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Variograms, which are frequently used in geostatistics, are of value also in the statistics of marked point processes. When the marks come from a random field which is independent of the point process, ideas of geostatistics suffice for the interpretation of point process variograms. When this model is not appropriate, interactions between the points lead to point process variograms having forms which are unusual in geostcistics. This is shown by three theoretical examples and one from forestry. 相似文献
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Questions: 1. Does random colonization predominate in early stages of primary succession? 2. Do pioneer species facilitate the establishment of later arriving species? 3. Does an initially random distribution change to an aggregated pattern with ongoing succession? Location: Lignite mining region of Lower Lusatia, eastern Germany. Methods: Individual plants were mapped along a 2 m × 28 m transect during three successive years and classified into two groups (1) the pioneer Corynephorus canescens and (2)‘all other species’. Using the pair‐correlation function, univariate point pattern analysis was carried out by applying a heterogeneous Poisson process as null model. Bivariate analysis and a toroidal shift null model were applied to test for independence between the spatial patterns of the two groups separately for each year, as well by exploring spatiotemporal patterns from different years. Results: In the first year Corynephorus and ‘all other species’ showed an aggregated pattern on a spatial scale > 40 cm and in the second and third years a significant attraction for distances between 4 and 12 cm, with an increasing radius in the third year. The analyses of interspecific spatiotemporal dynamics revealed a change from independence to attraction between distances of 4 cm and 16 cm when using Corynephorus as focal species. However, applying ‘all other species’ as focal points results in a significant attraction at distances up to 60 cm in the first year and a diminishing attraction in the second and third years with distances ≤ 6 cm. Conclusions: Facilitative species‐species interactions are present in early stages of primary succession, resulting mainly from pioneer species acting as physical barriers and their ability to capture diaspores being drifted by secondary dispersal along the substrate surface. However, due to gradual establishment of perennial species and their ability of lateral extension by vegetative dispersal, facilitation may influence spatial pattern formation predominantly on short temporal and fine spatial scales. 相似文献
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No methods proposed thus far have the capability to measure molecular flow in live cells at the single molecule level. Here, we review the potentiality of a newly established method based on the spatial correlation of fluorescence fluctuations at a pair of points in the sample (pair correlation method). The pair correlation function (pCF) offers a unique tool to probe the directionality of intracellular traffic, by measuring the accessibility of the cellular landscape and its role in determining the diffusive routes adopted by molecules. The sensitivity of the pCF method toward detection of barriers means that different structural elements of the cell can be tested in terms of penetrability and mechanisms of regulation imparted on molecular flow. This has been recently demonstrated in a series of studies looking at molecular transport inside live cells. Here, we will review the theory behind detection of barriers to molecular flow, the rules to interpret pCF data, and relevant applications to intracellular transport. 相似文献
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Phytogenic mounds (nebkhas) often are symptoms of desertification in arid regions. Interactions among nebkhas and between nebkhas and their environment are however poorly examined. To this end, three main hypotheses of nebkha pattern formation were evaluated in this study. These state that nebkha patterns are either shaped by: (i) biologically induced recruitment inhibiting zones, (ii) biologically induced recruitment encouraging zones, or (iii) by the spatial distribution of abiotic factors which are not biologically driven. Contrasting nebkha landscapes were examined: a highly dense New Mexican mesquite (Prosopis glandulosa) and snakeweed (Gutierrezia sarothrae and Gutierrezia microcephala) ecosystem, and a low-density mixed Tamarix aphylla and Calligonum comosum field in central Libya. Spatial second-order statistics of strategically chosen nebkha subpatterns were compared with those of null models in which observed patches were spatially randomized without overlap. Null model deviations were assessed with goodness-of-fit tests, and interpreted in terms of hypothesized mechanisms of nebkha pattern formation. Our results suggest that biologically induced recruitment inhibiting zones surround adult mesquite nebkhas. The configuration of Calligonum and Tamarix nebkhas may be driven by spatial dynamics of abiotic microsites which are not caused by nebkha interactions. Hence we conclude that both biotic and abiotic drivers can shape nebkha spatial patterns. 相似文献
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In clinical and observational studies, recurrent event data (e.g., hospitalization) with a terminal event (e.g., death) are often encountered. In many instances, the terminal event is strongly correlated with the recurrent event process. In this article, we propose a semiparametric method to jointly model the recurrent and terminal event processes. The dependence is modeled by a shared gamma frailty that is included in both the recurrent event rate and terminal event hazard function. Marginal models are used to estimate the regression effects on the terminal and recurrent event processes, and a Poisson model is used to estimate the dispersion of the frailty variable. A sandwich estimator is used to achieve additional robustness. An analysis of hospitalization data for patients in the peritoneal dialysis study is presented to illustrate the proposed method. 相似文献
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Abstract. Spatial heterogeneity is a characteristic of most natural ecosystems which is difficult to handle analytically, particularly in the absence of knowledge about the exogenous factors responsible for this heterogeneity. While classical methods for analysis of spatial point patterns usually require the hypothesis of homogeneity, we present a practical approach for partitioning heterogeneous vegetation plots into homogeneous subplots in simple cases of heterogeneity without drastically reducing the data. It is based on the detection of endogenous variations of the pattern using local density and second‐order local neighbour density functions that allow delineation of irregularly shaped subplots that could be considered as internally homogeneous. Spatial statistics, such as Ripley's K‐function adapted to analyse plots of irregular shape, can then be computed for each of the homogeneous subplots. Two applications to forest ecological field data demonstrate that the method, addressed to ecologists, can avoid misinterpretations of the spatial structure of heterogeneous vegetation stands. 相似文献
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This article is concerned with variance estimation for statistics that are computed from single recurrent event processes. Such statistics are important in diagnosis for each individual recurrent event process. The proposed method only assumes a semiparametric form for the first-order structure of the processes but not for the second-order (i.e., dependence) structure. The new variance estimator is shown to be consistent for the target parameter under very mild conditions. The estimator can be used in many applications in semiparametric rate regression analysis of recurrent event data such as outlier detection, residual diagnosis, as well as robust regression. A simulation study and application to two real data examples are used to demonstrate the use of the proposed method. 相似文献
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We derive semiparametric methods for estimating and testing treatment effects when censored recurrent event data are available over multiple periods. These methods are based on estimating functions motivated by a working \"mixed-Poisson\" assumption under which conditioning can eliminate subject-specific random effects. Robust pseudoscore test statistics are obtained via \"sandwich\" variance estimation. The relative efficiency of conditional versus marginal analyses is assessed analytically under a mixed time-homogeneous Poisson model. The robustness and empirical power of the semiparametric approach are assessed through simulation. Adaptations to handle recurrent events arising in crossover trials are described and these methods are applied to data from a two-period crossover trial of patients with bronchial asthma. 相似文献
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Abstract. This paper describes new methods for the detection of the characteristics of spatial point patterns, based on counting plants in the circumcircles of triangles defined by triplets of the points themselves. In addition to counting points in the circumcircle, a further refinement is to count also the points in a ring around the circumcircle of the same area. This approach can be applied in a univariate form, with one species or one kind of plant, to detect and evaluate the best‐defined patches of plants and gaps. In the bivariate form, the method can be used to investigate the spatial characteristics of the relationship between different kinds of plants. These methods are illustrated by application to several data sets. In particular, the method is shown to be useful in describing the spatial relationship between seedlings and trees, both when the seedlings are on the forest floor beneath the canopy trees and when the seedlings represent post‐fire regeneration. 相似文献
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Forestry statistics needs realistic models for non-homogeneously distributed trees in forests. For elder trees, non-homogeneous Poisson or Cox processes are not realistic models. Instead, non-homogeneous Gibbs processes are suggested, which are described by a fixed pair potential describing the short-range interaction of trees and a location dependent intensity function describing long-range variation of tree density. The application of this model is demonstrated for a hickory forest in North Carolina and an artificial forest stand. 相似文献
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This paper proposes an approximative method for maximum likelihood estimation of parameters of Neyman-Scott and similar point processes. It is based on the point pattern resulting from forming all difference points of pairs of points in the window of observation. The intensity function of this constructed point process can be expressed in terms of second-order characteristics of the original process. This opens the way to parameter estimation, if the difference pattern is treated as a non-homogeneous Poisson process. The computational feasibility and accuracy of this approach is examined by means of simulated data. Furthermore, the method is applied to two biological data sets. For these data, various cluster process models are considered and compared with respect to their goodness-of-fit. 相似文献
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G. A. Lienert 《Biometrical journal. Biometrische Zeitschrift》1981,23(2):167-173
It is shown that 3-point response curves from N individuals imply a second order correlation (triplet correlation) between the 3 series of repeated measurements if the curves are clustered as to their shapes. Coefficients are defined and tests are suggested for triplet correlations. Nonparametric alternatives to ANOVA are discussed for repeated measurement designs involving shapeclustered response curves. 相似文献
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Summary In this article, we propose a family of semiparametric transformation models with time‐varying coefficients for recurrent event data in the presence of a terminal event such as death. The new model offers great flexibility in formulating the effects of covariates on the mean functions of the recurrent events among survivors at a given time. For the inference on the proposed models, a class of estimating equations is developed and asymptotic properties of the resulting estimators are established. In addition, a lack‐of‐fit test is provided for assessing the adequacy of the model, and some tests are presented for investigating whether or not covariate effects vary with time. The finite‐sample behavior of the proposed methods is examined through Monte Carlo simulation studies, and an application to a bladder cancer study is also illustrated. 相似文献
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Summary . Longitudinal studies typically collect information on the timing of key clinical events and on specific characteristics that describe those events. Random variables that measure qualitative or quantitative aspects associated with the occurrence of an event are known as marks. Recurrent marked point process data consist of possibly recurrent events, with the mark (and possibly exposure) measured if and only if an event occurs. Analysis choices depend on which aspect of the data is of primary scientific interest. First, factors that influence the occurrence or timing of the event may be characterized using recurrent event analysis methods. Second, if there is more than one event per subject, then the association between exposure and the mark may be quantified using repeated measures regression methods. We detail assumptions required of any time-dependent exposure process and the event time process to ensure that linear or generalized linear mixed models and generalized estimating equations provide valid estimates. We provide theoretical and empirical evidence that if these conditions are not satisfied, then an independence estimating equation should be used for consistent estimation of association. We conclude with the recommendation that analysts carefully explore both the exposure and event time processes prior to implementing a repeated measures analysis of recurrent marked point process data. 相似文献
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Sani I. Doguwa 《Biometrical journal. Biometrische Zeitschrift》1989,31(4):451-459
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. 相似文献
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Questions: Fire appears to affect both replacement patterns and coexistence of Araucaria araucana‐Nothofagus pumilio forests in the Andean Araucarian region of south‐central Chile. A quantitative assessment of coexistence in the absence of recent fires, however, is lacking. In this study, we considered the life‐history attributes, time of recruitment and spatial pattern of individuals of both tree species to address the following questions. How regular has recruitment of both species been in time? Is there any temporal niche differentiation? Are the two species positively or negatively associated in space and, if so, at what scale and for what age and size classes? Is there any spatial niche differentiation? Location: Andean Araucarian region of Chile, Villarrica National Park (39°35′S, 71°31′W; 1300 m a.s.l.). Methods: We stem‐mapped and cored a total of 1073 trees in a 1‐ha plot in a late‐successional post‐fire stand to examine spatiotemporal patterns of establishment. We used semivariogram modelling and the pair‐correlation function to distinguish between regeneration modes and describe species interactions. Results: The two species differ in their regeneration mode: whereas A. araucana appeared to recruit more continuously in time and space, episodic pulses of establishment were dominant for N. pumilio. At small scales, younger age‐class stems of A. araucana were randomly distributed, while older age‐class stems were aggregated. This was in contrast to common patterns for temperate tree species, including N. pumilio, following processes of self‐thinning. Younger age classes of A. araucana were distributed independently of older trees of both species, but younger age classes of N. pumilio had a negative association with older conspecifics at scales similar to crown diameter. Conclusions: In the absence of recent fires, it is likely that A. araucana would dominate the stand alone, given its greater shade tolerance, greater longevity and continuous recruitment. However, while canopy closure is still incomplete, the shade‐intolerant N. pumilio will be able to recruit in those open areas after seed masting and will coexist with A. araucana. 相似文献