Detection of significant changes in short time series: applications to the analysis of annual routines in behavioural ecology and to the analysis of breaks in abundance N. Bru a , E. Biritxinaga a and F. D’Amico b a Laboratoire de Mathématiques et de leurs Applications de Pau UMR CNRS 5142- University of Pau et des Pays de l’Adour – France ; b UMR Ecobiop INRA-UPPA, Campus Montaury, University of Pau et des Pays de l’Adour – France Email: noelle.bru@univ-pau.fr Abstract: The aim of this paper is to identify significant changes, otherwise known as change-points, in short time series. The practical application that motivated this work concerns the detection of change-point differences in behavioural annual routines of living organisms (i.e. how they schedule activities in a regular way over the year). Our study case focuses on the annual routine of a specialist river bird species, the European Dipper (Cinclus cinclus), coping with drastic environmental changes in flow regime impacting their life-history stages. We compare behavioural data collected on a monthly basis in natural and altered rivers; they result in 12 values of so-called time-activity budgets expressed as mean percentage of time spent in each of 5 different behavioural activities. The methods used in this paper are based on statistical tests for detecting one or more points of breaks in time series. Different methods are compared on this first dataset : • The method of A. N. Pettitt (1979) which is based on the Mann and Whitney statistical test for comparing two samples thus 2 segmentations of the original time series; • The method of P. Hubert et al. (1989) for which the test statistic considers the squared difference between the series and a fixed segmentation. In this algorithm all possible segmentations of a time series are tested and the optimal segmentation is selected using the method of contrasts introduced by Scheffe (1959); • The method developed recently by L. Bordes et al. (2010) whose statistics do not depend on parametric assumptions on the distribution of the data. The thresholds of statistical inference in this paper are determined by a Monte Carlo method. Most of these methods were developed and used on long time series of statistical index (including hydrology and climatology applications). Thus, they have to be adapted to the study of phenomena on short duration, i.e. small samples size through resampling techniques. In addition, to take into account the dependence between successive observations induced by the fact that they are time series, bootstrapping techniques for dependent data are implemented to adjust statistical inference (due to the specific nature of the data). The irrespective interest of these methods is demonstrated on the studied original dataset (i.e. the Dipper behavioural annual routine). It is shown that significant differences in annual routine exist for 3 of the 5 behavioural categories between the two contrasting environments (natural vs altered flow regime), thus mathematically confirming the biological predictions made independently. We also present another application of these methods to historical time series (about 30 years) of annual abundance of European Eel in France. The advantage of this kind of application is to determine potential dates of any sudden change of abundance and to link them to external phenomena where significant decrease/increase occurs, such as accidental pollutions, immediate effect of regulatory management, disease outbreak, and more generally to any field of ecology where analysis of change-point along annual routine is necessary. Keywords: change-points, time dependent data, segmentation, Cinclus cinclus, Anguilla anguilla, block bootstrap, Monte Carlo method. 19th International Congress on Modelling and Simulation, Perth, Australia, 12–16 December 2011 http://mssanz.org.au/modsim2011 2211