Skip to main content

Advertisement

Log in

Hierarchical spatial point process analysis for a plant community with high biodiversity

  • Published:
Environmental and Ecological Statistics Aims and scope Submit manuscript

Abstract

A complex multivariate spatial point pattern of a plant community with high biodiversity is modelled using a hierarchical multivariate point process model. In the model, interactions between plants with different post-fire regeneration strategies are of key interest. We consider initially a maximum likelihood approach to inference where problems arise due to unknown interaction radii for the plants. We next demonstrate that a Bayesian approach provides a flexible framework for incorporating prior information concerning the interaction radii. From an ecological perspective, we are able both to confirm existing knowledge on species’ interactions and to generate new biological questions and hypotheses on species’ interactions.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Armstrong P (1991) Species patterning in the heath vegetation of the northern sandplain. Honours thesis, University of Western Australia

  • Baddeley A, Møller J, Waagepetersen R (2000) Non- and semi-parametric estimation of interaction in inhomogeneous point patterns. Statistica Neerlandica 54: 329–350

    Article  Google Scholar 

  • Baddeley AJ, Turner R (2005) Spatstat: an R package for analyzing spatial point patterns. J Stat Software 12: 1–42

    Google Scholar 

  • Barndorff-Nielsen OE (1978) Information and exponential families in statistical theory. Wiley, Chichester

    Google Scholar 

  • Beard J (1984) Biogeography of the Kwongan. In: Pate J, Beard J (eds) Kwongan – plant life of the sandplains. University of Western Australia Press, Nedlands, pp 1–26

    Google Scholar 

  • Berman M, Turner R (1992) Approximating point process likelihoods with GLIM. Appl Stat 41: 31–38

    Article  Google Scholar 

  • Burslem D, Garwood N, Thomas S (2001) Tropical forest diversity – the plot thickens. Science 291: 606–607

    Article  PubMed  CAS  Google Scholar 

  • Callaway RM (1995) Positive interactions among plants. Bot Rev 61: 306–349

    Article  Google Scholar 

  • Crawley M (1997) Biodiversity. In: Crawley M (ed) Plant Ecology. Blackwell Publishing, pp 325–358

  • Dale M, Dixon P, Fortin M, Legendre P, Myers D, Rosenberg M (2002) Conceptional and mathematical relationships among methods for spatial analysis. Ecography 25: 558–577

    Article  Google Scholar 

  • Diggle P (2003) Statistical analysis of spatial point patterns, 2nd edn. Oxford University Press, Oxford

    Google Scholar 

  • Durrett R, Levin S (1998) Spatial aspects of interspecific competition. Theor Popul Biol 53: 30–43

    Article  PubMed  CAS  Google Scholar 

  • Elkington J (1991) Report on the vegetation at Cooljarloo W.A. Unpublished report for TI02 Corporation, Ekomin Pty. Ltd., South Perth

  • Gelman A, Meng XL, Stern HS (1996) Posterior predictive assessment of model fitness via realized discrepancies (with discussion). Stat Sinica 6: 733–807

    Google Scholar 

  • Grabarnik P, Särkkä A (2008) Modelling of the spatial structure of a forest stand by Gibbs point processes with hierarchical interactions (in preparation)

  • Gratzer G, Waagepetersen R, Splechtna BE, Laister M, Coomes D (2008) The influence of seed dispersal and environmental heterogeneity for generation of spatial patterns of seedlings in a spruce beech fir old growth forest (in preparation)

  • Greig-Smith P (1983) Quantitative plant ecology. Blackwell Scientific, Oxford

    Google Scholar 

  • Herben T, During H, Law R (2000) Spatio-temporal patterns in grassland communities. In: Dieckmann U, Law R, Metz J(eds) The geometry of ecological interactions: Simplifying spatial complexity. Cambridge University Press, Cambridge, pp 11–27

    Google Scholar 

  • Högmander H, Särkkä A (1999) Multitype spatial point patterns with hierarchical interactions. Biometrics 55: 1051–1058

    Article  PubMed  Google Scholar 

  • Kühlmann-Berenzon S, Heikkinen J, Särkkä A (2005) An additive edge correction for the influence potential of trees. Biometrical J 47: 517–526

    Article  Google Scholar 

  • Kuuluvainen T, Pukkala T (1889) Effect of scots pine seed trees on the density of ground vegetation and tree seedlings. Silva Fennica 23: 159–167

    Google Scholar 

  • Law R, Herben T, Dieckmann U (1997) Non-manipulative estimates of competition coefficients in grassland communities. Ecology 85: 505–517

    Article  Google Scholar 

  • Law R, Murrell D, Dieckmann U (2003) Population growth in space and time: spatial logistic equations. Ecology 84: 252–262

    Article  Google Scholar 

  • Liebhold A, Gurevitch J (2002) Integrating the statistical analysis of spatial data in ecology. Ecography 25: 553–557

    Article  Google Scholar 

  • Loreau M, Naeem S, Inchausti P, Bengtsson J, Grime J, Hector A, Hooper D, Huston M, Raffaelli D, Schmid B, Tilman D, Wardle D (2001) Biodiversity and ecosystem functioning: current knowledge and future challenges. Science 294: 804–808

    Article  PubMed  CAS  Google Scholar 

  • Magurran A (1988) Ecological diversity and its measurement. University Press, Cambridge

    Google Scholar 

  • Mateu J, Usó J, Montes F (1998) The spatial pattern of a forest ecosystem. Ecol Model 108: 163–174

    Article  Google Scholar 

  • Miina J, Pukkala T (2002) Application of ecological field theory in distance-dependent growth modelling. Forest Ecol Manag 161: 101–107

    Article  Google Scholar 

  • Møller J, Waagepetersen R (2003) Statistical inference and simulation for spatial point processes. Chapman and Hall/CRC, Boca Raton

    Google Scholar 

  • Murrell D, Purves D, Law R (2001) Uniting pattern and process in plant ecology. Trends Ecol Evol 16: 529–530

    Article  Google Scholar 

  • Økland RH, Rydgren K, Økland T (1999) Single-tree influence on understorey vegetation in Norwegian boreal spruce forest. Oikos 87: 488–498

    Article  Google Scholar 

  • Richardson D, Cowling R, Lamont B, van Hensbergen H (1995) Coexistence of banksia species in southwestern australia: The role of regional and local processes. J Veg Sci 6: 329–342

    Article  Google Scholar 

  • Robert CP, Casella G (1999) Monte carlo statistical methods. Springer-Verlag, New York

    Google Scholar 

  • Schoenberg FP (2005) Consistent parametric estimation of the intensity of a spatial-temporal point process. J Stat Plan Infer 128: 79–93

    Article  Google Scholar 

  • Stoll P, Weiner J (2000) A neighbourhood view of interactions among individual plants. In: Dieckmann U, Law R, Metz J(eds) The geometry of ecological interactions: simplifying spatial complexity. Cambridge University Press, Cambridge, pp 11–27

    Google Scholar 

  • Uriarte M, Condit R, Canham C, Hubbell S (2004) A spatially explicit model of sapling growth in a tropical forest: does indentity of neighbours matter. J Ecol 92: 348–360

    Article  Google Scholar 

  • Waagepetersen R (2005) Posterior propriety for Poisson processes. Manuscript available at http://www.math.aau.dk/~rw+

  • Waagepetersen R (2007) An estimating function approach to inference for inhomogeneous Neyman-Scott processes. Biometrics 63: 252–258

    Article  PubMed  Google Scholar 

  • Wiegand T, Moloney K (2004) Rings, circles, and null-models for point pattern analysis in ecology. Oikos 104: 209–229

    Article  Google Scholar 

  • Wu H, Sharpe PJH, Walker J, Penridge LK (1985) Ecological field theory: a spatial analysis of resource interference among plants. Ecol Model 29: 215–243

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Janine B. Illian.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Illian, J.B., Møller, J. & Waagepetersen, R.P. Hierarchical spatial point process analysis for a plant community with high biodiversity. Environ Ecol Stat 16, 389–405 (2009). https://doi.org/10.1007/s10651-007-0070-8

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10651-007-0070-8

Keywords

Navigation