Marked Point Patterns Research Articles

Prevalence of Inter-Tree Competition and Its Role in Shaping the Community Structure of a Natural Mongolian Scots Pine (Pinus sylvestris var. mongolica) Forest

Inter-tree competition is considered one of the most important ecological processes of forest development. However, its importance in structuring the spatial patterns of plant communities remains controversial. We collected observational data from two plots in a natural Mongolian Scots pine forest to study the contribution of competition to tree growth, mortality, and size inequality. We used the nearest neighbour method to determine the presence of competition, and unmarked and marked spatial point pattern analyses to test the density-dependent mortality effects and the spatial autocorrelation of tree size. We identified significant positive correlations between tree canopy diameter and nearest neighbour distance in both plots, which were more evident in the denser plot. The pair correlation functions of both plots indicated regular distribution patterns of living trees, and trees living in more crowded environments were more likely to die. However, the mark differentiation characteristics showed weak evidence of a negative spatial autocorrelation in tree size, particularly in the high-density plot. The high mortality rate of suppressed trees and weak asymmetric competition may have accounted for the lack of dissimilarity in tree size. This study showed that inter-tree competition is an important determinant of the development of Mongolian Scots pine forests.

Factors influencing the dispersion ofArceuthobium oxycedriinCentralSpain: evaluation with a new null model for marked point patterns

SummaryThe dwarf mistletoe,Arceuthobium oxycedri, is found on populations ofJuniperus oxycedrus, in central Spain. This species can have negative effects on the physiology of its host, including mortality. Understanding the mechanisms that control its distribution and dispersal is critical to assessing its potential for spread. We assessed dwarf mistletoe distribution within a population ofJ. oxycedrus, including infected and uninfected host individuals. A new null model of parasitic dispersion was built using two dispersal kernel forms that were simulated with lower and upper envelopes for second‐order functions to summarize a point pattern, such as Ripley'sK, nearest‐neighbour distribution and pair correlation functions. Nine dispersal scenarios were constructed with half‐bandwidth kernels (10, 20, 30 m) and initial population of infected trees (P0 = 05, 10 and 20). These scenarios were compared with the observed pattern and evaluated using the goodness‐of‐fit test. Significant differences at short distance (r < 10 m) were found between the observed pattern and simulated patterns, corresponding to the range of seed dispersal of the dwarf mistletoe. Interactions between infected and uninfected hosts patterns at all scales were identified, suggesting thatA. oxycedriuses other mechanisms in addition to ballistic seed shooting as secondary dispersal agents to spread to distances greater than 20 m. Given that the seed characteristics facilitate dispersal by adhesion, we infer that spread between host individuals is amplified by seed transport by birds or small mammals.

Analysis of shape and spatial interaction of synaptic vesicles using data from focused ion beam scanning electron microscopy (FIB-SEM).

The spatial interactions of synaptic vesicles in synapses were assessed after a detailed characterization of size, shape, and orientation of the synaptic vesicles. We hypothesized that shape and orientation of the synaptic vesicles are influenced by their movement toward the active zone causing deviations from spherical shape and systematic trends in their orientation. We studied three-dimensional representations of synapses obtained by manual annotation of focused ion beam scanning electron microscopy (FIB-SEM) images of male mouse brain. The configurations of synaptic vesicles were regarded as marked point patterns, where the points are the centers of the vesicles, and the mark of a vesicle is given by its size, shape, and orientation characteristics. Statistics for marked point processes were employed to study spatial interactions between vesicles. We found that the synaptic vesicles in excitatory synapses appeared to be of oblate ellipsoid shape and in inhibitory synapses appeared to be of cigar ellipsoid shape, and followed a systematic pattern regarding their orientation toward the active zone. Moreover, there was strong evidence of spatial alignment in the orientations of pairs of synaptic vesicles, and of repulsion between them only in excitatory synapses, beyond that caused by their physical extent.

Unravelling conflicting density‐ and distance‐dependent effects on plant reproduction using a spatially explicit approach

Summary Density‐ and distance‐dependent (DDD) mechanisms are important determinants of plant reproductive success (PRS). Different components of sequential PRS can operate either in the same or in different directions and thus reinforce or neutralize each other, and they may also operate at different spatial scales. Thus, spatially explicit approaches are needed to detect such complex DDD effects across multiple PRS components and spatial scales. To reveal DDD effects of different components of early PRS of the Iberian pear (Pyrus bourgaeana) sampled over three consecutive years, we used marked point pattern analysis. Our special interest is to identify conflicting processes that regulate populations at different spatial scales, for example whether DDD on fruit initiation and on fruit development acted in opposite directions. To evaluate the significance of observed mark correlation functions based on empirical data (e.g. fruiting success), we compared them to expectations given by spatially explicit null models. Diverse DDD processes affected several aspects of PRS in a variable extent over the three seasons. First, fruit initiation was higher for individuals with more neighbours at small distances (i.e. up to 40 m). However, P. bourgaeana fruit development decreased with increasing number of nearby neighbours, but these effects cancelled for overall fruit set that did not show DDD effects. Secondly, the absolute number of fruits produced (crop sizes) by trees showed positive density dependence in 2011 and 2012 but not in 2013. Finally, the total number of seeds produced did not show DDD effects, indicating that conflicting demographic processes can disrupt the initial spatial pattern of tree investment in reproduction. Synthesis. Understanding complex spatial effects of DDD processes requires dissection of component processes to attain the complete picture since contrasting DDD processes may be hidden behind a single cumulative measure of reproductive success. The combination of novel and classic mark correlation functions used here constitutes a powerful spatially explicit tool that can be broadly applied to unravel conflicting mechanisms of DDD regulating the persistence of sessile organisms at a range of spatial scales. Our findings help to explain why some authors failed to find expected DDD of PRS and highlight the importance of detailed multiyear field studies on plant reproductive success.

Analysis of massive marked point patterns with stochastic partial differential equations

In this paper we describe a novel approach to modelling marked point patterns based on recent computational developments for Bayesian inference. We use the flexible class of log-Gaussian Cox Processes to model the intensity of the different observed point patterns. We propose several types of models to account for spatial variability and provide a modelling framework that allows for a common spatial component to all point processes (regardless of the mark) and also for a mark-specific spatial components. In this way, we provide a method of assessing whether all processes share a common spatial distribution or there are specific features.In order to fit these models, we have resorted to the Integrated Nested Laplace Approximation (INLA) method and the Stochastic Partial Differential Equation (SPDE) approach. This defines a connection between point process and geostatistics, as we model a point pattern by means of a continuous spatial process.Our new approach to spatial modelling is applied to a massive dataset on the occurrence of tornados in the United States. We have divided the tornados in the 1950–2013 period according to their magnitude and fitted our proposed models.

Impact of Eradication Programs on the Temporal and Spatial Dynamics of Plum pox virus on Prunus spp. in Pennsylvania and Ontario, Canada.

The goals of this research were to quantify the impacts of the Pennsylvania and Ontario Plum pox virus (PPV) eradication programs on the spatial and temporal dynamics of PPV epidemics on Prunus spp. The incidence of PPV-positive trees detected over time decreased in both Pennsylvania (-ln 0.85 units per year) and Ontario (-ln 0.51 units per year); however, PPV incidence per year decreased only 60% as fast in Ontario as in Pennsylvania. Marked point pattern analysis revealed that PPV-positive Prunus blocks in Pennsylvania were clustered for distances of 0.7 to 4.3 km, whereas PPV-positive blocks in Ontario were clustered for distances of 1.0 to 25.0 km. Multiyear spatiotemporal analyses revealed that the locations of PPV-positive blocks detected were spatially dependent upon the locations of PPV-positive blocks detected during the previous year. In Pennsylvania, between 2002 and 2006, distances to 95% of newly detected PPV-positive blocks occurred within 10 and 20 km from the previous year's PPV-positive blocks. In Ontario, 95% of new PPV-positive blocks occurred within 500 to 900 m from PPV-positive blocks detected the previous year. Until 2011, the PPV eradication policy for Prunus blocks in Ontario was triggered by a threshold incidence or PPV-positive tests for three consecutive years. Although the Ontario program was highly successful in reducing PPV incidence from 2001 to 2008, PPV was not eradicated. This study provides important quantitative information concerning the impact of PPV eradication programs on the spatial and temporal dynamics of PPV epidemics in Pennsylvania and Ontario. The analyses employed in this study may help to improve the effectiveness of present and future PPV eradication programs.

An Analysis of an Incomplete Marked Point Pattern of Heat-Related 911 Calls

We analyze an incomplete marked point pattern of heat-related 911 calls between the years 2006–2010 in Houston, TX, to primarily investigate conditions that are associated with increased vulnerability to heat-related morbidity and, secondarily, build a statistical model that can be used as a public health tool to predict the volume of 911 calls given a time frame and heat exposure. We model the calls as arising from a nonhomogenous Cox process with unknown intensity measure. By using the kernel convolution construction of a Gaussian process, the intensity surface is modeled using a low-dimensional representation and properly adheres to circular domain constraints. We account for the incomplete observations by marginalizing the joint intensity measure over the domain of the missing marks and also demonstrate model based imputation. We find that spatial regions of high risk for heat-related 911 calls are temporally dynamic with the highest risk occurring in urban areas during the day. We also find that elderly populations have an increased probability of calling 911 with heat-related issues than younger populations. Finally, the age of individuals and hour of the day with the highest intensity of heat-related 911 calls varies by race/ethnicity. Supplementary materials are included with this article.

Deviation test construction and power comparison for marked spatial point patterns

Deviation tests play an important role in testing distributional hypotheses in point process statistics. Such tests are based on differences between empirical summary functions and their theoretical counterparts, which depend on a distance variable r in a user-specified interval I. These differences are summarized to a single number, which serves then as the test statistic u. Statistical experience indicates that different distances r have different influence on u. We propose scalings of the differences to equalize the influence of the distances and show that the power of deviation tests can be improved by them. We further study how the power is affected by the other elements of deviation tests, which are the choice of the summary function, the deviation measure and the interval I. We consider in detail the construction of deviation tests for the particular case of testing the random labeling hypothesis, i.e. independence of the marks of a marked point process. By a large simulation study we come to clear statements about the role of the test elements. Furthermore, we demonstrate the potential of scaling by a data example from the literature.

Asymptotic goodness-of-fit tests for the Palm mark distribution of stationary point processes with correlated marks

We consider spatially homogeneous marked point patterns in an unboundedly expanding convex sampling window. Our main objective is to identify the distribution of the typical mark by constructing an asymptotic $\chi^{2}$-goodness-of-fit test. The corresponding test statistic is based on a natural empirical version of the Palm mark distribution and a smoothed covariance estimator which turns out to be mean square consistent. Our approach does not require independent marks and allows dependences between the mark field and the point pattern. Instead we impose a suitable $\beta$-mixing condition on the underlying stationary marked point process which can be checked for a number of Poisson-based models and, in particular, in the case of geostatistical marking. In order to study test performance, our test approach is applied to detect anisotropy of specific Boolean models.

Wombling Analysis of Childhood Tumor Rates in Florida

The Florida Association of Pediatric Tumor Program (FAPTP) is a statewide network charged with the responsibility to monitor and evaluate children’s cancer care in Florida. As part of this responsibility, the FAPTP collects data about the race, gender, age, ZIP code tabulation area of residence, and year of diagnosis for cancer cases across Florida. In accord with the goals of the FAPTP, this article seeks to identify spatial, temporal, and covariate regions of rapid change in the rate of cancer occurrence with the goal of understanding important spatial and demographic factors that determine the occurrence of childhood cancer. Herein, the FAPTP data are modeled as a marked point pattern (process) with an unknown intensity function. By estimating the intensity function from data, regions of high cancer occurrences and boundaries denoting rapid increases (or decreases) in the corresponding cancer rates can be identified. Results indicate that regions of high cancer risk vary with race. Furthermore, younger populations are found to have the highest risk.

Quantifying spatial phylogenetic structures of fully stem-mapped plant communities

Analysis of the phylogenetic similarity of co-occurring species at different spatial scales is increasingly used for decoding community assembly rules. Here, we integrated the analysis of phylobetadiversity and marked point pattern analysis to yield a new metric, the phylogenetic mark correlation function, kd(r), to quantify spatial phylogenetic structure of fully stem-mapped communities. kd(r) is defined as the expected phylogenetic distance of two heterospecifics separated by spatial distance r, and normalized with the expected phylogenetic distance of two heterospecifics taken randomly from a study area. It measures spatial phylogenetic turnover relative to spatial species turnover and is closely related with the spatially explicit Simpson index. We used simulated fully stem-mapped plant communities with known spatial phylogenetic structures to assess type I and II errors of the phylogenetic mark correlation function kd(r) under a null model of random phylogenetic spatial structure, and to test the ability of the kd(r) to detect scale-dependent signals of phylogenetic spatial structure. We also compared the performance of the kd(r) with two existing measures of phylobetadiversity that have been previously used to analyse fully stem-mapped plots. Finally, we explored the spatial phylogenetic structure of a 24-ha fully stem-mapped subtropical forest in China. Simulation tests showed that the new metric yielded correct type I and type II errors and accurately detected the spatial scales at which various processes (e.g. habitat filtering and competition) were invoked to generate spatial phylogenetic structures. The power of the kd(r) was not affected by a phylogenetic signal in species abundance and different topologies of the phylogenetic tree. Replacing phylogenetic distance by functional distance allows for application of the kd(r) to estimate spatial correlations in functional community structure. Thus, the kd(r) allows trait and phylogenetic structure to be analysed in the same framework. The phylogenetic mark correlation function is a powerful and accurate tool for revealing scale-dependent phylogenetic/functional footprints in community assemblages and allows ecologists to keep up with the increasingly available data of fully stem-mapped plots, functional traits and community phylogenies.

Long-term hurricane effects on populations of two epiphytic orchid species from Guanahacabibes Peninsula, Cuba

Disturbances affect the spatial and temporal dynamics of ecosystems. The lack of long-term demographic data affects our understanding the effects of high intensity disturbances such as hurricanes. In this paper we assess population recovery of two epiphytic orchids, Broughtonia cubensis (Lindl.) Cogn. and Dendrophylax lindenii (Lindl.) Bentham ex Rolfe, for 7-8 years after Hurricane Ivan (September 2004, category 5, Saffir-Simpson scale). To analyze some spatial components, we applied recent techniques of marked point pattern analysis to ask two questions: 1) at level of phorophytes, was the height and basal diameter (DBH) related to the damage caused by hurricane Ivan, and 2) was the height of epiphytic orchids on phorophytes related to the damage, too? We found that phorophyte damage caused by the hurricane depends on the ecosystem in which the trees were found. Furthermore, damage to individuals of B. cubensis was independent of their height above ground, in contrast to those of D. lindenii. To assess orchid recovery we compared pre- and post-hurricane measures of vegetative traits: number of leaves and leaf area for B. cubensis and number of living roots and mean root length for the leafless D. lindenii. We also compared changes in the production of inflorescences, flowers, and fruits over this recovery period. We found that vegetative parts of B. cubensis recovered, whereas those of D. lindenii did not. However, neither reproductive effort nor success returned to pre-hurricane levels for either species. The greatest decline in fruit set was by D. lindenii, which may reflect a significant decline in availability of their sphingid pollinators. The relative population growth rate from 2004 to 2012 for B. cubensis indicates that the population has stabilized. Unfortunately, analysis of our eight-year data set (2003-2011) for D. lindenii shows negative population growth. Despite an evolutionary history exposed to severe periodic storms not all orchid species are resilient.

Spatial dynamics of cone production in Mediterranean climates: A case study of Pinus pinea L. in Portugal

Seed production of trees is key to natural regeneration of forests and to successful conservation management. Despite its importance no spatially explicit analyses of seed production have so far been carried out in this important field. Analyses like these are particularly important in areas with regular summer droughts. We used Pinus pinea L. as a model species and analysed a short time series comprising four replicated plots in the Alcácer do Sal region in Portugal. In 2003, all trees in four plots with a size between 0.6 and 1.6 ha were mapped. Crown diameters were established in 2003 and cone weights were measured annually from 2003 to 2005. The marked point patterns formed by tree locations, crown diameters and cone weights were analysed with three second-order characteristics. As expected there was good correlation between crown diameters and coning. We found considerable variability in cone production, which was larger between plots than between years. It was confirmed that there is fairly regular spacing with distances larger than 10 m between mature trees. This is mainly a consequence of a climate with regular summer droughts and of poor soils. The mark correlation function revealed strong mutual stimulation of coning between trees around 10 and 23 m. According to our field observation recruitment of Pinus pinea and cork oak mainly occurs in the vicinity of large, mature Pinus pinea trees causing negative autocorrelation and benefitting from semi-shade and increased soil moisture. Pinus pinea cone production and recruitment are strongly influenced by tree spacing. Depending on the water holding capacity of soils, spacing between mature trees needs to be optimised for successful coning. Local forest owners and managers are aware of this and have developed a system of adaptive management.

Correct testing of mark independence for marked point patterns

Spatial pattern analysis provides valuable information on ecological processes. Many ecological systems can be described by marked point processes. One of the key issues in the statistical application of marked point processes is the question of spatial correlations of the marks. Therefore, the first step of analysis is a test of independence of marks. Many researchers use for this purpose the popular envelope test. However, this may lead to unreasonably high type I error probabilities, because in this test spatial correlations are inspected for a range of distances simultaneously. The paper discusses in detail the use of deviation tests for testing hypotheses of mark independence. Additionally, it demonstrates how the envelope test can be refined so that it becomes a valuable tool both for statistical inference and for understanding the reasons of possible rejections of the independence hypothesis. Two examples from forest ecology illustrate the application of both test types.

Marked point pattern analysis on genetic paternity data for uncertainty assessment of pollen dispersal kernels

Summary 1. Obtaining accurate estimates of the pollen dispersal kernel is central to a wide range of ecological studies. Assessing their statistical uncertainty is as important, but rarely considered. 2. We developed a new method of marked point processes for nonparametric estimation of dispersal kernels based on data of genetic paternity analysis that does not require assumptions about the shape of the dispersal distribution. This allows for construction of Monte Carlo simulation envelopes of a given null model, such as random mating, and for uncertainty assessment of the observed dispersal kernel. 3. We applied our method to characterize spatial patterns of pollen flow in an isolated population of Populus nigra in Central Germany and to assess the associated statistical uncertainty in estimates of within-population dispersal kernels. We compared our nonparametric within-population kernel estimate with that of established methods of parametric kernel fitting including: (i) a general mating model, (ii) a simplified mating model using categorical paternity data and (iii) least-squares regression of the nonparametric kernel estimate. 4. Our analysis showed a significant departure from the random mating null model. We found a highly significant excess of mating events at short distances ( 2000 m), indicating large uncertainty on the detailed shape of the kernel’s tail. 5. Results of the point pattern analysis were consistent with kernel fits using published maximum-likelihood mating models. Model selection revealed that two-component pollen dispersal kernels were the most parsimonious functions. 6. Synthesis. Our approach of nonparametric kernel estimation could be widely applied for dispersal data from genetic paternity analysis and complements traditional kernel estimation by providing a nonparametric kernel estimate and effective methods for an uncertainty assessment in kernel estimation. Our results indicate that statistical model fitting may substantially underestimate the uncertainty in kernel estimation, especially at larger distances.

A MULTISCALE APPROACH TO THE REPRESENTATION OF 3D IMAGES, WITH APPLICATION TO POLYMER SOLAR CELLS

A multiscale approach to the description of geometrically complex 3D image data is proposed which distinguishes between morphological features on a ‘macro-scale’ and a ‘micro-scale’. Since our method is mainly tailored to nanostructures observed in composite materials consisting of two different phases, an appropriate binarization of grayscale images is required first. Then, a morphological smoothing is applied to extract the structural information from binarized image data on the ‘macro-scale’. A stochastic algorithm is developed for the morphologically smoothed images whose goal is to find a suitable representation of the macro-scale structure by unions of overlapping spheres. Such representations can be interpreted as marked point patterns. They lead to an enormous reduction of data and allow the application of well-known tools from point-process theory for their analysis and structural modeling. All those voxels which have been ‘misspecified’ by the morphological smoothing and subsequent representation by unions of overlapping spheres are interpreted as ‘micro-scale’ structure. The exemplary data sets considered in this paper are 3D grayscale images of photoactive layers in hybrid solar cells gained by electron tomography. These composite materials consist of two phases: a polymer phase and a zinc oxide phase. The macro-scale structure of the latter is represented by unions of overlapping spheres.

Patterns of house infestation dynamics by non-domiciliatedTriatoma dimidiatareveal a spatial gradient of infestation in rural villages and potential insect manipulation byTrypanosoma cruzi

Chagas disease is a major vector-borne parasitic disease in Latin America, primarily transmitted to humans by triatomine vectors. Non-domiciliated triatomine species such as Triatoma dimidiata in the Yucatan peninsula, Mexico, can transiently invade houses and are emerging as a major challenge to control Trypanosoma cruzi transmission to humans. We analyzed the spatio-temporal spreading of house infestation by T. dimidiata in four rural villages. Triatomines were collected in four rural villages over a 2 years period, and the spatio-temporal patterns of infestation were analyzed. Triatomines were consistently more abundant at the periphery of villages than in centers, indicating a much higher risk of T. cruzi transmission at the periphery. Male T. dimidiata were found further in the center of the village, while females remained closer to the periphery, suggesting differential dispersal capabilities between sexes, although the timing of dispersal appeared identical. Surprisingly, infected females were consistently collected in houses much further from the surrounding bushes than non-infected females, while the distribution of males was unaffected by their T. cruzi infection status, suggesting an increased dispersal capability in infected females. The spatial structure of infestation should be taken into account for the prioritization of vector control activities within villages, and spatially targeted interventions may be explored. A potential vector manipulation by T. cruzi, observed for the first time in triatomines, may favor parasite transmission to new hosts.

ANALYSIS OF MINNESOTA COLON AND RECTUM CANCER POINT PATTERNS WITH SPATIAL AND NONSPATIAL COVARIATE INFORMATION.

Colon and rectum cancer share many risk factors, and are often tabulated together as "colorectal cancer" in published summaries. However, recent work indicating that exercise, diet, and family history may have differential impacts on the two cancers encourages analyzing them separately, so that corresponding public health interventions can be more efficiently targeted. We analyze colon and rectum cancer data from the Minnesota Cancer Surveillance System from 1998-2002 over the 16-county Twin Cities (Minneapolis-St. Paul) metro and exurban area. The data consist of two marked point patterns, meaning that any statistical model must account for randomness in the observed locations, and expected positive association between the two cancer patterns. Our model extends marked spatial point pattern analysis in the context of a log Guassian Cox process to accommodate spatially referenced covariates (local poverty rate and location within the metro area), individual-level risk factors (patient age and cancer stage), and related interactions. We obtain smoothed maps of marginal log-relative intensity surfaces for colon and rectum cancer, and uncover significant age and stage differences between the two groups. This encourages more aggressive colon cancer screening in the inner Twin Cities and their southern and western exurbs, where our model indicates higher colon cancer relative intensity.

Spatial—temporal marked point processes: a spectrum of stochastic models

AbstractMany processes that develop through space and time do so in response not only to their own individual growth mechanisms but also in response to interactive pressures induced by their neighbours. The growth of trees in a forest which compete for light and nutrient resources, for example, provides a classic illustration of this general spatial—temporal growth‐interaction process. Not only has its mathematical representation proved to be a powerful tool in the study and analysis of marked point patterns since it may easily be simulated, but it has also been shown to be highly flexible in terms of its application since it is robust with respect to incorrect choice of model selection. Moreover, it is highly amenable to maximum likelihood and least squares parameter estimation techniques. Currently the algorithm comprises deterministic growth and interaction coupled with a stochastic arrival and departure mechanism. So for systems with a fixed number of particles there is an inherent lack of randomness. A variety of different stochastic approaches are therefore presented, from the exact event—time model through to the associated stochastic differential equation, taking in time‐increment and Tau‐ and Langevin‐Leaping approximations en route. The main algorithm is illustrated through application to forest management and high‐intensity packing of hard particle systems, and comparisons are made with the established force biased approach. Copyright © 2009 John Wiley & Sons, Ltd.

Modelling Tree Roots in Mixed Forest Stands by Inhomogeneous Marked Gibbs Point Processes

The aim of the paper is to apply point processes to root data modelling. We propose a new approach to parametric inference when the data are inhomogeneous replicated marked point patterns. We generalize Geyer's saturation point process to a model, which combines inhomogeneity, marks and interaction between the marked points. Furthermore, the inhomogeneity influences the definition of the neighbourhood of points. Using the maximum pseudolikelihood method, this model is then fitted to root data from mixed stands of Norway spruce (Picea abies (L.) Karst.) and European beech (Fagus sylvatica L.) to quantify the degree of root aggregation in such mixed stands. According to the analysis there is no evidence that the two root systems are not independent.