S. (1977). Population distribution in and around selected British cities. Census Research Unit Working Paper No. 11, Department of Geography, University of Durham.
40.
Taaffe, E.J., Morrill, R.L. and Gould, P.R. (1963). Transport extension in underdeveloped countries: a comparative analysis. Geographical Review, Vol. 53: 503-29.
41.
Termote, M.G. (1978). Migration and commuting in Losch's central-place system. In R. Funck and J. B. Parr (eds.), The Analysis of Regional Structure: Essays in Honour of August Lösch. London: Pion. 83-90.
42.
Transport Studies Unit (1984). Transport, land use and energy interaction. Unpublished note, Transport Studies Unit, University College London.
43.
Ullman, E.L. and Dacey, M.F. (1962). The minimum requirements approach to the urban economic base. Lund Studies in Human Geography, Series B, No. 24: 121-143.
44.
Ville De Montreal (1964). La Vague d'Expansion Metropolitaine (Bulletin Technique, No. 1). Montreal: Service d'Urbanisme.
45.
Vining, R. (1955). A description of certain spatial aspects of an economic system. Economic Development and Cultural Change , Vol. 3: 147-95.
46.
Zielinski, K. (1979). Experimental analysis of eleven models of urban population density, Environment and Planning A, Vol. 11: 629-41.
