Detecting autocorrelation problems from GPS collar data in livestock studies

Uneven use of grasslands and savannas by livestock has a significant impact on ecosystem productivity, biodiversity, and function. In studies of livestock distribution, global positioning systems (GPS) collars are frequently used and the rapid rate of technological improvement has brought new opportunities to collect extremely large amounts of very accurate spatial information. However, these advances also pose statistical challenges associated with the analysis of large, temporally correlated, datasets. Our main goal was to find the optimal sampling time intervals for GPS collar schedules when studying livestock distribution in semi-arid ecosystems. The schedule must provide maximum spatio-temporal information while avoiding problems of autocorrelation of sequential locations to provide a methodology that is both practical and statistically valid. We used GPS collar data collected in the Southwestern region of the United States. In each study cattle were tracked and data were recorded every 5 min. Location information from the 5-min GPS fixes were subsampled into 10, 20, 30, 60, 90, 120, 150, 180, 240, 300, 360, and 420-min regular intervals. We calculated the Euclidean distance between pairs of successive locations then conducted correlation analyses to determine the degree of similarity between successive traveled distances. We then selected two correlated and two non-correlated time-interval datasets to compare estimates of kernel home range and minimum convex polygon areas. Successive Euclidean distances between GPS locations were significantly correlated when time intervals were <120 min. The calculated distance traveled was significantly reduced as time intervals between successive locations increased. Kernel home range values were smaller in correlated than in non-correlated datasets yet minimum convex polygon values were greater in correlated data than in non-correlated data sets. Our study shows the importance of considering different livestock sampling time intervals using GPS to achieve accurate and meaningful results on animal distributions especially in semi-arid ecosystems. Circumstances in which researchers may elect to use short-time interval autocorrelated data sets are also discussed.     

A radar-Doppler autocorrelation analysis of insect activity

ABSTRACT. A novel actograph is described which utilizes radar-Doppler methods to monitor continuously the activity of one or a group of insects. By means of autocorrelation analysis of the output of the radar-Doppler detector changes in the rate of movement can be followed. Components of the activity of an individual insect such as flight and walking can also be distinguished using radar-Doppler autocorrelation. Some applications of this method are illustrated in experiments on the following species: Periplaneta americana L., Musca domestica L., Calliphora erythrocephala Mg., Drosophila melanogaster Mg.     

The nature and context of exploratory experimentation: an introduction to three case studies of exploratory research

My aim in this article is to introduce readers to the topic of exploratory experimentation and briefly explain how the three articles that follow, by Richard Burian, Kevin Elliott, and Maureen O'Malley, advance our understanding of the nature and significance of exploratory research. I suggest that the distinction between exploratory and theory-driven experimentation is multidimensional and that some of the dimensions are continuums. I point out that exploratory experiments are typically theory-informed even if they are not theory-driven. I also distinguish between research programs and experiments. Research programs that are largely exploratory, such as the ones discussed in these case studies, can involve both exploratory and theory-driven experimentation.     

Evaluating spatial autocorrelation and depletion in pitfall-trap studies of environmental gradients

Studies of environmental gradients like edge effects commonly employ designs where samples are collected at unequal distances within transects. This approach risks confounding species patterns caused by the environmental gradient with patterns resulting from the spatial arrangement of the sampling scheme. Spatial autocorrelation and depletion (reduced catch) have the potential to influence pitfall-trap collections of invertebrates. Readily available control data from a study of edge and riparian effects on forest litter beetles was used to assess autocorrelation and depletion effects. Data from control transects distant from the treatment transects located at habitat edges and streams were screened to determine whether the study design (pitfall traps at varying distances within transects) was imposing patterns on the data attributable to differential autocorrelation or depletion. Autocorrelation in species composition and assemblage structure was not detected within the 99 m transects. The abundance and species richness of beetles were not lower where traps were in closer proximity, indicating that the transect design was not causing measurable depletion or resulting in differential trap catch. These findings indicate that spatial autocorrelation and depletion are unlikely to impair further analyses of edge and riparian effects on litter beetles.     

Iterative kriging for removing spatial autocorrelation in analysis of forest genetic trials

Conventional analysis of spatially correlated data in inadequately blocked field genetic trials may give erroneous results that would seriously affect breeding decisions. Forest genetic trials are commonly very large and strongly heterogeneous, so adjustments for micro-environmental heterogeneity become indispensable. This study explores the use of geostatistics to account for the spatial autocorrelation in four Pinus pinaster Ait. progeny trials established on hilly and irregular terrains with a randomized complete block design and large blocks. Data of five different traits assessed at age 8 were adjusted using an iterative method based on semivariograms and kriging, and the effects on estimates of variance components, heritability, and family effects were evaluated in relation to conventional analysis. Almost all studied traits showed nonrandom spatial structures. Therefore, after the adjustments for spatial autocorrelation, the block and family × block variance components, which were extremely high in the conventional analysis, almost disappeared. The reduction of the interaction variance was recovered by the family variance component, resulting in higher heritability estimates. The removal of the spatial autocorrelation also affected the estimation of family effects, resulting in important changes in family ranks after the spatial adjustments. Comparison among families was also greatly improved due to higher accuracy of the family effect estimations. The analysis improvement was larger for growth traits, which showed the strongest spatial heterogeneity, but was also evident for other traits such as straightness or number of whorls. The present paper demonstrates how spatial autocorrelation can drastically affect the analysis of forest genetic trials with large blocks. The iterative kriging procedure presented in this paper is a promising tool to account for this spatial heterogeneity.     

An exploratory analysis of multiple mutation spectra

The last decade has witnessed a remarkable increase in the number of mutations identified both in human disease-related genes and mutation reporter genes including those in mammalian cells and transgenic animals. This has led to the curation of a number of computerised databases, which make mutation data freely available for analysis. A primary interest of both the clinical researcher and the genetic toxicologist is determination of location and types of mutation within a gene of interest. Collections of mutation data observed for a disease-related gene or, for a gene exposed to a particular chemical, permits discovery of regions of sequence along the gene prone to mutagenesis and may provide clues to the origin of a mutation. The principal tool for visualising the distribution pattern of mutant data along a gene is the mutation spectrum: the distribution and frequency of mutations along a nucleotide sequence. In genetic toxicology, the current wealth of mutation data available allows us to construct many mutation spectra of interest to investigate the mutagenic mechanisms and mutational sites for one or a group of mutagens. Using the multivariate statistical methods principal components analysis (PCA) and cluster analysis (CA) we have tested the ability of these methods to establish the underlying patterns within and between 60 UV-induced, mitomycin C-induced and spontaneous mutations in the supF gene. The spectra were derived from human, monkey and mouse cells including both repair efficient and repair deficient cell lines. We demonstrate and support the successful application of multivariate statistical methods for exploring large sets of mutation spectra to reveal underlying patterns, groupings and similarities. The methods clearly demonstrate how different patterns of spontaneous and UV-induced supF mutation spectra can result from variation in plasmid, culture medium, species origin of cell line and whether mutations arose in vivo or in vitro.     

VIS-O-BAC: exploratory visualization of functional genome studies from bacteria

SUMMARY: The visualization-aided exploration of complex datasets will allow the research community to formulate novel functional hypotheses leading to a better understanding of biological processes at all levels. Therefore, we have developed a web resource termed VIS-O-BAC designed for the functional investigation of expression data for model systems, such as bacterial pathogens based on a graphical display. Genome-scale datasets derived from typical 'omic' approaches can directly be explored with respect to three biologically relevant aspects, the genome structure (operon organization), the organization of genes in pathways (KEGG) and the gene function with Gene Ontology (GO) terms. The integrated viewers can be used in parallel and combine expression data and functional annotations from different external data repositories. The graphical visualizations evidently accelerate both the validation of regulatory information and the detection of affected biological processes. AVAILABILITY: http://leger2.gbf.de/cgi-bin/vis-o-bac.pl. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.     

Multivariate exploratory tools for microarray data analysis

The ultimate success of microarray technology in basic and applied biological sciences depends critically on the development of statistical methods for gene expression data analysis. The most widely used tests for differential expression of genes are essentially univariate. Such tests disregard the multidimensional structure of microarray data. Multivariate methods are needed to utilize the information hidden in gene interactions and hence to provide more powerful and biologically meaningful methods for finding subsets of differentially expressed genes. The objective of this paper is to develop methods of multidimensional search for biologically significant genes, considering expression signals as mutually dependent random variables. To attain these ends, we consider the utility of a pertinent distance between random vectors and its empirical counterpart constructed from gene expression data. The distance furnishes exploratory procedures aimed at finding a target subset of differentially expressed genes. To determine the size of the target subset, we resort to successive elimination of smaller subsets resulting from each step of a random search algorithm based on maximization of the proposed distance. Different stopping rules associated with this procedure are evaluated. The usefulness of the proposed approach is illustrated with an application to the analysis of two sets of gene expression data.     

Study of xylem pressure potential daily dynamics by means of autocorrelation analysis

The xylem pressure potential (Ψ_xylem) of the leaves ofQuercus cerris, Acer campestre andCarpinus betulus was measured under anticyclonic weather types. The autocorrelation analysis revealed the daily course of the Ψ_xylem values approaching the stationary random process. A close statistical relation was found between the results obtained in three successive measurements of the Ψ_xylem (interval 2 h). A close statistical relation also between the value of the base potential (Ψ_b) measured at dawn and the actual values of the Ψ_xylem allowed the prediction of the Ψ_xylem values on the base of the known Ψ_b-values by means of a simple linear regression model.     

Prediction of protein helix content from an autocorrelation analysis of sequence hydrophobicities

It is demonstrated that protein α-helix content can be predicted from an autocorrelation analysis of the protein hydrophobicity sequence. The Fourier transform of the autocorrelation function yields the spectral densities or weights of the various frequencies contributing to the autocorrelation function. Using sequence and secondary structure data from more than 160 proteins and domains, a linear relationship was found between spectral density at periodicity 3.7 and protein α-helix content (r = 0.83). This relation permits prediction of the helix content (x) of proteins of known sequence to within ± 15%, i.e., as (x ± 15)%. Predictions based on the autocorrelation procedure are compared with values obtained by other methods.     

The statistical implications of autocorrelation for detection in environmental health assessment

Many environmental health and risk assessment techniques and models aim at estimating the fluctuations of selected biological endpoints through the time domain as a means of assessing changes in the environment or the probability of a particular measurement level occurring. In either case, estimates of the sample variance and mean of the sample variance are crucial to making appropriate statistical inferences. The commonly employed statistical techniques for estimating both measures presume the data were generated by a covariance stationary process. In such cases, the observations are treated as independently and identically distributed and classical statistical testing methods are applied. However, if the assumption of covariance stationarity is violated, the resulting sample variance and variance of the sample mean estimates are biased. The bias compromises statistical testing procedures by increasing the probability of detecting significance in tests of mean and variance differences. This can lead to inappropriate decisions being made about the severity of environmental damage. Accordingly, it is argued that data sets be examined for correlation in the time domain and appropriate adjustments be made to the required estimators before they are used in statistical hypothesis testing. Only then can credible and scientifically defensible decisions be made by environmental decision makers and regulators.     

Discovery of protein phosphorylation motifs through exploratory data analysis

Background

The need for efficient algorithms to uncover biologically relevant phosphorylation motifs has become very important with rapid expansion of the proteomic sequence database along with a plethora of new information on phosphorylation sites. Here we present a novel unsupervised method, called Motif Finder (in short, F-Motif) for identification of phosphorylation motifs. F-Motif uses clustering of sequence information represented by numerical features that exploit the statistical information hidden in some foreground data. Furthermore, these identified motifs are then filtered to find “actual” motifs with statistically significant motif scores.

Results and Discussion

We have applied F-Motif to several new and existing data sets and compared its performance with two well known state-of-the-art methods. In almost all cases F-Motif could identify all statistically significant motifs extracted by the state-of-the-art methods. More importantly, in addition to this, F-Motif uncovers several novel motifs. We have demonstrated using clues from the literature that most of these new motifs discovered by F-Motif are indeed novel. We have also found some interesting phenomena. For example, for CK2 kinase, the conserved sites appear only on the right side of S. However, for CDK kinase, the adjacent site on the right of S is conserved with residue P. In addition, three different encoding methods, including a novel position contrast matrix (PCM) and the simplest binary coding, are used and the ability of F-motif to discover motifs remains quite robust with respect to encoding schemes.

Conclusions

An iterative algorithm proposed here uses exploratory data analysis to discover motifs from phosphorylated data. The effectiveness of F-Motif has been demonstrated using several real data sets as well as using a synthetic data set. The method is quite general in nature and can be used to find other types of motifs also. We have also provided a server for F-Motif at http://f-motif.classcloud.org/, http://bio.classcloud.org/f-motif/ or http://ymu.classcloud.org/f-motif/.     

Automatic analysis of the spectra of extracellular proteins based on their autocorrelation characteristics

Hardware and software for the automatic comparison of densitograms, based on the evaluation of their autocorrelation characteristics, can be used for establishing the characteristics of circulating staphylococcal populations and for their epidemiological marking.     

Spatial autocorrelation analysis allows disentangling the balance between neutral and niche processes in metacommunities

One of the most popular approaches for investigating the roles of niche and neutral processes driving metacommunity patterns consists of partitioning variation in species data into environmental and spatial components. The logic is that the distance decay of similarity in communities is expected under neutral models. However, because environmental variation is often spatially structured, the decay could also be attributed to environmental factors that are missing from the analysis. Here, we use a spatial autocorrelation analysis protocol, previously developed to detect isolation‐by‐distance in allele frequencies, to evaluate patterns of species abundances under neutral dynamics. We show that this protocol can be linked with variation partitioning analyses. Moreover, in an attempt to test the neutral model, we derive three predictions to be applied both to original species abundances and to abundances predicted by a pure spatial model species abundances will be uncorrelated; Moran's I correlograms will reveal similar short‐distance autocorrelation patterns; an increasing degree of non‐neutrality will tend to generate patterns of correlation among abundances within groups of species with similar correlograms (i.e. within species with neutral and non‐neutral dynamics). We illustrate our protocol by analyzing spatial patterns in abundance of 28 terrestrially breeding anuran species from Central Amazonia. We recommend that researchers should investigate spatial autocorrelation patterns of abundances predicted by pure spatial models to identify similar patterns of spatial autocorrelation at short distances and lack of correlation between species abundances. Therefore, the hypothesis that spatial patterns in abundances are primarily due to pure neutral dynamics (rather than to missing spatiallystructured environmental factors) can be confirmed after taking environmental variables into account.     

Detecting clinal and balanced selection using spatial autocorrelation analysis under kin-structured migration

Recently spatial autocorrelation has been employed to infer microevolutionary processes from patterns of genetic variation. In theory, different processes should show characteristic signature correlograms; e. g., clinal selection should produce correlograms decreasing from positive to negative autocorrelation, whereas uniform balanced selection should lead to no spatial autocorrelation. The ability of a statistical method such as spatial autocorrelation analysis to distinguish between these selective regimes or even to detect departures from neutrality is dependent on the strength of the evolutionary force and the population structure. Weak selection or migration will not be apparent against the expected background of stochastic noise. Moreover, the population structure may generate sufficient stochastic variation such that even strong evolutionary forces may fail to be detected. This study uses computer simulation to examine the effects of kin-structured migration and three different selective regimes on the shape of spatial correlograms to assess the ability of this technique to detect different microevolutionary processes. Genetic variation among 8 loci is simulated in a linear set of 25 artificial populations. Kin-structured stepping-stone migration among adjacent populations is modeled; directional, balanced, and clinal selection, as well as neutral loci are considered. These experiments show that strong selection produces correlograms of the predicted shape. However, with an anthropologically reasonable population structure, considerable stochastic variation among correlograms for different alleles may still exist. This suggests the need for caution in inferring genetic process from spatial patterns. © 1994 Wiley-Liss, Inc.     

Spatial autocorrelation of ecological phenomena

Ecological variables often fluctuate synchronously over wide geographical areas, a phenomenon known as spatial autocorrelation or spatial synchrony. Development of statistical approaches designed to test for spatial autocorrelation combined with the increasing accessibility of long-term, large-scale ecological datasets are now making it possible to document the patterns and understand the causes of spatial synchrony at scales that were previously intractable. These developments promise to foster significant future advances in understanding population regulation, metapopulation dynamics and other areas of population ecology.     

An evaluation of three statistics of structured exploratory data analysis

The power of structured exploratory data analysis (SEDA) to discriminate among major genic, polygenic, and nongenetic determination of phenotypes was investigated using computer simulation. Three classes of SEDA indices (the major gene index, the offspring between parents function, and the midparent-child correlation coefficient) were evaluated. These three statistics, in combination, were reasonably sensitive in detecting the presence of a major locus and in discriminating between phenotypes with genetic effects and those with no genetic component. However, they were unable to discriminate between major genic and polygenically determined phenotypic models.