Contributions of spatial point process modelling to biodiversity theory

Illian, Janine; Burslem, David

Journal de la Société française de statistique & Revue de statistique appliquée, Tome 148 (2007) no. 1, pp. 9-29.

Les dernières décennies ont connu une chute de la biodiversité sans précédent, qui soulève des inquiétudes quant à ses conséquences pour le fonctionnement des écosystèmes. Les recherches en écologie des communautés cherchent à établir les mécanismes permetttant la coexistence d'un grand nombre d'espèces et le maintien de la biodiversité. Les processus mis en jeu au sein des communautés végétales sont principalement des interactions locales et prennent place dans un contexte spatial. Ils doivent donc être modélisés à l'échelle des individus. Plusieurs théories ont été proposées pour la coexistence des plantes, parmi lesquelles la théorie de la niche écologique et la théorie neutraliste sont prédominantes. Ces théories diffèrent principalement par le degré auquel les différences fonctionnelles entre espèces sont jugées nécessaires pour limiter l'exclusion compétitive. Il en résulte des prédictions différentes concernant les interactions entre espèces et entre les plantes et l'environnement. De grands jeux de données spatialisées sont à présent disponibles sur des communautés végétales, comportant la localisation de chaque plante. Cet article discute comment les prédictions des différentes théories peuvent être évaluées à l'aide de modèles de processus ponctuels et comment l'approche peut être appliquée à ces jeux de données pour contribuer à la discussion.

Recent decades have seen an unprecedented decline in biodiversity that has led to a growing concern about the consequences of biodiversity loss for the functioning of ecosystems. Key research in plant community ecology seeks to reveal the mechanisms that allow a large number of species to coexist and sustain biodiversity. Processes in plant communities are predominantly local and interactions take place in a spatial context. They thus need to be modelled from the individual plants' perspective. Several ecological theories of plant species coexistence have been proposed with niche theory and neutral theory being the most prominent. They differ mainly in the extent to which functional differences between species are considered necessary for preventing competitive exclusion. This results in different predictions about interactions among the plants and between the plants and the environment. Extensive spatially explicit data sets of plant communities have become available. This paper outlines how the theories' predictions may be assessed using spatial point process modelling and how this approach may be suitably applied to these data sets to contribute to the discussion.

[1] Adler R. (1981). The Geometry of Random Fields. Wiley, New York. | MR | Zbl

[2] Armstrong P. (1991). Species patterning in the heath vegetation of the Northern Sandplain. Honours thesis, University of Western Australia.

[3] Baddeley A., J. Møller and R. Waagepetersen (2000). Non- and semiparametric estimation of interaction in inhomogenous point patterns. Statistica Neerlandica 54, 329-350. | MR | Zbl

[4] Bell G. (2001). Neutral macroecology. Science 293, 2413-2418.

[5] Cardinale B. J., A. Ives and P. Inchausti (2004). Effects of species diversity on the primary productivity of ecosystems: extending our spatial and temporal scales of inference. Oikos 104, 437-450.

[6] Chave J. (2004). Neutral theory and community ecology. Ecology Letters 7, 241-253.

[7] Chesson P. L. (2000). Mechanisms of maintenance of species diversity. Annual Review of Ecology and Systematics 31, 343-366.

[8] Condit R., P. S. Ashton, P. Baker, S. Bunyavejchewin, S. Gunatilleke, N. Gunatilleke, S. Hubbell, R. Foster, A. Itoh, J. Lafrankie, H. Lee, E. Losos, N. Manokaran, R. Sukumar, and T. Yamakura (2000). Spatial patterns in the distribution of tropical tree species. Science 288, 1414-1418.

[9] Condit, R., N. Pitman, E. G. Leigh Jr., J. Chave, J. Terborgh, R. B. Foster, P. Nunez, S. Aguilar, R. Valencia, G. Villa, H. C. Müller-Landau, E. Losos, and S. P. Hubbell (2002). Beta diversity in tropical forest trees. Science 295, 666-669.

[10] Connell J. (1971). On the role of natural enemies in preventing competitive exclusion in some marine animals and in rainforest trees. In P. den Boer and G. Gradwell (Eds.), Dynamics of Populations, pp. 298-313. Centre for Agricultural Publishing and Documentation, Wageningen, The Netherlands.

[11] Coomes D. A., M. Rees and L. Turnbull (1999). Identifying aggregation and association in fully mapped spatial data. Ecology 80, 554-565.

[12] Cox D. R. (1955). Some statistical models related with series of events. Journal of the Royal Statistical Society Series B 17, 883-904. | MR

[13] Crawley M. (1997). The structure of plant communities. In M. Crawley (Ed.), Plant Ecology, pp. 475-531. Blackwell Publishing, Oxford.

[14] Daley D. J. and D. Vere-Jones (1988). An Introduction to the theory of point patterns. Springer-Verlag, New York. | MR | Zbl

[15] De Mazancourt C. (2001). Consequences of community drift. Science 293, 1772.

[16] Deangelis D. L. and L. J. Gross (1992). Individual based Models and Approaches in Ecology: Populations, Communities and Ecosystems. Chapman & Hall, London.

[17] Dieckmann U., R. Law and J. Metz (2000). The Geometry of Ecological Interactions - Simplifying spatial complexity. Cambridge University Press, Cambridge.

[18] Diggle P. (1983). Statistical Analysis of Spatial Point Patterns. Academic Press, London. | MR | Zbl

[19] Diggle P. (2003). Statistical Analysis of Spatial Point Patterns, 2nd ed. Hodder Arnold, London. | Zbl

[20] Diggle P. J., V. Gómez-Rubio, P. E. Brown, and A. G. Chetwynd (2006). Second-order analysis of inhomogeneous spatial point processes using case-control data. Biometrics. | Zbl

[21] Dixon K. (2005). Personal communication.

[22] Duivenvoorden J. F., J. C. Svenning and S. J. Wright (2002). Beta diversity in tropical forests. Science 295, 636-637.

[23] Durrett R. and S. Levin (1998). Spatial aspects of interspecific competition. Theoretical Population Biology 53, 30-43. | Zbl

[24] Elton C. (1927). Animal Ecology. Sidgwick and Jackson, London.

[25] Gaston K. J. and S. L. Crown (2005). Editorial: Neutrality and the niche. Functional Ecology 19, 1-6.

[26] Grinnell J. (1917). The niche relationships of the Californian thrasher. Auk 34, 427-433.

[27] Grubb P. J. (1977). The maintenance of species-richness in plant communities: the importance of the regeneration niche. Biological Reviews 52, 107-145.

[28] Harms K. E., R. Condit, S. P. Hubbell and R. B. Foster (2001). Habitat associations of trees and shrubs in a 50-ha neotropical forest plot. Journal of Ecology 89, 947-959.

[29] Hector A., B. Schmid, C. Beierkuhnlein, M. Caldeira, M. Diemer, P. Dimitrakopoulos, J. Finn, H. Freitas, P. Giller, J. Good, R. Harris, P. Hogberg, K. H. Danell, J. Joshi, A. Jumpponen, C. Krner, P. Leadley, M. Loreau, A. Minns, C. Mulder, G. O. G, S. Otway, J. Pereira, A. Prinz, D. Read, M. S. Lorenzen, E. Schulze, A. Siamantziouras, E. Spehn, A. Terry, A. Troumbis, F. Woodward, S. Yachi, and J. Lawton (1999). Plant diversity and productivity experiments in European grasslands. Science 286, 1123-1127.

[30] Hubbell S. (2001). The Unified Neutral Theory of Biodiversity and Biogeography. Monographs in Population Biology 32, Princeton University Press.

[31] Hubbell S. P. (1979). Tree dispersion, abundance and diversity in a tropical dry forest. Science 203, 1299-1309.

[32] Huston M., D. L. Deangelis, and W. M. Post (1988). New computer model unify ecologcal theory. BioScience 38, 682-691.

[33] Hutchinson G. E. (1957). Concluding remarks. Cold Spring Habor Symposium on Quantitative Biology 22, 415-457.

[34] Hutchinson G. E. (1959). Homage to santa rosalia, or why are there so many kinds of animals? American Naturalist 93, 145-159.

[35] Illian J. B. (2006). Spatial point process modelling of a biodiverse plant community. PhD thesis, University of Abertay Dundee.

[36] Illian J. B., E. Benson, J. Crawford, and H. J. Staines (2004). Multivariate methods for spatial point processes - a simulation study. In A. Baddeley, P. Gregori, J. Mateu, R. Stoica, and D. Stoyan (Eds.), Spatial point process modelling and its applications, pp. 125-130. Castelló de la Plana: Publicacions de la Universitat Jaume I.

[37] Illian J. B., E. Benson, J. Crawford, and H. Staines (2006). Principal component analysis for spatial point patterns. In A. Baddeley, P. Gregori, J. Mateu, R. Stoica, and D. Stoyan (Eds.), Case studies in spatial point process modelling. Springer, New York. | MR

[38] Illian J. B., J. Møller, and R. P. Waagepetersen (2007). Spatial point process models for a complex plant community. To appear in Journal of Ecological and Environmental Statistics. | MR

[39] Janzen D. H. (1970). Herbivores and the number of tree species in tropical forests. American Naturalist 104, 501-528.

[40] Judson O. (1994). The rise of the individual-based model in ecology. TREE 9, 9-14.

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

[42] Loreau M. (2000). Biodiversity and ecosystem functioning: recent theoretical advances. Oikos 91, 3-17.

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

[44] Mateu J., J. L. Us'O, and F. Montes (1998). The spatial pattern of a forest ecosystem. Ecological Modelling 108, 163-174.

[45] Møller J. and R. Waagepetersen (2003a). An introduction to simulation-based inference for spatial point processes. In J. Møller (Ed.), Lecture Notes in Statistics 137, pp. 143-198. Springer-Verlag, New York. | MR | Zbl

[46] Møller J. and R. Waagepetersen (2003b). Statistical Inference and Simulation for Spatial Point Processes. Chapman & Hall/CRC, Boca Raton. | Zbl

[47] Mouquet N., J. L. Moore, and M. Loreau (2002). Plant species richness and community productivity: why the mechanism that promotes coexistence matters. Ecology Letters 5, 56-65.

[48] Murrell D. J., D. W. Purves, and R. Law (2001). Uniting pattern and process in plant ecology. Trends in Ecology and Evolution 16, 529-530.

[49] Purves D. and R. Law (2003). Heteromyopia and the spatial coexistence of similar competitors. Ecology letters 6, 48-59.

[50] Purves D. W. and S. W. Pacala (2005). Ecological drift in niche-strucured communities: neutral pattern does not imply neutral process. In D. Burslem, M. Pinard, and S. Hartley (Eds.), Biotic Interactions in the Tropics, pp. 107-138. Cambridge University Press, Cambridge.

[51] Ramsay J. and B. Silverman (1997). Functional data analysis. Springer, New York. | MR | Zbl

[52] Ramsay J. and B. Silverman (2002). Applied functional data analysis. Springer, New York. | MR | Zbl

[53] Regan H., R. Lupia, and M. Burgmann (2001). The currency and tempo of extinction. American Naturalist 157, 1-10.

[54] Ripley B. (1976). The second-order analysis of stationary point processes. Journal of Applied Probability 13, 255-266. | MR | Zbl

[55] Schlather M. (2001). On the second-order characteristics of marked point patterns. Bernoulli 7, 99-117. | MR | Zbl

[56] Schoener T. W. (1989). The ecological niche. In J. Cherrett (Ed.), Ecological Concepts, pp. 79-113. Blackwell Scientific Publications, Oxford.

[57] Stoll P. and J. Weiner (2000). A neighbourhood view of interactions among individual plants. In U. Dieckmann, R. Law, and J. Metz (Eds.), The Geometry of Ecological Interactions: Simplifying Spatial Complexity, pp. 11-27. Cambridge University Press, Cambridge.

[58] Stoyan D., W. Kendall, and J. Mecke (1995). Stochastic Geometry and its Applications (2nd ed.). John Wiley & Sons, London. | MR | Zbl

[59] Stoyan D. and A. Penttinen (2000). Recent applications of point process methods in forestry statistics. Statistical Science 1, 61-78. | MR

[60] Stoyan D. and H. Stoyan (1994). Fractals, random Shapes and Point Fields. John Wiley & Sons, London. | MR | Zbl

[61] Tilman D. (1994). Competition and biodiversity in spatially structured habitats. Ecology 75, 2-16.

[62] Tilman D., P. B. Reich, J. Knops, D. Wedin, T. Mielke, and C. Lehman (2001). Diversity and productivity in a long-term grassland experiment. Science 294, 843-845.

[63] Tilman D., D. Wedin, and J. Knops (1996). Productivity and sustainability influenced by biodiversity in grassland ecostystems. Nature 379, 718-720.

[64] Turkington R. A. and J. L. Harper (1979). The growth, distribution and neighbour relationships of Trifolium repens in a permanent pasture. I ordination, pattern and contact. Journal of Ecology 67, 201-208.

[65] Van Lieshout M. (2000). Markov point processes and their applications. Imperial College Press, London. | MR | Zbl