Abstract
The spatial distributions of two species of tree result in a bivariate pattern. This pattern characterizes biological mechanism involved within a forest with the spatial localization of the trees. If we consider simultaneously two species, the main question is not to describe the marginal distribution of each species but to describe the relationship between the repartitions of the two species under study. The relationship between two clouds of points can be described in various ways and therefore many indices can be defined. Each index will give a specific information about these relationships and will greatly depends on the ecological mechanisms, i.e., the point process that leads to the observed repartition. The aim of this article is to review the leading indices in ecology and to provide guidelines for practical use. To mimic ecological situations, we simulated 13 point process that can model classical relationships between two species of trees and compute nine classical indices. The interest of the various indices are discussed. A R package for simulating the point process and to compute the indices is available on request. The package is available upon request at picard@cirad.fr or avner@inapg.fr
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References
Baddeley A, Silverman BW (1984) A cautionary example on the use of second-order methods for analysing point patterns. Biometrics 40:1089–1093
Barot S, Gignoux J, Menaut JC (1999) Demography of a savanna palm tree: predictions from comprehensive spatial pattern analyses. Ecology 80(6):1987–2005
Batista JLF, Maguire DA (1998) Modeling the spatial structure of tropical forests. Forest Ecol Manage 110(1–3):293–314
Besag J (1977) Some methods of statistical analysis for spatial data. Bull Int Stat Inst 47(2):77–92. In: Proceedings of the 41st session, New Delhi
Brillinger DR (1976) Measuring the association of point processes: a case history. Am Math Month 83:16–22
Brix A, Chadoeuf J (2002) Spatio-temporal modelling of weeds by shot-noise G Cox processes. Biom J 44(1):83–99
Cailliez F, Pagès JP (1976) Introduction à l’analyse de données, SMASH
Cassie RM. (1962) Frequency distribution models in the ecology of plankton and other organisms. J Anim Ecol 31: 65–91
Cressie N (1991) Statistics for spatial data. Wiley, New York
Cuzick J, Edwards R (1990) Spatial clustering for inhomogeneous populations. J Roy Statl Soc, Ser B 52(1):73–104
Dale MRT (2000) Lacunarity analysis of spatial pattern: a comparison Landscape ecol 15(5):467–478
Dale MRT, Blundon DJ (1991) Quadrat covariance analysis and the scales of interspecific association during primary succession. J Veg Sci 2:103–112
Dale MRT, Powell RD (1994) Scales of segregation and aggregation of plants of different kinds. Can J Bot 72(4):448–453
Diggle PJ, Chetwynd AG (1991) Second-order analysis of spatial clustering for inhomogeneous populations. Biometrics 47:1155–1163
Diggle PJ, Cox TF (1983) Some distance-based tests of independence for sparsely-sampled multivariate spatial point patterns. Int Stat Rev 51:11–23
Diggle PJ, Milne RK (1983) Bivariate Cox processes: some models for bivariate spatial point patterns. J Roy Stat Soc Ser B 45:11–21
Dixon P (1994) Testing spatial segregation using a nearest-neighbor contingency table. Ecology 75(7):1940–1948
Ford ED (1975) Competition and stand structure in some even-aged plant monocultures. J Ecol 63:311–333
Forget PM, Mercier F, Collinet F (1999) Spatial patterns of two rodent-dispersed rain forest trees Carapa procera (Meliaceae) and Vouacapoua americana (Caesalpiniaceae) at Paracou, French Guiana. J Trop Ecol 15(3):301–313
Forman RTT, Hahn DC (1980) Spatial patterns of trees in a caribbean semievergreen forest. Ecology 61(6):1267–1274
Galiano EF (1982) Pattern detection in plant populations through the analysis of plant-to-all-plants distances. Vegetatio 49:39–43
Goodall DW (1965) Plot-less tests of interspecific association. J Ecol 53:197–210
Goodall DW (1974) A new method for the analysis of spatial pattern by random pairing of quadrats. Vegetatio 29(2):135–146
Goreaud F, Courbaud B, Collinet F (1998) Spatial structure analysis applied to modelling of forest dynamics: a few examples. In: Empirical and process based models for forest tree stand growth simulation. Proceedings of the IUFRO workshop, 21–27 September 1997, Oeiras, Portugal
Goreaud F, Pélissier R (2003) Avoiding misinterpretation of biotic interactions with the intertype K12-function: population independence vs. random labelling hypotheses. J Veg Sci 14(5):681–692
Greig-Smith P (1952) The use of random and contiguous quadrats in the study of the structure of plant communities. Ann Bot N. S. 16(62):293–316
Greig-Smith P (1964) Quantitative plant ecology, 2 edn. Butterworths, London
Harkness RD, Isham V (1983) A bivariate spatial point pattern of ants’ nests. Appl Stat 32(3):293–303
Hill MO (1973) The intensity of spatial pattern in plant communities. J Ecol 61:225–235 Evocation de l’analyse spectrale (p 231)
Kershaw KA (1957) The use of cover and frequency in the detection of pattern in plant communities. Ecology 38(2):291–299
Kershaw KA (1960) The detection of pattern and association. J Ecol 48:233–242
Lee Y (1979) A nearest-neighbour spatial association measure for the analysis of firm interdependence. Environ Plann Ser A 11:169–176 Lu, pas recupere.
Lepš J (1990a) Can underlying mechanisms be deduced from observed patterns? In: Krahulec F, Agnew ADQ, Agnew S, Willem JH (eds) Spatial processes in plant communities. SPB Academic Publishing, The Hague pp 1–11
Lepš J (1990b) Comparison of transect methods for the analysis of spatial pattern. In: Krahulec F, Agnew ADQ, Agnew S, Willem JH (eds), Spatial processes in plant communities. SPB Academic Publishing, The Hague, pp 71–82
Lotwick HW (1984) Some models for multitype spatial point processes, with remarks on analysing multitype patterns. J Appl Probab 21:575–582
Lotwick HW, Silverman BW (1982) Methods for analysing spatial processes of several types of points. J Roy Stat Soc Ser B 44(3):406–413
Ludwig JA, Goodall DW (1978) Comparison of paired with blocked quadrat variance methods for the analysis of spatial pattern. Vegetatio 38(1):49–59
Meagher TR, Burdick DS (1980) The use of nearest neighbor frequency analyses in studies of association. Ecology 61(5):1253–1255
Moeur M (1993) Characterizing spatial patterns of trees using stem-mapped data Forest Sci 39(4):756–775
Møller J, Waagepetersen RP (2004) Statistical inference and simulation for spatial point processes, number 100 In: Monographs on statistics and applied probability. Chapman & Hall/CRC, Boca Raton
Moran PAP (1976) Another quasi-Poisson plane point process. Zeitschrift fur Wahrscheinlichkeitstheorie und Verwandte Gebiete 33:269–272
Parrott L, Lange H (2004) Use of interactive forest growth simulation to characterise spatial stand structure. Forest Ecol Manage 194 (1–3):29–47
Patil GP, Stiteler WM (1974) Concepts of aggregation and their quantification: a critical review with some new results and applications. Res Population Ecol 15:238–254
Pélissier R (1998) Tree spatial patterns in three contrasting plots of a southern Indian tropical moist evergreen forest. J Trop Ecol 14(1): 1–16
Penttinen A, Stoyan D, Henttonen HM (1992) Marked point processes in forest statistics. Forest Sci 38(4):806–824
Persson O (1964) Distance methods. The use of distance measurements in the estimation of seedling density and open space frequency. Studia Forestalia Suecica 15:1–68
Peterson CH (1976) Measurement of community pattern by indices of local segregation and species diversity. J Ecol 64:157–169
Pielou EC (1961) Segregation and symmetry in two-species populations as studied by nearest-neighbour relationships. J Ecol 49:255–269
Pielou EC (1962) The use of plant-to-neighbour distances for the detection of competition. J Ecol 50:357–367
Pielou EC (1969) An introduction to mathematical ecology. Wiley, New York
R Development Core Team (2003) R: a language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria
Rathbun SL, Cressie N (1994) A space-time survival point process for a longleaf pine forest in southern Georgia. J Am Stat Assoc 89(428):1164–1174
Stoyan D, Penttinen A (2000) Recent applications of point process methods in forestry statistics. Stat Sci 15(1):61–78
Stoyan D, Stoyan H (1994) Fractals, random shapes and point fields. Wiley, Chichester
Upton G, Fingleton B (1985) Spatial data analysis by example—Vol. I: Point pattern and quantitative data. Wiley, Chichester
Usher MB (1969) The relation between mean square and block size in the analysis of similar patterns. J Ecol 57:505–514
van Lieshout MNM, Baddeley AJ (1999) Indices of dependence between types in multivariate point patterns. Scand J Stat 26:511–532
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Bar-Hen, A., Picard, N. Simulation study of dissimilarity between point process. Computational Statistics 21, 487–507 (2006). https://doi.org/10.1007/s00180-006-0008-x
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DOI: https://doi.org/10.1007/s00180-006-0008-x