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A Space-Time Survival Point Process for a Longleaf Pine Forest in Southern Georgia

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Abstract

A marked spatial point pattern of trees and their diameters is the result of a dynamic biological process that takes place over time as well as space. Such patterns can be modeled as realizations of marked space-time survival point processes, where trees are born at some random location and time and then live, grow, and produce offspring in a random fashion. A model for a marked space-time survival point process is fit to data from a longleaf pine ( Pinus palustris ) forest in southern Georgia. The space-time survival point process is divided into three components: a birth process, a growth process, and a survival process. Each of the component processes is analyzed individually, from which conclusions regarding the dynamic ecological processes can be made. By using this reductionist approach, questions concerning each individual process can be addressed that might not have been answerable otherwise.
... To provide context for the changes in forest structure and spatial pattern from selection treatments in second growth forests, we also incorporate data from a well-studied 200-ha old-growth longleaf pine woodland on the Wade Tract in Thomasville GA (30.75 • N 84.00 • W; Platt et al., 1988;Platt and Rathbun, 1993;Rathbun and Cressie, 1994). Although the Wade Tract experienced grazing and other minor disturbances (Engstrom et al., in press), recent records indicate no extensive clearing or plowing, and limited selective logging or salvaging of some lightning struck trees (Platt et al., 1988). ...
... Thus, the Wade Tract is thought to be a representative example of old-growth longleaf pine woodlands of the Tallahassee Red Hills. We use a publicly available dataset of the Wade Tract analyzed in Rathbun and Cressie (1994) available in the spatstat package in R (Baddeley and Turner, 2005). This dataset includes point locations and dbh for 584 trees in a 4 ha area ca. ...
... To determine how selection treatments altered the spatial pattern of overstory trees, we used a point process-based approach (Rathbun and Cressie, 1994). We tested whether trees within each treatment were distributed randomly, uniformly, or aggregated by using the distancedependent univariate pair correlation function, g(r) (Dale and Fortin, 2014). ...
Article
Natural disturbance-based silviculture emphasizes harvest methods that emulate the timing and structural changes of natural disturbances. Longleaf pine woodlands are ecologically important ecosystems of the southeastern U.S. that support high biodiversity. Options for multi-aged silviculture include individual tree and group selection methods to promote regeneration—the latter method may be modified by retention of reserve trees. To explore the extent to which selection methods are congruent with natural disturbance regimes, we evaluated how treatments in mature second-growth longleaf pine woodlands affected overstory structure, pattern, and dynamics, and we made comparisons to an old-growth longleaf stand. In 2010, stands were harvested using individual tree selection, group selection, or group selection with reserves. We compared treatment effects on spatial pattern of residual trees, recruitment of trees into the 10 cm diameter class (hereafter “recruitment”), and tree mortality 8 years after harvest. Basal area and residual volume were similar among treatments, but the individual tree selection treatment had lower density and a unimodal rather than bimodal diameter distribution compared to other treatments. Group selection and group selection with reserves increased spatial aggregation, compared to individual tree selection which reduced aggregation. Recruitment was similar across treatments but usually occurred near existing trees in the group selection treatments and was further from existing trees in the individual tree selection treatment. Tree mortality primarily occurred as single trees rather than tree groups for all treatments. These results indicate that natural disturbance-based treatments vary in their effects on overstory spatial pattern and alter forest dynamics. In longleaf pine woodlands, the rationale for individual tree selection emphasizes maintaining a continuous input of needles as fine fuels for control of resprouting hardwoods with prescribed fire. This method, may simplify overstory spatial structure and alter forest dynamics after initial harvest. Maintenance of vertical and horizontal complexity is a central tenet of natural disturbance-based management, thus attention to spatial pattern must be given when individual tree selection methods are used. In longleaf pine woodlands, natural disturbance-based techniques such as group selection with reserves may better mimic spatial patterns seen in old-growth stands while preserving continuity of fine fuels.
... We next consider treatment decisions for egos in a social network, where each individual may have more than one neighbour. In particular, we consider five types of fixed network: (i) a ring consisting of points on a circle, (ii) a square lattice, (iii) an Erdős-Rényi (ER) network realization, (iv) a Barabási-Albert (BA) network realization, and (v) the Longleaf Pines (Rathbun & Cressie, 1994) spatial network. The ring and the square lattices are simple network structures with a constant degree. ...
Article
Precision medicine describes health care where patient‐level data are used to inform treatment decisions. Within this framework, dynamic treatment regimes (DTRs) are sequences of decision rules that take individual patient information as input data and then output treatment recommendations. DTR estimation from observational data typically relies on the assumption of no interference: i.e., the outcome of one individual is unaffected by the treatment assignment of others. However, in many social network contexts, such as friendship or family networks, and for many health concerns, such as infectious diseases, this assumption is questionable. We investigate the DTR estimation method of dynamic weighted ordinary least squares (dWOLS), which boasts of easy implementation and the so‐called double‐robustness property, but relies on the assumption of no interference. We define a network propensity function and build on it to establish an implementation of dWOLS that remains doubly robust under interference associated with network links. The method's properties are demonstrated via simulation and applied to data from the Population Assessment of Tobacco and Health (PATH) study to investigate cigarette dependence within two‐person household networks. La médecine de précision est une discipline médicale qui vise à dresser le portrait de soins de santé d'un patient en se fiant à ses données spécifiques pour prendre une décision éclairée quant aux traitement et soins à lui prodiguer. Dans ce contexte, les régimes de traitement dynamiques (RTD) sont des suites de règles de décision qui se servent des données individuelles du patient pour produire des recommandations de traitement personnalisé. L'estimation de RTD à partir de données d'observation repose généralement sur l'hypothèse de non‐interférence, dans le sens que, le résultat d'un patient n'est pas affecté par le traitement prescrit à d'autres patients. Cependant, dans de nombreux contextes de réseaux sociaux, tels que les réseaux d'amis ou de proches, et pour de nombreux problèmes de santé, tels que les maladies infectieuses, cette hypothèse est questionable. Les auteurs de ce travail étudient la méthode éstimation de RTD par les moindres carrés ordinaires pondérés dynamiques (dWOLS), méthode qui repose sur l'hypothèse de non‐interférence tout en étant facile à mettre en œuvre et jouit de la propriété dite de double robustesse. Pour ce faire, ils définissent une fonction de propension de réseau sur laquelle ils s'appuient pour établir une mise en œuvre des dWOLS qui reste doublement robuste même en présence ínterférence associée aux liens réseaux. Les propriétés de la méthode sont illustrées par simulation, et appliquées aux données de l'étude PATH (Population Assessment of Tobacco and Health) pour étudier la dépendance à la cigarette au sein de réseaux de ménages de deux personnes.
... We illustrate the above on a real dataset as suggested in Example 5.3 of Taddy and Kottas (2012). The suggested dataset, longleaf is part of the R package spatstat (Baddeley and Turner 2005) and a detailed space-time survival analysis based on this was developed in Rathbun and Cressie (1994). The observations are locations of 584 pine trees in a 200 × 200 square and the marks are diameters of the trees at breast height (only for trees having this diameter greater than 2 cm). ...
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Predictive recursion (PR) is a fast, recursive algorithm that gives a smooth estimate of the mixing distribution under the general mixture model. However, the PR algorithm requires evaluation of a normalizing constant at each iteration. When the support of the mixing distribution is of relatively low dimension, this is not a problem since quadrature methods can be used and are very efficient. But when the support is of higher dimension, quadrature methods are inefficient and there is no obvious Monte Carlo-based alternative. In this paper, we propose a new strategy, which we refer to as PRticle filter, wherein we augment the basic PR algorithm with a filtering mechanism that adaptively reweights an initial set of particles along the updating sequence which are used to obtain Monte Carlo approximations of the normalizing constants. Convergence properties of the PRticle filter approximation are established and its empirical accuracy is demonstrated with simulation studies and a marked spatial point process data analysis.
... Given the importance of longleaf pine ecosystems, a thorough understanding of stand dynamics of the species seems to be needed for its restoration. Research on the spatial patterns of trees in longleaf pine forests has been limited (Platt et al., 1988;Rathbun and Cressie 1994). Spatial patterns of trees would give many ideas on the stand dynamics of longleaf pine forests. ...
... Cox-process models (Møller et al., 1998), and these are difficult and time-consuming to fit (Teng et al., 2017). A CAR model as a random effect on a grid is a fast approximation for the spatial point process intensity surface (Rathbun and Cressie, 1994), and still provides an MCMC sample from the posterior distribution (Besag, 1994). A sensitivity analysis could be performed (Kéry and Royle, 2016, p. 415) on hexagon size, and ultimately, the coarsest-scale grid that meets objectives should be adopted as the fastest method. ...
Article
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... See, for example, Besag [4,5] and Besag [6], for some early studies. For some recent studies over the past three decades, see, for example, Rathban and Cressie [14], Heagerty and Lele [9], Lin and Clayton [11], and Ainsworth et al. [1]. As far as the model for spatial binary data is concerned, these existing studies mostly used the CAR [6], BPM [9], and WCQL [11] models to accommodate spatial binary correlations. ...
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