PubMed Health⌕ Search

PubMed · 12265195

Spatial aggregation in gravity models: 2. One-dimensional population density models.

Abstract

"This paper, the second of four, is concerned with applying a methodology for analysing the spatial aggregation problem in gravity models outlined in the first paper. The methodology is based on a consistent framework for linking measures of pattern in interaction data to the derivation and estimation of related interaction models using spatial information. In this quest, a link is forged between information in data and the parameters of an associated model.... This relationship can be formalised for the case of the continuous one-dimensional interaction model such as the population density model, and this paper is concerned with demonstrating such an application to aggregations of zones in the Reading [England] region."

Explore related subjects

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

M Batty, P K Sikdar. 1982. Spatial aggregation in gravity models: 2. One-dimensional population density models.. https://doi.org/10.1068/a140525

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related citations

On treatment of tuberculosis in heterogeneous populations.

Global eradication of tuberculosis (TB) is an international agenda. Thus understanding effects of treatment of TB in different settings is crucial. In previous work, we introduced the framework for a mathematical model of epidemic TB in demographically distinct, heterogeneous populations. Simulations showed the importance of genetic susceptibility in determining endemic prevalence levels. In the work presented here, we include treatment and investigate different strategies for treatment of latent and active TB disease in heterogeneous populations. We illustrate how the presence of a genetically susceptible subpopulation dramatically alters effects of treatment in the same way a core population does in the setting of sexually transmitted diseases. In addition, we evaluate treatment strategies that focus specifically on this subpopulation, and our results indicate that genetically susceptible subpopulations should be accounted for when designing treatment strategies to achieve the greatest reduction in disease prevalence.

Demography↗

Demography, recombination hotspot intensity, and the block structure of linkage disequilibrium.

BACKGROUND: Effective gene mapping based on genetic association data will require detailed knowledge of patterns of linkage disequilibrium (LD) in human populations. It has been recently suggested that linkage disequilibrium in humans may be organized in a block-like structure, with islands of high LD separated by regions of rapid breakdown of LD due to recombination hotspots. The experimental data to date, however, are limited, and fundamental questions remain about the implications of recombination rate heterogeneity. Here, we use computer simulations to evaluate how such heterogeneity influences patterns of LD, and we develop formal criteria to assess whether the patterns are functionally block like in the context of association mapping. RESULTS: Our analyses suggest that, even in models of extreme recombination rate heterogeneity, some human populations will have a functionally block-like structure to the pattern of LD, but others will not, depending on their precise demographic histories. In fact, for many models, we find that, following an LD-generating event, populations may move through discrete phases that can be functionally described as pre-block, block, and post-block. An analysis of observed and expected patterns of LD surrounding hotspots within the MHC Class II region confirms these theoretical expectations. CONCLUSIONS: Even if highly punctuated patterns of recombination are the rule, patterns of LD are still likely to show differences among populations and among genomic regions that are of practical importance in the design of genetic association studies. The notion that the average extent of LD is a useful concept for the design of association studies must be abandoned in light of the experimental and theoretical evidence.

Demography↗