Short communication Prediction of ungulates abundance through local linear algorithms Mauro Bianchi, Giorgio Corani * , Giorgio Guariso, Ciro Pinto Dipartimento di Elettronica ed Informazione, Politecnico di Milano, Via Ponzio 34/5, 20133 Milano, Italy Received 29 August 2005; received in revised form 4 April 2006; accepted 4 April 2006 Available online 6 June 2006 Abstract We use a local learning algorithm to predict the abundance of the Alpine ibex population living in the Gran Paradiso National Park, Northern Italy. Population abundance, recorded for a period of 40 years, have been recently analyzed by [Jacobson, A., Provenzale, A., Von Hardenberg, A., Bassano, B., Festa-Bianchet, M., 2004. Climate forcing and density dependence in a mountain ungulate population. Ecology 85, 1598e1610], who showed that the rate of increase of the population depends both on its density and snow depth. In the same paper, a threshold linear model is proposed for predicting the population abundance. In this paper, we identify a similar linear model in a local way, using a lazy learning algorithm. The advantages of the local model over the traditional global model are: improved forecast accuracy, easier understanding of the role and behaviour of the parameters, effortless way to keep the model up-to-date. Both data and software used in this work are of public domain; therefore, experiments can be easily replicated and further discussions are welcome. Ó 2006 Elsevier Ltd. All rights reserved. Keywords: Lazy learning; Population dynamics; Alpine ibex; Time series analysis; Nonparametric regression Software availability Name of software: Lazy Learning Toolbox for use with Matlab. Website: http://iridia.ulb.ac.be/Projects/lazy.html. Developer: Mauro Birattari and Gianluca Bontempi. Affiliation: IRIDIA e Universite ´ Libre de Bruxelles e Brus- sels, Belgium. Year first available: 1999. Software required: MatlabÓ(www.mathworks.com) and a C compiler. Program language: The ‘‘Lazy Learning Toolbox for use with Matlab’’ consists of four functions, written in C lan- guage for computational efficiency. They are de- signed to be compiled and subsequently invoked from a Matlab shell. Availability and cost: Open source software, publicly avail- able from the website. Further notes: A more recent implementation of Lazy Learn- ing, realized by the same authors, is provided for R, an open source language for data analysis and graphics. The lazy package for R is available from http://cran.r-project.org/src/contrib/Descriptions/lazy. html. 1. Introduction We study the population of Alpine ibex (Capra ibex, Fig. 1), a medium size ungulate living in the Gran Paradiso National Park (Northern Italy). The Park sizes about 703 km 2 ; hunting is not allowed inside or close to the Park, and large predators have been absent over the past 100 years. According to the literature overview presented in Jacobson et al. (2004), if large predators are rare or absent, the changes in ungulate populations can be modelled by considering * Corresponding author. Tel.: þ39 02 2399 3562; fax: þ39 02 2399 3412. E-mail address: corani@elet.polimi.it (G. Corani). 1364-8152/$ - see front matter Ó 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.envsoft.2006.04.001 Environmental Modelling & Software 21 (2006) 1508e1511 www.elsevier.com/locate/envsoft