An estimating function approach to inference for inhomogeneous Neyman-Scott processes

This article is concerned with inference for a certain class of inhomogeneous Neyman-Scott point processes depending on spatial covariates. Regression parameter estimates obtained from a simple estimating function are shown to be asymptotically normal when the "mother" intensity for the Neyman-Scott process tends to infinity. Clustering parameter estimates are obtained using minimum contrast estimation based on the K-function. The approach is motivated and illustrated by applications to point pattern data from a tropical rain forest plot.     

Genome Comparison In Silico in Neisseria Suggests Integration of Filamentous Bacteriophages by their Own Transposase

We have identified filamentous prophages, Nf (Neisserial filamentousphages), during an in silico genome comparison in Neisseria.Comparison of three genomes of Neisseria meningitidis and oneof Neisseria gonorrhoeae revealed four subtypes of Nf. Elevenintact copies are located at different loci in the four genomes.Each intact copy of Nf is flanked by duplication of 5'-CT and,at its right end, carries a transposase homologue (pivNM/irg)of RNaseH/Retroviral integrase superfamily. The phylogeny ofthese putative transposases and that of phage-related proteinson Nfs are congruent. Following circularization of Nfs, a promoter-likesequence forms. The sequence at the junction of these predictedcircular forms (5'-atCTtatat) was found in a related plasmid(pMU1) at a corresponding locus. Several structural variantsof Nfs—partially inverted, internally deleted and truncated—werealso identified. The partial inversion seems to be a productof site-specific recombination between two 5'-CTtat sequencesthat are in inverse orientation, one at its end and the otherupstream of pivNM/irg. Formation of internally deleted variantsprobably proceeded through replicative transposition that alsoinvolved two 5'-CTtat sequences. We concluded that the PivNM/Irgtransposase on Nfs integrated their circular forms into thechromosomal 5'-CT-containing sequences and probably mediatedthe above rearrangements.     

Regression analysis of mean quality-adjusted lifetime with censored data

In clinical trials of chronic diseases such as acquired immunodeficiency syndrome, cancer, or cardiovascular diseases, the concept of quality-adjusted lifetime (QAL) has received more and more attention. In this paper, we consider the problem of how the covariates affect the mean QAL when the data are subject to right censoring. We allow a very general form for the mean model as a function of covariates. Using the idea of inverse probability weighting, we first construct a simple weighted estimating equation for the parameters in our mean model. We then find the form of the most efficient estimating equation, which yields the most efficient estimator for the regression parameters. Since the most efficient estimator depends on the distribution of the health history processes, and thus cannot be estimated nonparametrically, we consider different approaches for improving the efficiency of the simple weighted estimating equation using observed data. The applicability of these methods is demonstrated by both simulation experiments and a data example from a breast cancer clinical trial study.     

Bayesian Wombling for Spatial Point Processes

Summary In many applications involving geographically indexed data, interest focuses on identifying regions of rapid change in the spatial surface, or the related problem of the construction or testing of boundaries separating regions with markedly different observed values of the spatial variable. This process is often referred to in the literature as boundary analysis or wombling. Recent developments in hierarchical models for point‐referenced (geostatistical) and areal (lattice) data have led to corresponding statistical wombling methods, but there does not appear to be any literature on the subject in the point‐process case, where the locations themselves are assumed to be random and likelihood evaluation is notoriously difficult. We extend existing point‐level and areal wombling tools to this case, obtaining full posterior inference for multivariate spatial random effects that, when mapped, can help suggest spatial covariates still missing from the model. In the areal case we can also construct wombled maps showing significant boundaries in the fitted intensity surface, while the point‐referenced formulation permits testing the significance of a postulated boundary. In the computationally demanding point‐referenced case, our algorithm combines Monte Carlo approximants to the likelihood with a predictive process step to reduce the dimension of the problem to a manageable size. We apply these techniques to an analysis of colorectal and prostate cancer data from the northern half of Minnesota, where a key substantive concern is possible similarities in their spatial patterns, and whether they are affected by each patient's distance to facilities likely to offer helpful cancer screening options.     

呼中林区火烧点格局分析及影响因素

林火是森林生态系统景观格局、动态和生态过程的重要自然驱动力,理解林火发生空间格局与影响因素对于林火安全管理具有重要的作用。采用点格局分析方法,以黑龙江大兴安岭呼中林区1990-2005年火烧数据为研究案例,分析了火烧点空间格局及其影响因素。结果表明,火烧点在空间上的分布是不均匀的,呈现聚集分布,存在一些火烧高发区和低发区。呼中林区火烧概率是0.004-0.012次/(km² · a),平均火烧概率为0.0077次/(km² · a)。人类活动因子、地形因子和植被因子对林火的发生均具有重要作用。应用空间点格局分析方法表明,距离居民点和道路的距离、高程、坡度和林型是影响林火发生的显著因子。因此在进行森林防火管理时,仅仅通过控制人类活动对于降低林火火险的效果是有限的,地形和林型也是林火防控时重点要考虑的因素。     

Temporal Analogues to Spatial K Functions

In this article, the spatial statistic known as the K function is adapted for temporal processes and patterns. The (optimal) K-function estimator is used in a testing procedure to determine whether behavior patterns of exposed rats versus control rats are different. Specifically, the temporal analogue to the K function is given and an approximately optimal estimator is developed. Next, a testing procedure, to determine whether a group of point patterns is generated from complete temporal randomness, is given. Finally, a testing procedure, to compare pairwise two groups of point patterns to each other, is given. The testing procedures are illustrated with rat-behavior data from both a control-control experiment as well as an exposed-control experiment, where in the latter case a difference in behavior is known to exist.     

Generalized additive models for cancer mapping with incomplete covariates

Maps depicting cancer incidence rates have become useful tools in public health research, giving valuable information about the spatial variation in rates of disease. Typically, these maps are generated using count data aggregated over areas such as counties or census blocks. However, with the proliferation of geographic information systems and related databases, it is becoming easier to obtain exact spatial locations for the cancer cases and suitable control subjects. The use of such point data allows us to adjust for individual-level covariates, such as age and smoking status, when estimating the spatial variation in disease risk. Unfortunately, such covariate information is often subject to missingness. We propose a method for mapping cancer risk when covariates are not completely observed. We model these data using a logistic generalized additive model. Estimates of the linear and non-linear effects are obtained using a mixed effects model representation. We develop an EM algorithm to account for missing data and the random effects. Since the expectation step involves an intractable integral, we estimate the E-step with a Laplace approximation. This framework provides a general method for handling missing covariate values when fitting generalized additive models. We illustrate our method through an analysis of cancer incidence data from Cape Cod, Massachusetts. These analyses demonstrate that standard complete-case methods can yield biased estimates of the spatial variation of cancer risk.     

植物空间分布格局中邻体距离的概率分布模型及参数估计

最近邻体法是一类有效的植物空间分布格局分析方法,邻体距离的概率分布模型用于描述邻体距离的统计特征,属于常用的最近邻体法之一。然而,聚集分布格局中邻体距离(个体到个体)的概率分布模型表达式复杂,参数估计的计算量大。根据该模型期望和方差的特性,提出了一种简化的参数估计方法,并利用遗传算法来实现参数优化,结果表明遗传算法可以有效地估计的该模型的两个参数。同时,利用该模型拟合了加拿大南温哥华岛3个寒温带树种的空间分布数据,结果显示:该概率分布模型可以很好地拟合美国花旗松(P.menziesii)和西部铁杉(T.heterophylla)的邻体距离分布,但由于西北红柏(T.plicata)存在高度聚集的团簇分布,拟合结果不理想;美国花旗松在样地中近似随机分布,空间聚集参数对空间尺度的依赖性不强,但西北红柏和西部铁杉空间聚集参数具有尺度依赖性,随邻体距离阶数增加而变大。最后,讨论了该模型以及参数估计方法的优势和限制。     

A new non‐parametric method for analyzing replicated point patterns in ecology

Most ecological studies that involve point pattern analyses are based on a single plot, which prevent the separation of the effects of various processes that could act simultaneously, as well as limiting the conclusions that can be extracted from these studies. However, considering the spatial distribution of individuals in several plots as replicates of the same process could help to differentiate its specific effects from those of other confounding processes. Thus, we introduce a new method for analyzing spatial point patterns that are replicated according to a two‐factorial design. By summarizing the spatial patterns as K‐functions, the proposed method computes the average K‐functions for each level of the two factors (i.e. predictors) and for each combination of levels, before estimating the sum of squared deviations from the overall mean K‐function. Inferences of the strength of the relationship between the predictors, their interaction, and the spatial structure are made based on a non‐parametric bootstrap procedure, which considers the dependency among spatial scales. We illustrate the proposed approach based on an analysis of the effects of altitude (with two levels: low and high) and slope (with two levels: flat and steep slopes) on the spatial pattern of Croton wagneri, a dominant shrub in an Andean dry scrubland. Our method detected a significant effect of the interaction between slope and altitude, which could not have been detected using current point pattern analysis methodology. The prevalence of single‐plot analysis in ecological studies may be due to a lack of familiarity with appropriate methods for replicated point patterns, as well as the greater complexity of these methods and the absence of appropriate software. Our approach can be applied to a significant number of ecological questions while maintaining a simple, understandable, and easily reportable methodological framework.     

On Bayesian inference for the K function

The K function is a summary of spatial dependence in spatial point processes. In practice one observes a realization of the spatial point process, called a spatial point pattern. Although the K function of a spatial point process is typically unknown, several estimators of the process K function have been put forth. These estimators, however, are based upon empirical averages; the complicated distributional properties of the estimators unfortunately complicates interval estimation. In this paper, we propose a Bayesian inferential framework, allowing inference for the K function of the spatial point process (including interval estimation). Of particular interest is the unique use of the posterior predictive distribution to (efficiently) enable such inferences. To demonstrate our technique, the well known Swedish pine sapling data (Strand, 1972) is analyzed, including a discussion on evaluating model fit.     

Using flowViz to visualize flow cytometry data

Summary: Automated analysis of flow cytometry (FCM) data isessential for it to become successful as a high throughput technology.We believe that the principles of Trellis graphics can be adaptedto provide useful visualizations that can aid such automation.In this article, we describe the R/Bioconductor package flowVizthat implements such visualizations. Availability: flowViz is available as an R package from theBioconductor project: http://bioconductor.org Contact: dsarkar{at}fhcrc.org Associate Editor: Olga Troyanskaya     

Spatial patterns on the sagebrush steppe/Western juniper ecotone

Analysis of the spatial patterns of woody plants is important to better understand the ecological processes that govern the worldwide expansion of woody plants across semi-arid ecosystems. Second-order characteristics of a marked spatial point pattern of western juniper (Juniperus occidentalis subsp. occidentalis) were analyzed using Ripley’s K-functions and the pair-correlation function g. The marked point process of crown diameters was produced via two-dimensional wavelet analysis of a fine scale aerial photograph at the woodland-steppe ecotone in the Reynolds Creek watershed in the Owyhee Mountains, southwestern Idaho. Colonization of J. occidentalis stems from mature juniper trees growing in rocky, fire resistant areas. Although these areas introduce components of natural heterogeneity within the landscape, the selected study area is situated within a single soil type, and we modeled the expansion of juniper plants into previously juniper-free sagebrush steppe as a homogeneous point process with constant intensity. Through this research we have identified two statistically significant spatial scales characteristic of J. occidentalis on the woodland/steppe ecotone: (1) We observed inhibition between J. occidentalis plants at distances <15 m, resulting in a regular pattern, rather than clumped or random. This short-distance inhibition can be attributed to competition for water and other resources. Recruitment of young J. occidentalis occurs significantly more often in a direction away from older plants, maximizing the utilization of water and light resources, and perpetuating the spread of the species into previously juniper-free shrub-steppe. (2) J. occidentalis on the ecotone exhibits significant clustering within a 30–60 m radius. Bivariate point pattern analyses provide evidence that, within a distance of 50–70 m, there is a spatial dependence in tree size such that medium trees are more likely than small trees to be close to large trees. We attribute these phenomena to the fact that juniper seeds are commonly dispersed by berry-eating birds with small territories (0.3–1 ha). Beyond a distance of 50–70 m, juniper plants are randomly distributed, suggesting that additional long-range seed dispersal processes are at work. We further acknowledge the importance of including a reference to spatial scale when formulating hypotheses in statistical analysis of spatio-temporal point patterns.     

On the Estimation of the Nearest Neighbour Distribution,G(t), for Point Processes

A new method is proposed for estimating G(t), the distribution function of the distance from an object to its nearest neighbour in a spatial point process. The new method makes more complete use of the information available and has a smaller mean squared error than that of the existing alternatives. The method appears equally effective with random, clustered and regular patterns.     

Detecting spatial aggregation from distance sampling: a probability distribution model of nearest neighbor distance

Spatial point pattern is an important tool for describing the spatial distribution of species in ecology. Negative binomial distribution (NBD) is widely used to model spatial aggregation. In this paper, we derive the probability distribution model of event-to-event nearest neighbor distance (distance from a focal individual to its n-th nearest individual). Compared with the probability distribution model of point-to-event nearest neighbor distance (distance from a randomly distributed sampling point to the n-th nearest individual), the new probability distribution model is more flexible. We propose that spatial aggregation can be detected by fitting this probability distribution model to event-to-event nearest neighbor distances. The performance is evaluated using both simulated and empirical spatial point patterns.     

Methods for Fitting the Right-Truncated Weibull Distribution to Life-Test and Survival Data

This paper develops mathematical and computational methods for fitting, by the method of maximum likelihood (ML), the two-parameter, right-truncated Weibull distribution (RTWD) to life-test or survival data. Some important statistical properties of the RTWD are derived and ML estimating equations for the scale and shape parameters of the RTWD are developed. The ML equations are used to express the scale parameter as an analytic function of the shape parameter and to establish a computationally useful lower bound on the ML estimate of the shape parameter. This bound is a function only of the sample observations and the (known) truncation point T. The ML equations are reducible to a single nonlinear, transcendental equation in the shape parameter, and a computationally efficient algorithm is described for solving this equation. The practical use of the methods is illustrated in two numerical examples.     

Optimizing surveys for marsh songbirds: does timing matter?

Analysis of data from point counts, a common method for monitoring bird population trends, has evolved to produce estimates of various population parameters (e.g., density, abundance, and occupancy) while simultaneously estimating detection probability. An important consideration when designing studies using point counts is to maximize detection probability while minimizing variation in detection probability both within and between counts. Our objectives were to estimate detection probabilities for three marsh songbirds, including Marsh Wrens (Cistothorus palustris), Swamp Sparrows (Melospiza georgiana), and Yellow‐headed Blackbirds (Xanthocephalus xanthocephalus), as a function of weather covariates and to evaluate temporal variability in detection probability of these three species. We conducted paired, unlimited radius, 10‐min point counts during consecutive morning and evening survey periods for our three focal species at 56 wetlands in Iowa from 20 April to 10 July 2010. Mean detection probabilities ranged from 0.272 (SE = 0.042) for Marsh Wrens to 0.365 (SE = 0.052) for Swamp Sparrows. Time of season was positively correlated with detection probability for Swamp Sparrows, but was negatively correlated with detection probability for Yellow‐headed Blackbirds, suggesting that detection probability increased during the breeding season for Swamp Sparrows and was highest early in the breeding season for Yellow‐headed Blackbirds. Understanding how detection probabilities of marsh songbirds vary throughout the breeding season allows targeted survey efforts that maximize detection probabilities for these species. Furthermore, consistent detection probabilities of marsh songbirds during morning and evening survey periods mean that investigators have more time to conduct surveys for these birds, allowing greater flexibility to increase spatial and temporal replication of surveys that could provide more precise estimates of desired population parameters.     

On Second Order Neighbourhood Analysis of Mapped Point Patterns

Getis and Franklin (1987), introduced a technique based on second order methods, called second order neighbourhood method, which is used to quantify clustering at various spatial scales. Variants of this method are introduced for testing whether a spatial point pattern is consistent with the hypothesis of a Poisson process. These variants are applied to point location data for a sample of Ponderosa pine (Pinus ponderosa) trees.     

A new digital method of data collection for spatial point pattern analysis in grassland communities

A major objective of plant ecology research is to determine the underlying processes responsible for the observed spatial distribution patterns of plant species. Plants can be approximated as points in space for this purpose, and thus, spatial point pattern analysis has become increasingly popular in ecological research. The basic piece of data for point pattern analysis is a point location of an ecological object in some study region. Therefore, point pattern analysis can only be performed if data can be collected. However, due to the lack of a convenient sampling method, a few previous studies have used point pattern analysis to examine the spatial patterns of grassland species. This is unfortunate because being able to explore point patterns in grassland systems has widespread implications for population dynamics, community‐level patterns, and ecological processes. In this study, we developed a new method to measure individual coordinates of species in grassland communities. This method records plant growing positions via digital picture samples that have been sub‐blocked within a geographical information system (GIS). Here, we tested out the new method by measuring the individual coordinates of Stipa grandis in grazed and ungrazed S. grandis communities in a temperate steppe ecosystem in China. Furthermore, we analyzed the pattern of S. grandis by using the pair correlation function g(r) with both a homogeneous Poisson process and a heterogeneous Poisson process. Our results showed that individuals of S. grandis were overdispersed according to the homogeneous Poisson process at 0–0.16 m in the ungrazed community, while they were clustered at 0.19 m according to the homogeneous and heterogeneous Poisson processes in the grazed community. These results suggest that competitive interactions dominated the ungrazed community, while facilitative interactions dominated the grazed community. In sum, we successfully executed a new sampling method, using digital photography and a geographical information system, to collect experimental data on the spatial point patterns for the populations in this grassland community.     

Assessing Habitat Use by Snapper (Chrysophrys auratus) from Baited Underwater Video Data in a Coastal Marine Park

Baited Underwater Video (BUV) systems have become increasingly popular for assessing marine biodiversity. These systems provide video footage from which biologists can identify the individual fish species present. Here we explore the relevance of spatial dependence and marine park boundaries while estimating the distribution and habitat associations of the commercially and recreationally important snapper species Chrysophrys auratus in Moreton Bay Marine Park during a period when new Marine National Parks zoned as no-take or “green” areas (i.e., areas with no legal fishing) were introduced. BUV studies typically enforce a minimum distance among BUV sites, and then assume that observations from different sites are independent conditional on the measured covariates. In this study, we additionally incorporated the spatial dependence among BUV sites into the modelling framework. This modelling approach allowed us to test whether or not the incorporation of highly correlated environmental covariates or the geographic placement of BUV sites produced spatial dependence, which if unaccounted for could lead to model bias. We fitted Bayesian logistic models with and without spatial random effects to determine if the Marine National Park boundaries and available environmental covariates had an effect on snapper presence and habitat preference. Adding the spatial dependence component had little effect on the resulting model parameter estimates that emphasized positive association for particular coastal habitat types by snapper. Strong positive relationships between the presence of snapper and rock habitat, particularly rocky substrate composed of indurated freshwater sediments known as coffee rock, and kelp habitat reinforce the consideration of habitat availability in marine reserve design and the design of any associated monitoring programs.