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, 1598–1610], 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.

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 – Université Libre de Bruxelles – Brussels, Belgium.

Year first available:

1999.

Software required:

Matlab©(www.mathworks.com) and a C compiler.

Program language:

The “Lazy Learning Toolbox for use with Matlab” consists of four functions, written in C language for computational efficiency. They are designed to be compiled and subsequently invoked from a Matlab shell.

Availability and cost:

Open source software, publicly available from the website.

Further notes:

A more recent implementation of Lazy Learning, 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.

Article Outline

Nomenclature

1. Introduction

2. A threshold population model

3. The local linear prediction algorithm

4. Simulation results

5. Conclusions

References