Key words: Urban Spatial Dynamics, Urban Structure, Residential Segregation, GIS, Population Census
The measurement of urban residential patterns is aimed at providing a background for verifying social theories and models of urban dynamics (Allen, 1998; Portugali, 1999). With some exceptions (Wadorf, 1992; Schnell, 1999), these patterns are described and measured for population groups over predetermined partitions of the studied area. This is not enough for verifying the theories and models of urban dynamics, which differ in characterizing form and location of homogeneous or heterogeneous population domains. To verify the models we have to know the inherent properties of the residential distribution, which are available at high resolution only. This is especially important for agent-based models of residential dynamics (Benenson, 1998), where the dependence of agents' behaviour on segregation situation within the neighbourhood is the driving force of urban dynamics.
In order to validate the social theories and corresponding models, high-resolution geo-referenced data are necessary (Boal, 1987). These data became available only recently. Beginning in 1995, the population censuses in several European countries, including Israel, are based on exact location of householders and households in the GIS frame (Israeli Central Statistical Bureau, 2000). Consequently, we are now able to develop an individual-based approach to residential segregation and to estimate the exposure, isolation, etc., of a single individual relative to his/her neighbours in the house, within the neighbourhood of the closest houses, and so on. A human being exists in several spatial aggregates concurrently and experiences transitions between them. Proceeding with the individual-based approach, we immediately understand that a person can exist simultaneously in strong segregation regarding the rest of the residents of a house and in weak segregation regarding the population of the neighbouring houses, thus exhibiting different levels of segregation at different units of space. As a result, the series of residential patterns representing, say, exposure of the individuals to their neighbours within the neighbourhood of varying sizes or their isolation from the neighbours within these neighbourhoods should be constructed in order to describe the state of an urban system.
The aim of this paper is to suggest an individual-based framework for description of the multi-level spatial relations between individuals and estimating corresponding urban patterns. The framework is based on hierarchical representation of urban residential space and estimation and comparison of several indices of local spatial segregation at different levels of the proposed hierarchy. We apply this approach to the data of the Israeli population census of 1995, which are geo-referenced at the level of householders and households. We study residential patterns in the Tel-Aviv City based on the census database.
It is shown that the administrative divisions do not properly reflect the pattern of the city's residential distribution. The latter is adequately represented according to the proposed hierarchical scheme and is characterized by a number of relatively homogeneous domains of individuals having extreme characteristics - high or low income or high or low education level, etc. The rest of the city area, where the inhabitants are, on average, at intermediate levels of income, education, etc., are highly heterogeneous.
The general hypothesis, which stems from the above study, is: if an area in the city is homogeneous according to a given population characteristic, then the value of this characteristic over this area is either extremely high or low. If the mean value of the characteristic over some area is intermediate, then an area is highly heterogeneous. Possible confirmations of this hypothesis by means of agent-based model of individual residential activity are discussed.