Yongtao Guan | Search PubMed

PubMed2006

Tests for independence between marks and points of a marked point process.

A convenient assumption while modeling a marked point process is that the observations (i.e., marks) and the locations (i.e., points) are independent. We propose new graphical and formal testing approaches to test for this assumption. The proposed graphical procedures are easy to obtain and can be used to diagnose the nature and range of dependence between marks and points. The formal testing procedures require only minimal conditions on marks and thus can be applied to a variety of settings. We illustrate these procedures through a simulation study and an application to some real data.

Computer Graphics↗

PubMed2006

Assessing isotropy for spatial point processes.

A common assumption while analyzing spatial point processes is direction invariance, i.e., isotropy. In this article, we propose a formal nonparametric approach to test for isotropy based on the asymptotic joint normality of the sample second-order intensity function. We derive an L(2) consistent subsampling estimator for the asymptotic covariance matrix of the sample second-order intensity function and use this to construct a test statistic with a chi(2) limiting distribution. We demonstrate the efficacy of the approach through simulation studies and an application to a desert plant data set, where our approach confirms suspected directional effects in the spatial distribution of the desert plant species.

Anisotropy↗

PubMed2005

Spatial self-organization in a cyclic resource-species model.

Biological communities are remarkable in their ability to form cooperative ensembles that lead to coexistence through various types of niche partitioning, usually intimately tied to spatial structure. This is especially true in microbial settings where differential expression and regulation of genes allows members of a given species to alter their lifestyle so as to fill a functional role within the community. The resulting species interactions can involve feedback, as in the case of some bacterial consortia that participate in the cooperative degradation of a given resource in a succession of steps and in such a way that certain "later" species provide catalytic support for the primary degrader. We seek to capture the essential features of such spatially extended biological systems by introducing a lattice-based stochastic spatial model (interacting particle system) with cyclic local dynamics. Here, a given site progresses through a sequence of resource and species states in a prescribed order. Furthermore, this succession of states (at a site) is assumed to form a cyclic pattern due to a natural feedback mechanism. We explore conditions under which all the species are able to coexist and consider the extent to which this coexistence requires the development of spatio-temporal patterns, including spiral waves. This self-organization, if it occurs, results when synchronization of the dynamics at the microscopic level leads to macroscopic patterns. These patterns result in consumer-driven resource fluctuations that generate a form of spatio-temporal niche partitioning. As with most models of this complexity, we employ a mixture of mathematical analysis and simulations to develop an understanding of the resulting dynamics.

Adaptation, Biological↗