Modelling Forest Dynamics: A Perspective from Point Process Methods

This paper reviews the main applications of (marked) point process theory in forestry including functions to analyse spatial variability and the main (marked) point process models. Although correlation functions do describe spatial variability at distinct range of scale, they are clearly restricted to the analysis of few dominant species since they are based on pairwise analysis. This has over-simplified the spatial analysis of complex forest dynamics involving "large" number of species. Moreover, although process models can reproduce, to some extent, real forest spatial patterns of trees, the biological forest-ecological interpretation of the resulting spatial structures is difficult since these models usually lack of biological realism. This problem gains in strength as usually most of these point process models are defined in terms of purely spatial relationships, though in real life, forest develop through time. We thus aim to discuss the applicability of such formulations to analyse and simulate "real" forest dynamics and unwrap their shortcomes. We present a unified approach of modern spatially explicit forest growth models. Finally, we focus on a continuous space-time stochastic process as an alternative approach to generate marked point patterns evolving through space and time.

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

[2]  R. Monserud,et al.  A basal area increment model for individual trees growing in even- and uneven-aged forest stands in Austria , 1996 .

[3]  R. Leemans,et al.  Canopy gaps and establishment patterns of spruce (Picea abies (L.) Karst.) in two old-growth coniferous forests in central Sweden , 1991, Vegetatio.

[4]  Melinda Moeur,et al.  Characterizing Spatial Patterns of Trees Using Stem-Mapped Data , 1993, Forest Science.

[5]  D. Botkin.  Forest Dynamics: An Ecological Model , 1993 .

[6]  Uta Berger,et al.  A new approach to spatially explicit modelling of forest dynamics: spacing, ageing and neighbourhood competition of mangrove trees , 2000 .

[7]  Preston R. Aldrich,et al.  Spatial dispersion of trees in an old-growth temperate hardwood forest over 60 years of succession , 2003 .

[8]  Thomas Fiksel,et al.  Estimation of Parametrized Pair Potentials of Marked and Non-marked Gibbsian Point Processes , 1984, J. Inf. Process. Cybern..

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

[10]  D. Stoyan,et al.  Non-Homogeneous Gibbs Process Models for Forestry — A Case Study , 1998 .

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

[12]  Marja Kolström,et al.  Ecological simulation model for studying diversity of stand structure in boreal forests , 1998 .

[13]  A. Baddeley,et al.  A non-parametric measure of spatial interaction in point patterns , 1996, Advances in Applied Probability.

[14]  H. Shugart.  A Theory of Forest Dynamics , 1984 .

[15]  Jorge Mateu,et al.  The spatial pattern of a forest ecosystem , 1998 .

[16]  Hans Pretzsch,et al.  The single tree-based stand simulator SILVA: construction, application and evaluation , 2002 .

[17]  R. Wolpert,et al.  Poisson/gamma random field models for spatial statistics , 1998 .

[18]  B. Ripley.  Statistical inference for spatial processes , 1990 .

[19]  van Marie-Colette Lieshout,et al.  Mixture formulae for shot noise weighted point processes , 2004 .

[20]  Rasmus Waagepetersen,et al.  Log Gaussian Cox processes: A statistical model for analyzing stand structural heterogeneity in forestry , 1997 .

[21]  P. J. Clark,et al.  Distance to Nearest Neighbor as a Measure of Spatial Relationships in Populations , 1954 .

[22]  Noel A Cressie,et al.  Statistics for Spatial Data. , 1992 .

[23]  Gregory S. Biging,et al.  Evaluation of Competition Indices in Individual Tree Growth Models , 1995, Forest Science.

[24]  Renzo Motta,et al.  Stand structure and dynamics in a mixed and multilayered forest in the Upper Susa Valley, Piedmont, Italy , 2005 .

[25]  T. Pukkala,et al.  A spatial yield model for optimizing the thinning regime of mixed stands of Pinus sylvestris and Picea abies , 1998 .

[26]  Robert A. Monserud,et al.  Applicability of the forest stand growth simulator PROGNAUS for the Austrian part of the Bohemian Massif , 1997 .

[27]  B. Ripley.  Modelling Spatial Patterns , 1977 .

[28]  A. Degenhardt.  Description of Tree Distribution Patterns and Their Development Through Marked Gibbs Processes , 1999 .

[29]  Eric Renshaw,et al.  The analysis of marked point patterns evolving through space and time , 2006, Comput. Stat. Data Anal..

[30]  S. Pacala,et al.  Forest models defined by field measurements: I. The design of a northeastern forest simulator , 1993 .

[31]  J. Heikkinen,et al.  Modeling a Poisson forest in variable elevations: a nonparametric Bayesian approach. , 1999, Biometrics.

[32]  Bruce C. Larson,et al.  Forest Stand Dynamics , 1990 .

[33]  L. V. Pienaar,et al.  A stand table projection approach to yield prediction in unthinned even-aged stands , 1988 .

[34]  Dietrich Stoyan,et al.  On Variograms in Point Process Statistics, II: Models of Markings and Ecological Interpretation , 2000 .

[35]  A. Youngblood,et al.  Stand structure in eastside old-growth ponderosa pine forests of Oregon and northern California , 2004 .

[36]  E. Renshaw,et al.  Gibbs point processes for studying the development of spatial-temporal stochastic processes , 2001 .

[37]  Aila Särkkä,et al.  Modelling interactions between trees by means of field observations , 1998 .

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

[39]  Alfred Stein,et al.  A spatial statistical analysis of cork oak competition in two Portuguese silvopastoral systems , 2002 .

[40]  Ulrich Pofahl,et al.  Simulation of natural evolution of stem number and tree distribution pattern in a pure pine stand , 2000 .

[41]  F. J. Richards.  A Flexible Growth Function for Empirical Use , 1959 .

[42]  J. R. Wallis,et al.  Some ecological consequences of a computer model of forest growth , 1972 .

[43]  E. Renshaw,et al.  The Interpretation of Process from Pattern Using Two‐Dimensional Spectral Analysis: Methods and Problems of Interpretation , 1983 .

[44]  Dietrich Stoyan,et al.  Trunk-top relations in a Siberian pine forest , 1993 .

[45]  D. Reichle,et al.  Dynamic properties of forest ecosystems , 2004, Vegetatio.

[46]  Peter J. Diggle,et al.  Competition for Light in a Plant Monoculture Modelled as a Spatial Stochastic Process , 1981 .

[47]  Luis Gil,et al.  Spatial stochastic modeling of resin yield from pine stands , 2001 .

[48]  D. Stoyan,et al.  Fractals, random shapes and point fields : methods of geometrical statistics , 1996 .

[49]  Thomas Curt,et al.  Modeling mid-elevation Scots pine growth on a volcanic substrate , 2000 .

[50]  Dietrich Stoyan,et al.  The use of marked point processes in ecological and environmental forest studies , 1995, Environmental and Ecological Statistics.

[51]  Noel A Cressie,et al.  A space-time survival point process for a longleaf pine forest in Southern Georgia , 1994 .

[52]  Jorge Mateu,et al.  Estimating Mark Functions Through Spectral Analysis for Marked Point Patterns , 2006 .

[53]  Vladimir L. Gavrikov.  A model of collisions of growing individuals: a further development , 1995 .

[54]  Raphaël Pélissier,et al.  Tree spatial patterns in three contrasting plots of a southern Indian tropical moist evergreen forest , 1998 .

[55]  D. Stoyan,et al.  Stochastic Geometry and Its Applications , 1989 .

[56]  Jiquan Chen,et al.  Forest structure in space: a case study of an old growth spruce-fir forest in Changbaishan Natural Reserve, PR China , 1999 .

[57]  Thomas M. Smith,et al.  The potential for application of individual-based simulation models for assessing the effects of global change , 1992 .

[58]  Elizabeth A. Freeman,et al.  Spatial and population characteristics of dwarf mistletoe infected trees in an old-growth Douglas-fir - western hemlock forest , 2005 .

[59]  Andrew Park,et al.  Spatial relationships and tree species associations across a 236-year boreal mixedwood chronosequence , 2005 .

[60]  Eric Renshaw,et al.  Spectral techniques in spatial analysis , 1997 .

[61]  Eric Renshaw,et al.  Two-dimensional spectral analysis for marked point processes , 2002 .

[62]  D. Cox.  Some Statistical Methods Connected with Series of Events , 1955 .

[63]  Dietrich Stoyan,et al.  Marked Point Processes in Forest Statistics , 1992, Forest Science.

[64]  van Marie-Colette Lieshout,et al.  Shot-noise-weighted processes : a new family of spatial point processes , 1995 .

[65]  Jerzy Szwagrzyk,et al.  Spatial patterns of trees in natural forests of East‐Central Europe , 1993 .

[66]  Seppo Kellomäki,et al.  Näkökohtia puuston tiheyden ja puiden koon välisestä suhteesta. , 1983 .

[67]  Douglas A. Maguire,et al.  Modeling the spatial structure of topical forests , 1998 .

[68]  William R. Wykoff,et al.  A Basal Area Increment Model for Individual Conifers in the Northern Rocky Mountains , 1990, Forest Science.

[69]  E. Renshaw,et al.  The interpretation of process from pattern using two-dimensional spectral analysis: modelling single species patterns in vegetation , 2004, Vegetatio.

[70]  Marie-Josée Fortin,et al.  Spatial pattern of subalpine forest-alpine grassland ecotones in the Spanish Central Pyrenees , 2000 .

[71]  A. Baddeley,et al.  Area-interaction point processes , 1993 .

[72]  Eric Renshaw,et al.  Disentangling mark/point interaction in marked-point processes , 2007, Comput. Stat. Data Anal..

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

[74]  I. Bella,et al.  A New Competition Model for Individual Trees , 1971 .

[75]  Thomas M. Smith,et al.  A review of forest patch models and their application to global change research , 1996 .

[76]  D. G. Chapman.  Statistical Problems in Dynamics of Exploited Fisheries Populations , 1961 .

[77]  Kenichiro Shimatani.  Multivariate point processes and spatial variation of species diversity , 2001 .

[78]  L. Bertalanffy.  Problems of Organic Growth , 1949, Nature.

[79]  Melinda Moeur,et al.  Spatial models of competition and gap dynamics in old-growth Tsuga heterophylla/Thuja plicata forests , 1997 .

[80]  John D. Aber,et al.  Predicting the Effects of Rotation Length, Harvest Intensity, and Fertilization on Fiber Yield From Northern Hardwood Forests in New England , 1982 .

[81]  Changhui Peng,et al.  Growth and yield models for uneven-aged stands: past, present and future , 2000 .

[82]  W. B. Smith.  An Appreciation of Anant M. Kshirsagar , 2006 .

[83]  D. Tilman.  Plant Strategies and the Dynamics and Structure of Plant Communities. (MPB-26), Volume 26 , 1988 .

[84]  Eric Renshaw.  Modelling biological populations in space and time , 1990 .

[85]  B. Ripley.  The Second-Order Analysis of Stationary Point Processes , 1976 .

[86]  Juli G. Pausas,et al.  A FOREST SIMULATION MODEL FOR PREDICTING EUCALYPT DYNAMICS AND HABITAT QUALITY FOR ARBOREAL MARSUPIALS , 1997 .