Spatial Autocorrelation Structure Research Articles

大気環境における構造用鋼材の腐食表面性状とその経時性予測

Many severe corrosion damages have been observed in steel structures constructed in a period of high economic growth. To ensure the safety of such structures, it is important to devise a method how corrosion develops in the service. In our research, semi-variogram analyses were carried out on time-dependent corrosion surfaces of unpainted steel plates exposed to atmospheric environment in order to quantitatively clarify the spatial autocorrelation structures and their time-dependence. In addition, by using the spatial statistics and an ordinary kriging technique, numerical simulation for the time-dependent corrosion surfaces in atmospheric environments was proposed and the validity was confirmed by comparing with corrosion surfaces obtained in various exposure fields.

A Bayesian localized conditional autoregressive model for estimating the health effects of air pollution

Estimation of the long-term health effects of air pollution is a challenging task, especially when modeling spatial small-area disease incidence data in an ecological study design. The challenge comes from the unobserved underlying spatial autocorrelation structure in these data, which is accounted for using random effects modeled by a globally smooth conditional autoregressive model. These smooth random effects confound the effects of air pollution, which are also globally smooth. To avoid this collinearity a Bayesian localized conditional autoregressive model is developed for the random effects. This localized model is flexible spatially, in the sense that it is not only able to model areas of spatial smoothness, but also it is able to capture step changes in the random effects surface. This methodological development allows us to improve the estimation performance of the covariate effects, compared to using traditional conditional auto-regressive models. These results are established using a simulation study, and are then illustrated with our motivating study on air pollution and respiratory ill health in Greater Glasgow, Scotland in 2011. The model shows substantial health effects of particulate matter air pollution and nitrogen dioxide, whose effects have been consistently attenuated by the currently available globally smooth models.

Development and comparative evaluation of a stochastic analog method to downscale daily GCM precipitation

Abstract. There are a number of statistical techniques that downscale coarse climate information from general circulation models (GCMs). However, many of them do not reproduce the small-scale spatial variability of precipitation exhibited by the observed meteorological data, which is an important factor for predicting hydrologic response to climatic forcing. In this study a new downscaling technique (Bias-Correction and Stochastic Analog method; BCSA) was developed to produce stochastic realizations of bias-corrected daily GCM precipitation fields that preserve both the spatial autocorrelation structure of observed daily precipitation sequences and the observed temporal frequency distribution of daily rainfall over space. We used the BCSA method to downscale 4 different daily GCM precipitation predictions from 1961 to 1999 over the state of Florida, and compared the skill of the method to results obtained with the commonly used bias-correction and spatial disaggregation (BCSD) approach, a modified version of BCSD which reverses the order of spatial disaggregation and bias-correction (SDBC), and the bias-correction and constructed analog (BCCA) method. Spatial and temporal statistics, transition probabilities, wet/dry spell lengths, spatial correlation indices, and variograms for wet (June through September) and dry (October through May) seasons were calculated for each method. Results showed that (1) BCCA underestimated mean daily precipitation for both wet and dry seasons while the BCSD, SDBC and BCSA methods accurately reproduced these characteristics, (2) the BCSD and BCCA methods underestimated temporal variability of daily precipitation and thus did not reproduce daily precipitation standard deviations, transition probabilities or wet/dry spell lengths as well as the SDBC and BCSA methods, and (3) the BCSD, BCCA and SDBC methods underestimated spatial variability in daily precipitation resulting in underprediction of spatial variance and overprediction of spatial correlation, whereas the new stochastic technique (BCSA) replicated observed spatial statistics for both the wet and dry seasons. This study underscores the need to carefully select a downscaling method that reproduces all precipitation characteristics important for the hydrologic system under consideration if local hydrologic impacts of climate variability and change are going to be reasonably predicted. For low-relief, rainfall-dominated watersheds, where reproducing small-scale spatiotemporal precipitation variability is important, the BCSA method is recommended for use over the BCSD, BCCA, or SDBC methods.

Genetic inference of epiphytic orchid colonization; it may only take one

Colonization of vacant habitat is a fundamental ecological process that affects the ability of species to persist and undergo range modifications in continually shifting landscapes. Thus, understanding factors that affect and limit colonization has important ecological and conservation implications. Epiphytic orchids are increasingly threatened by various factors, including anthropogenic habitat disturbance. As cleared areas (e.g. pastures) are recolonized by suitable host trees, the establishment and genetic composition of epiphytic orchid populations are likely a function of their colonization patterns. We used genetic analyses to infer the prevailing colonization pattern of the epiphytic orchid, Brassavola nodosa. Samples from three populations (i.e. individuals within a tree) from each of five pastures in the dry forest of Costa Rica were genotyped with neutral nuclear and chloroplast markers. Spatial autocorrelation and hierarchical genetic structure analyses were used to assess the relatedness of individuals within populations, among populations within pastures and among populations in different pastures. The results showed significant relatedness within populations (mean r=0.166) and significant but lower relatedness among populations within a pasture (mean r=0.058). Our data suggest that colonization of available habitats is by few individuals with subsequent population expansion resulting from in situ reproduction, and that individuals within a tree are not a random sample of the regional seed pool. Furthermore, populations within a pasture were likely colonized by seeds produced by founders of a neighbouring population within that pasture. These results have important ramifications for understanding conservation measures needed for this species and other epiphytic orchids.

지구통계학적 기법에 의한 강원폐광부지 중금속의 공간적 분포 양상 예측 연구

This study was performed to evaluate the spatial distribution of heavy metals using principal component analysis and Ordinary Kriging technique in the Gangwon Mine site. In the soils from the sub soil, the contents of Zn and Ni in the PC1 were gradually dispersed from south to north direction, while the components of Cd and Hg in the PC2 showed an increase significantly from middle-south area in the Gangwon Mine site. According to the cluster analysis, pollutant metals of As and Cu were presented a strong spatial autocorrelation structure in cluster D. The concentration of As was 0.83mg/kg and shown to increase from the south to north direction. The spatial distribution maps of the soil components using geostatistical method might be important in future soil remediation studies and help decision-makers assess the potential health risk affects of the abandoned mining sites.

Characterization of ambient air pollution measurement error in a time-series health study using a geostatistical simulation approach

In recent years, geostatistical modeling has been used to inform air pollution health studies. In this study, distributions of daily ambient concentrations were modeled over space and time for 12 air pollutants. Simulated pollutant fields were produced for a 6-year time period over the 20-county metropolitan Atlanta area using the Stanford Geostatistical Modeling Software (SGeMS). These simulations incorporate the temporal and spatial autocorrelation structure of ambient pollutants, as well as season and day-of-week temporal and spatial trends; these fields were considered to be the true ambient pollutant fields for the purposes of the simulations that followed. Simulated monitor data at the locations of actual monitors were then generated that contain error representative of instrument imprecision. From the simulated monitor data, four exposure metrics were calculated: central monitor and unweighted, population-weighted, and area-weighted averages. For each metric, the amount and type of error relative to the simulated pollutant fields are characterized and the impact of error on an epidemiologic time-series analysis is predicted. The amount of error, as indicated by a lack of spatial autocorrelation, is greater for primary pollutants than for secondary pollutants and is only moderately reduced by averaging across monitors; more error will result in less statistical power in the epidemiologic analysis. The type of error, as indicated by the correlations of error with the monitor data and with the true ambient concentration, varies with exposure metric, with error in the central monitor metric more of the classical type (i.e., independent of the monitor data) and error in the spatial average metrics more of the Berkson type (i.e., independent of the true ambient concentration). Error type will affect the bias in the health risk estimate, with bias toward the null and away from the null predicted depending on the exposure metric; population-weighting yielded the least bias.

Infant mortality in Brazil, 1980-2000: a spatial panel data analysis.

BackgroundInfant mortality is an important measure of human development, related to the level of welfare of a society. In order to inform public policy, various studies have tried to identify the factors that influence, at an aggregated level, infant mortality. The objective of this paper is to analyze the regional pattern of infant mortality in Brazil, evaluating the effect of infrastructure, socio-economic, and demographic variables to understand its distribution across the country.MethodsRegressions including socio-economic and living conditions variables are conducted in a structure of panel data. More specifically, a spatial panel data model with fixed effects and a spatial error autocorrelation structure is used to help to solve spatial dependence problems. The use of a spatial modeling approach takes into account the potential presence of spillovers between neighboring spatial units. The spatial units considered are Minimum Comparable Areas, defined to provide a consistent definition across Census years. Data are drawn from the 1980, 1991 and 2000 Census of Brazil, and from data collected by the Ministry of Health (DATASUS). In order to identify the influence of health care infrastructure, variables related to the number of public and private hospitals are included.ResultsThe results indicate that the panel model with spatial effects provides the best fit to the data. The analysis confirms that the provision of health care infrastructure and social policy measures (e.g. improving education attainment) are linked to reduced rates of infant mortality. An original finding concerns the role of spatial effects in the analysis of IMR. Spillover effects associated with health infrastructure and water and sanitation facilities imply that there are regional benefits beyond the unit of analysis.ConclusionsA spatial modeling approach is important to produce reliable estimates in the analysis of panel IMR data. Substantively, this paper contributes to our understanding of the physical and social factors that influence IMR in the case of a developing country.

The Effects of Spatial Patterns in Low Resolution Thematic Maps on Geostatistical Downscaling

This paper investigates the effects of spatial autocorrelation structures in low resolution data on downscaling without ground measurements or secondary data, as well as the potential of geostatistical downscaling. An advanced geostatistical downscaling scheme applied in this paper consists of two analytical steps: the estimation of the point-support spatial autocorrelation structure by variogram deconvolution and the application of area-to-point kriging. Point kriging of block data without variogram deconvolution is also applied for a comparison purpose. Experiments using two low resolution thematic maps derived from remote sensing data showing very different spatial patterns are carried out to discuss the objectives. From the experiments, it is demonstrated that the advanced geostatistical downscaling scheme can generate the downscaling results that well preserve overall patterns of original low resolution data and also satisfy the coherence property, regardless of spatial patterns in input low resolution data. Point kriging of block data can produce the downscaling result compatible to that by area-to-point kriging when the spatial continuity in block data is strong. If heterogeneous local variations are dominant in input block data, the treatment of the low resolution data as point data cannot generate the reliable downscaling result, and this simplification should not be applied to donwscaling.

Interpreting Spatial Patterns: An Inquiry Into Formal and Cognitive Aspects of Tobler's First Law of Geography

The characterization, identification, and understanding of spatial patterns are central concerns of geography. Deeply rooted in the notion that geographic location matters, one testable assumption is that near things are more related than distant things—a concept often referred to as Tobler's first law of geography. One means of quantifying this assumption is using measures of spatial autocorrelation. Several such measures have been developed to test whether a pattern is indeed clustered, or dispersed, or whether it is, from a statistical perspective, random. To shed light on how spatial patterns are understood from a cognitive perspective, this article reports results from studies of spatial pattern interpretation represented in maps. For the purpose of experimental validation, we used a two-color map. We systematically varied the ratio of the colors as well as the level of significance of clustering and dispersion; we targeted two groups: experts and nonexperts. The task for both experts and nonexperts was to sort patterns according to five specified categories of spatial autocorrelation structures. The results show clearly that patterns are understood on the basis of the dominant color, by both experts and nonexperts. A third experiment, using a free classification paradigm, confirmed the dominance of the color effect. These results are important, as they point to critical aspects of pattern perception and understanding that need to be addressed from the perspective of spatial thinking, especially how people relate concepts of randomness with spatial patterns (represented in maps).

Spatial-temporal disease mapping of illicit drug abuse or dependence in the presence of misaligned ZIP codes

Geo-referenced data often are collected in small, administrative units such as census enumeration districts or postal code areas. Such areas vary in geographic area and population size and may change over time. In research into drug-related health issues within the United States, U.S. Postal Service ZIP codes represent a commonly used unit for data collection, storage, and spatial analysis because of their widespread availability in health databases through patient contact and billing information. However, the ZIP code was developed for the specific purpose of delivering mail and may be changed at any time, and its design and development does not take into consideration problems that may arise in data collection, analysis, and presentation in health studies. In this paper, we propose a spatial hierarchical modeling approach to quantify trends within ZIP-code based counts when some fraction of ZIP codes change over the study period, that is, when the data are spatially misaligned across time. We propose a data vector approach and adjust the spatial auto-correlation structure within our Bayesian hierarchical model to provide inference for our misaligned data. We motivate and illustrate our approach to explore spatio-temporal patterns of amphetamine abuse and/or dependence in Tracy, California over the years 1995-2005. Uncertainty associated with misaligned data is modeled, quantified, and visualized. The approach offers a framework for further investigation into other risk factors in order to more fully understand the dynamics of illicit drug abuse or dependence across time and space in imperfectly measured data.

Permeability in the Mushy Zone

When modeled at macroscopic length scales, the complex dendritic network in the solid-plus-liquid region of a solidifying alloy (the “mushy zone”) has been modeled as a continuum based on the theory of porous media. The most important property of a porous medium is its permeability, which relates the macroscopic pressure gradient to the throughput of fluid flow. Knowledge of the permeability of the mushy zone as a function of the local volume-fraction of liquid and other morphological parameters is thus essential to successfully modeling the flow of interdendritic liquid during alloy solidification. In current continuum models, the permeability of the mushy zone is given as a deterministic function of (1) the local volume fraction of liquid and (2) a characteristic length scale such as the primary dendrite arm spacing or the reciprocal of the specific surface area of the solid-liquid interface. Here we first provide a broad overview of the experimental data, mesoscale numerical flow simulations, and resulting correlations for the deterministic permeability of both equiaxed and columnar mushy zones. A extended view of permeability in mushy zones which includes the stochastic nature of permeability is discussed. This viewpoint is the result of performing extensive numerical simulations of creeping flow through random microstructures. The permeabilities obtained from these simulations are random functions with spatial autocorrelation structures, and variations in the local permeability are shown to have dramatic effects on the flow patterns observed in such microstructures. Specifically, it is found that “lightning-like” patterns emerge in the fluid velocity and that the flows in such geometries are strongly sensitive to small variations in the solid structure. We conclude with a comparison of deterministic and stochastic permeabilities which suggests the importance of incorporating stochastic descriptions of the permeability of the mushy zone in solidification modeling.

Estimating commercial property prices: an application of cokriging with housing prices as ancillary information

A vast majority of the recent literature on spatial hedonic analysis has been concerned with residential property values, with only very few examples of studies focused on commercial property prices. The dearth of studies can be attributed to some of the challenges faced in the analysis of commercial properties, in particular the scarcity of information compared to residential transactions. In order to address this issue, in this paper we propose the use of cokriging and housing prices as ancillary information to estimate commercial property prices. Cokriging takes into account the spatial autocorrelation structure of property prices, and the use of more abundant information on housing prices helps to improve the accuracy of property value estimates. A case study of Toledo in Spain, a city for which commercial activity stemming from tourism is one of the key elements of the economy in the city, demonstrates that substantial accuracy and precision gains can be obtained from the use of cokriging.

A geostatistical approach for the stock assessment of the edible sea urchin, Paracentrotus lividus, in four coastal zones of Southern and West Sardinia (SW Italy, Mediterranean Sea)

Quantitative surveys of the edible sea urchin, Paracentrotus lividus, were conducted in four fishing zones of Sardinia (Southern Italy, Mediterranean Sea), in Autumn 2007. A total of 120 stations were geo-located along a bathymetric gradient ranging from 0 to 10 m. A geostatistical method was used to evaluate spatial patterns in density and to estimate harvestable stocks. Variographic analyses showed that the isotropic Gaussian and spherical models successfully explained the spatial structure of sea urchin assemblages in these areas. Density maps obtained by punctual kriging showed that sea urchin populations tend to be patchy rather than uniform in their density distribution. A combination of mapping and size categories was used to generate diverse scenarios of harvestable stocks (specimens ≥50 mm in diameter) before the start of the current fishing season. We conclude that the geostatistical approach, which takes into consideration the spatial autocorrelation structure of the populations in small areas, seems to be a good estimator of P. lividus density and biomass and for the assessment of its harvestable stocks, and thus provides an initial step towards a scientific approach to the management of local sea urchin fisheries.

Spatial autocorrelation and statistical tests: Some solutions

Spatial dependence or spatial autocorrelation often occurs in ecological data and can be a serious problem in analysis, affecting the significance rates of statistical tests, making them too liberal when the dependence is positive. Ecological phenomena often are patchy and give data with a wave structure, producing autocorrelation that cycles between positive and negative with increasing distance, further complicating the situation. This article describes the essentials of dealing with this problem as commonly encountered in analyzing ecological data for two variables. We investigated two related approaches to correcting statistical tests for data with spatial autocorrelation from one-dimensional sampling schemes like the transects used in plant ecology, the example of interest here. Both approaches estimate the “effective sample size” based on the observed autocorrelation structures of the variables. We examined tests of correlation and bivariate goodness-of-fit tests, as well as extensions beyond both of these test classes. The correction methods prove to be robust for a wide range of spatial autocorrelation structures in one-dimensional data and provide reliable corrections in most cases. They fail only when the data have strong and consistent waves that cause persistent cycles in the autocorrelation as a function of distance. By examining the spatial autocorrelation structure of the ecological data, we can predict the likelihood of successful correction for these bivariate tests.

Spatial Behavior of Phosphorus and Nitrogen in a Subtropical Wetland

Complex spatial patterns of biogeochemical properties such as soils are generated in wetlands as a result of internal cycling of nutrients, natural forcing functions (e.g., hydrologic flow paths), and anthropogenic impacts (e.g., nutrient inputs). To preserve ecosystem health and the functions of a wetland ecosystem, it is critical to maintain a soil nutrient status that resembles natural reference conditions and to preserve biogeochemical variability. We investigated the spatial behavior of total P (TP) and total N (TN) in a subtropical wetland in Florida that historically has been impacted by nutrient influx. Our specific objectives were to: (i) assess the spatial autocorrelation structure and spatial variability of TP and TN across a subtropical wetland given a dense observation set (n = 266); and (ii) assess the information loss associated with underlying spatial autocorrelations and spatial variability in TP and TN under various scenarios of reduced sampling densities (n = 175–50). Both properties showed contrasting spatial metrics with long spatial autocorrelations for TP (7240 m) and much shorter ones for TN (1007 m). The contrasting spatial metrics of TP and TN along trajectories of sparser observation sets translated into different responses in spatial patterns that disintegrated dramatically for TN and less so for TP when compared with the reference set (n = 266). In this subtropical wetland, a sampling set of n > 75 (0.036 samples ha−1) for TP and n > 125 (0.0260 samples ha−1) for TN yielded satisfactory results to resemble spatial patterns of the reference set. This study provided insight into the spatial behavior and patterns of two important soil nutrients in wetlands.

Pollen dispersal and genetic structure of the tropical tree Dipteryx panamensis in a fragmented Costa Rican landscape

In the face of widespread deforestation, the conservation of rainforest trees relies increasingly on their ability to maintain reproductive processes in fragmented landscapes. Here, we analysed nine microsatellite loci for 218 adults and 325 progeny of the tree Dipteryx panamensis in Costa Rica. Pollen dispersal distances, genetic diversity, genetic structure and spatial autocorrelation were determined for populations in four habitats: continuous forest, forest fragments, pastures adjacent to fragments and isolated pastures. We predicted longer but less frequent pollen movements among increasingly isolated trees. This pattern would lead to lower outcrossing rates for pasture trees, as well as lower genetic diversity and increased structure and spatial autocorrelation among their progeny. Results generally followed these expectations, with the shortest pollen dispersal among continuous forest trees (240 m), moderate distances for fragment (343 m) and adjacent pasture (317 m) populations, and distances of up to 2.3 km in isolated pastures (mean: 557 m). Variance around pollen dispersal estimates also increased with fragmentation, suggesting altered pollination conditions. Outcrossing rates were lower for pasture trees and we found greater spatial autocorrelation and genetic structure among their progeny, as well as a trend towards lower heterozygosity. Paternal reproductive dominance, the pollen contributions from individual fathers, did not vary among habitats, but we did document asymmetric pollen flow between pasture and adjacent fragment populations. We conclude that long-distance pollen dispersal helps maintain gene flow for D. panamensis in this fragmented landscape, but pasture and isolated pasture populations are still at risk of long-term genetic erosion.

Spatial models for inferring topographic controls on historical low-severity fire in the eastern Cascade Range of Washington, USA

Fire regimes are complex systems that represent an aggregate of spatial and temporal events whose statistical properties are scale dependent. Despite the breadth of research regarding the spatial controls on fire regime variability, few datasets are available with sufficient resolution to test spatially explicit hypotheses. We used a spatially distributed network of georeferenced fire-scarred trees to investigate the spatial structure of fire occurrence at multiple scales. Mantel’s tests and geostatistical analysis of fire-occurrence time series led to inferences about the mechanisms that generated spatial patterns of historical fire synchrony (multiple trees recording fire in a single year) in eastern Washington, USA. The spatial autocorrelation structure of historical fire regimes varied within and among sites, with clearer patterns in the complex rugged terrain of the Cascade Range than in more open and rolling terrain further north and east. Results illustrate that the statistical spatial characteristics of fire regimes change with landform characteristics within a forest type, suggesting that simple relationships between fire frequency, fire synchrony, and forest type do not exist. Quantifying the spatial structures in fire occurrence associated with topographic variation showed that fire regime variability depends on both landscape structure and the scale of measurement. Spatially explicit fire-scar data open new possibilities for analysis and interpretation, potentially informing the design and application of fire management on landscapes, including hazardous fuel treatments and the use of fire for ecosystem restoration.

Type and spatial structure of distribution data and the perceived determinants of geographical gradients in ecology: the species richness of African birds

ABSTRACTAim Studies exploring the determinants of geographical gradients in the occurrence of species or their traits obtain data by: (1) overlaying species range maps; (2) mapping survey‐based species counts; or (3) superimposing models of individual species’ distributions. These data types have different spatial characteristics. We investigated whether these differences influence conclusions regarding postulated determinants of species richness patterns.Location Our study examined terrestrial bird diversity patterns in 13 nations of southern and eastern Africa, spanning temperate to tropical climates.Methods Four species richness maps were compiled based on range maps, field‐derived bird atlas data, logistic and autologistic distribution models. Ordinary and spatial regression models served to examine how well each of five hypotheses predicted patterns in each map. These hypotheses propose productivity, temperature, the heat–water balance, habitat heterogeneity and climatic stability as the predominant determinants of species richness.Results The four richness maps portrayed broadly similar geographical patterns but, due to the nature of underlying data types, exhibited marked differences in spatial autocorrelation structure. These differences in spatial structure emerged as important in determining which hypothesis appeared most capable of explaining each map's patterns. This was true even when regressions accounted for spurious effects of spatial autocorrelation. Each richness map, therefore, identified a different hypothesis as the most likely cause of broad‐scale gradients in species diversity.Main conclusions Because the ‘true’ spatial structure of species richness patterns remains elusive, firm conclusions regarding their underlying environmental drivers remain difficult. More broadly, our findings suggest that care should be taken to interpret putative determinants of large‐scale ecological gradients in light of the type and spatial characteristics of the underlying data. Indeed, closer scrutiny of these underlying data — here the distributions of individual species — and their environmental associations may offer important insights into the ultimate causes of observed broad‐scale patterns.

Spatial patterns of kangaroo density across the South Australian pastoral zone over 26 years: aggregation during drought and suggestions of long distance movement

Summary Wildlife surveys usually focus on estimating population size, and management actions such as commercial harvesting, culling and poison baiting are referenced commonly to population size alone, without taking into account the way in which those animals are distributed. This paper outlines how point‐based aerial survey data can be converted to continuous density surfaces using spatial analysis techniques. Using this approach, we describe and explore the spatial patterns of density of two species of kangaroos in an area exceeding 200 000 km2 in South Australia over a 26‐year period. Densities of red and western grey kangaroos were estimated in 2 km2 segments along aerial survey transect lines, yielding point density estimates. Universal kriging provided an unbiased interpolation of these data using the spatial autocorrelation structure described by the semi‐variogram. The Getis statistic identified clusters of high and low kangaroo density. Considerable year‐to‐year variation in the spatial patterns of kangaroo density was observed. In many cases, annual rates of increase over large areas were too high to be explained by vital rates alone, implying immigration from surrounding areas. These large shifts in distribution were occasionally to areas that had received better rainfall than the surrounding areas. For both species, there was no obvious local spatial autocorrelation pattern or clustering of kangaroo density beyond that described by average density and the present set of management regions, suggesting the latter are appropriate divisions for harvest management. Data for both species fitted the power law relationship extremely well. During dry times, red kangaroos, but not western grey kangaroos, were more aggregated, supporting past ground observations at a fine spatial scale. Synthesis and applications. Kriged density surfaces enable estimation of kangaroo density on individual properties, which are the management units at which harvest quotas or culling approvals are allocated. These estimates will be marked improvements over systematic sampling estimates when sampling intensity is low. Predictions of shifts in kangaroo distribution using rainfall or satellite imagery will allow more accurate allocation of harvest quotas. Similarly, predictions of more even kangaroo dispersion following high rainfall will allow managers to anticipate downturns in harvest rate.

Genetic Mapping of Developmental Instability: Design, Model and Algorithm

Developmental instability or noise, defined as the phenotypic imprecision of an organism in the face of internal or external stochastic disturbances, has been thought to play an important role in shaping evolutionary processes and patterns. The genetic studies of developmental instability have been based on fluctuating asymmetry (FA) that measures random differences between the left and the right sides of bilateral traits. In this article, we frame an experimental design characterized by a spatial autocorrelation structure for determining the genetic control of developmental instability for those traits that cannot be bilaterally measured. This design allows the residual environmental variance of a quantitative trait to be dissolved into two components due to permanent and random environmental factors. The degree of developmental instability is quantified by the relative proportion of the random residual variance to the total residual variance. We formulate a mixture model to estimate and test the genetic effects of quantitative trait loci (QTL) on the developmental instability of the trait. The genetic parameters including the QTL position, the QTL effects, and spatial autocorrelations are estimated by implementing the EM algorithm within the mixture model framework. Simulation studies were performed to investigate the statistical behavior of the model. A live example for poplar trees was used to map the QTL that control root length growth and its developmental instability from cuttings in water culture.