Inferences from fluctuations in the local variogram about the assumption of stationarity in the variance

Geostatistics is commonly used to describe and predict the variation of soil properties over the landscape. However, many geostatistical methods require the assumption that our observed data are a realization of a random function which is intrinsically stationarity. Under stationarity, observations of a single realization of the random function at different positions can be treated as a form of replication. There are various ways in which a random function may breach the assumption of intrinsic stationarity and numerous geostatistical techniques have been developed that are able to cope with some forms of non-stationarity. What is currently needed is a set of diagnostic tools capable of detecting and identifying when data cannot plausibly be treated as a realization of a process which is stationary in the variance.In this paper, we propose an inferential method that can identify when stationarity in the variance cannot plausibly be assumed. The basis of our approach is to obtain a model for the random function under the assumption of intrinsic stationarity. If the global dataset can be regarded as a realization of a Gaussian process (perhaps after transformation), then the global variogram is sufficient for this purpose. By using a window-based method to locally estimate variograms, we can define some statistic of homogeneity of the sample variation of the data. This allows us to obtain a sample distribution for this statistic, under the null hypothesis of intrinsic stationarity, by generating multiple realizations of the postulation random function at the original sample points using Monte Carlo methods and recomputing the statistic for each realization. We selected as statistics the interquartile ranges of: i) the spatial dependence ratio (s), the proportion c₁ / (c₀ + c₁), ii) a distance parameter (a), which is the maximum lag over which the random function is autocorrelated for variograms like the spherical, and iii) the local variances (v; c₀ + c₁), where (c₀) is the nugget component and (c₁) the spatially structured component. We demonstrated this method using data from the large scale sampling (n = 1341 over 8248 km²) of the Florida Everglades, United States.     

Airborne radiometric survey data and a DTM as covariates for regional scale mapping of soil organic carbon across Northern Ireland

Soil scientists require cost-effective methods to make accurate regional predictions of soil organic carbon (SOC) content. We assess the suitability of airborne radiometric data and digital elevation data as covariates to improve the precision of predictions of SOC from an intensive survey in Northern Ireland. Radiometric data (K band) and, to a lesser extent, altitude are shown to increase the precision of SOC predictions when they are included in linear mixed models of SOC variation. However the statistical distribution of SOC in Northern Ireland is bimodal and therefore unsuitable for geostatistical analysis unless the two peaks can be accounted for by the fixed effects in the linear mixed models. The upper peak in the distribution is due to areas of peat soils. This problem may be partly countered if soil maps are used to classify areas of Northern Ireland according to their expected SOC content and then different models are fitted to each of these classes. Here we divide the soil in Northern Ireland into three classes, namely mineral, organo-mineral and peat. This leads to a further increase in the precision of SOC predictions and the median square error is 2.2 %². However a substantial number of our observations appear to be mis-classified and therefore the mean squared error in the predictions is larger (30.6 %²) since it is dominated by large errors due to mis-classification. Further improvement in SOC prediction may therefore be possible if better delineation between areas of large SOC (peat) and small SOC (non-peat) could be achieved.     

Non-homogeneity of variance components from spatially nested sampling of the soil

Spatially nested sampling and the associated nested analysis of variance by spatial scale is a well-established methodology for the exploratory investigation of soil variation over multiple, disparate scales. The variance components that can be estimated this way can be accumulated to approximate the variogram. This allows us to identify the important scales of variation, and the general form of the spatial dependence, in order to plan more detailed sampling by design-based or model-based methods. Implicit in the standard analyses of nested sample data is the assumption of homogeneity in the variance, i.e. that all variations from sub-station means at some scale represent a random variable of uniform variance. If this assumption fails then the comparable assumption of stationarity in the variance, which is an important assumption in geostatistics, will also be implausible. However, data from nested sampling may be analysed with a linear mixed model in which the variance components are parameters which can be estimated by residual maximum likelihood (REML). Within this framework it is possible to propose an alternative variance parameterization in which the variance depends on some auxiliary variable, and so is not generally homogeneous. In this paper we demonstrate this approach, using data from nested sampling of chemical and biogeochemical soil properties across a region in central England, and use land use as our auxiliary variable to model non-homogeneous variance components. We show how the REML analysis allows us to make inferences about the need for a non-homogeneous model. Variances of soil pH and cation exchange capacity at different scales differ between these land uses, but a homogeneous variance model is preferable to such non-homogeneous models for the variance of soil urease activity at standard concentrations of urea.     

Ectopic hepatocellular carcinoma in a dog

CASE HISTORY: A 14-year-old neutered male Bearded Collie was presented with a history of recurrent, intermittent urinary incontinence of 7 years duration.

CLINICAL FINDINGS: A large, firm, non-painful mass was found in the mid-abdominal region on palpation. Ultrasonography of the mass revealed a compartmentalised structure with mixed echogenicity, and which did not appear to be associated with any of the abdominal organs. Ultrasound-guided fine needle aspirates contained several clusters of epithelial cells with cytological features of hepatocytes. At exploratory laparotomy, the mass was found in the gastrosplenic ligament within the greater omentum.

PATHOLOGICAL FINDINGS AND DIAGNOSIS: Histopathologically, the mass consisted of sheets of hepatocytes, but without the characteristic hepatic architecture. The cells showed moderate variation in nuclear size and were sometimes binucle- ate. A diagnosis of hepatocellular carcinoma (HCC) in the mesentery was made.

CLINICAL RELEVANCE: The presence of ectopic hepatic tissue has been reported rarely in man and cats, but not in the dog. Neoplastic transformation of ectopic hepatic tissue is seen in man. This is the first report of the presentation, clinical findings and treatment of a dog with ectopic HCC.     

Safety of temperature sensitive mutant Mycoplasma gallisepticum vaccine

A temperature sensitive (ts) vaccine strain designated ts-11 was selected after exposure of a low passage culture of the immunogenic Australian field isolate (strain 80083) of Mycoplasma gallisepticum to 100 mg/ml of N-methyl-N-nitro-N-nitrosoguanidine. Viable counts (assayed as colour changing units (CCU)/25 microliters) of a thawed stock culture of ts-11 were typically log10 3 to log10 5 higher when incubated at 33 degrees C (the permissive temperature) than duplicate viable counts incubated at 39.5 degrees C (the restrictive temperature). Doses of approximately 2 x 10(7) CCU of ts-11 caused no gross lesions or loss of egg production when inoculated into the air sacs of susceptible chickens and no clinical or pathological signs of sinusitis when inoculated into the infraorbital sinuses of susceptible turkey poults, whereas the parent strain 80083 was demonstrably pathogenic. However, 1 of 10 poults inoculated intra-abdominally with approximately 2 x 10(7) CCU of ts-11 did show signs of mild airsacculitis. Eight-week-old pullets were vaccinated by eye drop with up to 1.4 x 10(7) CCU of ts-11 and simultaneously subjected to several stressful management practices, without apparent ill effects. Administration by coarse aerosol of 5 ml of ts-11 vaccine/25 day-old broilers, with or without 25 doses of infectious bronchitis virus vaccine caused no obvious signs of respiratory disease. The non virulent ts phenotype was maintained after 3 passages of strain ts-11 in chickens. Chickens vaccinated 3 weeks previously with ts-11 or with strain 80083 were placed in contact with susceptible chickens for a period of 2 weeks.(ABSTRACT TRUNCATED AT 250 WORDS)