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Journal of the American Statistical Association

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.

Content uploaded by Stephen Rathbun

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All content in this area was uploaded by Stephen Rathbun on Apr 29, 2015

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... Competition for belowground resources may have been occurring; belowground competition among trees was observed >15 m into openings in a previous study near the same site (Pecot et al., 2007). Despite the exact mechanism of competition remaining unclear, our empirical finding of competition among mature pines was consistent with stocking chart predictions and other observations in longleaf pine woodlands (Rathbun & Cressie, 1994). The finding of some positive effects of hardwood neighbors on mature pine growth rates was surprising, particularly given that hardwoods can exert intense competition against juvenile longleaf pines (Pecot et al., 2007). ...

... Our finding that longleaf pine growth essentially decreased monotonically as dbh increased cannot therefore provide support for a possible link between shade tolerance and size at maximum growth rate. Furthermore, our findings contrast with those from an old-growth longleaf pine stand <100 km distant where growth increased with size for juveniles and subadults then decreased for adults (Rathbun & Cressie, 1994). We hypothesize that differing stand histories may have played a role: the old-growth stand underwent minimal cutting (Platt et al., 1988), whereas most canopy trees at the site of the present study established in open conditions after heavy cutting early in the 20th century, which may account for the rapid early growth we observed. ...

Abstract Longleaf pine woodlands of the North American Coastal Plain are proposed to be resilient to climate change impacts, but little is known about changes in limiting factors to longleaf pine growth as climate has changed in late 20th century and early 21st century. Moreover, the role that neighborhood trees play in the context of climate change remains largely unexplored. We used static and moving window tree ring and climatic analyses to measure the effects of climate on longleaf pine growth at a site in southwest Georgia, USA. We then performed maximum likelihood analysis to examine the influence of neighboring hardwoods on the response of longleaf pine growth to the joint effects of competition and climate. Analysis of climate data from local stations in southwest Georgia over six decades indicated that mean air temperature decreased until the late 20th century then began to rise, and that the variability of spring and summer precipitation has increased. Tree ring and climate analyses indicated longleaf pine radial growth is sensitive to precipitation and air temperature, and that the strength of correlation of longleaf pine growth to summer air temperature and summer precipitation increased since the 1950s. Likelihood models, which were applied over a shorter (23‐year) period and explicitly incorporated competition, did not support a link between summer temperature and growth but did indicate summer precipitation increased growth. Furthermore, basal area (BA) of neighboring hardwoods was correlated with greater pine growth per millimeter of precipitation. BA of neighboring longleaf pine negatively affected growth of conspecific trees; the presence of hardwoods increased the competitive effect when BA of neighboring pine trees was low (

... This is surprising considering that other studies have found that silvicultural thinning can increase cone production in longleaf pine (Brockway et al., 2006) and many other pines (Krannitz & Duralia, 2004;Moreno-Fernández et al., 2013;Ayari & Khouja, 2014). Competition among mature longleaf trees in open forests is relatively small compared with earlier life stages (Rathbun & Cressie, 1994); thus, removal of neighbors may have minimal impact on resource availability and cone production in the low-density New Phytologist (2023) www.newphytologist.com stands examined here. ...

Many trees exhibit masting – where reproduction is temporally variable and synchronous over large areas. Several dominant masting species occur in tropical cyclone (TC)‐prone regions, but it is unknown whether TCs correlate with mast seeding.
We analyzed long‐term data (1958–2022) to test the hypothesis that TCs influence cone production in longleaf pine ( Pinus palustris ). We integrate field observations, weather data, satellite imagery, and hurricane models to test whether TCs influence cone production via: increased precipitation; canopy density reduction; and/or mechanical stress from wind.
Cone production was 31% higher 1 yr after hurricanes and 71% higher after 2 yr, before returning to baseline levels. Cyclone‐associated precipitation was correlated with increased cone production in wet years and cone production increased after low‐intensity winds (≤ 25 m s ⁻¹ ) but not with high‐intensity winds (> 25 m s ⁻¹ ).
Tropical cyclones may stimulate cone production via precipitation addition, but high‐intensity winds may offset any gains. Our study is the first to support the direct influence of TCs on reproduction, suggesting a previously unknown environmental correlate of masting, which may occur in hurricane‐prone forests world‐wide.

... This is surprising considering that other studies have found that silvicultural thinning can increase cone production in longleaf pine (Brockway et al., 2006) and many other pines (Krannitz & Duralia, 2004;Moreno-Fernández et al., 2013;Ayari & Khouja, 2014). Competition among mature longleaf trees in open forests is relatively small compared with earlier life stages (Rathbun & Cressie, 1994); thus, removal of neighbors may have minimal impact on resource availability and cone production in the low-density New Phytologist (2023) www.newphytologist.com stands examined here. ...

... 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). ...

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.

Aim
Accounting for biotic interactions in species distribution models is complicated by the fact that interactions occur at the individual‐level at unknown spatial scales. Standard approaches that ignore individual‐level interactions and focus on aggregate scales are subject to the modifiable aerial unit problem (MAUP) in which incorrect inferences may arise about the sign and magnitude of interspecific effects.
Location
Global (simulation) and North Carolina, United States (case study).
Taxon
None (simulation) and Aves (case study).
Methods
We present a hierarchical species distribution model that includes a Markov point process in which the locations of individuals of one species are modelled as a function of both abiotic variables and the locations of individuals of another species. We applied the model to spatial capture‐recapture (SCR) data on two ecologically similar songbird species—hooded warbler ( Setophaga citrina ) and black‐throated blue warbler ( Setophaga caerulescens )—that segregate over a climate gradient in the southern Appalachian Mountains, USA.
Results
A simulation study indicated that the model can identify the effects of environmental variation and biotic interactions on co‐occurring species distributions. In the case study, there were strong and opposing effects of climate on spatial variation in population densities, but spatial competition did not influence the two species' distributions.
Main Conclusions
Unlike existing species distribution models, the framework proposed here overcomes the MAUP and can be used to investigate how population‐level patterns emerge from individual‐level processes, while also allowing for inference on the spatial scale of biotic interactions. Our finding of minimal spatial competition between black‐throated blue warbler and hooded warbler adds to the growing body of literature suggesting that abiotic factors may be more important than competition at low‐latitude range margins. The model can be extended to accommodate count data and binary data in addition to SCR data.

We introduce a new fully non-parametric two-step adaptive bandwidth selection method for kernel estimators of spatial point process intensity functions based on the Campbell–Mecke formula and Abramson’s square root law. We present a simulation study to assess its performance relative to other adaptive and global bandwidth selectors, investigate the influence of the pilot estimator and apply the technique to two data sets: A pattern of trees and an earthquake catalogue.

Bayesian latent Gaussian models are Bayesian hierarchical models that assign Gaussian prior densities to the latent parameters. In this chapter, we present three subclasses within the class of Bayesian latent Gaussian models, namely, Bayesian Gaussian–Gaussian models, Bayesian latent Gaussian models with a univariate link function, and Bayesian latent Gaussian models with a multivariate link function. The structure of each subclass is described along with methods to infer the parameters of these models. The construction of prior densities for the latent parameters and the hyperparameters is described. Several examples are given to demonstrate how to apply models from these subclasses to real datasets.

Species interactions and abiotic factors are important determinants of abundance and distribution, but accounting for biotic interactions is complicated by the fact that interactions occur at the individual-level at unknown spatial scales. Ignoring individual-level interactions can yield incorrect conclusions about biotic interactions when analyzing aggregated count data or presence-absence data. We present a hierarchical species distribution model that includes a Markov point process in which an individual’s location is dependent upon both abiotic variables and the locations of individuals of another species. The model can be regarded as a thinned point process in which encounter probability is a function of the distance between individual activity centers and survey locations. We applied the model to spatial capture-recapture data on two ecologically similar songbird species – hooded warbler ( Setophaga citrina ) and black-throated blue warbler ( Setophaga caerulescens ) – that segregate over a climate gradient in the southern Appalachian Mountains, USA. In spite of coarse spatial segregation and many ecological similarities between the two species, we found minimal evidence of spatial competition. There were strong, and opposing effects of climate on spatial variation in population densities, but spatial competition did not influence their distributions. A small simulation study indicated that the model can identify the distinct effects of environmental variation and biotic interactions on co-occurring species distributions. Unlike previous statistical models that attempt to infer competition from species-level co-occurrence data, the framework proposed here can be used to investigate how population-level patterns emerge from individual-level processes, while also allowing for inference on the spatial scale of biotic interactions. Our finding of minimal spatial competition between black-throated blue warbler and hooded warbler adds to the growing body of literature suggesting that, contrary to early theory from biogeography, abiotic factors may be more important than competition at low-latitude range margins.

When spatial data are repeatedly collected over a short period of time, they
exhibit two-way correlations. More specifically at a given point of time the
neighboring responses from a spatial family become pair-wise spatially correlated,
and over time each of these familial responses become longitudinally
correlated, leading to a two-way multivariate spatial longitudinal correlation
model. Recently, this type of two-way multivariate correlation model was
studied by Sutradhar (2021, Sankhya A, 83, 206-244) for linear longitudinal
spatial data. However, as the binary correlations can not be obtained directly
from linear correlations, the construction of spatial longitudinal model for
binary data requires special efforts mainly for combining the two structures,
spatial and longitudinal, those are themselves complex for binary data. In
this paper we resolve this challenge by using first a conditional (on spatial
family-based random effects) binary dynamic logits (CBDL) model for longitudinal
binary data, and then integrating out the family-based random
effects over their distributional properties those used originally to generate
spatial correlations. For inferences for the proposed model, we develop
the so-called generalized quasi-likelihood (GQL) and method of moments
approaches. Asymptotic properties such as consistency of the estimators of
all parameters and asymptotic normality for the GQL estimators of main
regression parameters are discussed in details.

In an old-growth longleaf pine population in which all trees of at least 2 cm in dbh were mapped and tagged, the population was of uneven age and size; tree size correlated positively with tree age. Large or old trees were only loosely aggregated, forming a background matrix that filled the forest. Juvenile trees were highly aggregated, located in areas of low adult densities. Recruitment thus occurs primarily within open spaces created by the deaths of large trees. Variable time lags may occur before the colonization of open spaces, however, because of temporal variation in seed production and occurrence of summer ground fires. Recruitment within the mapped plot has occurred frequently for at least the past 250 yr. Temporal variation in adult mortality and recruitment into open spaces, coupled with strong negative interactions between cohorts of different ages, appears likely to produce alternating phases of population growth and decline that are highly variable in length and magnitude. An upper bound to population size occurs when all available space is filled with trees; but no lower bound exists, and extinction probabilities may be increased at very low densities. The population is buffered from declines to very low densities, however, by the tendency for small trees to recruit into openings created by the deaths of adults. Longleaf pine possibly maintains the environment in an open state suitable for its own regeneration by transmuting a localized disturbance (lightning) into a widespread disturbance (ground fires). Fire facilitation results in an extended, but indefinite, increase in the persistence of environmental conditions in which longleaf pine, but no other tree species, can survive and reproduce. -from Authors

In previous papers (1976), (1977) limit theorems were obtained for the classical Ising model in the absence of an external magnetic field, thereby providing a basis for asymptotic inference. The present paper extends these results to arbitrary external magnetic fields. Statistical inference for this model is important because its nearest-neighbour interactions provide a natural first approximation to spatial interaction among binary variables located on square lattices.
The most interesting behaviour occurs in zero field and at or beyond the critical point. In this case, the central limit result for nearest-neighbour interactions requires an unusual norming, the limiting variances may depend on the nature of the boundary conditions, and there cannot be any central limit result for external magnetic field. The implications of these phenomena for statistical inference are also discussed. In particular, the maximum likelihood estimator of magnetic field is not consistent. Rather it appears to have a non-trivial asymptotic distribution.

A definition of the Markovian property is given for a lattice process and a Gaussian Markovian lattice process is constructed on a torus lattice. From this a Gaussian Markovian process is constructed for a lattice in the plane and its properties are studied.

From certain points of view, the range of probability models currently available for describing the joint behaviour of two point processes is rather limited. In this paper we explore the structure of some further models and apply our results to the statistical analysis of bivariate spatial point patterns.

B. Kaufmann's exact characterization of the partition function for the classical Ising model is used to obtain limit theorems for the sample correlation between nearest neighbors in the non-critical case. This provides a basis for the asymptotic testing and estimation (by confidence intervals) of the correlation between nearest neighbors.

In Pickard (1976) limit theorems were obtained for the classical Ising model at non-critical points. These determined the asymptotic distribution of the sample nearest-neighbour correlation, thereby providing a basis for statistical inference by confidence intervals. In this paper, these limit theorems are extended to the statistically significant case of different vertical and horizontal interactions. Results at critical points are also obtained. Critical points clearly have the potential to seriously distort statistical inferences, especially in their immediate neighbourhoods. For our Ising model it turns out that such distortion is relatively minor. Surprisingly, in the two-parameter case the correlation between the sufficient statistics exhibits peculiar asymptotic behaviour resulting in a singular covariance matrix at critical points in the central limit theorem. Finally, at critical points, unusual norming constants are required for the central limit theorem, and our results are much more sensitive to the relative rate at which m,n tend to infinity.

In previous papers (1976), (1977) limit theorems were obtained for the classical Ising model in the absence of an external magnetic field, thereby providing a basis for asymptotic inference. The present paper extends these results to arbitrary external magnetic fields. Statistical inference for this model is important because its nearest-neighbour interactions provide a natural first approximation to spatial interaction among binary variables located on square lattices.
The most interesting behaviour occurs in zero field and at or beyond the critical point. In this case, the central limit result for nearest-neighbour interactions requires an unusual norming, the limiting variances may depend on the nature of the boundary conditions, and there cannot be any central limit result for external magnetic field. The implications of these phenomena for statistical inference are also discussed. In particular, the maximum likelihood estimator of magnetic field is not consistent. Rather it appears to have a non-trivial asymptotic distribution.

Cluster point processes are defined and studied using the probability generating functional. Necessary and sufficient conditions for the existence of a cluster process are proved and applied to particular cases. A result on mixing in cluster processes is established.

Recent yearly bole growth of individual trees, as estimated from height and annual growth ring measurements, is considered as a function of the number, distance and size of neighbours in a young Pinus rigida stand in New Jersey. Results are consistent with a model in which the growth of an individual is inversely related to the total effect of interference, and the contribution of each neighbour to this effect is additive in proportion to its size and inversely proportional to the square of its distance. While results show, as expected, that the effect of a neighbour decreases with its distance, they do not allow one to distinguish between alternative formulations with confidence, but a modified version of the model in which the effect of a neighbour decreases with its distance always resulted in a slightly improved fit over the original formulation in which a neighbour's effect decreases with the square of its distance. -from Author