An important issue in the study of cities is defining a metropolitan area, as different definitions affect the statistical distribution of urban activity. A commonly employed method of defining a metropolitan area is the Metropolitan Statistical Areas (MSA), based on rules attempting to capture the notion of city as a functional economic region, and is constructed using experience. The MSA is time-consuming and is typically constructed only for a subset (few hundreds) of the most highly populated cities. Here, we introduce a new method to designate metropolitan areas, denoted the "City Clustering Algorithm" (CCA). The CCA is based on spatial distributions of the population at a fine geographic scale, defining a city beyond the scope of its administrative boundaries. We use the CCA to examine Gibrat's law of proportional growth, postulating that the mean and standard deviation of the growth rate of cities are constant, independent of city size. We find that the mean growth rate of a cluster utilizing the CCA exhibits deviations from Gibrat's law, and that the standard deviation decreases as a power-law with respect to the city size. The CCA allows for the study of the underlying process leading to these deviations, shown to arise from the existence of long-range spatial correlations in the population growth. These results have socio-political implications, such as those pertaining to the location of new economic development in cities of varied size.
Effect of decreasing population growth-rate on deforestation and population sustainability
我们考虑了非常数参数对“Deforestation and world population sustainability：a quantitative analysis”[1]中引入的人-林相互作用Logistic模型以及人类技术增长的影响。事实上，近年来，人口增长率已经出现下降，自1960年以来每年下降约1.7%，这与联合国对2100年之前的未来几十年的最新预测相吻合[2]。因此，我们在这里考虑人口增长率下降对上述模型的影响，并评估其对人类文明在不经历人口灾难性崩溃的情况下生存的可能性的影响。我们发现，对于地球人口承载能力的现实值（由参数β测量），这种减少不会影响以前的结果，导致避免灾难性崩溃的概率很低。相反，对于更大更乐观的β值，增长率的下降将使概率倾向于积极的结果，即从10-20%上升到甚至95%的避免崩溃的可能性。
