Two‐Dimensional Spectral Analysis for Marked Point Processes

Spectral analysis has already been shown to be a powerful tool in the interrogation of lattice patterns, since it assumes no structural characteristics in the data (such as isotropy) prior to analysis. Here we extend the analysis to non‐lattice data for which both points and marks can exhibit spatial structure. Both distance‐ and spectral‐based measures are introduced, and theoretical comparisons are made between lattice and mark spectra. Simulated examples suggest a high degree of independence between point and mark spectra, and a real example is presented for the spatial structure of 584 tree locations and diameters at breast height of longleaf pine trees in southern Georgia.     

A modified pseudolikelihood approach for analysis of longitudinal data

We consider the analysis of longitudinal data when the covariance function is modeled by additional parameters to the mean parameters. In general, inconsistent estimators of the covariance (variance/correlation) parameters will be produced when the "working" correlation matrix is misspecified, which may result in great loss of efficiency of the mean parameter estimators (albeit the consistency is preserved). We consider using different "working" correlation models for the variance and the mean parameters. In particular, we find that an independence working model should be used for estimating the variance parameters to ensure their consistency in case the correlation structure is misspecified. The designated "working" correlation matrices should be used for estimating the mean and the correlation parameters to attain high efficiency for estimating the mean parameters. Simulation studies indicate that the proposed algorithm performs very well. We also applied different estimation procedures to a data set from a clinical trial for illustration.     

Using neutral landscapes to identify patterns of aggregation across resource points

Many organisms are aggregated within resource patches and aggregated spatially across landscapes with multiple resources. Such patchy distributions underpin models of population regulation and species coexistence, so ecologists require methods to analyse spatially‐explicit data of resource distribution and use. I describe a method for analysing maps of resources and testing hypotheses about how resource distribution influences the distribution of organisms, where resource patches can be described as points in a landscape and the number of organisms on each resource point is known. Using a mark correlation function and the linearised form of Ripley's K‐function, this version of marked point pattern analysis can characterise and test hypotheses about the spatial distribution of organisms (marks) on resource patches (points). The method extends a version of point pattern analysis that has wide ecological applicability, it can describe patterns over a range of scales, and can detect mixed patterns. Statistically, Monte Carlo permutations are used to estimate the difference between the observed and expected values of the mark correlation function. Hypothesis testing employs a flexible neutral landscape approach in which spatial characteristics of point patterns are preserved to some extent, and marks are randomised across points. I describe the steps required to identify the appropriate neutral landscape and apply the analysis. Simulated data sets illustrate how the choice of neutral landscape can influence ecological interpretations, and how this spatially‐explicit method and traditional dispersion indices can yield different interpretations. Interpretations may be general or context‐sensitive, depending on information available about the underlying point pattern and the neutral landscape. An empirical example of caterpillars exploiting food plants illustrates how this technique might be used to test hypotheses about adult oviposition and larval dispersal. This approach can increase the value of survey data, by making it possible to quantify the distribution of resource points in the landscape and the pattern of resource use by species.     

南极半岛北部南极磷虾渔业空间点格局特征

南极磷虾作为南极生态系统中的关键物种,在空间分布上常表现出集群特征.这也反映到磷虾渔业生产的空间格局特征上.为了探讨捕捞能力有明显差异的船队在高/低单位捕捞努力量渔获量(CPUE)的情况下空间点分布格局特征及其生态学效应,基于南极半岛北部海域的两艘中国南极磷虾渔船(船A为专业南极磷虾渔船,船B为在智利竹筴鱼渔场与南极磷虾渔场转换的兼作渔船)的磷虾渔业数据,从空间点格局的角度出发,分别从两船的高、低CPUE的空间点格局在不同尺度上聚集特征,高、低CPUE在不同尺度上的二元点格局相关关系,以及CPUE点标记格局下的相关性关系等3个方面进行了分析.Ripley的L函数和标记相关函数分析结果表明: 研究对象在空间窗口所有尺度上的空间格局均表现为聚集性,高、低CPUE下均有聚集发生;在15 km尺度上,聚集强度近最大,在15~50 km尺度下,聚集程度稳定;总体上点格局分布的聚集强度依次为:船A高CPUE>船B低CPUE>船B高CPUE>船A低CPUE.船A高、低CPUE在0~75 km尺度上为正相关关系,在大于75 km尺度上为随机关系;船B在所有尺度上的高、低CPUE均为正相关,说明了低CPUE点事件伴随高CPUE的点事件同步发生,两者在大部分尺度下均显著相关.这是磷虾集群模式的动态性和复杂性造成.船A各点的CPUE值在0~44 km尺度上呈正相关,在44~80 km尺度上呈负相关;船B各点的CPUE值在50~70 km尺度上呈负相关,在其他尺度上无显著相关性;正相关反映了磷虾密集集群的种群分布特性,而负相关表明了磷虾群间由于食物和空间原因存在一定的竞争关系.捕捞能力强的船A和捕捞能力较弱的船B在点格局分布上存在较大差异.专业南极磷虾渔船更适于开展磷虾作业空间点格局分析及相关科学调查工作.     

Mark-mark scatterplots improve pattern analysis in spatial plant ecology

Point process statistics provides valuable tools for many ecological studies, where ‘points’ are commonly determined to represent the locations of plants or animals and ‘marks’ are additional items such as species or size. In the statistical analysis of marked point patterns, various correlation functions are used such as the mark variogram or the mark correlation function. Often the interpretation of these functions is not easy and the non-spatial ecologist is in need of support. In order to make the analysis of spatial point patterns more accessible to ecologists, we introduced and tested a new graphical method, the mark-mark scatterplot. This plot visualises the marks of point pairs of inter-point distances r smaller than some small distance r_max. We tested the application of the mark-mark scatterplot by reconsidering three quite different tree patterns: a pattern of longleaf pine trees from the southern US which was strongly influenced by fires, a tropical tree pattern of the species Shorea congestiflora from Sri Lanka and a Scots pine pattern from Siberia (Russia). The new method yielded previously undetected cause-effect information on mark behaviour at short inter-point distances and thus improved the analysis with mark correlation functions as well as complemented the information they provided. We discovered important new correlations in clusters of trees at close proximity. The application of the mark-mark scatterplot will facilitate the interpretation of point process summary statistics and will make point process analysis more accessible to ecologists not specialized in point process statistics.     

Nonparametric estimation of the joint distribution of a survival time subject to interval censoring and a continuous mark variable

This article considers three nonparametric estimators of the joint distribution function for a survival time and a continuous mark variable when the survival time is interval censored and the mark variable may be missing for interval-censored observations. Finite and large sample properties are described for the nonparametric maximum likelihood estimator (NPMLE) as well as estimators based on midpoint imputation (MIDMLE) and coarsening the mark variable (CMLE). The estimators are compared using data from a simulation study and a recent phase III HIV vaccine efficacy trial where the survival time is the time from enrollment to infection and the mark variable is the genetic distance from the infecting HIV sequence to the HIV sequence in the vaccine. Theoretical and empirical evidence are presented indicating the NPMLE and MIDMLE are inconsistent. Conversely, the CMLE is shown to be consistent in general and thus is preferred.     

Analyzing wearable device data using marked point processes

This paper introduces two sets of measures as exploratory tools to study physical activity patterns: active‐to‐sedentary/sedentary‐to‐active rate function (ASRF/SARF) and active/sedentary rate function (ARF/SRF). These two sets of measures are complementary to each other and can be effectively used together to understand physical activity patterns. The specific features are illustrated by an analysis of wearable device data from National Health and Nutrition Examination Survey (NHANES). A two‐level semiparametric regression model for ARF and the associated activity magnitude is developed under a unified framework using the marked point process formulation. The inactive and active states measured by accelerometers are treated as a 0‐1 point process, and the activity magnitude measured at each active state is defined as a marked variable. The commonly encountered missing data problem due to device nonwear is referred to as “window censoring,” which is handled by a proper estimation approach that adopts techniques from recurrent event data. Large sample properties of the estimator and comparison between two regression models as measurement frequency increases are studied. Simulation and NHANES data analysis results are presented. The statistical inference and analysis results suggest that ASRF/SARF and ARF/SRF provide useful analytical tools to practitioners for future research on wearable device data.     

Some Remarks on the Estimation of the Pair-Correlation Function for Point Processes

Doguwa (1990) proposed kernel based pair-correlation function estimators for Point processes. These estimators transport a part of the probability mass into the negative or left, to a hard-core distance. The reflection technique is used to provide an alternative estimator of the pair-correlation function, which drastically reduces the bias inherent in these estimators for the case of random and clustered point patterns. However, the drastic reduction in bias, is at the cost of a much larger variance.     

Improved methods for estimating abundance and related demographic parameters from mark‐resight data

Over the past decade, there has been much methodological development for the estimation of abundance and related demographic parameters using mark‐resight data. Often viewed as a less‐invasive and less‐expensive alternative to conventional mark recapture, mark‐resight methods jointly model marked individual encounters and counts of unmarked individuals, and recent extensions accommodate common challenges associated with imperfect detection. When these challenges include both individual detection heterogeneity and an unknown marked sample size, we demonstrate several deficiencies associated with the most widely used mark‐resight models currently implemented in the popular capture‐recapture freeware Program MARK. We propose a composite likelihood solution based on a zero‐inflated Poisson log‐normal model and find the performance of this new estimator to be superior in terms of bias and confidence interval coverage. Under Pollock's robust design, we also extend the models to accommodate individual‐level random effects across sampling occasions as a potentially more realistic alternative to models that assume independence. As a motivating example, we revisit a previous analysis of mark‐resight data for the New Zealand Robin (Petroica australis) and compare inferences from the proposed estimators. For the all‐too‐common situation where encounter rates are low, individual detection heterogeneity is non‐negligible, and the number of marked individuals is unknown, we recommend practitioners use the zero‐inflated Poisson log‐normal mark‐resight estimator as now implemented in Program MARK.     

Population Estimation Techniques for Lekking Species

Abstract: With the decline of many lekking species, the need to develop a rigorous population estimation technique is critical for successful conservation and management. We employed mark—resight methods to estimate population size for 2 lekking species: greater sage-grouse (Centrocercus urophasianus) and Gunnison sage-grouse (Centrocercus minimus). We evaluated 2 different estimators: Bowden's estimator and the mixed logit-normal mark—resight model. We captured and marked 75 greater sage-grouse. We counted marked and unmarked birds as they attended 15 known leks. We used 36 and 37 marked Gunnison sage-grouse to estimate population size in 2003 and 2004, respectively. We observed marked and unmarked Gunnison sage-grouse daily as they attended 6 leks in 2003 and 3 leks in 2004. Based on our examination of the assumptions of each mark—resight estimator, relative to behavior and biology of these species, we concluded the mixed logit-normal mark—resight model is preferred. We recommend wildlife managers employ mark—resight approaches when statistically rigorous population estimates are required for management and conservation of lekking species.     

Weighted rank regression for clustered data analysis

Summary .   We consider ranked-based regression models for clustered data analysis. A weighted Wilcoxon rank method is proposed to take account of within-cluster correlations and varying cluster sizes. The asymptotic normality of the resulting estimators is established. A method to estimate covariance of the estimators is also given, which can bypass estimation of the density function. Simulation studies are carried out to compare different estimators for a number of scenarios on the correlation structure, presence/absence of outliers and different correlation values. The proposed methods appear to perform well, in particular, the one incorporating the correlation in the weighting achieves the highest efficiency and robustness against misspecification of correlation structure and outliers. A real example is provided for illustration.     

Generalization of the Mantel-Haenszel estimating function for sparse clustered binary data

We extend the Mantel-Haenszel estimating function to estimate both the intra-cluster pairwise correlation and the main effects for sparse clustered binary data. We propose both a composite likelihood approach and an estimating function approach for the analysis of such data. The proposed estimators are consistent and asymptotically normally distributed. Simulation results demonstrate that the two approaches are comparable in terms of bias and efficiency; however, the estimating equation approach is computationally simpler. Analysis of the Georgia High Blood Pressure survey is used for illustration.     

Development of a local size hierarchy causes regular spacing of trees in an even-aged Abies forest: analyses using spatial autocorrelation and the mark correlation function

Background and Aims

During the development of an even-aged plant population, the spatial distribution of individuals often changes from a clumped pattern to a random or regular one. The development of local size hierarchies in an Abies forest was analysed for a period of 47 years following a large disturbance in 1959.

Methods

In 1980 all trees in an 8 × 8 m plot were mapped and their height growth after the disturbance was estimated. Their mortality and growth were then recorded at 1- to 4-year intervals between 1980 and 2006. Spatial distribution patterns of trees were analysed by the pair correlation function. Spatial correlations between tree heights were analysed with a spatial autocorrelation function and the mark correlation function. The mark correlation function was able to detect a local size hierarchy that could not be detected by the spatial autocorrelation function alone.

Key Results

The small-scale spatial distribution pattern of trees changed from clumped to slightly regular during the 47 years. Mortality occurred in a density-dependent manner, which resulted in regular spacing between trees after 1980. The spatial autocorrelation and mark correlation functions revealed the existence of tree patches consisting of large trees at the initial stage. Development of a local size hierarchy was detected within the first decade after the disturbance, although the spatial autocorrelation was not negative. Local size hierarchies that developed persisted until 2006, and the spatial autocorrelation became negative at later stages (after about 40 years).

Conclusions

This is the first study to detect local size hierarchies as a prelude to regular spacing using the mark correlation function. The results confirm that use of the mark correlation function together with the spatial autocorrelation function is an effective tool to analyse the development of a local size hierarchy of trees in a forest.Key words: Abies, local size hierarchy, mark correlation function, pair correlation function, regenerating forest, regular spacing, spatial autocorrelation     

Plasma protein N-glycan profiles are associated with calendar age, familial longevity and health

The development of medical interventions for the preservation of disease-free longevity would be facilitated by markers that predict healthy aging. Altered protein N-glycosylation patterns have been found with increasing age and several disease states. Here we investigate whether glycans derived from the total glycoprotein pool in plasma mark familial longevity and distinguish healthy from unhealthy aging. Total plasma N-glycan profiles of 2396 middle aged participants in the Leiden Longevity Study (LLS) were obtained by glycan release, labeling, and subsequent HPLC analysis with fluorescence detection. After normalization and batch correction, several regression strategies were applied to evaluate associations between glycan patterns, familial longevity, and healthy aging. Two N-glycan features (LC-7 and LC-8) were identified to be more abundant in plasma of the offspring of long-lived individuals as compared to controls. These results were not confounded by the altered lipid status or glucose homeostasis of the offspring. Furthermore, a decrease in levels of LC-8 was associated with the occurrence of myocardial infarction (p = 0.049, coefficient = -0.065), indicating that plasma glycosylation patterns do not only mark familial longevity but may also reflect healthy aging. In conclusion, we describe two glycan features, of which increased levels mark familial longevity and decreased levels of one of these features mark the presence of cardiovascular disease.     

Improved confidence intervals for a difference of two cause-specific cumulative incidence functions estimated in the presence of competing risks and random censoring

A cause-specific cumulative incidence function (CIF) is the probability of failure from a specific cause as a function of time. In randomized trials, a difference of cause-specific CIFs (treatment minus control) represents a treatment effect. Cause-specific CIF in each intervention arm can be estimated based on the usual non-parametric Aalen–Johansen estimator which generalizes the Kaplan–Meier estimator of CIF in the presence of competing risks. Under random censoring, asymptotically valid Wald-type confidence intervals (CIs) for a difference of cause-specific CIFs at a specific time point can be constructed using one of the published variance estimators. Unfortunately, these intervals can suffer from substantial under-coverage when the outcome of interest is a rare event, as may be the case for example in the analysis of uncommon adverse events. We propose two new approximate interval estimators for a difference of cause-specific CIFs estimated in the presence of competing risks and random censoring. Theoretical analysis and simulations indicate that the new interval estimators are superior to the Wald CIs in the sense of avoiding substantial under-coverage with rare events, while being equivalent to the Wald CIs asymptotically. In the absence of censoring, one of the two proposed interval estimators reduces to the well-known Agresti–Caffo CI for a difference of two binomial parameters. The new methods can be easily implemented with any software package producing point and variance estimates for the Aalen–Johansen estimator, as illustrated in a real data example.     

Nonparametrically Weighted Least Squares Estimation in Heteroscedastic Linear Regression

The weights used in iterative weighted least squares (IWLS) regression are usually estimated parametrically using a working model for the error variance. When the variance function is misspecified, the IWLS estimates of the regression coefficients β are still asymptotically consistent but there is some loss in efficiency. Since second moments can be quite hard to model, it makes sense to estimate the error variances nonparametrically and to employ weights inversely proportional to the estimated variances in computing the WLS estimate for β. Surprisingly, this approach had not received much attention in the literature. The aim of this note is to demonstrate that such a procedure can be implemented easily in S-plus using standard functions with default options making it suitable for routine applications. The particular smoothing method that we use is local polynomial regression applied to the logarithm of the squared residuals but other smoothers can be tried as well. The proposed procedure is applied to data on the use of two different assay methods for a hormone. Efficiency calculations based on the estimated model show that the nonparametric IWLS estimates are more efficient than the parametric IWLS estimates based on three different plausible working models for the variance function. The proposed estimators also perform well in a simulation study using both parametric and nonparametric variance functions as well as normal and gamma errors.     

The structure of yeast tRNA(Asp). A model for tRNA interacting with messenger RNA

The anticodon of yeast tRNA(Asp), GUC, presents the peculiarity to be self-complementary, with a slight mismatch at the uridine position. In the orthorhombic crystal lattice, tRNA(Asp) molecules are associated by anticodon-anticodon interactions through a two-fold symmetry axis. The anticodon triplets of symmetrically related molecules are base paired and stacked in a normal helical conformation. A stacking interaction between the anticodon loops of two two-fold related tRNA molecules also exists in the orthorhombic form of yeast tRNA(Phe). In that case however the GAA anticodon cannot be base paired. Two characteristic differences can be correlated with the anticodon-anticodon association: the distribution of temperature factors as determined from the X-ray crystallographic refinements and the interaction between T and D loops. In tRNA(Asp) T and D loops present higher temperature factors than the anticodon loop, in marked contrast to the situation in tRNA(Phe). This variation is a consequence of the anticodon-anticodon base pairing which rigidifies the anticodon loop and stem. A transfer of flexibility to the corner of the tRNA molecule disrupts the G19-C56 tertiary interactions. Chemical mapping of the N3 position of cytosine 56 and analysis of self-splitting patterns of tRNA(Asp) substantiate such a correlation.     

A diatom based transfer function for reconstructing sea ice concentrations in the North Atlantic

A diatom based sea ice transfer function is developed using 99 surface sediment samples from the North Atlantic and the associated modern sea ice concentrations. Canonical correspondence analysis (CCA) is applied to the species assemblages of the surface sediment samples and the association of the species with two environmental parameters, August sea surface temperature and May sea ice concentration, is assessed. The results of this analysis indicate negative correlation between sea ice and sea surface temperature and that a group of diatom species is strongly associated with sea ice, especially May sea ice concentration. The results of the CCA legitimate the development of a diatom based sea ice transfer function. The maximum likelihood method has been applied as the transfer function method, as it has been proven most suitable with this particular data set. The newly developed transfer function is then used to reconstruct May sea ice concentration in three cases, each focusing on a different time period: the Last Glacial Maximum, the Younger Dryas and the Holocene. In all three cases the transfer function produces reasonable results when compared to other paleoclimatic proxy results. This suggests that the sea ice concentration reconstructed by the diatom based sea ice transfer function is a valid and reliable method, which can be applied as a valid proxy for May sea ice concentration.     

Point pattern analysis under conditions of replicated sampling北大核心CSCD

Aims: The analysis of point patterns, which deals with data sets consisting of mapped locations of organisms in a study region, is especially important to plant ecological studies because the locations of plants can often be approximated as points. However, few studies used point pattern analysis with data collected by replicated sampling. a principle procedure of acquiring data in ecological research. Therefore, we explore the applicability of point pattern analysis under conditions of replicated sampling in this study. Methods: Three replicated 5 m × 5 m plots of homogenous communities were established on a site with eight years of restoration in Nei Mongol steppe. In each plot, the locations of individuals in Leymus chinensis and Stipa grandis populations were mapped. O-Ring function was used to describe the population patterns and species association between L. chinensis and S. grandis for each plot as well as the integrative data of the three replicates. Important findings: Population patterns and species associations differed among the three replicated plots. This illustrates that if point pattern analysis was applied to describe the population patterns and species associations only by using data from a single plot sampling, the results could be misleading. Whereas it would be more reliable to integrate the data of replicated plots in the point pattern analysis because in this way the resulting O-Ring function is a weighted average, where the weight is the number of points in the replicate i divided by the total number of points in all replicated plots.     

A statistical study of the multivariate structure and race-sex differences of American white and Negro fetal skeletons

The techniques of factor analysis and discriminant analysis have been applied to 21 measurements of 115 fetal, American White and Negro skeletons. It was found that the factor patterns of the race-sex groups are similar and that two factors describe approximately 85% of the total variance of the multivariate structure of the skeleton. Discriminant analyses showed that differences between the sexes are more marked than those between the races. A function was obtained by which the sex of fetal skeletons may be classified.