A Family of Relaxed Spatial Interaction Models

In traditional, constrained spatial interaction models, the number of predicted movers leaving origins and entering destinations is constrained to match exactly the observed number. In relaxed models, these constraints are allowed to vary over a range of values in order to provide greater flexibility in calibration. This paper identifies a new, seven-member family of relaxed spatial interaction models, based upon the generalization of the constraint sets used in model derivation. Three categories are suggested, including single and doubly relaxed models, cost-relaxed models, and totally relaxed models. This paper introduces these relaxed models as entropy-maximizing ones, proposes a terminology for them, and describes empirical situations in which they are useful.     

Formulating a General Spatial Segregation Measure*

Most traditional segregation measures, such as the index of dissimilarity D, fail to distinguish spatial patterns effectively. Previously proposed spatial measures modifying D suffer from several shortcomings. This article describes a general spatial segregation index based upon the concept of composite population counts, which are derived from grouping people in neighboring areas together to account implicitly for spatial interaction of groups across unit boundaries. The suggested spatial index can overcome the disadvantages of previous indices and can assess the spatial extent of the segregated clusters. The results offer a more comprehensive depiction of spatial segregation of a region.     

Where Non-academic Geographers are Employed

In traditional, constrained spatial interaction models, the number of predicted movers leaving origins and entering destinations is constrained to match exactly the observed number. In relaxed models, these constraints are allowed to vary over a range of values in order to provide greater flexibility in calibration. This paper identifies a new, seven-member family of relaxed spatial interaction models, based upon the generalization of the constraint sets used in model derivation. Three categories are suggested, including single and doubly relaxed models, cost-relaxed models, and totally relaxed models. This paper introduces these relaxed models as entropy-maximizing ones, proposes a terminology for them, and describes empirical situations in which they are useful.     

WARPED SPACE: A GEOGRAPHY OF DISTANCE DECAY*

Distance decay is one of geography's core concepts, yet its own spatial properties have been largely neglected. We illustrate the use of the expansion method in assessing the spatial variation of distance-decay parameters within the general context of gravity models. The approach enables the portrayal of “space warping,” said to occur when equivalent distances have spatially uneven effects on interaction. The concepts are examined empirically through the estimation of a competing destination model for out-migration from five State Economic Areas over the 1965–70 period. Four of the five origins are found to have spatially unstable frictions of distance. We conclude by suggesting that distance decay is a contextual, rather than a universal, effect.     

空间相互作用模型中的目的地竞争效应 ——基于中国城市间铁路客流数据的实证研究

目的地竞争模型是空间相互作用领域的重要进展之一,但其有效性尚未得到一致认可,且缺乏基于中国的实证依据。基于中国2010年城市间铁路客流数据,采用目的地竞争模型进行实证分析,并与传统空间相互作用模型相比较,以检验目的地竞争模型在实际应用中的有效性。结果表明：① 空间结构对中国城市间铁路客流存在显著影响,目的地之间存在较强的竞争效应;② 目的地竞争模型的引入显著地减弱了距离衰减参数的空间自相关程度,较大程度上改善了传统空间相互作用模型的距离衰减参数标定偏误问题;③ 既有研究中在区域尺度下对传统空间相互作用模型（即重力模型）参数的标定及实证分析可能会存在偏误,目的地竞争模型这一改进模型具备应用价值。     

基于空间互动模型的兰州市乡村旅游网络中心性分析

基于传统“引力模型”,引入通勤时间、旅游潜力等指标,构建了“旅游空间互动模型”,并以兰州市47个乡村旅游发展重点村为例,采用社会网络分析法剖析了兰州市乡村旅游网络中心性特征,发现：① 兰州市各村庄的度中心值均高于中介中心,中介中心值均高于向量中心,且主城区周边村庄的中心性普遍高于西北部永登县、东南部榆中县及其他县区所辖村庄的中心性;② 兰州市乡村旅游网络发育不成熟,空间结构呈现局部紧凑、整体稀疏且发展不均衡的特点;③ 当前兰州市乡村旅游发展以第二层级村庄为主,急需培育第一层级村庄以完善旅游网络中的核心节点。最后,提出优化兰州市乡村旅游网络结构的对策。     

Spatial interaction: a statistical mechanism model

1 IntroductionSpatial interaction is an important problem in modern geography. A. Wilson (1970) has deduced the mathematical formulation of spatial interaction from the principle of maximum entropy; but the mechanism is not clear. In the past 10 years the basis of the model of maximum entropy is challenged, since one considers geographical system as an open system. In an open system, it is meanless for the entropy of the system to reach maximum. The basic aspect of this paper, which is based …     

都市区空间结构与经济发展的互动关系研究

文章采用结构方程模型实证检验空间结构与经济发展的互动关系。研究发现,中国都市区已经进入多中心分散阶段,空间结构与经济发展存在因果关系,即经济发展水平的提高会扩大人口规模,规模增加则导致集聚不经济上升,并促进空间结构多中心化。多中心化后的空间结构由于降低了集聚不经济而进一步提高生产率。因而,传统地理学中关于两者互动发展的描述得到实证支持;同时明确了多中心化的直接动力是人口规模的增加,而不是经济发展水平的提高。这些发现对于优化当前中国的城市与区域空间战略具有重要的启示。     

Imposing Age and Spatial Structures on Inadequate Migration‐Flow Datasets*

With the elimination of the long‐form questionnaire from future decennial censuses and its replacement by a much smaller continuous monthly sampling survey (the American Community Survey), students of territorial mobility may find it necessary to deal with inadequate, missing, or inaccurate sample data on migration by adopting an approach that “improves” such data using information from different geographical areas, time periods, and data sources. We develop such an approach in this article and illustrate it with interregional migration flow data reported by the U.S. decennial censuses of 1980 and 1990 and by the 1985 Current Population Survey.     

基于引力模型的中心镇空间联系测度研究——以浙江省金华市25个中心镇为例

根据中心镇之间经济社会要素空间流动特征,对引力模型和断裂点公式进行改进与整合,形成基于引力模型的中心镇空间联系测度方法体系,并将其应用于金华市25个中心镇空间联系强度和空间引力范围的定量测度。结果显示：① 金华市中心镇空间联系强度呈现出明显的组团化空间格局,中心镇发展可进行“两轴线、四组团”的空间整合;② 市域中心镇空间联系强度具有显著的空间分异规律,需采取差别化的措施促进中心镇协同发展;③ 金华市中心镇空间引力范围差异较大,中部中心镇组团空间引力范围最大,东南部、西部组团次之,北部组团最小;④ 中心镇与断裂点之间的距离关系,可作为判断中心镇组团内核心中心镇及关键节点中心镇的重要依据。     

城市空间相互作用理论模型的演进与机理

城市空间相互作用理论是城市地理学的重要基础理论。由于城市空间相互作用模型发端于西方,我国这方面的研究相对较晚,主要是引进和实证,在理论研究上还有待深入。本文分析了几种主要城市空间相互作用理论模型的机制和原理,考虑到断裂点模型应用较广,经过了较多的实践验证,重点探讨了该模型的缺陷、演进和扩展形式,从理论上论证了将空间分割原理和断裂点模型结合的扩展模型的科学性和合理性。对城市空间相互作用理论模型的研究,不仅可以为城市规划、城市影响空间和城市经济区的划分以及行政区划调整提供理论基础,而且对物流分析、设施选址、市场影响力的分析等也具有重要的指导作用。从分析城市空间相互作用理论模型演进的过程中还可以得到深刻的启发：地理学以复杂的自然、人文现象为研究对象,是一门边缘学科,又是一门实践性很强的学科。地理学应积极借鉴其他学科最新的理论、技术与方法是十分必要的,是推动其自身发展的关键所在。     

论京津空间相互作用

在对京津空间相互作用的历史、现状及趋势分析的基础上，着重剖析了距离、规模、互补性及介入机会等空间相互作用的影响因素在京津空间相互作用中的影响，并将具有中国特色的制度因素对京津关系的影响引入空间相互作用理论，以期为京津联合发展提供决策参考。     

近20年珠三角城市群城市空间相互作用时空演变

利用改进的引力模型和潜力模型,结合GIS空间分析方法,从地级市和县域两个空间尺度分析了近20 a珠三角地区城市间相互作用的时空演变。结果表明:珠三角地级城市空间联系总体逐步加强,并充分体现出广州的中心城市地位;县域尺度上,空间联系强度较大的主要是各地市市区之间及广-佛都市区的县市间和各地市市区与其所辖县市之间,其它县市间联系强度则较小;珠三角核心区内大部分县市之间联系总体呈逐渐增强趋势,核心区外的县市之间及其与核心区内的县市间联系强度有升有降,规律性不明显。广-佛都市区和深圳-东莞-惠州都市区的城市潜力较大且变动较大,对外辐射带动作用强,其它城市潜力相对较小且变化不明显;珠三角城市潜力的区域不平衡态势明显,城市潜力的空间分异和空间辐射的特征与演变规律明显。     

Incorporating Spatial Dependence in Predictive Vegetation Models: Residual Interpolation Methods*

Predictive vegetation modeling can be used statistically to relate the distribution of vegetation across a landscape as a function of important environmental variables. Often these models are developed without considering the spatial pattern that is inherent in biogeographical data, resulting from either biotic processes or missing or misspecified environmental variables. Including spatial dependence explicitly in a predictive model can be an efficient way to improve model accuracy with the available data. In this study, model residuals were interpolated and added to model predictions, and the resulting prediction accuracies were assessed. Adding kriged residuals improved model accuracy more often than adding simulated residuals, although some alliances showed no improvement or worse accuracy when residuals were added. In general, the prediction accuracies that were not increased by adding kriged residuals were either rare in the sample or had high nonspatial model accuracy. Regression interpolation methods can be an important addition to current tools used in predictive vegetation models as they allow observations that are predicted well by environmental variables to be left alone, while adjusting over‐ and underpredicted observations based on local factors.     

Mobile Communications,Social Networks,and Urban Travel: Hypertext as a New Metaphor for Conceptualizing Spatial Interaction*

The widespread use of mobile communications is leading to new practices in family life and social life, and these changes have significant implications for the study of urban travel. Because of the adoption of new modes of space‐time coordination, changing time use and increasing mobility, changing use of existing urban nodes, the blurring of boundaries between home and work, the importance of social networks and social capital, and the shift to person‐to‐person connectivity, the spatial structure and processes of interaction among individuals have become much more complicated in this age of mobile communications. Static spatial frameworks based on fixed points (e.g., home or workplace) and distances among them are no longer adequate for understanding urban travel. The study of urban travel now needs new conceptualizations and new methodologies.     

城乡过渡带空间演进与空间交互强度分析

采用NPP/VIIRS夜间灯光数据提取广州市城乡过渡带边界,利用基于sDNA模型修正的引力模型测算2012—2019年广州市城乡过渡带的空间交互强度,分析其空间演进特征与社会经济发展的关系。研究表明：1）2012—2019年广州市城乡过渡带总体呈扩大趋势,以北偏东方向发展为主,破碎区块逐渐演变为连续区域;2）广州市城乡过渡带之间的空间交互网络结构呈现“多方向化”趋势,从最初的西南侧单线网络结构逐步发育成多方向闭合网络联结结构,目前演变为南北两支、东西向的强空间交互态势,以白云区为代表的北部区域和以番禺区为代表的南部区域是广州市城乡过渡带的重要战略节点地域;3）广州市城乡过渡带社会经济优势度呈现出由内向外的3个空间层级结构,并由城市核心区辐射带动,向北、东北与东南3个方向推动发展为城乡过渡带;4）各城乡过渡带的发展速度不均衡现象仍较明显,广州市应结合本区域优势产业和自然资源,走联合与互补发展并存的道路,重视城乡过渡带区域发展引擎,增强其与周边地区联系的潜力。     

东北三省人口流失的测算及演化格局研究

东北三省养育了全国8%的人口,但是改革开放以来人口不断外迁和流出,东北三省人口流失问题受到广泛关注。基于2000年以来的人口普查和抽样统计资料,系统地测算东北三省人口流失量,从省级和县市2个空间尺度分析东北三省人口流失的演化格局。主要结论包括：① 2000~2015年,东北三省人口出现持续流失,并且不断加剧。② 东北三省并不是中国人口流失最严重的地区。③ 东北三省内部出现较多人口流失的县市,空间范围呈现扩张。④ 经济动能不足是东北三省人口流失的主要原因。⑤ 东北三省人口发展的真正问题不在数量,而在人口质量和结构,包括人才流失严重、人口老龄化加剧、人口空间结构高度极化等。     

HISPANIC MIGRATION AND POPULATION REDISTRIBUTION IN THE UNITED STATES*

The US Hispanic population has grown rapidly over the last two decades and remains geographically concentrated in nine states. Redistribution away from core states through internal migration has been largely offset by heavy immigration to traditional areas of Hispanic concentration. Geographical patterns of Hispanic miration show broad similarities to overall patterns of population redistribution in the United States. New York and California serve as key spatial redistributors or pivots in the Hispanic migration system.     

长江三角洲人口迁移空间格局、模式及启示

本文运用修正后的重力模型和城市之间最短通行时间的O-D矩阵,模拟长江三角洲人口迁移节点联系状态,判断吸引中心的从属结构,划分人口迁移引力体系的等级结构。结果表明:至2005年,长三角共形成上海、南京、杭州、宁波、温州5个一级人口吸引中心,无锡、徐州2个二级吸引中心,连云港、淮安、扬州等9个三级吸引中心;这些吸引中心共同构成5个Ⅰ级引力体系,7个Ⅱ级引力体系和14个Ⅲ级引力体系。在此基础上,归纳出人口迁移空间结构演变的一般模式:即"单核集聚"—"多核结构"—"单中心体系"—"多中心网络"。通过吸引中心等时圈分析,认为区域快速交通体系布局对人口流动空间格局的形成起着重要的引导和支撑作用。最后从城市轨道交通、地方行政壁垒和中心城市发展角度对长江三角洲不同层次的规划提出了相应的建议。     

基于空间相互作用模型的商业布局——以北京市海淀区为例

在分析北京市海淀区人口增长与商业发展的基础上,运用空间相互作用理论和模型, 定量地测算了海淀区各个街乡的人口潜能与商业吸引力,对该区的人口与商业分布状况及其空间互动关系进行了分析,并根据人口增长的组合预测结果对未来海淀区各个街乡商业配置进行了具体的测算,在为商业发展布局规划提供决策支持的同时,探讨一种城市商业活动的空间分析框架。