中国人口疏密区分界线的历史变迁及数学拟合与地理意义

采用历史时间断面方法和现代空间分析方法,对中国西汉、西晋、唐代、北宋、明代、清代、现代7个时间断面的人口分布进行分析。结果发现：① 中国人口疏密区的分界线就是中国农牧区的分界线,中国人口分布的大格局由中国农耕区和畜牧区的空间分异奠定,理论上中国人口疏密区分界线就是中国农牧交错带的拟合线。② 两千多年的历史证明,中国农牧交错带是一个弧状地带,不能用直线拟合,只能用弧线拟合;“沈天大弧线”（沈阳—天水—大理弧线）是该交错带的函数拟合线,“山兰防弧线”（山海关—兰州—防城港弧线）是该交错带的内缘拟合线,也是中原王朝衰弱时期的农牧分界线;“沈兰西弧线”（沈阳—兰州—西双版纳弧线）是该交错带的外缘拟合线,也是中原王朝强盛时期的农牧分界线;直线的“爱辉—腾冲线”理论上不能拟合弧状的中国农牧交错带,但因为它碰巧是中国农牧交错带的函数拟合线的切线,因而也能较好地刻画中国人口的宏观分异格局。③ 中国人口疏密区分界线有着丰富的地理学意义：一是分界线本身就是农牧业分界线;二是分界线与海岸线围成的区域是中国的“国家核心区”;三是分界线最大限度地刻画了中国东南和西北的自然地理和人文地理的分异。

The historical change,mathematical fitting and geographical significance of demographic borderlines in China

By the methods of historical temporal section and modern spatial analysis, this paper analyzes the change of population distribution in China since the past 2000 years ago, such as the Western Han Dynasty (the representative year A.D. 2), the Western Jin Dynasty (A.D. 280), the Tang Dynasty (A.D. 742), the Northern Song Dynasty (A.D. 1102), the Ming Dynasty (A.D. 1460), the Qing Dynasty (A.D. 1820), and the present (A.D. 2010). It is found that China demographic borderlines dividing sparsely and densely populated areas are the borderlines which divide farming and pastoral areas, and the pattern of China's population distribution depends on the spatial differentiation of China's farming and pastoral areas. Therefore, theoretically the fitting curve of sparse-dense borderlines of China's population distribution in various times can be seen as the fitting curve of the farming-pastoral ecotone. The history has proved that China's farming-pastoral ecotone is an arc-shaped belt, so it can not be fitted by straight line but by arc-curve. Shenyang-Tianshui-Dali Arc is a function fitting line of the ecotone; Shanhaiguan-Lanzhou-Fangchenggang Arc is a fitting of the inner edge curve of the ecotone, which is a farming-pastoral borderline when the empire's rule was not so strong; Shenyang-Lanzhou-Xishuangbanna Arc is a fitting of the outer edge curve of the ecotone, which is another farming-pastoral borderline when the empire’s rule was very strong. As for Aihui-Tengchong Line, theoretically, it cannot fit the arc-shaped farming-pastoral ecotone, but coincidentally, because of being the tangent of Shenyang-Tianshui-Dali Arc, it can also depict the macro pattern of China's population distribution. China's demographic borderline dividing sparsely and densely populated areas is of geographical significance: first, the line is an farming-pastoral borderline of historical China; second, it, along with the coastline, encircles the "National Core Area" of China, in term of political geography; third, it, to the greatest extent, distinguishes the natural and human geographical differences existing in the northwestern and southeastern China.