Spatial distribution of the active surveillance of sheep scrapie in Great Britain: an exploratory analysis
© Crown copyright; licensee BioMed Central Ltd. 2009
Received: 05 October 2008
Accepted: 16 July 2009
Published: 16 July 2009
This paper explores the spatial distribution of sampling within the active surveillance of sheep scrapie in Great Britain. We investigated the geographic distribution of the birth holdings of sheep sampled for scrapie during 2002 – 2005, including samples taken in abattoir surveys (c. 83,100) and from sheep that died in the field ("fallen stock", c. 14,600). We mapped the birth holdings by county and calculated the sampling rate, defined as the proportion of the holdings in each county sampled by the surveys. The Moran index was used to estimate the global spatial autocorrelation across Great Britain. The contributions of each county to the global Moran index were analysed by a local indicator of spatial autocorrelation (LISA).
The sampling rate differed among counties in both surveys, which affected the distribution of detected cases of scrapie. Within each survey, the county sampling rates in different years were positively correlated during 2002–2005, with the abattoir survey being more strongly autocorrelated through time than the fallen stock survey. In the abattoir survey, spatial indices indicated that sampling rates in neighbouring counties tended to be similar, with few significant contrasts. Sampling rates were strongly correlated with sheep density, being highest in Wales, Southwest England and Northern England. This relationship with sheep density accounted for over 80% of the variation in sampling rate among counties. In the fallen stock survey, sampling rates in neighbouring counties tended to be different, with more statistically significant contrasts. The fallen stock survey also included a larger proportion of holdings providing many samples.
Sampling will continue to be uneven unless action is taken to make it more uniform, if more uniform sampling becomes a target. Alternatively, analyses of scrapie occurrence in these datasets can take account of the distribution of sampling. Combining the surveys only partially reduces uneven sampling. Adjusting the distribution of sampling between abattoirs to reduce the bias in favour of regions with high sheep densities could probably achieve more even sampling. However, any adjustment of sampling should take account of the current understanding of the distribution of scrapie cases, which will be improved by further analysis of this dataset.
Since 2002, the European Union has required that each Member State must test a representative sample of its sheep population to monitor scrapie prevalence . In Great Britain, during the period 2002–2005, this active surveillance on sheep older than 18 months included samples taken in abattoir surveys (AS, c. 132,000)  and from sheep that died in the field (fallen stock (FS), c. 19,600) . These samples are used for surveillance of both classical and atypical scrapie, which are distinct prion diseases of sheep. Classical scrapie has been recorded in Britain for over 200 years, while atypical scrapie was only recently recognized, but has probably existed for a long time . With respect to surveillance, the main difference between the diseases is that sheep with atypical scrapie develop clinical symptoms and die older than sheep with classical scrapie, so that they are more likely to survive to an age at which they are sent to abattoir as mature animals . Of the two surveys, the abattoir survey is closer to a random sample, because selection at abattoirs is potentially random and farmers do not know which, if any of their sheep will be sampled. The fallen stock survey provides a higher proportion of samples positive for classical scrapie .
The Animal Movements Licensing System (AMLS) in England and Wales has recorded all movements of batches of sheep and other animals, including movements from Scotland, since 2001, being kept as a digital database (AMLS2) since 2005. Recent tracing of birth holdings using AMLS2  provided the opportunity to evaluate the "representativeness" attribute of the active component of the scrapie surveillance . Most directly, tracing the holdings of origin allowed evaluation of the spatial distribution of sampling.
There have been several studies of spatial patterns of scrapie reporting and disease in Great Britain [9–12]. All these studies assessed the spatial distribution either on data from postal surveys, which had low spatial resolution, or from the statutory reporting of clinical cases, which had unknown self-reporting bias. The active surveillance data offers high spatial resolution and more opportunities to analyse the distribution of sampling. Spatial analysis of sampling may allow the detection of under-sampling or over-sampling at the spatial unit of choice. Local sampling intensities can also be used to correctly estimate the local prevalence estimates obtained from surveys . Studies in France have already demonstrated that the design and geographic distribution of sampling surveys could bias their results [13, 14].
Although the pitfalls of spatial visualization have long been recognized [15, 16], it is widely acknowledged for its value in exploration and analysis of spatial data . An example is the use of area cartograms, which are particularly well suited to displaying sampling rates and denominator populations together. A cartogram is a map transformed so that regional areas are proportional to a measure of interest (i.e. the number of sheep holdings in a county), rather than actual land area . We used this method to emphasize counties according to their weight in the sheep population, while still making them readily recognizable. A further advantage was that the cartograms could display more information, for example the number of holdings was represented by county area, while sampling rate was displayed by use of colour scales.
Our primary goal was to assess whether sampling in Great Britain was uniformly distributed in space relative to the population of sheep holdings. Uniform sampling rate would contribute to achieving representative sampling as required by European legislation, and would help against failing to detect clusters of infection that coincided with areas with low sampling rate. We achieved this primary goal through visualization, by mapping county sampling rates. Having demonstrated uneven sampling, we made a preliminary spatial analysis to assess overall and local spatial and temporal autocorrelation, and to investigate apparent correlations between sampling rate and sheep density.
We traced birth holdings by comparing flock marks from identity tags of sampled sheep with flock marks recorded against sheep movements in the Animal Movements Licensing System (AMLS2) database in the period January 2005 to February 2006 inclusive. For each movement record, AMLS2 records the flock marks of the sheep being moved and the identity of the holding they are leaving. The birth holding for a flock mark was identified as the holding most frequently recorded as moving off sheep with that flock mark. Comparison of traces known to be reliable from corroborating evidence with traces of unknown reliability allowed definition of criteria by which traces were selected to increase reliability. These criteria were based on the number of departures of a flock tag from the presumed birth holding and the number of departures from other holdings. This technique was called 'shotgun' tracing . Scottish Animal Movement System (SAMS) data was not used because of problems with the availability of flock mark data. This meant that we could not use data on movements wholly within Scotland, which may have reduced tracing of Scottish holdings, but we had the opportunity to check the impact of tracing on the denominator population, as explained below.
We used two sources of denominator data at the holding level. The first was the 2004 June Agricultural Survey of England, Scotland and Wales (referred to here as the 'agricultural survey') and the second was the shotgun tracing. The agricultural survey is probably the most accurate source of holding level data currently available, but involves a degree of sampling and interpolation. The alternative was to use the criteria for selecting traces in the shotgun method to generate a list of all holdings that could be traced as birth holdings of sampled sheep. The list of traceable holdings was the appropriate denominator population, because it included all holdings that might be identified as sampled and no others. To check regional bias introduced by tracing, we compared the number of holdings on the list of traceable holdings against the number in the agricultural survey in each county, by using a scatter plot and calculating their correlation.
Identifying locations for veterinary records and samples is not a trivial problem . From the AMLS database we were able to obtain a county parish holding ID (CPH), with postcode, map reference, or easting and northing coordinates for each traced holding. Usually the location was for a mailbox in a farmhouse associated with a particular group of sheep, so it would be close to the animals, although probably not in the centre of their grazing area. Each location was checked against the parish identified by the first five digits of the CPH. If the location was outside the parish, it was corrected to the parish centroid. Thus every holding was located within the parish and therefore the county identified by its CPH.
Sampled proportions and cartograms
The unit for control of scrapie is the farm or holding, so we focused our analyses on the proportion of holdings sampled within each county (holding sampling rate). The holding sampling rate was the number of holdings sampled in a given county divided by the number of traceable sheep holdings in the county. Sampling rates were calculated for the AS and FS surveys separately, and combined. However, in case sampling was more closely related to the number of sheep in a region, rather than the number of holdings, maps for 2002–2005 were also prepared to show the number of samples from each county as a proportion of the county's adult sheep population. Agricultural survey information was used to provide the denominator population for these maps, because it was the only source for numbers of sheep.
All maps were produced using ArcMap http://www.esri.com. Most maps were cartograms, which were transformed so that the area of each county was proportional to the number of holdings in it, using the CartogramCreator script http://arcscripts.esri.com/, which applies a "rubber sheet" method [20, 21]. The maps of proportions of sheep sampled were also used to display the locations of abattoirs used for sampling, so they were presented as regular land area based maps.
Uneven sample distribution among counties could result from temporary and/or local causes, but broad regional trends that were consistent through time and space might have more impact and be easier to adjust. We therefore assessed whether there was evidence of spatial correlation in sampling between counties across Great Britain and of temporal correlation between years. Because global measures tend to conceal local variation, we also looked for individual counties with significantly high or low sampling rates, taking account of the trend in their neighbourhoods.
where n = the number of counties; = the mean of the sampling rate across all counties; x i , x j = sampling rates in counties i and j respectively; w ij ∈ W = the weighting for the covariance between counties i and j; finally σ(x) = the sampling rate standard deviation.
The weight matrix W defines the neighbourhood structure in accordance with Tobler's First Law  by which measures at locations close to each other will tend to be more similar than measures at distant locations. We set elements of the weight matrix, w ij to be inversely proportional to the distance between the centroids of counties i and j. This weighting avoided assigning islands zero weights because they had no adjacent neighbours, which would have occurred if we had used a common alternative by which elements of the weight matrix would equal one if counties shared a boundary and zero otherwise. In addition, the elements are normalized so that row totals equal one. Our null hypothesis for testing the presence of spatial autocorrelation was that the observed sampling rates were randomly and independently assigned to counties. The expected value of Moran's I, E [I] = -1/(n-1) with I > -1/(n-1) indicating positive and I < indicating negative spatial autocorrelation.
LISA statistics assess local associations by comparing local averages to global averages. The local statistic is large and positive when a county's sampling rate and the sampling rate in its neighbourhood are both substantially above the global average, or when both are substantially below the global average, which are termed "over-sampling" and "under-sampling clusters" respectively. The local Moran statistic is large and negative when a county's sampling rate is substantially above the global average while its neighbourhood's is substantially below average, or vice-versa, suggesting "outliers". Each county's local Moran statistic, I i is an indication of whether it is part of a local cluster or contrast with its neighbours.
Local and global statistics were calculated using Geoda http://www.geoda.uiuc.edu/, an open source spatial analysis system, and visualized on LISA cluster maps using ArcGIS http://www.esri.com. Both were compared to reference distributions that would be expected under the null hypothesis of no spatial correlation, which were generated randomly using Monte-Carlo simulations and a pseudo significance level .
Distribution of sheep
A dilemma in the analysis of the distribution of sampling rates was the distinction between the sampling rate of sheep and the sampling rate of holdings. If sheep were individually selected at random at abattoirs, we would expect higher sampling rates from holdings with many sheep than holdings with few sheep. Therefore our analysis of sampling required consideration of the distribution of sheep as well as holdings. In addition to maps of the holding sampling rate, we mapped the distributions of sheep density and holding size (sheep per holding), as well as the sheep sampling rate. There were three measures of sheep density: areal sheep density (ha-1), holding density (km-2) and holding size (sheep/holding). Although these three measures were likely to be correlated with each other and were algebraically related, they were all identified as being potential factors influencing local sampling rate.
For both the AS and FS surveys, a generalized linear model with logit link was applied using Stata (Stata Corporation Ltd.) to model the number of holdings u i sampled during 2002–2005 in each county i containing w i holdings, as a binomially distributed variable related to the three measures of sheep density. The model was investigating the contribution of sheep density to local sampling rate, not attempting a complete explanation of variations in local sampling rate. Therefore significant deviation from the model fit was expected, so standard errors were scaled using the square root of the deviance-based dispersion. To assess the contribution of sheep density to the observed variance in sampling rate, squared deviations from the GLM model were calculated and compared with squared deviations from a null model that assumed the sampling rate u i /w i was constant.
Number of holdings sampled each year.
# Selected samples
# Distinct holdings1
Samples per holding
Proportions of holdings sampled and case distribution
Correlation matrix for county sampling rates of sheep holdings for the abattoir and fallen stock surveys.
Global Moran I statistics and relative standard deviation (RSD) for the active surveillance programme 2002 – 2005.
Combined FS & AS
Relationship between sampling and sheep distribution
Correlation matrix for county sampling rates and sheep density measures in active surveillance 2002–2005.
AS sample rate
FS sample rate
AS sample rate
FS sample rate
Coefficients from fitting a GLM regression model for sampling rate to three measures related to sheep density.
95% confidence interval
Fallen stock survey
95% confidence interval
-3.05 – -2.20
-3.42 – -1.97
Holding size (sheep)
0.0033 – 0.0059
0.0005 – 0.0043
Sheep density (ha-1)
-0.15 – 0.36
-0.62 – 0.34
Holding density (km-2)
0.62 – 2.22
-2.12 – 0.91
% Deviance from uniform explained
There was clear evidence that sampling of sheep holdings by both the abattoir survey and the fallen stock survey was unevenly distributed. Moreover, this uneven sampling apparently affected the distribution of detected cases of scrapie. Apart from the relatively small fallen stock survey in 2002, both spatial distributions were consistent through the years 2002–2005, so that the same regions continued to be over-sampled or under-sampled each year. Although there was some evidence that sampling rates in the fallen stock survey became more uniform during 2003–2005, it is likely that similar spatial distributions will continue if not actively corrected in sympathy with disease occurrence. The consistent relatively low sampling rates in the South-east may deserve especial attention, given the historically high incidence of scrapie as detected by passive surveillance and postal survey in that part of Britain [12, 28].
Positive global Moran statistics indicated that the abattoir survey sampling was not only uneven, but was spatially autocorrelated at the county level, suggesting broad regional trends. In contrast, there was weaker evidence of spatial correlation at the county level in the fallen stock survey, and sampling by the fallen stock survey could be negatively correlated in neighbouring counties as well as positively correlated, suggesting that factors influencing fallen stock sampling were more local. Combining the two surveys reduced the contrast between heavily sampled counties and lightly sampled counties, but the combined surveys in 2002–2005 still sampled holdings unevenly across Great Britain in a pattern that was consistent between years and spatially autocorrelated.
In the abattoir survey, the variation of holding sampling between counties was strongly related to aspects of sheep distribution, including sheep density, holding density and holding size. The observed strongest regression was with holding density and holding size, whose product is sheep density. The relationship with sheep distribution was so strong that it must have included much of the spatial correlation in sampling among neighbouring counties. The impact of holding size was expected, because the probability that a sheep randomly selected from the British flock comes from a particular holding will be in proportion to the number of sheep in that holding. However, the additional relationship with holding density cannot be so easily explained. Counties with dense sheep populations were sampled disproportionately, so that individual sheep within holdings in those counties were more likely to be sampled than sheep in counties with sparser populations. The dominance of sampling by a small number of large abattoirs may be an important factor, because economies of scale may encourage large abattoirs to source their sheep directly or indirectly from areas with dense animal populations. Large abattoirs were bound to be selected for sampling, because the survey aimed to potentially sample most sheep over 18 months old. This relationship between sampling and animal population distribution may have widespread significance. Variation in local population density is one of the most fundamental characteristics of most national animal populations worldwide, so over-sampling of locally dense populations may be an issue in many surveys that rely on samples taken from pre-existing gathering points, such as abattoirs.
The evidence presented in this study has two applications: to allow interpretation of case distribution taking account of the sample distribution  and to allow design for future sampling, ideally relative to disease occurrence, which would maintain the ability to detect cases as the disease becomes rare. In the latter case, the strong regional trend of the AS would make it easier to adjust its sampling than the FS, which has a much patchier distribution with local contrasts. Del Rio Vilas et al. (2005)  reported a large variation in the number of samples from each holding in the FS, which was not necessarily correlated with holding size, and suggested that sampling could be arbitrary rather than random. The large numbers of submissions from some holdings to the FS may even reflect exploitation of the free disposal scheme of carcasses under the FS. Such exploitation may be diluting the high-risk nature of the surveillance stream and reducing the value of this targeted approach . The AS, on the other hand, appeared to have achieved a better control of the number of samples taken per holding. However, since 2005, the number of fallen stock samples per holding has been restricted as much as possible.
There have been previous attempts to study the representativeness of the active surveillance of scrapie in other countries. In France, Morignat et al. (2006)  simulated the effects of three biases, namely the lack of random sampling at the abattoir, the presence of spatial heterogeneity in the sampling rate and the use of different diagnostic tests, to assess their impact on the surveillance results. The latter two accounted for significant differences in their results, indicating their importance in the design of the sampling. Lynn et al. (2007)  conducted an evaluation of the active scrapie surveillance in the U.S. Spatial unevenness was also evident in their study with large disparities in the sampling proportion between states, but they claimed that the representativeness of their surveillance appeared in general to be fair, although the basis of this evaluation was unclear. They suggested further analysis to define more accurately the adequacy of sampling.
One issue in this present study was the potential impact on the sampling distribution of the nearly 40% of the AS samples and about 25% of the FS samples that could not be traced. A higher proportion of FS samples were traced for several reasons. Their collection locations, which were likely to be their birth locations as well, were known, staff collecting FS had more training and time for recording data than staff at abattoirs, and most FS were collected in 2004 and 2005, when recording standards had improved. Comparison with numbers of holdings recorded in each county by the agricultural survey showed that tracing from Shetland, the Western Isles and Highland was poor, but that tracing from other counties was relatively uniform. Using the traceable holdings as the denominator population partly compensated for remaining differences in tracing between counties.
We went beyond cartographic presentation by testing for evidence of spatial correlation among the sampling rates of neighbouring counties. Within the spatial analysis presented here, Moran's I, as a global measure, was adequate to demonstrate the presence of spatial autocorrelation in the abattoir survey, which distinguished its geographic distribution from the distribution of the fallen stock survey. However, the local LISA measures were also useful in identifying local patterns in the fallen stock survey, while confirming that there were few exceptions to the broad regional trends in the abattoir survey. The weak spatial autocorrelation in the fallen stock survey at the county level, despite the differences in sampling between counties, suggests that further spatial structure could be revealed by spatial analysis at a finer resolution.
A full understanding of the corrections required in the surveys must depend on some understanding of the distribution of scrapie cases. For example, the importance of under-sampling of small flocks due to sampling bias strongly depends on whether sheep in small flocks are more or less likely to have scrapie than sheep in larger flocks. These first steps to identifying the sample distribution have given us the opportunity to investigate such issues, adding to our understanding of the disease epidemiology as well as its surveillance.
Visualizing the distribution of holdings sampled in the scrapie surveys demonstrated their unevenness at the county level, and that the distribution of sampling differed between the two surveys. The distribution of sampling was positively correlated from year to year, suggesting that uneven sampling will continue unless actively corrected. An alternative to correcting uneven sampling is to take account of the distribution of sampling when analysing survey results, now that we have the information. Combining the two surveys reduced the difference between the most heavily sampled counties and the most lightly sampled counties, but levels of sampling still differed substantially between counties. A large proportion of holdings providing many samples was an issue with the fallen stock survey, which will affect its effectiveness for scrapie surveillance. Initial spatial analysis at the coarse, county level indicated significant spatial autocorrelation of sampling in the abattoir survey. Abattoir survey sampling was strongly positively related to parameters of sheep distribution, including sheep density, holding density and numbers of sheep per holding, so that sheep in counties with high sheep densities were more likely to be sampled. We suggest that this positively density-dependent sampling may be caused by most samples coming from a few, large abattoirs. Modifying the distribution of sampling between abattoirs appears to be the most practicable option to achieve more uniform sampling, so the next step will be more detailed analysis of abattoir catchments.
This research was funded by the Department for Environment, Food and Rural Affairs (Defra) under project SE0243.
- Anon: Commission Regulation (EC) No 1248/2001. Official Journal of the European Communities. 2001, L 173: 12-22.Google Scholar
- Elliott H, Gubbins S, Ryan J, Ryder S, Tongue S, Watkins G, Wilesmith JW: Prevalence of scrapie in sheep in Great Britain estimated from abattoir surveys during 2002 and 2003. The Veterinary Record. 2005, 157: 418-419.View ArticlePubMedGoogle Scholar
- Del Rio Vilas VJ, Ryan J, Elliott HG, Tongue SC, Wilesmith JW: Prevalence of scrapie in sheep: results from fallen stock surveys in Great Britain in 2002 and 2003. The Veterinary Record. 2005, 157: 744-745.View ArticlePubMedGoogle Scholar
- Green DM, Del Rio Vilas VJ, Birch CPD, Johnson J, Kiss IZ, McCarthy ND, Kao RR: Demographic risk factors for classical and atypical scrapie in Great Britain. Journal of General Virology. 2007, 88: 3486-3492.PubMed CentralView ArticlePubMedGoogle Scholar
- McIntyre KM, Del Rio Vilas VJ, Gubbins S: No temporal trends in the prevalence of atypical scrapie in British sheep, 2002–2006. BMC Vet Res. 2008, 4: 13.PubMed CentralView ArticlePubMedGoogle Scholar
- Del Rio Vilas V, Hopp P, Nunes T, Ru G, Sivam K, Ortiz-Pelaez A: Explaining the heterogeneous scrapie surveillance figures across Europe: a meta-regression approach. BMC Veterinary Research. 2007, 3: 13PubMed CentralView ArticlePubMedGoogle Scholar
- Birch CPD, Del Rio Vilas VJ, McDonald R, Chikukwa AC: The distribution of sheep sampled for scrapie in Great Britain. Proceedings of Prion 2006: Strategies, advances and trends towards protection of society: 4–6 October 2006, Torino, Italy. 2006, 52-[http://www.neuroprion.org/resources/pdf_docs/conferences/prion2006/abstract_book.pdf]Google Scholar
- Romaguera RA, German R, Klaucke D: Evaluating Public Health Surveillance. Principles and Practice of Public Health Surveillance. 2nd edition. Edited by: Teutsch SM, Churchill RM. New York: Oxford University Press; 2000:176-194.Google Scholar
- McLean AR, Hoek A, Hoinville LJ, Gravenor MB: Scrapie transmission in Britain: a recipe for a mathematical model. Proceedings of the Royal Society of London B Biological Sciences. 1999, 266: 2531-2538.View ArticleGoogle Scholar
- Hoinville LJ, Hoek A, Gravenor MB, McLean AR: Descriptive epidemiology of scrapie in Great Britain: results of a postal survey. The Veterinary Record. 2000, 146: 455-46.View ArticlePubMedGoogle Scholar
- Sivam SK, Baylis M, Gravenor MB, Gubbins S: Descriptive analysis of the results of an anonymous postal survey of the occurrence of scrapie in Great Britain in 2002. The Veterinary Record. 2006, 158: 501-506.View ArticlePubMedGoogle Scholar
- Del Rio Vilas VJ, Guitian J, Pfeiffer DU, Wilesmith JW: Analysis of data from the passive surveillance of scrapie in Great Britain between 1993 and 2002. The Veterinary Record. 2006, 159: 799-804.PubMedGoogle Scholar
- Ducrot C, Roy P, Morignat E, Baron T, Calavas D: How the surveillance system may bias the results of analytical epidemiological studies on BSE prevalence among dairy versus beef suckler cattle breeds in France. Veterinary Research. 2003, 34: 185-192.View ArticlePubMedGoogle Scholar
- Morignat E, Cazeau G, Biacage AG, Vinard JL, Bencsik A, Madec JY, Ducrot C, Baron T, Calavas D: Estimates of the prevalence of transmissible spongiform encephalopathies in sheep and goats in France in 2002. The Veterinary Record. 2006, 158: 683-687.View ArticlePubMedGoogle Scholar
- Monmonier M: How to Lie with Maps. Chicago: University of Chicago Press; 1991.Google Scholar
- Plaisant C: The Challenges of Information visualization evaluation. Proceedings of the Conference on Advanced Visual Interfaces: 25 – 28 May 2004; Gallipoli. Edited by: Costabile MF. ACM Press; 2004:109-116.View ArticleGoogle Scholar
- Andrienko N, Andrienko G: Exploratory Analysis of Spatial and Temporal Data – A Systematic Approach. Berlin: Springer-Verlag; 2005.Google Scholar
- Dorling D: Area Cartograms: Their Use and Creation. Concepts and Techniques in Modern Geography (CATMOG). 1996, 59: 1-69.Google Scholar
- Durr PA, Froggatt AE: How best to geo-reference farms? A case study from Cornwall, England. Preventive Veterinary Medicine. 2002, 56: 51-62.View ArticlePubMedGoogle Scholar
- Dougenik JA, Chrisman NR, Niemeyer DR: An algorithm to construct continuous area cartograms. Professional Geographer. 1985, 37: 75-81.View ArticleGoogle Scholar
- Wolf EB: Creating contiguous cartograms in ArcGIS 9. proceedings of 25th Annual ESRI International Users Conference, 25–29. 2005, [http://gis.esri.com/library/userconf/proc05/papers/pap1155.pdf]July ; San DiegoGoogle Scholar
- Moran PA: Notes on continuous stochastic phenomena. Biometrika. 1950, 37: 17-23.View ArticlePubMedGoogle Scholar
- Tobler WR: A computer movie simulating urban growth in the Detroit region. Economic Geography. 1970, 46: 234-240.View ArticleGoogle Scholar
- Fotheringham AS, Brunsdon C, Charlton M: Quantitative Geography: Perspectives on Spatial Data Analysis. London: SAGE; 2000.Google Scholar
- Ping JL, Green CJ, Zatman RE, Bronson KF: Exploring spatial dependence of cotton yield using global and local autocorrelation statistics. Field Crops Research. 2004, 89: 219-236.View ArticleGoogle Scholar
- Anselin L: Local Indicators of Spatial Association – LISA. Geographic Analysis. 1995, 27: 93-115.View ArticleGoogle Scholar
- Anselin L: Computing environments for spatial data analysis. Journal of Geographical Systems. 2000, 2: 201-220.View ArticleGoogle Scholar
- McIntyre KM, Gubbins S, Sivam SK, Baylis M: Flock-level risk factors for scrapie in Great Britain: analysis of a 2002 anonymous postal survey. BMC Veterinary Research. 2006, 2: 25.PubMed CentralView ArticlePubMedGoogle Scholar
- Lynn TJ, Grannisa M, Williams K, Millera E, Bush , Bruntza S: An evaluation of scrapie surveillance in the United States. Preventive Veterinary Medicine. 2007, 81: 70-79.View ArticlePubMedGoogle Scholar
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