Statistical Science

Recent applications of point process methods in forestry statistics

Antti Penttinen and Dietrich Stoyan

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Abstract

Forestry statistics is an important field of applied statistics with a long tradition. Many forestry problems can be solved by means of point processes or marked point processes. There, the “points ”are tree locations and the “marks ” are tree characteristics such as diameter at breast height or degree of damage by environmental factors. Point process characteristics are valuable tools for exploratory data analysis in forestry, for describing the variability of forest stands and for understanding and quantifying ecological relationships. Models of point processes are also an important basis of modern single-tree modeling, that gives simulation tools for the investigation of forest structures and for the prediction of results of forestry operations such as plantation and thinning.

Article information

Source
Statist. Sci. Volume 15, Number 1 (2000), 61-78.

Dates
First available in Project Euclid: 24 December 2001

Permanent link to this document
http://projecteuclid.org/euclid.ss/1009212674

Digital Object Identifier
doi:10.1214/ss/1009212674

Mathematical Reviews number (MathSciNet)
MR1842237

Zentralblatt MATH identifier
1195.94036

Keywords
Point process mark modeling ecology intensity variability indices second order characteristic correlation single-tree model Cox process Gibbs process

Citation

Stoyan, Dietrich; Penttinen, Antti. Recent applications of point process methods in forestry statistics. Statist. Sci. 15 (2000), no. 1, 61--78. doi:10.1214/ss/1009212674. http://projecteuclid.org/euclid.ss/1009212674.


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References

  • Avery, T. E. and Burkhart, H. E. (1983). Forest Measurements, 3rd ed. McGraw-Hill, New York.
  • Baddeley, A. J. (1998). Spatial samplingand censoring. In Stochastic Geometry: Likelihood and Computation (O. E. Barndorff-Nielsen, W. S. Kendall and M. N. M. van Lieshout, eds.) 37-78. CRC Press/Chapman and Hall, London.
  • Baddeley, A. J. and Gill, R. D. (1997). Kaplan-Meier estimators of distance distributions for spatial point processes. Ann. Statist. 25 263-292.
  • Baddeley, A. J., Møller, J. and Waagepetersen, R (1998). Nonand semiparametric estimation of interaction in inhomogeneous point patterns. R-98-2019, Dept. Mathematics, Inst. Electronic Systems, Univ. Aalborg.
  • Besag, J. (1978). Some methods of statistical analysis for spatial data. Bull. Internat. Statist. Inst. 47 77-92.
  • Biging, G. S. and Dobbertin, M. (1992). A comparison of distance-dependent competition measures for height and basal area growth of individual conifer trees. Forest Science 38 695-720.
  • Biging, G. S. and Dobbertin, M. (1995). Evaluation of competition indices in individual tree growth models. Forest Science 41 360-377.
  • Bitterlich, W. (1948). Die Winkelz¨ahlprobe. Allgemeine Forstund Holzwirtschaftliche Zeitung 59 4-5.
  • Bitterlich, W. (1952). Die Winkelz¨ahlprobe. Forstwissenschaftliches Centralblatt 71 215-225.
  • Cannon, A. and Cressie, N. (1997). Temporal analogues to spatial K functions. Biometrical J. 37 351-373.
  • Chiu, S. N. and Stoyan, D. (1998). Estimates of distance distributions for spatial patterns. Statist. Neerlandica 52 239-246.
  • Clark, P. J. and Evans, F. C. (1954). Distance to the nearest neighbor as a measure of spatial relationships in populations. Ecology 35 445-453.
  • Cox, F. (1971). Dichtebestimmungund Strukturanalyse von Pflanzenpopulationen mit Hilfe von Abstandsmessungen. Mitt. Bundesforsch. Anst. Forstund Holzwirtsch., Reinbek b. Hamburg 87 1-184.
  • Cressie, N. (1993). Statistics for Spatial Data, rev. ed. Wiley, New York.
  • Degenhardt, A. (1999). Description of tree distribution and their development through marked Gibbs processes. Biometrical J. 41 457-470.
  • Diggle, P. J. (1983). Statistical Analysis of Spatial Point Patterns. Academic Press, London.
  • Diggle, P. J. and Chetwynd, A. G. (1993). Second-order analysis of spatial clusteringfor inhomogeneous populations. Biometrics 47 1153-1163. Diggle, P. J., Fiksel, T., Grabarnik, P., Ogata, Y., Stoyan,
  • D. and Tanemura, M. (1994). On parameter estimation for pairwise interaction point processes. Internat. Statist. Rev. 92 99-117.
  • Diggle, P. J. and Milne, R. K. (1983). Bivariate Cox processes: some models for bivariate spatial point-patterns. J. Roy. Statist. Soc. Ser. B 45 11-21.
  • Dralle, K. and Rudemo, M. (1996). Stem number estimation by kernel smoothingof aerial photos. Canad. J. For. Res. 26 1228-1236. F ¨uldner, K., Sattler, S., Zucchini, W. and von Gadow,
  • K. (1996). Modellierungpersonenabh¨angiger Auswahlwahrscheinlichkeiten bei der Durchforstung. Allg. Forstund Jagdzeitung 167 159-162.
  • Gavrikov, V. L. and Stoyan, D. (1995). The use of marked point processes in ecological and environmental forest studies. Environ. Ecolog. Statist. 2 331-344.
  • Geyer, C. (1998). Likelihood inference for spatial point processes. In Stochastic Geometry: Likelihood and Computation (O. E. Barndorff-Nielsen, W. S. Kendall and M. N. M. van Lieshout, eds.) 79-40. CRC Press/Chapman and Hall, London.
  • Geyer, C. J. and Møller, J. (1994). Simulation and likelihood inference for spatial point processes. Scand. J. Statist. 21 359-373.
  • Goulard, M., S¨arkk¨a, A. and Grabarnik, P. (1996). Parameter estimation for marked Gibbs point processes through the maximum pseudo-likelihood method. Scand. J. Statist. 23 365-379.
  • Heikkinen, J. and Arjas, E. (1998). Nonparametric Bayesian estimation of a spatial Poisson intensity. Scand. J. Statist. 25 435-450.
  • Heikkinen, J. and Arjas, E. (1999). Modelinga Poisson forest in variable elevation: a nonparametric Bayesian approach. Biometrics 55 738-745.
  • Heikkinen, J. and Penttinen, A. (1999). Bayesian smoothingin the estimation of the pair potential function of Gibbs point processes. Bernoulli 5. To appear.
  • Ickstadt, K. and Wolpert, R. L. (1997). Multiresolution assessment of forest inhomogeneity. Case Studies in Bayesian Statistics. Lecture Notes in Statist. 3 371-386. Springer, Berlin.
  • Jensen, E. B. V. and Nielsen, L. S. (1998). Inhomogeneous Markov point processes by transformation. Research Report 2, Lab. Computational Stochastics, Dept. Mathematical Sciences, Univ. Aarhus.
  • Kelly, F. P. and Ripley, B. D. (1976). A note on Strauss's model for clustering. Biometrika 63 357-360.
  • Kimmins, J. P. (1993). Scientific foundations for the simulation of ecosystem function and menagement in FOTCYTE-11. Information Report NOR-X-328, Forestry Canada, Northwest Region Northern Forestry Centre.
  • K ¨onig, G. (1835). Die Forst-Mathematik. Beckersche Buchhandlung, Gotha.
  • Krebs, C. J. (1989). Ecological Methodology. HarperCollins, New York. Kuuluvainen, T., Penttinen, A., Leinonen, K. and Nygren, M.
  • (1996). Statistical opportunities for comparingstand structural heterogeneity in managed and primeval forests: An example from boreal spruce forest in southern Finland. Silva Fennica 30 315-328.
  • Lep s, J. (1990). Can underlyingmechanisms be deduced from observed patterns? In Spatial Processes in Plant Communities (F. Krahulec, A. D. Q. Agnew and J. H. Willems, eds.) 1-11. Academia, Prague.
  • Lep s, J. and Kindlmann, P. (1987). Models of the development of spatial pattern of an even-aged plant population over time. Ecological Modelling 39 45-57.
  • Liu, J. and Ashton, P. S. (1995). Individual-based simulation models for forest succession and management. Forest Ecology and Management 73 157-175.
  • Mat´ern, B. (1960). Spatial variation. Meddelanden fr an Statens Skogsforskningsinstitut 49 1-144. Lecture Notes in Statist. 36. Springer, Berlin. [2nd ed. (1986)] Møller, J., Syversveen, A. R. and Waagepetersen, R. P.
  • (1997). LogGaussian Cox Processes: a statistical model for analysingstand structural heterogeneity in forestry. In Proceedings First European Conference for Information Technology in Agriculture (H. Kure, I. Thysen and A. R. Kristensen, eds.) 339-342. Dept. Mathematics and Physics, Royal Veterinary and Agricultural Univ., Denmark.
  • Møller, J., Syversveen, A. R. and Waagepetersen, R. P. (1998). LogGaussian Cox processes. Scand. J. Statist. 25 451-482.
  • Newnham, R. M. (1964). The development of a stand model for Douglas-fir. Ph.D. thesis, Univ. British Columbia, Vancouver.
  • Odum, E. P. (1971). Fundamentals of Ecology. Saunders, Philadelphia.
  • Ogata, Y. and Tanemura, M. (1984). Likelihood analysis of spatial point-patterns. J. Roy. Statist. Soc. Ser. B 46 496-518.
  • Ogata, Y. and Tanemura, M. (1985). Estimation of interaction potentials of marked spatial point-patterns through the maximum-likelihood method. Biometrics 41 315-338.
  • Ogata, Y. and Tanemura, M. (1986). Likelihood estimation of interaction potentials and external fields of inhomogeneous spatial point patterns. In Proceedings Pacific Statistical Congress 1985 (I. S. Francis, B. F. J. Manly and F. C. Lam, eds.) 150-154.
  • Ohser, J. and Stoyan, D. (1981). On the second-order and orientation analysis of planar point processes. Biometrical J. 23 523-533.
  • Overton, W. S. and Stehman, S. V. (1995). The Horvitz- Thompson theorem as a unifyingperspective for probability sampling: with examples from natural resource sampling. Amer. Statist. 49 261-268. Pacala, S. W., Canham, C. D., Saponara, J., Silsander, J. A.,
  • Kobe, R. K. and Ribbens, E. (1996). Forest models defined by field measurements: estimation, error analysis and dynamics. Ecological Monogr. 66 1-43.
  • Penttinen, A. (1988). A random field approach to Bitterlich sampling. Ann. Acad. Sci. Fenn. Ser. A I Math. 13 259-268.
  • Penttinen, A. K., Stoyan, D. and Henttonen, H. M. (1992). Marked point processes in forest statistics. Forest Sci. 38 806-824.
  • Pielou, E. C. (1977). Mathematical Ecology. Wiley, New York.
  • Pohtila, E. (1980). Spatial distribution development in young tree stands in Lapland. Comm. Inst. Forestalis Fennicae 98 1-35.
  • Pretzsch, H. (1993). Analyse und Reproduktion r¨aumlicher Bestandesstrukturen. Versuche mit dem Strukturgenerator STRUGEN. Schriften aus der Forstlichen Fakult¨at der Universit¨at G¨ottingen and der Nieders. Forstl. Versuchsanstalt 114. J. D. Sauerl¨anders, Frankfurt.
  • Pretzsch, H. (1997). Analysis and modelingof spatial stand structures. Methological considerations based on mixed beech-larch stand in Lower Saxony. Forest Ecol. Manag. 97 237-253.
  • Rathbun, S. L. (1996). Estimation of Poisson intensity usingpartially observed concomitant variables. Biometrics 52 226-242.
  • Rathbun, S. L. and Cressie, N. (1994). A space-time survival point process for a longleaf pine forest in Southern Georgia. J. Amer. Statist. Assoc. 89 1164-1174.
  • Ripley, B. D. (1976). The second-order analysis of stationary point processes. J. Appl. Probab. 13 255-266.
  • Ripley, B. D. (1977). Modellingspatial patterns (with discussion). J. Roy. Statist. Soc. Ser. B 39 172-212.
  • Ripley, B. D. (1981). Spatial Statistics. Wiley, New York.
  • Ripley, B. D. (1988). Statistical Inference for Spatial Processes. Cambridge Univ. Press.
  • Salonen, V., Penttinen, A. and S¨arkk¨a, A. (1992). Plant colonization of a bare peat surface: population changes and spatial patters. J. Vegetation Sci. 3 113-118.
  • S¨arkk¨a, A. and Tomppo, E. (1998). Modellinginteractions between trees by means of field observations. Forest Ecol. Manag. 108 57-62.
  • Schlather, M. (1999). On the second order characteristics of marked point processes. Bernoulli. To appear.
  • Schreuder, H. T., Gregoire, T. G. and Wood, G. B. (1993). Sampling Methods for Multiresource Forest Inventory. Wiley, New York.
  • Serra, J. (1982). Image Analysis and Mathematical Morphology. Academic Press, London.
  • Stoyan, D., Kendall, W. S. and Mecke, J. (1995). Stochastic Geometry and Its Applications, 2nd ed. Wiley, Chichester.
  • Stoyan, D. and Stoyan, H. (1994). Fractals, Random Shapes and Point Fields. Wiley, Chichester.
  • Stoyan, D. and Stoyan, H. (1996). Estimatingpair correlation functions of planar cluster processes. Biometrical J. 38 259- 271.
  • Stoyan, D. and W¨alder, O. (1999). On variograms in point process statistics II. Biometrical J. To appear.
  • Strauß, D. J. (1975). A model for clustering. Biometrika 63 467-475.
  • Svedberg, T. (1922). Ett bidragtill de statistika metodernas anv¨andninginom v¨axtbiologien. Svensk. Botanisk. Titskrift 16 1-8.
  • Tilman, D. (1988). Plant Strategies and the Dynamics and Structure of Plant Communities. Princeton Univ. Press.
  • Tomppo, E. (1986). Models and methods for analysingspatial patterns of trees. Comm. Inst. Forestalis Fennicae 138.
  • Turner, M. G. and Gardner, R. H. (1991). Quantitative Methods in Landscape Ecology. Springer, Berlin.
  • Van Lieshout, M. N. M. and Baddeley, A. J. (1996). A nonparametric measure of spatial interaction in point-patterns. Statist. Neerland. 50 344-361.
  • W¨alder, O. and Stoyan, D. (1996). On variograms in point process statistics. Biometrical. J. 38 395-905.
  • Warren, W. G. (1972). Point processes in forestry. In Stochastic Point Processes, Statistical Analysis, Theory and Application (P. A. W. Lewis, ed.) 85-116. Wiley, New York.
  • Wolpert, R. L. and Ickstadt, K. (1998). Poisson/Gamma random field models for spatial statistics. Biometrika 85 251- 267.