Ecology, 90(11), 2009, pp. 3245–3257 Ó 2009 by the Ecological Society of America Statistical performance and information content of time lag analysis and redundancy analysis in time series modeling DAVID G. ANGELER, 1,2,3 OLGA VIEDMA, 1 AND JOSE ´ M. MORENO 1 1 Institute of Environmental Sciences (ICAM), University of Castilla–La Mancha, Avda. Carlos III s/n, E-45071 Toledo, Spain 2 Swedish University of Agricultural Sciences, Department of Aquatic Sciences and Assessment, P.O. Box 7050, SE-750 07 Uppsala, Sweden Abstract. Time lag analysis (TLA) is a distance-based approach used to study temporal dynamics of ecological communities by measuring community dissimilarity over increasing time lags. Despite its increased use in recent years, its performance in comparison with other more direct methods (i.e., canonical ordination) has not been evaluated. This study fills this gap using extensive simulations and real data sets from experimental temporary ponds (true zooplankton communities) and landscape studies (landscape categories as pseudo-communi- ties) that differ in community structure and anthropogenic stress history. Modeling time with a principal coordinate of neighborhood matrices (PCNM) approach, the canonical ordination technique (redundancy analysis; RDA) consistently outperformed the other statistical tests (i.e., TLAs, Mantel test, and RDA based on linear time trends) using all real data. In addition, the RDA-PCNM revealed different patterns of temporal change, and the strength of each individual time pattern, in terms of adjusted variance explained, could be evaluated. It also identified species contributions to these patterns of temporal change. This additional information is not provided by distance-based methods. The simulation study revealed better Type I error properties of the canonical ordination techniques compared with the distance- based approaches when no deterministic component of change was imposed on the communities. The simulation also revealed that strong emphasis on uniform deterministic change and low variability at other temporal scales is needed to result in decreased statistical power of the RDA-PCNM approach relative to the other methods. Based on the statistical performance of and information content provided by RDA-PCNM models, this technique serves ecologists as a powerful tool for modeling temporal change of ecological (pseudo-) communities. Key words: canonical ordination; community ecology; distance-based methods; principal coordinate of neighborhood matrices (PCNM); statistical power; temporal dynamics. INTRODUCTION Many tools underlying different statistical methodol- ogies are available for ecologists to measure the temporal change (i.e., cyclical, stochastic, and/or direc- tional) of ecological communities (examples in Millar et al. [2005]). Collins et al. (2000) introduced a method, time lag analysis (TLA), which regresses community dissimilarity against increasing time lags. Time lag analysis provides measures of model fit and statistical significance that allow the quantification of the strength of temporal community change in a numerical frame- work, while permitting comparison of model perfor- mance with other methods. Despite their common use in the spatial and temporal analysis of ecological communities, distance-based approaches have limitations. First, as an indirect method they do not provide taxonomic detail (i.e., species identities are lost in the process of distance/dis- similarity calculations), which does not allow them to reveal which species contribute most importantly to the observed trends (Warton and Hudson 2004). Conse- quently, some authors have preferred a redundancy analysis approach (van den Brink and ter Braak 1998) or Procrustes analysis (Peres-Neto and Jackson 2001) over distance-based statistics. Second, distance-based results depend on the choice of the dissimilarity/distance measure used for calculating distance matrices (Faith et al. 1987, Clarke 1993, Legendre and Legendre 1998, McArdle and Anderson 2001, Kent et al. 2006). For example, the method of Collins et al. (2000) is based on Euclidean distance as a measure of dissimilarity but this measure has been criticized because its geometrical properties (squaring of differences) make multivariate solutions prone to distortion by outliers. Euclidean distance also leads to a species abundance paradox (Legendre and Legendre 1998) because it is dominated by sample totals (two sample sites without any shared species may show smaller distances than pairs of sites that share species). Yet Legendre and Gallagher (2001) have shown that the problems arising from Euclidean Manuscript received 8 March 2007; revised 6 February 2009; accepted 2 March 2009. Corresponding Editor: J. A. Jones. 3 E-mail: david.angeler@vatten.slu.se 3245