Imaging platforms for generating highly multiplexed histological images are being continually developed and improved. Significant improvements have also been made in the accuracy of methods for automated cell segmentation and classification. However, less attention has focused on the quantification and analysis of the resulting point clouds, which describe the spatial coordinates of individual cells. We focus here on a particular spatial statistical method, the cross-pair correlation function (cross-PCF), which can identify positive and negative spatial correlation between cells across a range of length scales. However, limitations of the cross-PCF hinder its widespread application to multiplexed histology. For example, it can only consider relations between pairs of cells, and cells must be classified using discrete categorical labels (rather than labeling continuous labels such as stain intensity). In this paper, we present three extensions to the cross-PCF which address these limitations and permit more detailed analysis of multiplex images: topographical correlation maps can visualize local clustering and exclusion between cells; neighbourhood correlation functions can identify colocalization of two or more cell types; and weighted-PCFs describe spatial correlation between points with continuous (rather than discrete) labels. We apply the extended PCFs to synthetic and biological datasets in order to demonstrate the insight that they can generate.

Generators of space-time dynamics in bioimaging have become essential to build ground truth datasets for image processing algorithm evaluation such as biomolecule detectors and trackers, as well as to generate training datasets for deep learning algorithms. In this contribution, we leverage a stochastic model, called birth-death-move (BDM) point process, in order to generate joint dynamics of biomolecules in cells. This particle-based stochastic simulation method is very flexible and can be seen as a generalization of well-established standard particle-based generators. In comparison, our approach allows us: (1) to model a system of particles in motion, possibly in interaction, that can each possibly switch from a motion regime (e.g., Brownian) to another (e.g., a directed motion); (2) to take into account finely the appearance over time of new trajectories and their disappearance, these events possibly depending on the cell regions but also on the current spatial configuration of all existing particles. This flexibility enables to generate more realistic dynamics than standard particle-based simulation procedures, by for example accounting for the colocalization phenomena often observed between intracellular vesicles. We explain how to specify all characteristics of a BDM model, with many practical examples that are relevant for bioimaging applications. As an illustration, based on real fluorescence microscopy datasets, we finally calibrate our model to mimic the joint dynamics of Langerin and Rab11 proteins near the plasma membrane, including the well-known colocalization occurrence between these two types of vesicles. We show that the resulting synthetic sequences exhibit comparable features as those observed in real microscopy image sequences.

Helminthiases are a class of neglected tropical diseases that affect at least 1 billion people worldwide, with a disproportionate impact on resource-poor areas with limited disease surveillance. Geospatial methods can offer valuable insights into the burden of these infections, particularly given that many are subject to strong ecological influences on the environmental, vector-borne or zoonotic stages of their life cycle. In this study, we screened 6829 abstracts and analysed 485 studies that use maps to document, infer or predict transmission patterns for over 200 species of parasitic worms. We found that quantitative mapping methods are increasingly used in medical parasitology, drawing on One Health surveillance data from the community scale to model geographic distributions and burdens up to the regional or global scale. However, we found that the vast majority of the human helminthiases may be entirely unmapped, with research effort focused disproportionately on a half-dozen infections that are targeted by mass drug administration programmes. Entire regions were also surprisingly under-represented in the literature, particularly southern Asia and the Neotropics. We conclude by proposing a shortlist of possible priorities for future research, including several neglected helminthiases with a burden that may be underestimated.

The Strait of Sicily in the middle of the Mediterranean Sea is considered a crossroads between the western and the eastern basins for species immigrating from the Atlantic Ocean and Lessepsian species. Among the latter, the African sailfin flyingfish Parexocoetus mento was recently collected from Lampedusa Island in November 2017, and represents the first documented record in Italian waters. In this paper, the morphological and meristic characteristics of this specimen are reported and discussed, compared with the other species of the genus Parexocoetus. Furthermore, as mapping and monitoring the distribution of invasive species is crucial to understanding their establishment and spread and then to manage the invasion process, the occurrences distribution of P. mento in the Mediterranean Sea was studied. The application of GIS-based spatial statistics allowed to identify significant clustering areas and dispersion areas of the species, summarizing the key characteristics, and underlining directional trends of distribution. GIS analysis identified two similar groups of records (1935/1966 and 1986/2017 time period), showing a change of distribution spatial pattern over time. An earlier spread direction in the Mediterranean east coast and a settled area of P. mento were found. The analysis also includes the specimen caught in Italian waters.

Archaeologists have struggled to combine remotely sensed datasets with preexisting information for landscape-level analyses. In the American Southeast, for example, analyses of lidar data using automated feature extraction algorithms have led to the identification of over 40 potential new pre-European-contact Native American shell ring deposits in Beaufort County, South Carolina. Such datasets are vital for understanding settlement distributions, yet a comprehensive assessment requires remotely sensed and previously surveyed archaeological data. Here, we use legacy data and airborne lidar-derived information to conduct a series of point pattern analyses using spatial models that we designed to assess the factors that best explain the location of shell rings. The results reveal that ring deposit locations are highly clustered and best explained through a combination of environmental conditions such as distance to water and elevation as well as social factors.

Localized network processes are central to the study of political science, whether in the formation of political coalitions and voting blocs, balancing and bandwagoning, policy learning, imitation, diffusion, tipping-point dynamics, or cascade effects. These types of processes are not easily modeled using traditional network approaches, which focus on global rather than local structures within networks. We show that localized network processes, in which network edges form in response to the formation of other edges, are best modeled by shifting from the traditional theoretical framework of nodes-as-actors to what we term a nodes-as-actions framework, which allows for zeroing in on relationships among network connections. We show that the proposed theoretical framework is statistically compatible with a local structure graph model (LSGM). We demonstrate the properties of LSGMs using a Monte Carlo experiment and explore action–reaction processes in two empirical applications: formation of alliances among countries and legislative cosponsorships in the US Senate.

Bush encroachment has serious consequences on ecosystem functioning through alteration of species composition and ecosystem productivity. However, little is known regarding the spatial patterning of invading shrubs in semi-arid savannas. Cartesian coordinates of two invading woody species (Vachellia karroo and V. nilotica), were recorded in a 20 × 20-m plot on a grassland at Matopos research station, south-west Zimbabwe. We recorded a total of 308 plants including both saplings and shrubs from the two study plant species. Second-order spatial statistics was applied in order to understand the spatial pattern of encroaching plants. We predicted that the encroaching plants would be spatially aggregated because of facilitation that occurs in harsh environmental conditions. Consistent with our predictions, the two species were aggregated, with no evidence of inter- and intra specific species competition. This study demonstrates that encroaching trees in semi-arid savanna generally do not show self organization during early growth stages.

Geostatistical methods were used to describe and map nonrandom distribution and variation (standard deviation) of shoot density and root growth across a well-established patch of Canada thistle, a perennial weed. Semivariogram functions and kriging, an interpolation method, were used to prepare isoarithmic contour maps and associated error maps. Maps consisted of interpolated contours of uniform weed density and other measured or calculated regionalized variables between measured X-Y control points, as well as maps of error (standard deviation) associated with contour estimation. Mapped regions of greatest shoot density across a patch not only had the greatest underlying root biomass and, often, greatest density of adventitious root buds, but also had more deeply growing root biomass.

This research was aimed at understanding how far and how fast glyphosate-resistant (GR) Palmer amaranth will spread in cotton and the consequences associated with allowing a single plant to escape control. Specifically, research was conducted to determine the collective impact of seed dispersal agents on the in-field expansion of GR Palmer amaranth, and any resulting yield reductions in an enhanced GR cotton system where glyphosate was solely used for weed control. Introduction of 20,000 GR Palmer amaranth seed into a 1-m2 circle in February 2008 was used to represent survival through maturity of a single GR female Palmer amaranth escape from the 2007 growing season. The experiment was conducted in four different cotton fields (0.53 to 0.77 ha in size) with no history of Palmer amaranth infestation. In the subsequent year, Palmer amaranth was located as far as 114 m downslope, creating a separate patch. It is believed that rainwater dispersed the seeds from the original area of introduction. In less than 2 yr after introduction, GR Palmer amaranth expanded to the boundaries of all fields, infesting over 20% of the total field area. Spatial regression estimates indicated that no yield penalty was associated with Palmer amaranth density the first year after introduction, which is not surprising since only 0.56% of the field area was infested with GR Palmer amaranth in 2008. Lint yield reductions as high as 17 kg ha−1 were observed 2 yr after the introduction (in 2009). Three years after the introduction (2010), Palmer amaranth infested 95 to 100% of the area in all fields, resulting in complete crop loss since it was impossible to harvest the crop. These results indicate that resistance management options such as a “zero-tolerance threshold” should be used in managing or mitigating the spread of GR Palmer amaranth. This research demonstrates the need for proactive resistance management.

The distributions of parasitic diseases are determined by complex factors, including many that are distributed in space. A variety of statistical methods are now readily accessible to researchers providing opportunities for describing and ultimately understanding and predicting spatial distributions. This review provides an overview of the spatial statistical methods available to parasitologists, ecologists and epidemiologists and discusses how such methods have yielded new insights into the ecology and epidemiology of infection and disease. The review is structured according to the three major branches of spatial statistics: continuous spatial variation; discrete spatial variation; and spatial point processes.

Spatial data sets can be analysed by counting the number of objects in equally sized bins. The bin counts are related to the Pólya urn process, where coloured balls (for example, white or black) are removed from the urn at random. If there are insufficient white or black balls for the prescribed number of trials, the Pólya urn process becomes untenable. In this case, we modify the Pólya urn process so that it continues to describe the removal of volume within a spatial distribution of objects. We determine when the standard formula for the variance of the standard Pólya distribution gives a good approximation to the true variance. The variance quantifies an index for assessing whether a spatial point data set is at its most randomly distributed state, called the complete spatial randomness (CSR) state. If the bin size is an order of magnitude larger than the size of the objects, then the standard formula for the CSR limit is indicative of when the CSR state has been attained. For the special case when the object size divides the bin size, the standard formula is in fact exact.

We propose an image-based framework to evaluate the uncertainty in the estimation of the volume fraction of specific microstructures based on the observation of a single section. These microstructures consist of cubes organized on a cubic mesh, such as monocrystalline nickel base superalloys. The framework is twofold: a model-based stereological analysis allows relating two-dimensional image observations to three-dimensional microstructure features, and a spatial statistical analysis allows computing approximate confidence bounds while assessing the representativeness of the image. The reliability of the method is assessed on synthetic models. Volume fraction estimation variances and approximate confidence intervals are computed on real superalloy images in the context of material characterization.

The red fox Vulpes vulpes is usually classified as being territorial, dispersing or transient. Past studies have focused almost exclusively on territorial or dispersing foxes, leaving transient foxes out of the analysis. In this paper, we present spatial-statistical methods for the classification of free-ranging foxes, using 95% fixed kernels and 100% minimum convex polygons. By means of these procedures we classify individual foxes on the basis of their spatial behaviour, using home-range size and home range shift. Also, we make a methodological comparison between these classification procedures and interpret the composition of these classes ethologically. The procedures apply to a sample of 24 foxes, radio-tracked in the dune area of the Netherlands from January 1997 to June 1999. We analysed size of home range and successive 3-month overlap using a geographical information system (GIS). Classifying the sample using 95% fixed kernel home ranges resulted in two classes of foxes: a class of 20 territorial foxes with relatively small home ranges (<250 ha), and a class of four dispersing and transient foxes with relatively large home ranges (400–600 ha). This study shows that a fox population can be divided into different classes of individuals in a quantitative statistical way, honouring measured characteristics. This is a clear extension of more informal ways relying on expert judgement applied so far.

A generalization of Markov point processes is introduced in which interactions occur between connected components of the point pattern. A version of the Hammersley-Clifford characterization theorem is proved which states that a point process is a Markov interacting component process if and only if its density function is a product of interaction terms associated with cliques of connected components. Integrability and superpositional properties of the processes are shown and a pairwise interaction example is used for detailed exploration.

The paper describes the main drawbacks in the application of conventional acoustics in shallow waters, and reviews the advantages and limitations that existing multibeam sonar present in these ecosystems. New techniques and methods for adapting multibeam sonar to shallow waters are proposed and discussed. A method for analysing acoustic data from shallow waters through image analysis process is presented and some examples are considered. The results show that scattered fish can be observed individually and counted, and that schools are described in their morphology and behaviour. From these results an ‘ideal’ acoustic device is defined: a sonar operating at more than 400 kHz with a coverage of at least 120° in one direction and, depending on the needs of the user, 15° or 1° (which can be modified easily) in the perpendicular plane. The beam opening–angle is 0.5° in the centre beam, increasing to 1.0° at the 60° steer–angle, giving a total of 240 beams. Multibeam sonar data could be used for several purposes in shallow waters, in particular to estimate fish density and biomass, and study spatial and temporal behaviour of fish.

Suppose n particles xi in a region of the plane (possibly representing biological individuals such as trees or smaller organisms) have a joint density proportional to exp{-∑i<jϕ(n(xi-xj))}, with ℝd; a specified function of compact support. We obtain a Poisson process limit for the collection of rescaled interparticle distances as n becomes large. We give corresponding results for the case of several types of particles, representing different species, and also for the area-interaction (Widom-Rowlinson) point process of interpenetrating spheres.

The spatial distribution of two rain forest tree species, Carapa procera (Meliaceae) and Vouacapoua americana (Caesalpiniaceae) was analysed within and between plots of different sizes (6.25 and 25 ha) at Paracou, French Guiana. The L(d) function was used to characterize spatial patterns, and the Lij(d) intertype to study independancy between young and adult trees. Although both species are known to be dispersed by caviomorph rodents within short distances (c. 10–20 m and up to 50 m) of parent tree crowns, the analysis of tree positions led to different spatial patterns between species depending on soil drainage characteristics. Overall, while V. americana showed a strongly aggregated spatial distribution, C. procera had a weaker propensity to depart from complete spatial randomness (CSR). A complex distribution, sometimes clustered in areas with hydromorphic soils (swamps and around streams) and sometimes very near CSR outside these areas characterized the C. procera population. When C. procera tree aggregation occurred, there was a slight attraction between juveniles and adults. The aggregation of V. americana trees was evidenced at different levels depending on the scale of investigation. Within small plots (6.25 ha), a first level of aggregation with short distance radii of c. 10–25 m giving small clusters, and a second level which is composed of small clusters aggregated at c. 40–50 m distance radius, were observed. A third level of aggregation was suggested by analysing the tree population at the larger scale (25 ha) whose boundaries outside the plot were not delimited. Aggregation of V. americana trees at all levels was enhanced by a strong attraction between juveniles and adults. These results were discussed in light of seed and seedling ecology, especially with regard to seedling and sapling gap-dependence and soil drainage, which likely affected the recruitment of juvenile trees, and henceforth final tree spatial pattern.