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Part of the book series: NATO ASI Series ((ASIG,volume 22))

Abstract

Numerical methods are presented that represent three different approaches to biogeographic problems. The first approach is multivariate data analysis. The delineation of biogeographic “provinces” or areas is a type of descriptive analysis that can be accomplished by clustering faunal data (with or without spatial contiguity constraint) and drawing the resulting choropleth map. On the other hand, ecological biogeographers like to use ordinations of sampling localities and interpret the main axes of variation in terms of environmental gradients; canonical ordination, where a species presence or abundance data table and an environmental data matrix are both analyzed simultaneously, can be used with profit in this context. Secondly, the analysis of spatial patterns can help identify the type of spatial distribution of the biological material, both at the population and at the community level, while Mantel tests and other derived analyses make it possible to test hypotheses concerning causal factors possibly responsible for the observed spatial structures. Finally, phylogenetic-tree reconstruction methods, as well as other techniques, can be used for historical biogeographic studies; these include the study of taxa cladograms and of area cladograms.

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References

  • Adams EN III (1972) Consensus techniques and the comparison of taxonomic trees. Syst Zool 21: 390–397

    Article  Google Scholar 

  • Bock CE, Root TL (1981) Winter abundance patterns of landbirds in the United States and southern Canada. Amer Birds 35: 891–897

    Google Scholar 

  • Bray RJ, Curtis JT (1957) An ordination of the upland forest communities of southern Wisconsin. Ecol Monogr 27: 325–349

    Article  Google Scholar 

  • Brooks DR, Thorson TB, Mayes MA (1981) Freshwater stingrays (Potamotrygonidae) and their helminth parasites; testing hypotheses of evolution and coevolution. pp. 147–175. In: Funk VA, Brooks DR (eds) Advances in cladistics, 1. Columbia Univ. Press, New York

    Google Scholar 

  • Brooks DR, McLennan DA (1990) Historical ecology as a research program. In: Mayden RL (ed) Historical ecology and phylogeny of North American freshwater fishes. Stanford Univ. Press, Stanford

    Google Scholar 

  • Burgess TM, Webster R, McBratney AB (1981) Optimal interpolation and isarithmic mapping of soil properties. IV. Sampling strategy. J Soil Sci 32: 643–659

    Article  Google Scholar 

  • Burgman MA (1987) An analysis of the distribution of plants on granite outcrops in southern Western Australia using Mantel tests. Vegetado 71: 79–86

    Google Scholar 

  • Burrough PA (1987) Spatial aspects of ecological data. Chapter 7, pp. 213–251. In: Jongman RHG, ter Braak CJF, van Tongeren OFR (eds) Data analysis in community and landscape ecology. Pudoc, Wageningen

    Google Scholar 

  • Cliff AD, Ord JK (1981) Spatial processes: models and applications. Pion Limited, London

    Google Scholar 

  • Croizat L (1952) Manual of phytogeography. Junk, The Hague

    Google Scholar 

  • Croizat L (1958) Panbiogeography. Published by the author, Caracas, Venezuela

    Google Scholar 

  • Croizat L (1981) Biogeography: past, present, and future, pp. 501–523. In: Nelson G, Rosen DE (eds) Vicariance biogeography, a critique. Columbia Univ. Press, New York

    Google Scholar 

  • Day WHE (1986) Foreword: comparison and consensus classifications. J Classif 3: 183–185

    Article  Google Scholar 

  • Edgington ES (1987) Randomization tests, 2nd ed. Marcel Dekker Inc., New York

    Google Scholar 

  • Edwards AWF, Cavalli-Sforza LL (1963) The reconstruction of evolution. Ann Hum Genet 27: 105

    Google Scholar 

  • Edwards AWF, Cavalli-Sforza LL (1964) Reconstruction of evolutionary trees, pp. 67–76. In: Heywood VH, McNeill J (eds) Phenetic and phylogenetic classification. Systematic Association Publ No. 6, London

    Google Scholar 

  • Estabrook GF (1972) Cladistic methodology: a discussion of the theoretical basis for the induction of evolutionary history. Ann Rev Ecol Syst 3: 427–456

    Article  Google Scholar 

  • Farris JS (1972) Estimating phylogenetic trees from distance matrices. Amer Nat 106: 645–668

    Article  Google Scholar 

  • Felsenstein J (1982) Numerical methods for inferring evolutionary trees. Quart Rev Biol 57: 379–404

    Article  Google Scholar 

  • Fitch WM, Margoliash E (1967) Construction of phylogenetic trees. Science 155: 279–284

    Article  PubMed  CAS  Google Scholar 

  • Fortin M-J (1985) Analyse spatiale de la répartition des phénomènes écologiques: méthodes d’analyse spatiale, théorie de l’échantillonnage. Mémoire de Maîtrise, Université de Montréal

    Google Scholar 

  • Gower JC (1987) Introduction to ordination techniques, pp. 3–64. In: Legendre P, Legendre L (eds) Developments in Numerical Ecology. NATO ASI Series, Vol. G 14. Springer-Verlag, Berlin

    Google Scholar 

  • Gower JC, Legendre P (1986) Metric and Euclidean properties of dissimilarity coefficients. J Classif 3: 5–48

    Article  Google Scholar 

  • Griffith DA (1987) Spatial autocorrelation — A primer. Resource Publications in Geography, Association of American Geographers, Washington, D.C.

    Google Scholar 

  • Hennig W (1950) Grundzüge einer Theorie der phylogenetischen Systematik. Deutscher Zentralverlag, Berlin

    Google Scholar 

  • Hennig W (1966) Phylogenetic systematics. University of Illinois Press, Urbana, Illinois

    Google Scholar 

  • Hudon C, Lamarche G (1989) Niche segregation between American lobster Homarus americanus and rock crab Cancer irroratus. Mar Ecol Prog Ser 52:155–168

    Article  Google Scholar 

  • Humphries CJ, Ladiges PY, Roos M, Zandee M (1988) Cladistic biogeography. pp. 371–404. In: Myers AA, Giller PS (eds) Analytical biogeography — An integrated approach to the study of animal and plant distributions. Chapman and Haul, London

    Google Scholar 

  • Jongman RHG, ter Braak CJF, van Tongeren OFR (eds) (1987) Data analysis in community and landscape ecology. Pudoc, Wageningen

    Google Scholar 

  • Kluge AG, Farns JS (1969) Quantitative phyletics and the evolution of anurans. Syst Zool 18: 1–32

    Article  Google Scholar 

  • Lapointe F-J, Legendre P — A statistical framework to test the consensus of two nested classifications. Syst Zool 39: 1–14

    Google Scholar 

  • Lebart L (1978) Programme d’agrégation avec contraintes (C.A.H. contiguïté). Cah Anal Données 3: 275–287

    Google Scholar 

  • Leduc A, Drapeau P, Bergeron Y, Legendre P (submitted) Importance of spatial phenomena in the explanation of forest cover variations.

    Google Scholar 

  • Le Gros Clark WE, Sonntag CF (1926) A monograph of Orycteropus afer. III. The skull. Proc Gen Meet Sci Bus, Zool Soc London 1926: 445–485

    Google Scholar 

  • Lefkovitch LP (1978) Cluster generation and grouping using mathematical programming. Math Biosci 41: 91–110

    Article  Google Scholar 

  • Lefkovitch LP (1980) Conditional clustering. Biometrics 36: 43–58

    Article  Google Scholar 

  • Lefkovitch LP (1982) Conditional clusters, musters, and probability. Math Biosci 60: 207–234

    Article  Google Scholar 

  • Lefkovitch LP (1987) Species associations and conditional clustering: clustering with or without pairwise resemblances, pp. 309–331. In: Legendre P, Legendre L (eds) Developments in Numerical Ecology. NATO ASI Series, Vol. G 14. Springer-Verlag, Berlin

    Google Scholar 

  • Legendre L, Legendre P (1983) Numerical ecology. Developments in environmental modelling, 3. Elsevier, Amsterdam

    Google Scholar 

  • Legendre L, Legendre P (1984a) Ecologie numérique, 2ième éd. Tome 2: La structure des données écologiques. Masson, Paris et les Presses de l’Université du Québec

    Google Scholar 

  • Legendre P (1986) Reconstructing biogeographic history using phylogenetic-tree analysis of community structure. Syst Zool 35: 68–80

    Article  Google Scholar 

  • Legendre P (1987) Constrained clustering, pp. 289–307. In: Legendre P, Legendre L (eds) Developments in Numerical Ecology. NATO ASI Series, Vol. G 14. Springer-Verlag, Berlin

    Google Scholar 

  • Legendre P, Fortin M-J (1989) Spatial pattern and ecological analysis. Vegetatio 80: 107–138

    Article  Google Scholar 

  • Legendre P, Legendre V (1984b) Postglacial dispersal of freshwater fishes in the Québec peninsula. Can J Fish Aquat Sci 41: 1781–1802

    Article  Google Scholar 

  • Legendre P, Oden NL, Sokal RR, Vaudor A, Kim J (1990) Approximate analysis of variance of spatially autoeorrelated regional data. J Classif 7: 53–75

    Article  Google Scholar 

  • Legendre P, Troussellier M (1988) Aquatic heterotrophic bacteria: modeling in the presence of spatial autocorrelation. Limnol Oceanogr 33: 1055–1067

    Article  Google Scholar 

  • Legendre P, Troussellier M, Jarry V, Fortin M-J (1989) Design for simultaneous sampling of ecological variables: from concepts to numerical solutions. Oikos 55: 30–42

    Article  CAS  Google Scholar 

  • LeQuesne WJ (1969) A method of selection of characters in numerical taxonomy. Syst Zool 18: 201–205

    Article  Google Scholar 

  • Mantel, N. 1967. The detection of disease clustering and a generalized regression approach. Cancer Res 27: 209–220.

    PubMed  CAS  Google Scholar 

  • McBratney AB, Webster R, Burgess TM (1981) The design of optimal sampling schemes for local estimation and mapping of regionalized variables. I. Theory and method. Computers & Geosciences 7: 331–334

    Article  Google Scholar 

  • McMorris FR (1975) Compatibility criteria for cladistic and qualitative taxonomic characters. pp. 399–415. In: Estabrook GF (ed) Proceedings of the Eight International Conference on Numerical Taxonomy. Freeman, San Francisco

    Google Scholar 

  • McMorris FR, Meronk DB, Neumann DA (1982) A view of some consensus methods for trees, pp. 122–126. In: Felsenstein J (ed) Numerical taxonomy. NATO ASI Series, Vol. G 1. Springer-Verlag, Berlin

    Google Scholar 

  • Mickevich MF (1981) Quantitative phylogenetic biogeography. pp. 209–222. In: Funk VA, Brooks DR (eds) Advances in cladistics, 1. Columbia Univ. Press, New York

    Google Scholar 

  • Mitchell PG (1901) On the intestinal tract of birds, with remarks on the valuation and nomenclature of zoological characters. Trans Linnean Soc London (Zool Ser 2) 8: 173–275

    Article  Google Scholar 

  • Myers AA, Giller PS (1988) Process, pattern and scale in biogeography. pp. 3–12. In: Myers AA, Giller PS (eds) Analytical biogeography — An integrated approach to the study of animal and plant distributions. Chapman and Hall, London

    Google Scholar 

  • Nelson G, Platnick NI (1981) Systematics and biogeography: cladistics and vicariance. Columbia Univ. Press, New York

    Google Scholar 

  • Oden NL, Sokal RR (1986) Directional autocorrelation: an extension of spatial correlograms to two dimensions. Syst Zool 35: 608–617

    Article  Google Scholar 

  • Odland J (1988) Spatial autocorrelation. Scientific Geography Series, Vol. 9. Sage Publications Inc., Newbury Park, California

    Google Scholar 

  • Odum EP (1950) Bird populations of the Highlands (North Carolina) plateau in relation to plant succession and avian invasion. Ecology 31: 587–605

    Article  Google Scholar 

  • Openshaw S (1974) A regionalisation program for large data sets. Computer Appl 3–4: 136–160

    Google Scholar 

  • Orlóci L (1978) Multivariate analysis in vegetation research, 2nd ed. Dr. W. Junk B.V., The Hague

    Google Scholar 

  • Page RDM (1987) Graphs and generalized tracks: quantifying Croizat’s panbiogeography. Syst Zool 36: 1–17

    Article  Google Scholar 

  • Page RDM (1988) Quantitative cladistic biogeography: constructing and comparing area cladograms. Syst Zool 37: 254–270

    Article  Google Scholar 

  • Platnick NI, Nelson G (1978) A method of analysis for historical biogeography. Syst Zool 27: 1–16

    Article  Google Scholar 

  • Ray DM, Berry BJL (1966) Multivariate socioeconomic regionalization: a pilot study in central Canada, pp. 75–130. In: Ostry S, Rymes T (eds) Papers on Regional Statistical Studies. Univ. of Toronto Press, Toronto

    Google Scholar 

  • Rosen DE (1978) Vicariant patterns and historical explanation in biogeography. Syst Zool 27: 159–188

    Article  Google Scholar 

  • Rosen DE (1979) Fishes from the uplands and intermontane basins of Guatemala: revisionary studies and comparative geography. Bull Am Mus Nat Hist 162: 267–376

    Google Scholar 

  • Schnell GD, Douglas ME, Hough DJ (1986) Geographic patterns of variation in offshore spotted dolphins (Stenella attenuata) of the eastern tropical Pacific Ocean. Marine Mammal Science 2: 186–213

    Article  Google Scholar 

  • Smouse PE, Long JC, Sokal RR (1986) Multiple regression and correlation extensions of the Mantel test of matrix correspondence. Syst Zool 35: 627–632

    Article  Google Scholar 

  • Sokal RR (1986) Spatial data analysis and historical processes, pp. 29–43. In: Diday E et al. (eds) Data analysis and informatics, IV. Proceedings of the Fourth International Symposium on Data Analysis and Informatics, Versailles, France, 1985. North-Holland, Amsterdam

    Google Scholar 

  • ter Braak CJF (1986) Canonical correspondence analysis: a new eigenvector technique for multivariate direct gradient analysis. Ecology 67: 1167–1179

    Article  Google Scholar 

  • ter Braak CJF (1987a) The analysis of vegetation-environment relationships by canonical correspondence analysis. Vegetatio 69: 69–77

    Article  Google Scholar 

  • ter Braak CJF (1987b) Ordination. Chapter 5, pp. 91–173. In: Jongman RHG, ter Braak CJF, van Tongeren OFR (eds) Data analysis in community and landscape ecology. Pudoc, Wageningen

    Google Scholar 

  • Theriot E (1989) Phylogenetic systematics for phycology. J Phycol 25:407–411

    Article  Google Scholar 

  • Webster R, Burrough PA (1972) Computer-based soil mapping of small areas from sample data. I. Multivariate classification and ordination. H Classification smoothing. J Soil Sci 23: 210–221, 222–234

    Article  CAS  Google Scholar 

  • Whittaker RH (1967) Gradient analysis of vegetation. Biol Rev 49: 207–264

    Article  Google Scholar 

  • Wiley EO (1988a) Vicariance biogeography. Ann Rev Ecol Syst 19: 513–542

    Article  Google Scholar 

  • Wiley EO (1988b) Parsimony analysis and vicariance biogeography. Syst Zool 37: 271–290

    Article  Google Scholar 

  • Williams WT, Lambert JM, Lance GN (1966) Multivariate methods in plant ecology. V. Similarity analyses and information-analysis. J Ecol 54: 427–445

    Article  Google Scholar 

  • Zandee M, Roos MC (1987) Component-compatibility in historical biogeography. Cladistics 3: 305–332

    Google Scholar 

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Legendre, P. (1990). Quantitative Methods and Biogeographic Analysis. In: Garbary, D.J., South, G.R. (eds) Evolutionary Biogeography of the Marine Algae of the North Atlantic. NATO ASI Series, vol 22. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-75115-8_2

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  • DOI: https://doi.org/10.1007/978-3-642-75115-8_2

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