Multivariate product‐shot‐noise Cox point process models

We introduce a new multivariate product-shot-noise Cox process which is useful for modeling multi-species spatial point patterns with clustering intra-specific interactions and neutral, negative, or positive inter-specific interactions. The auto- and cross-pair correlation functions of the process can be obtained in closed analytical forms and approximate simulation of the process is straightforward. We use the proposed process to model interactions within and among five tree species in the Barro Colorado Island plot.

[1]  N. Picard,et al.  Understanding the dynamics of an undisturbed tropical rain forest from the spatial pattern of trees , 2009 .

[2]  D. Stoyan,et al.  Recent applications of point process methods in forestry statistics , 2000 .

[3]  J. Illian,et al.  Ecological information from spatial patterns of plants: insights from point process theory , 2009 .

[4]  M. Emmerson,et al.  MEASUREMENT OF INTERACTION STRENGTH IN NATURE , 2005 .

[5]  J. Møller,et al.  Shot noise Cox processes , 2003, Advances in Applied Probability.

[6]  A. Gelfand,et al.  ANALYSIS OF MINNESOTA COLON AND RECTUM CANCER POINT PATTERNS WITH SPATIAL AND NONSPATIAL COVARIATE INFORMATION. , 2009, The annals of applied statistics.

[7]  Aila Särkkä,et al.  Modelling the spatial structure of forest stands by multivariate point processes with hierarchical interactions. , 2009 .

[8]  E. B. Jensen,et al.  Asymptotic Palm likelihood theory for stationary point processes , 2013 .

[9]  Valerie Isham,et al.  A Bivariate Spatial Point Pattern of Ants' Nests , 1983 .

[10]  D. Warton,et al.  Equivalence of MAXENT and Poisson Point Process Models for Species Distribution Modeling in Ecology , 2013, Biometrics.

[11]  Peter J. Diggle,et al.  Bivariate Cox Processes: Some Models for Bivariate Spatial Point Patterns , 1983 .

[12]  Nicolas Picard,et al.  The Multi‐scale Marked Area‐interaction Point Process: A Model for the Spatial Pattern of Trees , 2008 .

[13]  van Marie-Colette Lieshout,et al.  Indices of Dependence Between Types in Multivariate Point Patterns , 1999 .

[14]  Jorge Mateu,et al.  Modelling Forest Dynamics: A Perspective from Point Process Methods , 2007, Biometrical journal. Biometrische Zeitschrift.

[15]  Daryl J. Daley,et al.  An Introduction to the Theory of Point Processes , 2013 .

[16]  David F. R. P. Burslem,et al.  Contributions of spatial point process modelling to biodiversity theory , 2007 .

[17]  R. Waagepetersen,et al.  Decomposition of Variance for Spatial Cox Processes , 2013, Scandinavian journal of statistics, theory and applications.

[18]  Adrian Baddeley,et al.  spatstat: An R Package for Analyzing Spatial Point Patterns , 2005 .

[19]  Yongtao Guan,et al.  A Composite Likelihood Approach in Fitting Spatial Point Process Models , 2006 .

[20]  R. Waagepetersen,et al.  Two‐step estimation for inhomogeneous spatial point processes , 2009 .

[21]  A. Baddeley,et al.  Non‐ and semi‐parametric estimation of interaction in inhomogeneous point patterns , 2000 .

[22]  Donald L DeAngelis,et al.  Consumer-resource theory predicts dynamic transitions between outcomes of interspecific interactions. , 2009, Ecology letters.

[23]  Anders Brix,et al.  Space‐time Multi Type Log Gaussian Cox Processes with a View to Modelling Weeds , 2001 .

[24]  Michaela Prokešová,et al.  Lévy-based Cox point processes , 2008, Advances in Applied Probability.

[25]  Dietrich Stoyan,et al.  Deviation test construction and power comparison for marked spatial point patterns , 2013, 1306.1028.

[26]  Z. Luo,et al.  Spatial associations of tree species in a subtropical evergreen broad-leaved forest , 2012 .

[27]  Stephen J. Wright,et al.  Light-Gap disturbances, recruitment limitation, and tree diversity in a neotropical forest , 1999, Science.

[28]  Richard Condit,et al.  Tropical Forest Census Plots , 1998, Environmental Intelligence Unit.

[29]  R. Waagepetersen.  An Estimating Function Approach to Inference for Inhomogeneous Neyman–Scott Processes , 2007, Biometrics.

[30]  J. Møller,et al.  Log Gaussian Cox Processes , 1998 .

[31]  Thorsten Wiegand,et al.  Species Associations in a Heterogeneous Sri Lankan Dipterocarp Forest , 2007, The American Naturalist.