Assessing biodiversity profile through FDA


  • Tonio Di Battista Università degli Studi "Gabriele D'Annunzio", Chieti-Pescara
  • Francesca Fortuna Università degli Studi "Gabriele D'Annunzio", Chieti-Pescara



Diversity index, diversity profiles, functional data analysis, functional statistics, lichen biodiversity


The past few years have highlighted the need to protect diversity in its broader concept and, in particular, with reference to the ecological context for environmental protection. In this context, the problem of the definition and the measurement of diversity becomes fundamental. This paper provides a general picture of the main biodiversity indices proposed in literature and shows their limits in favor of diversity profiles. Since the diversity profile is a curve which expresses the diversity as a function of the relative abundance vector, it may be studied through the functional approach. In particular,we point out the advantages of the parametric FDA which, under suitable assumptions, allow us to obtain summary statistics of the same functional form of the observed data. Diversity profiles and parametric FDA approach have been applied to evaluate the diversity of epiphytic lichens in the province of Florence, providing an alternative way of understanding the biological diversity.


ANPA (2001). I.B.L. Indice di Biodiversità Lichenica. Manuali e Linee Guida. no. 2.

J. ASTA,W. ERHARDT,M. FERRETTI, F. FORNASIER, U. KIRSCHBAUM, P. L.NIMIS, O. W. PURVIS, S. PIRINTOS, C. SCHEIDEGGER, C. V. HALUWYN, V. WIRTH (2002). Mapping lichen diversity as an indicator of environmental quality. In P. L. NIMIS, C. SCHEIDEGGER, P. A. WOLSELEY (eds.), Monitoring with Lichens- Monitoring Lichens, Nato Science Program-IV, Kluwer Academic Publisher, The Netherlands, pp. 273–279.

M. E. CONTI, G. CECCHETTI (2001). Biological monitoring: lichens as bioindicators of air pollution assessment - a review. Environmental Pollution, 114, pp. 471–492.

F. CRISTOFOLINI, P.GIORDANI, E.GOTTARDINI, P.MODENESI (2008). The response of epiphytic lichens to air pollution and subsets of ecological predictors: a case study from the italian prealps. Environmental Pollution, 151, pp. 308–317.

T. DI BATTISTA, S. A. GATTONE, A. DE SANCTIS (2010). Dealing with fda estimation methods. In S. INGRASSIA, R. ROCCI, M. VICHI (eds.), New Perspectives in Statistical Modeling in Data Analysis, Springer, New York, pp. 357–365.

S. A. GATTONE, T. DI BATTISTA (2009). A functional approach to diversity profiles. Journal of the Royal Statistical Society, 58, pp. 267–284.

P. GIORDANI, G. BRUNIALTI, D. ALLETEO (2002). Effects of atmospheric pollution on lichen biodiversity (lb) in a mediterranean region (liguria, nw italy). Environmental Pollution, 118, pp. 53–64.

J. H. GOVE, G. P. PATIL, D. F. SWINDEL, C. TAILLIE (1994). Ecological diversity and forest management. In G. P. PATIL, C. R. RAO (eds.), Handbook of Statistics, vol.12, Environmental Statistics, Elsevier, Amsterdam, pp. 409–462.

H. NAGENDRA (2001). Using remote sensing to assess biodiversity. Int. J. Rem. Sens., 22, pp. 2377–2400.

L. NIMIS, A. CICCARELLI, G. LAZZARIN, R. BARGAGLI, A. BENEDET, M. CASTELLO, D. GASPARO, D. LAUSI, S. OLIVIERI, M. TRETTACH (1989). I licheni come bioindicatori di inquinamento atmosferico nell’area di schio-thienebreganze (vi). Bollettino del Museo Civico di Storia Naturale di Verona.

G. P. PATIL, C. TAILLIE (1979). An overview of diversity. In J. F. GRASSLE, G. P. PATIL, W. SMITH, C. TAILLIE (eds.), Ecological Diversity in Theory and Practice, International Co-operative Publishing House, Fairland, MD, pp. 23–48.

G. P. PATIL, C. TAILLIE (1982). Diversity as a concept and its measurement. Journal of the American Statistical Association, 77, pp. 548–567.

E. C. PIELOU (1975). Ecological Diversity. JohnWiley & Sons, New York.

J. O. RAMSAY, B.W. SILVERMAN (2005). Functional Data Analysis, 2nd edn. Springer, New York.

W. RUDIN (2006). Real and complex analysis. McGraw-Hill, New York.

C. SHANNON (1948). A mathematical theory of communication. Bell Syst. tech. J., 27, pp. 379–423.

E. H. SIMPSON (1949). Measurement of diversity. Nature, 163, p. 688.

S. K. THOMPSON, G. A. F. SEBER (1996). Adaptive sampling. JohnWiley&Sons,New York.

H. F. VAN DOBBEN, H. T.WOLTERBEEK, G.W.WAMELINK, C. J. T. BRAAK (2001). Relationship between epiphytic lichens, trace elements and gaseous atmospheric pollutants. Environmental Pollution, 112, no. 2, pp. 163–169.

J. H. WARD (1963). Hierarchical grouping to optimize an objective function. Journal of the American Statistical Association, 58, pp. 236–244.

J. E. WEGMAN, W. I. WRIGHT (1983). Splines in statistics. Journal of the American Statistical Association, 78, pp. 351–365.




How to Cite

Di Battista, T., & Fortuna, F. (2013). Assessing biodiversity profile through FDA. Statistica, 73(1), 69–85.