Improving the usability of spatial point process methodology: an interdisciplinary dialogue between statistics and ecology

The last few decades have seen an increasing interest and strong development in spatial point process methodology, and associated software that facilitates model fitting has become available. A lot of this progress has made these approaches more accessible to users, through freely available software. However, in the ecological user community the methodology has only been slowly picked up despite its obvious relevance to the field. This paper reflects on this development, highlighting mutual benefits of interdisciplinary dialogue for both statistics and ecology. We detail the contribution point process methodology has made to research on biodiversity theory as a result of this dialogue and reflect on reasons for the slow take-up of the methodology. This primarily concerns the current lack of consideration of the usability of the approaches, which we discuss in detail, presenting current discussions as well as indicating future directions.

[1]  van Marie-Colette Lieshout,et al.  Markov Point Processes and Their Applications , 2000 .

[2]  M. Uriarte,et al.  Multispecies coexistence of trees in tropical forests: spatial signals of topographic niche differentiation increase with environmental heterogeneity , 2013, Proceedings of the Royal Society B: Biological Sciences.

[3]  Tom Mens,et al.  On the Development and Distribution of R Packages: An Empirical Analysis of the R Ecosystem , 2015, ECSA Workshops.

[4]  Mevin B Hooten,et al.  Estimating animal resource selection from telemetry data using point process models. , 2013, The Journal of animal ecology.

[5]  Ecological processes maintaining differential tree species distributions in an Australian subtropical rain forest: implications for models of species coexistence , 2000, Journal of Tropical Ecology.

[6]  Harri HöUgmander,et al.  Multitype Spatial Point Patterns with Hierarchical Interactions , 1999 .

[7]  David Kenfack,et al.  An estimate of the number of tropical tree species , 2015, Proceedings of the National Academy of Sciences.

[8]  H. Rue,et al.  Scaling intrinsic Gaussian Markov random field priors in spatial modelling , 2014 .

[9]  Alan E. Gelfand,et al.  Modeling Space-Time Data Using Stochastic Differential Equations , 2009 .

[10]  Glenna F. Nightingale,et al.  Pairwise Interaction Point Processes for Modelling Bivariate Spatial Point Patterns in the Presence of Interaction Uncertainty , 2015 .

[11]  M. Cruz,et al.  Release of Juniperus thurifera woodlands from herbivore-mediated arrested succession in Spain , 2010 .

[12]  Sylvia Tippmann,et al.  Programming tools: Adventures with R , 2014, Nature.

[13]  Alain F. Zuur,et al.  A protocol for data exploration to avoid common statistical problems , 2010 .

[14]  A. Pocheville.  The Ecological Niche: History and Recent Controversies , 2015 .

[15]  D. Burslem,et al.  Habitat preferences of Aporosa in two Malaysian forests: Implications for abundance and coexistence , 2002 .

[16]  P. Diggle,et al.  Spatial patterns reveal negative density dependence and habitat associations in tropical trees. , 2011, Ecology.

[17]  François Goreaud,et al.  ads Package for R: A Fast Unbiased Implementation of the K-function Family for Studying Spatial Point Patterns in Irregular-Shaped Sampling Windows , 2015 .

[18]  Leonhard Held,et al.  Gaussian Markov Random Fields: Theory and Applications , 2005 .

[19]  Linda Altieri,et al.  A changepoint analysis of spatio-temporal point processes , 2015 .

[20]  A. Penttinen,et al.  Conditionally heteroscedastic intensity‐dependent marking of log Gaussian Cox processes , 2009 .

[21]  A. Magurran.  Ecological Diversity and Its Measurement , 1988, Springer Netherlands.

[22]  Visakan Kadirkamanathan,et al.  Point process modelling of the Afghan War Diary , 2012, Proceedings of the National Academy of Sciences.

[23]  Thorsten Wiegand,et al.  Analyzing the spatial structure of a Sri Lankan tree species with multiple scales of clustering. , 2007, Ecology.

[24]  Antti Penttinen,et al.  Modern Statistics for Spatial Point Processes. Commentary , 2007 .

[25]  Richard Condit,et al.  The impact of neutrality, niche differentiation and species input on diversity and abundance distributions , 2007 .

[26]  Thiago G. Martins,et al.  Penalising Model Component Complexity: A Principled, Practical Approach to Constructing Priors , 2014, 1403.4630.

[27]  R. Pélissier,et al.  Avoiding misinterpretation of biotic interactions with the intertype K12-function: population independence vs. random labelling hypotheses , 2003 .

[28]  Anne E. Magurran,et al.  Biological Diversity: Frontiers in Measurement and Assessment , 2011 .

[29]  Vincent Bretagnolle,et al.  Assessing the influence of environmental heterogeneity on bird spacing patterns: a case study with two raptors , 2006 .

[30]  R. Waagepetersen,et al.  Modern Statistics for Spatial Point Processes * , 2007 .

[31]  H. D. Cooper,et al.  A mid-term analysis of progress toward international biodiversity targets , 2014, Science.

[32]  Jesper Møller,et al.  An Introduction to Simulation-Based Inference for Spatial Point Processes , 2003 .

[33]  Y. Ogata,et al.  Estimation of Interaction Potentials of Marked Spatial Point Patterns Through the Maximum Likelihood Method , 1985 .

[34]  Michael R W Rands,et al.  Biodiversity Conservation: Challenges Beyond 2010 , 2010, Science.

[35]  Stephen P. Hubbell,et al.  Beta-Diversity in Tropical Forest Trees , 2002, Science.

[36]  J. Illian,et al.  Lianas and soil nutrients predict fine‐scale distribution of above‐ground biomass in a tropical moist forest , 2016 .

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

[38]  Janine B. Illian,et al.  Careful prior specification avoids incautious inference for log‐Gaussian Cox point processes , 2017, Journal of the Royal Statistical Society: Series C (Applied Statistics).

[39]  C. Geyer,et al.  Simulation Procedures and Likelihood Inference for Spatial Point Processes , 1994 .

[40]  A. Baddeley,et al.  Practical Maximum Pseudolikelihood for Spatial Point Patterns , 1998, Advances in Applied Probability.

[41]  A. Baddeley,et al.  Residual analysis for spatial point processes (with discussion) , 2005 .

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

[43]  Anne E. Magurran,et al.  Goodness‐of‐fit measures of evenness: a new tool for exploring changes in community structure , 2011 .

[44]  J. Møller,et al.  Statistical Inference and Simulation for Spatial Point Processes , 2003 .

[45]  T. Brooks,et al.  Global Biodiversity Conservation Priorities , 2006, Science.

[46]  Mevin B. Hooten,et al.  Restricted spatial regression in practice: geostatistical models, confounding, and robustness under model misspecification , 2015 .

[47]  Jérôme Chave,et al.  Neutral theory and community ecology , 2004 .

[48]  Thorsten Wiegand,et al.  Rings, circles, and null-models for point pattern analysis in ecology , 2004 .

[49]  D. Janzen.  Herbivores and the Number of Tree Species in Tropical Forests , 1970, The American Naturalist.

[50]  Calum Brown,et al.  Linking ecological processes with spatial and non‐spatial patterns in plant communities , 2011 .

[51]  Subhrendu K. Pattanayak,et al.  Money for Nothing? A Call for Empirical Evaluation of Biodiversity Conservation Investments , 2006, PLoS biology.

[52]  J. Symanzik.  Statistical Analysis of Spatial Point Patterns (2nd ed.) , 2005 .

[53]  J. Connell.  On the role of the natural enemies in preventing competitive exclusion in some marine animals and in rain forest trees , 1971 .

[54]  S. Wood.  Generalized Additive Models: An Introduction with R , 2006 .

[55]  Joshua B Plotkin,et al.  Seed Dispersal and Spatial Pattern in Tropical Trees , 2006, PLoS biology.

[56]  James Rosindell,et al.  Unified neutral theory of biodiversity and biogeography , 2010, Scholarpedia.

[57]  Stephen P. Hubbell,et al.  Habitat associations of trees and shrubs in a 50‐ha neotropical forest plot , 2001 .

[58]  J. Illian,et al.  Success of spatial statistics in determining underlying process in simulated plant communities , 2016 .

[59]  Haavard Rue,et al.  Going off grid: computationally efficient inference for log-Gaussian Cox processes , 2016 .

[60]  H. Rue,et al.  Approximate Bayesian inference for latent Gaussian models by using integrated nested Laplace approximations , 2009 .

[61]  V. Zadnik,et al.  Effects of Residual Smoothing on the Posterior of the Fixed Effects in Disease‐Mapping Models , 2006, Biometrics.

[62]  Peter J. Diggle,et al.  Statistical analysis of spatial point patterns , 1983 .

[63]  R. Law,et al.  Heteromyopia and the spatial coexistence of similar competitors , 2002 .

[64]  Ulf Dieckmann,et al.  Moment Approximations of Individual-based Models , 1999 .

[65]  Joseph S. Wright.  Plant diversity in tropical forests: a review of mechanisms of species coexistence , 2017, Oecologia.

[66]  Norman A. Bourg,et al.  CTFS‐ForestGEO: a worldwide network monitoring forests in an era of global change , 2015, Global change biology.

[67]  Michel Loreau,et al.  Biodiversity, Ecosystem Functioning, and Human Wellbeing: An Ecological and Economic Perspective , 2009 .

[68]  Adrian Baddeley,et al.  Spatial Point Patterns: Methodology and Applications with R , 2015 .

[69]  Haavard Rue,et al.  A toolbox for fitting complex spatial point process models using integrated nested Laplace approximation (INLA) , 2012, 1301.1817.

[70]  J. Forcada,et al.  Non-recovery of two spotted and spinner dolphin populations in the eastern tropical Pacific Ocean , 2005 .

[71]  J. Harper.  Population Biology of Plants , 1979 .

[72]  Avid,et al.  Point process models for spatio-temporal distance sampling data from a large-scale survey of blue whales , 2017 .

[73]  D. Burslem,et al.  Species–habitat associations in a Sri Lankan dipterocarp forest , 2006, Journal of Tropical Ecology.

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

[75]  Peter J. Diggle,et al.  Spatial and spatio-temporal Log-Gaussian Cox processes:extending the geostatistical paradigm , 2013, 1312.6536.

[76]  H. Rue,et al.  An explicit link between Gaussian fields and Gaussian Markov random fields: the stochastic partial differential equation approach , 2011 .

[77]  Stephen P. Hubbell,et al.  Soil nutrients influence spatial distributions of tropical tree species , 2007, Proceedings of the National Academy of Sciences.

[78]  Julia P. G. Jones,et al.  The Why, What, and How of Global Biodiversity Indicators Beyond the 2010 Target , 2011, Conservation biology : the journal of the Society for Conservation Biology.

[79]  M. Spalding,et al.  Measuring the extent and effectiveness of protected areas as an indicator for meeting global biodiversity targets , 2005, Philosophical Transactions of the Royal Society B: Biological Sciences.

[80]  Haavard Rue,et al.  Using INLA to fit a complex point process model with temporally varying effects – a case study , 2012 .

[81]  David Kenfack,et al.  Soil resources and topography shape local tree community structure in tropical forests , 2013, Proceedings of the Royal Society B: Biological Sciences.

[82]  D. Stoyan,et al.  Statistical Analysis and Modelling of Spatial Point Patterns , 2008 .

[83]  E. Leigh,et al.  Tropical forest diversity and dynamism : findings from a large-scale plot network , 2004 .

[84]  J. Hodges,et al.  Adding Spatially-Correlated Errors Can Mess Up the Fixed Effect You Love , 2010 .

[85]  Stephen P. Hubbell,et al.  Tree Dispersion, Abundance, and Diversity in a Tropical Dry Forest , 1979, Science.

[86]  A. Watt,et al.  Pattern and process in the plant community , 1947 .

[87]  Finn Lindgren,et al.  Bayesian Spatial Modelling with R-INLA , 2015 .

[88]  Achim Zeileis,et al.  Structured Additive Regression Models: An R Interface to BayesX , 2015 .

[89]  Martin Schlather,et al.  On the second-order characteristics of marked point processes , 2001 .

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

[91]  S. Wright,et al.  TESTING THE DISPERSION OF JUVENILES RELATIVE TO ADULTS: A NEW ANALYTIC METHOD' , 1986 .

[92]  P. Haase.  Spatial pattern analysis in ecology based on Ripley's K-function: Introduction and methods of edge correction , 1995 .

[93]  Nick Golding,et al.  Fast and flexible Bayesian species distribution modelling using Gaussian processes , 2016 .

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

[95]  Marti J. Anderson,et al.  Species abundance distributions: moving beyond single prediction theories to integration within an ecological framework. , 2007, Ecology letters.

[96]  Jay M Ver Hoef,et al.  A Model‐Based Approach for Making Ecological Inference from Distance Sampling Data , 2010, Biometrics.