Local Spatial Autocorrelation in a Biological Model

We review the recently developed local spatial autocorrelation statistics I_i, c_i, G_i, and G_i*. We discuss two alternative randomization assumptions, total and conditional, and then newly derive expectations and variances under conditional randomization for I_i and c_i, as well as under total randomization for c_i. The four statistics are tested by a biological simulation model from population genetics in which a population lives on a 21 × 21 lattice of stepping stones (sixty-four individuals per stone) and reproduces and disperses over a number of generations. Some designs model global spatial autocorrelation, others spatially random surfaces. We find that spatially random designs give reliable test results by permutational methods of testing significance. Globally autocorrelated designs do not fit expectations by any of the three tests we employed. Asymptotic methods of testing significance failed consistently, regardless of design. Because most biological data sets are autocorrelated, significance testing for local spatial autocorrelation is problematic. However, the statistics are informative when employed in an exploratory manner. We found that hotspots (positive local autocorrelation) and coldspots (negative local autocorrelation) are successfully distinguished in spatially autocorrelated, biologically plausible data sets.     

Local Spatial Autocorrelation Statistics: Distributional Issues and an Application

The statistics G_i(d) and G_i*(d), introduced in Getis and Ord (1992) for the study of local pattern in spatial data, are extended and their properties further explored. In particular, nonbinary weights are allowed and the statistics are related to Moran's autocorrelation statistic, I. The correlations between nearby values of the statistics are derived and verified by simulation. A Bonferroni criterion is used to approximate significance levels when testing extreme values from the set of statistics. An example of the use of the statistics is given using spatial-temporal data on the AIDS epidemic centering on San Francisco. Results indicate that in recent years the disease is intensifying in the counties surrounding the city.     

The Saddlepoint Approximation of Moran's I's and Local Moran's Ii's Reference Distributions and Their Numerical Evaluation

Global Moran's I and local Moran's I_i are the most commonly used test statistics for spatial autocorrelation in univariate map patterns or in regression residuals. They belong to the general class of ratios of quadratic forms for whom a whole array of approximation techniques has been proposed in the statistical literature, such as the prominent saddlepoint approximation by Offer Lieberman (1994). The saddlepoint approximation outperforms other approximation methods with respect to its accuracy and computational costs. In addition, only the saddlepoint approximation is capable of handling, in analytical terms, reference distributions of Moran's I that are subject to significant underlying spatial processes. The accuracy and computational benefits of the saddlepoint approximation are demonstrated for a set of local Moran's Ii statistics under either the assumption of global spatial independence or subject to an underlying global spatial process. Local Moran's I_i is known to have an excessive kurtosis and thus void the use of the simple approximation methods of its reference distribution. The results demonstrate how well the saddlepoint approximation fits the reference distribution of local Moran's I_i. Furthermore, for local Moran's I_i under the assumption of global spatial independence several algebraic simplifications lead to substantial gains in numerical efficiency. This makes it possible to evaluate local Moran's I_i's significance in large spatial tessellations.     

An Evaluative Technique for Categorical Maps

A method is developed that can be used to evaluate categorical maps quantitatively. The method is based on the conditional probability of the occurrence of a cell state, given the states of its neighbors, i.e., to determine the most likely state of a given cell. A zero-one loss function can then be used to calculate the total number of improbable cell states as well as category-by-category counts. Experiments with the technique show its ability to predict accurately the amount of pseudo random noise that is added to a test array of categorical data.     

Founder effect, drift, and adaptive change in domestic crop use in early Neolithic Europe

We document and quantify a significant reduction in crop diversity in the early central European Neolithic using a large multi-site database of archaeobotantical remains we compiled from published Neolithic sites across southwest Asia and Europe. Two hypotheses are proposed to account for the observed changes: one which claims that the different environmental conditions of central Europe selected for a different set of crop choices and strategies than in use in southeast and Mediterranean Europe; and a null hypothesis that explains the change as a drift process associated with a small founding population that subsequently undergoes rapid expansion. Through an agent-based simulation model, we test the null hypothesis and demonstrate that the drop in diversity exceeds that predicted by a drift process. We conclude by re-evaluating the possible adaptive changes underlying crop use in early Neolithic Europe.     

Local Indicators of Spatial Association—LISA

The capabilities for visualization, rapid data retrieval, and manipulation in geographic information systems (GIS) have created the need for new techniques of exploratory data analysis that focus on the “spatial” aspects of the data. The identification of local patterns of spatial association is an important concern in this respect. In this paper, I outline a new general class of local indicators of spatial association (LISA) and show how they allow for the decomposition of global indicators, such as Moran's I, into the contribution of each observation. The LISA statistics serve two purposes. On one hand, they may be interpreted as indicators of local pockets of nonstationarity, or hot spots, similar to the G_i and G*_i statistics of Getis and Ord (1992). On the other hand, they may be used to assess the influence of individual locations on the magnitude of the global statistic and to identify “outliers,” as in Anselin's Moran scatterplot (1993a). An initial evaluation of the properties of a LISA statistic is carried out for the local Moran, which is applied in a study of the spatial pattern of conflict for African countries and in a number of Monte Carlo simulations.     

The Analysis of Spatial Association by Use of Distance Statistics

Introduced in this paper is a family of statistics, G, that can be used as a measure of spatial association in a number of circumstances. The basic statistic is derived, its properties are identified, and its advantages explained. Several of the G statistics make it possible to evaluate the spatial association of a variable within a specified distance of a single point. A comparison is made between a general G statistic and Moran's I for similar hypothetical and empirical conditions. The empirical work includes studies of sudden infant death syndrome by county in North Carolina and dwelling unit prices in metropolitan San Diego by zip-code districts. Results indicate that G statistics should be used in conjunction with I in order to identify characteristics of patterns not revealed by the I statistic alone and, specifically, the G_i and G_i* statistics enable us to detect local “pockets” of dependence that may not show up when using global statistics.     

Modeling Strategies for Categorical Data: Examples from Housing and Tenure Choice

Models to investigate categorical data can be divided into preprocessing, limited parameterization, and formal logit models. To illustrate the advantages of preprocessing and limited parameterization models they are applied to a data set of tenure and type of housing choice before the data are examined with hierarchical logit and nested logit models. The preprocessing approaches are useful in selecting optimal subsets of independent variables with respect to the dependent variable. The ease of application and interpretation of a limited parameterization approach extends the clarity of the results from the preprocessing approaches. Because some variables are only relevant at specific levels of other independent variables, nonstandard (nested) logit models are necessary to understand the nested relationships.     

Exploring Goodness-of-Fit and Spatial Correlation Using Components of Tango's Index of Spatial Clustering

The ability to detect anomalies such as spatial clustering in data sets plays an important role in spatial data analysis, leading to interest in test statistics identifying patterns exhibiting significant levels of clustering. Toward this end, Tango (1995) proposed a statistic (and its associated distribution under a null hypothesis of no clustering) assessing overall patterns of spatial clustering in a set of observed regional counts. Rogerson (1999) observed that Tango's index may be decomposed into the summation of two distinct statistics, the first mirroring standard tests of goodness-of-fit (GOF), and the second an index of spatial association (SA) similar to Moran's I . In this article, we investigate the effectiveness of Rogerson's expression of Tango's statistic in separating GOF from SA in data sets containing clusters. We simulate data under the null hypothesis of no clustering as well as two alternative hypotheses. The first alternative hypothesis induces a poor fit from the null hypothesis while maintaining independent observations and the second alternative hypothesis induces spatial dependence while maintaining fit. Using Rogerson's decomposition and leukemia incidence data from upstate New York, we show graphically that one is unable to statistically distinguish poor fit from autocorrelation.     

Investigating Global and Local Categorical Map Configuration Comparisons Based on Coincidence Matrices

The simple and intuitive nature of the coincidence matrix has not only made it the current "gold standard" for accuracy assessment (based on a sample of map pixels), but also a common tool for describing difference between two categorical maps (when all pixels are enumerated). It is this latter case of map comparison that this article explores. Coincidence matrices, although providing significant information regarding thematic agreement between two categorical maps (composition), can lack significantly in terms of conveying information about differences or similarities in the spatial arrangement (configuration) of those map categories in geographic space. This article introduces means for distilling the available configuration information from a coincidence matrix while demonstrating some simple categorical map comparisons. Specifically, while the coincidence matrix summarizes per-pixel compositional persistence or change, the introduced technique further quantifies the global and local configurational uncertainty between compared maps. I demonstrate how this quantification of configurational uncertainty can be used to gauge which thematic mismatch types are most significant and how to measure/present local configurational uncertainty in a spatial context. Implementation is through a straightforward mathematical algorithm in R that is illustrated by several examples.     

A Simulation Study to Explore Inference about Global Moran's I with Random Spatial Indexes

Inference procedures for spatial autocorrelation statistics assume that the underlying configurations of spatial units are fixed. However, sometimes this assumption can be disadvantageous, for example, when analyzing social media posts or moving objects. This article examines for the case of point geometries how a change from fixed to random spatial indexes affects inferences about global Moran's I, a popular spatial autocorrelation measure. Homogeneous and inhomogeneous Matérn and Thomas cluster processes are studied and for each of these processes, 10,000 random point patterns are simulated for investigating three aspects that are key in an inferential context: the null distributions of I when the underlying geometries are varied; the effect of the latter on critical values used to reject null hypotheses; and how the presence of point processes affects the statistical power of Moran's I. The results show that point processes affect all three characteristics. Inferences about spatial structure in relevant application contexts may therefore be different from conventional inferences when this additional source of randomness is taken into account.     

Constructing the Spatial Weights Matrix Using a Local Statistic

Spatial weights matrices are necessary elements in most regression models where a representation of spatial structure is needed. We construct a spatial weights matrix, W , based on the principle that spatial structure should be considered in a two‐part framework, those units that evoke a distance effect, and those that do not. Our two‐variable local statistics model (LSM) is based on the G_i* local statistic. The local statistic concept depends on the designation of a critical distance, d_c, defined as the distance beyond which no discernible increase in clustering of high or low values exists. In a series of simulation experiments LSM is compared to well‐known spatial weights matrix specifications—two different contiguity configurations, three different inverse distance formulations, and three semi‐variance models. The simulation experiments are carried out on a random spatial pattern and two types of spatial clustering patterns. The LSM performed best according to the Akaike Information Criterion, a spatial autoregressive coefficient evaluation, and Moran's I tests on residuals. The flexibility inherent in the LSM allows for its favorable performance when compared to the rigidity of the global models.     

Detection of Dietary Changes by Intra-tooth Carbon and Nitrogen Isotopic Analysis: An Experimental Study of Dentine Collagen of Cattle (Bos taurus)

Hypsodont teeth potentially contain a record of dietary or environmental changes occurring during their growth. The aim of our study is to understand how a dietary change is recorded in dentine collagen. Analyses were conducted on five steers (Bos taurus) raised in an experimental farm. From birth until weaning the steers were fed on a C₃diet; after weaning they were fattened on a C₄/C₃mixed diet until slaughter. Dentine collagen was sampled on demineralized molars from top to bottom. The change from the C₃to the C₄/C₃diet and weaning are both reflected in intra-tooth variations in δ¹³C and δ¹⁵N values, respectively. The abrupt change in carbon isotopic composition of the diet is reflected by a progressive change of the dentine collagen δ¹³C values. The gradual change may reflect sampling strategy and/or gradual turnover of the metabolic nutrient pool. The weaning process is reflected by a decrease in δ¹⁵N that exactly coincides with increase in δ¹³C. This demonstrates that when steers are weaned to a protein-poor diet, δ¹⁵N traces the cessation of suckling. Archaeological applications of this study are considered, including determination of the duration of lactation in prehistoric herds, and detection of residential mobility in cattle herders.     

THE EFFECT OF LAND‐USE CONTROLS ON THE SPATIAL SIZE OF U.S. URBANIZED AREAS*

ABSTRACT On a sample of U.S. urbanized areas in 2000, we test theoretical hypotheses of the effect of land‐use controls on the spatial size of urban areas. We find that minimum lot‐size zoning and maximum FAR restrictions expand the urban area, while maximum lot‐size zoning, urban growth boundaries, minimum square footage limits, maximum building permit restrictions, minimum person per room controls, and impact fees contract the urban area. All of these findings are consistent with theoretical predictions although the effect of urban growth boundaries and minimum square footage limits are not statistically significant.     

Stable isotope evidence for dietary and cultural change over the Holocene at the Sabana de Bogotá region,Northern South America

The Sabana de Bogotá in the northern Andes is an interesting region to investigate temporal patterns of dietary variation because it counts with a vast archeological and osteological record for the last 10,000 years. In this paper, stable isotope data of human archeological bone collagen and apatite were used to study the evolution of diet and major subsistence transformations taking place during the Holocene (～9000–600 cal BP). Paleoenvironmental reconstructions and the isotopic ecology of the Sabana de Bogotá were used as an interpretative baseline. Stable isotope measurements (δ¹³C_col, δ¹³C_ap, δ¹⁵N, and Δ¹³C_col-ap) representing hunter-gatherers, horticulturalists, and agriculturalists (N = 134 individuals) were analyzed by using bivariate, regressional, and discriminant statistical techniques. Results show that early Holocene hunter-gatherers (9000–7000 cal BP) consumed mostly C₃ vegetal resources locally available. In contrast, animal protein was less important. Middle Holocene hunter-gatherers (6000–4500 cal BP) continued with the food foraging pattern observed in the earlier counterparts and presented a slight increase in C₃ animal protein intake. During the initial late Holocene ca. 4000 cal BP, important shifts in subsistence strategies occurred when populations presented a trend toward mixed C₃/C₄ diets, and by ca. 3500 cal BP, there is a clear signal of C₄ crops (i.e., maize) consumption concomitant with the introduction of ceramic technology. During the final late Holocene (last 2000 cal years BP), intensive agriculture was adopted and humans presented relatively diverse diets integrated by C₄ and C₃ crops, C₃-C₄ feeding animals, and freshwater resources. Such dietary change coincides with an increase in sociopolitical complexity, population size, and a general decline in health.     

Misconceptions and Complexities in the Study of China's Cities: Definitions,Statistics, and Implications

A noted American authority on urbanization and the household registration system in China reviews and clarifies factors leading to misunderstanding and misconceptions regarding the number of inhabitants of China's major cities. Principal sources of confusion linked to reliance on official statistical sources are the multi-layered meanings of the term "city" and, consequently, simultaneous publication and use of a multitude of official population statistics for the country's "cities." Other complicating factors analyzed by the author include the effects of the Chinese hukou (household registration) system and the rapid rate of urban growth and change over the last three decades. Systematic population and per capita GDP data for the years 2000 and 2005, all based on the multiple boundaries and systems for five major cities (Beijing, Shanghai, Chongqing, Guangzhou, and Shenzhen), are collected to illustrate both the countrywide situation and specific cases. Also included is a critique of several studies and popular accounts of Chinese cities to highlight misstatements and areas of misunderstanding based on inappropriate use of statistical data. Journal of Economic Literature, Classification Numbers: O18, O53, P20, R12. 2 figures, 6 tables, 130 references.     

Guanaco (Lama guanicoe) isotopic ecology in southern South America: spatial and temporal tendencies, and archaeological implications

We synthesize and discuss available isotopic data on Holocene guanaco samples from southern South America, extending from Tierra del Fuego Island to northern Patagonia and the Pampean region. We evaluate temporal and spatial tendencies on the basis of 91 samples (mainly based on δ¹³C_collagen values), presenting implications for paleodietary research in archaeology. We conclude that there are no strong correlations with latitude in the macro-spatial scale, while there is a set of interesting patterns at smaller regional scales. These patterns lead us to evaluate the role of ecologic and topographic variables (e.g. canopy effect, variations in altitude, ecotones) in structuring isotopic variability. Finally, on the basis of the present analysis we suggest a number of hypotheses and perspectives for the use of stable isotopes as geographic tracers of guanaco distribution in the past, and specific implications for the paleodietary study of human samples.     

Illustrating the Phaenomena: Celestial Cartography in Antiquity and the Middle Ages

Abstract

The Ordnance Survey's Boundary Survey, carried out between 1841 and 1888, was a major undertaking which resulted in the local administrative boundaries of the whole of Great Britain being reliably mapped for the first time. This was not achieved by imposition but by the use of local knowledge of boundaries, thus making permanent a communal memory of administrative geography and rendering it globally accessible through maps. The Boundary Survey aided the reform of local government areas, a process which started during the same period and provided derived data for the burgeoning collection of statistics in the nineteenth century.     

Inelastic Displacement Ratios for Seismic Assessment of Structures Subjected to Forward-Directivity Near-Fault Ground Motions

This article presents results of a statistical study focused on evaluating inelastic displacement ratios (i.e., ratio of maximum inelastic displacement with respect to maximum elastic displacement demand) of degrading and non degrading single-degree-of-freedom (SDOF) systems subjected to forward-directivity near-fault ground motions. C_R spectra are computed for normalized periods of vibration with respect to the predominant period of the ground motion to provide a better ground motion characterization. This period normalization allows reducing the record-to-record variability in the estimation of C_R. An equation to obtain estimates of C_R for the seismic assessment of structures exposed to forward-directivity near-fault ground motions is proposed.     

THE PRIORITY OF LARGE CITIES IN ZIPF RANK-SIZE RULE SYSTEMS

The author seeks to establish possible reasons for differences in the rates of growth of towns within urban systems with rank-size regularities. It is shown that a system follows Zipf s law if the growth of population N _i of the towns of the system follows the regularity M(ΔN _i )/N _i ～ (In N _i - c) where M is the mathematical expectation, ΔN _i is an increment of Ni over a short period of time, ～ stands for “directly proportional,” and c is a constant.